13173 lines
546 KiB
Cython
13173 lines
546 KiB
Cython
# This file is automatically generated by _generate_pyx.py.
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# Do not edit manually!
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from libc.math cimport NAN
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include "_ufuncs_extra_code_common.pxi"
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include "_ufuncs_extra_code.pxi"
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__all__ = ['agm', 'bdtr', 'bdtrc', 'bdtri', 'bdtrik', 'bdtrin', 'betainc', 'betaincc', 'betainccinv', 'betaincinv', 'boxcox', 'boxcox1p', 'btdtria', 'btdtrib', 'chdtr', 'chdtrc', 'chdtri', 'chdtriv', 'chndtr', 'chndtridf', 'chndtrinc', 'chndtrix', 'elliprc', 'elliprd', 'elliprf', 'elliprg', 'elliprj', 'entr', 'erfcinv', 'erfinv', 'eval_chebyc', 'eval_chebys', 'eval_chebyt', 'eval_chebyu', 'eval_gegenbauer', 'eval_genlaguerre', 'eval_hermite', 'eval_hermitenorm', 'eval_jacobi', 'eval_laguerre', 'eval_legendre', 'eval_sh_chebyt', 'eval_sh_chebyu', 'eval_sh_jacobi', 'eval_sh_legendre', 'expn', 'fdtr', 'fdtrc', 'fdtri', 'fdtridfd', 'gdtr', 'gdtrc', 'gdtria', 'gdtrib', 'gdtrix', 'huber', 'hyp0f1', 'hyp1f1', 'hyperu', 'inv_boxcox', 'inv_boxcox1p', 'kl_div', 'kn', 'kolmogi', 'kolmogorov', 'lpmv', 'nbdtr', 'nbdtrc', 'nbdtri', 'nbdtrik', 'nbdtrin', 'ncfdtr', 'ncfdtri', 'ncfdtridfd', 'ncfdtridfn', 'ncfdtrinc', 'nctdtr', 'nctdtridf', 'nctdtrinc', 'nctdtrit', 'ndtri', 'ndtri_exp', 'nrdtrimn', 'nrdtrisd', 'owens_t', 'pdtr', 'pdtrc', 'pdtri', 'pdtrik', 'poch', 'powm1', 'pseudo_huber', 'rel_entr', 'round', 'shichi', 'sici', 'smirnov', 'smirnovi', 'spence', 'stdtr', 'stdtridf', 'stdtrit', 'tklmbda', 'wrightomega', 'yn', 'geterr', 'seterr', 'errstate', 'jn', 'airy', 'airye', 'bei', 'beip', 'ber', 'berp', 'binom', 'exp1', 'expi', 'expit', 'exprel', 'gamma', 'gammaln', 'hankel1', 'hankel1e', 'hankel2', 'hankel2e', 'hyp2f1', 'it2i0k0', 'it2j0y0', 'it2struve0', 'itairy', 'iti0k0', 'itj0y0', 'itmodstruve0', 'itstruve0', 'iv', 'ive', 'jv', 'jve', 'kei', 'keip', 'kelvin', 'ker', 'kerp', 'kv', 'kve', 'log_expit', 'log_wright_bessel', 'loggamma', 'logit', 'mathieu_a', 'mathieu_b', 'mathieu_cem', 'mathieu_modcem1', 'mathieu_modcem2', 'mathieu_modsem1', 'mathieu_modsem2', 'mathieu_sem', 'modfresnelm', 'modfresnelp', 'obl_ang1', 'obl_ang1_cv', 'obl_cv', 'obl_rad1', 'obl_rad1_cv', 'obl_rad2', 'obl_rad2_cv', 'pbdv', 'pbvv', 'pbwa', 'pro_ang1', 'pro_ang1_cv', 'pro_cv', 'pro_rad1', 'pro_rad1_cv', 'pro_rad2', 'pro_rad2_cv', 'psi', 'rgamma', 'sph_harm', 'wright_bessel', 'yv', 'yve', 'zetac', 'sindg', 'cosdg', 'tandg', 'cotdg', 'i0', 'i0e', 'i1', 'i1e', 'k0', 'k0e', 'k1', 'k1e', 'y0', 'y1', 'j0', 'j1', 'struve', 'modstruve', 'beta', 'betaln', 'besselpoly', 'gammaln', 'gammasgn', 'cbrt', 'radian', 'cosm1', 'gammainc', 'gammaincinv', 'gammaincc', 'gammainccinv', 'fresnel', 'ellipe', 'ellipeinc', 'ellipk', 'ellipkinc', 'ellipkm1', 'ellipj', 'erf', 'erfc', 'erfcx', 'erfi', 'voigt_profile', 'wofz', 'dawsn', 'ndtr', 'log_ndtr', 'exp2', 'exp10', 'expm1', 'log1p', 'xlogy', 'xlog1py']
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cdef void loop_D_DDDD__As_DDDD_D(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
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cdef np.npy_intp i, n = dims[0]
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cdef void *func = (<void**>data)[0]
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cdef char *func_name = <char*>(<void**>data)[1]
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cdef char *ip0 = args[0]
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cdef char *ip1 = args[1]
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cdef char *ip2 = args[2]
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cdef char *ip3 = args[3]
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cdef char *op0 = args[4]
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cdef double complex ov0
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for i in range(n):
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ov0 = (<double complex(*)(double complex, double complex, double complex, double complex) noexcept nogil>func)(<double complex>(<double complex*>ip0)[0], <double complex>(<double complex*>ip1)[0], <double complex>(<double complex*>ip2)[0], <double complex>(<double complex*>ip3)[0])
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(<double complex *>op0)[0] = <double complex>ov0
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ip0 += steps[0]
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ip1 += steps[1]
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ip2 += steps[2]
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ip3 += steps[3]
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op0 += steps[4]
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sf_error.check_fpe(func_name)
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cdef void loop_D_DDDD__As_FFFF_F(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
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cdef np.npy_intp i, n = dims[0]
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cdef void *func = (<void**>data)[0]
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cdef char *func_name = <char*>(<void**>data)[1]
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cdef char *ip0 = args[0]
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cdef char *ip1 = args[1]
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cdef char *ip2 = args[2]
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cdef char *ip3 = args[3]
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cdef char *op0 = args[4]
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cdef double complex ov0
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for i in range(n):
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ov0 = (<double complex(*)(double complex, double complex, double complex, double complex) noexcept nogil>func)(<double complex>(<float complex*>ip0)[0], <double complex>(<float complex*>ip1)[0], <double complex>(<float complex*>ip2)[0], <double complex>(<float complex*>ip3)[0])
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(<float complex *>op0)[0] = <float complex>ov0
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ip0 += steps[0]
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ip1 += steps[1]
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ip2 += steps[2]
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ip3 += steps[3]
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op0 += steps[4]
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sf_error.check_fpe(func_name)
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cdef void loop_D_DDD__As_DDD_D(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
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cdef np.npy_intp i, n = dims[0]
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cdef void *func = (<void**>data)[0]
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cdef char *func_name = <char*>(<void**>data)[1]
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cdef char *ip0 = args[0]
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cdef char *ip1 = args[1]
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cdef char *ip2 = args[2]
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cdef char *op0 = args[3]
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cdef double complex ov0
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for i in range(n):
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ov0 = (<double complex(*)(double complex, double complex, double complex) noexcept nogil>func)(<double complex>(<double complex*>ip0)[0], <double complex>(<double complex*>ip1)[0], <double complex>(<double complex*>ip2)[0])
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(<double complex *>op0)[0] = <double complex>ov0
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ip0 += steps[0]
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ip1 += steps[1]
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ip2 += steps[2]
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op0 += steps[3]
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sf_error.check_fpe(func_name)
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cdef void loop_D_DDD__As_FFF_F(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
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cdef np.npy_intp i, n = dims[0]
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cdef void *func = (<void**>data)[0]
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cdef char *func_name = <char*>(<void**>data)[1]
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cdef char *ip0 = args[0]
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cdef char *ip1 = args[1]
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cdef char *ip2 = args[2]
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cdef char *op0 = args[3]
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cdef double complex ov0
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for i in range(n):
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ov0 = (<double complex(*)(double complex, double complex, double complex) noexcept nogil>func)(<double complex>(<float complex*>ip0)[0], <double complex>(<float complex*>ip1)[0], <double complex>(<float complex*>ip2)[0])
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(<float complex *>op0)[0] = <float complex>ov0
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ip0 += steps[0]
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ip1 += steps[1]
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ip2 += steps[2]
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op0 += steps[3]
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sf_error.check_fpe(func_name)
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cdef void loop_D_DD__As_DD_D(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
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cdef np.npy_intp i, n = dims[0]
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cdef void *func = (<void**>data)[0]
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cdef char *func_name = <char*>(<void**>data)[1]
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cdef char *ip0 = args[0]
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cdef char *ip1 = args[1]
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cdef char *op0 = args[2]
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cdef double complex ov0
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for i in range(n):
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ov0 = (<double complex(*)(double complex, double complex) noexcept nogil>func)(<double complex>(<double complex*>ip0)[0], <double complex>(<double complex*>ip1)[0])
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(<double complex *>op0)[0] = <double complex>ov0
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ip0 += steps[0]
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ip1 += steps[1]
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op0 += steps[2]
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sf_error.check_fpe(func_name)
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cdef void loop_D_DD__As_FF_F(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
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cdef np.npy_intp i, n = dims[0]
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cdef void *func = (<void**>data)[0]
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cdef char *func_name = <char*>(<void**>data)[1]
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cdef char *ip0 = args[0]
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cdef char *ip1 = args[1]
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cdef char *op0 = args[2]
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cdef double complex ov0
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for i in range(n):
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ov0 = (<double complex(*)(double complex, double complex) noexcept nogil>func)(<double complex>(<float complex*>ip0)[0], <double complex>(<float complex*>ip1)[0])
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(<float complex *>op0)[0] = <float complex>ov0
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ip0 += steps[0]
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ip1 += steps[1]
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op0 += steps[2]
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sf_error.check_fpe(func_name)
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cdef void loop_D_D__As_D_D(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
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cdef np.npy_intp i, n = dims[0]
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cdef void *func = (<void**>data)[0]
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cdef char *func_name = <char*>(<void**>data)[1]
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cdef char *ip0 = args[0]
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cdef char *op0 = args[1]
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cdef double complex ov0
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for i in range(n):
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ov0 = (<double complex(*)(double complex) noexcept nogil>func)(<double complex>(<double complex*>ip0)[0])
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(<double complex *>op0)[0] = <double complex>ov0
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ip0 += steps[0]
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op0 += steps[1]
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sf_error.check_fpe(func_name)
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cdef void loop_D_D__As_F_F(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
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cdef np.npy_intp i, n = dims[0]
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cdef void *func = (<void**>data)[0]
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cdef char *func_name = <char*>(<void**>data)[1]
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cdef char *ip0 = args[0]
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cdef char *op0 = args[1]
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cdef double complex ov0
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for i in range(n):
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ov0 = (<double complex(*)(double complex) noexcept nogil>func)(<double complex>(<float complex*>ip0)[0])
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(<float complex *>op0)[0] = <float complex>ov0
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ip0 += steps[0]
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op0 += steps[1]
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sf_error.check_fpe(func_name)
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cdef void loop_D_dD__As_dD_D(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
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cdef np.npy_intp i, n = dims[0]
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cdef void *func = (<void**>data)[0]
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cdef char *func_name = <char*>(<void**>data)[1]
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cdef char *ip0 = args[0]
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cdef char *ip1 = args[1]
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cdef char *op0 = args[2]
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cdef double complex ov0
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for i in range(n):
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ov0 = (<double complex(*)(double, double complex) noexcept nogil>func)(<double>(<double*>ip0)[0], <double complex>(<double complex*>ip1)[0])
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(<double complex *>op0)[0] = <double complex>ov0
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ip0 += steps[0]
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ip1 += steps[1]
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op0 += steps[2]
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sf_error.check_fpe(func_name)
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cdef void loop_D_dD__As_fF_F(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
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cdef np.npy_intp i, n = dims[0]
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cdef void *func = (<void**>data)[0]
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cdef char *func_name = <char*>(<void**>data)[1]
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cdef char *ip0 = args[0]
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cdef char *ip1 = args[1]
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cdef char *op0 = args[2]
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cdef double complex ov0
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for i in range(n):
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ov0 = (<double complex(*)(double, double complex) noexcept nogil>func)(<double>(<float*>ip0)[0], <double complex>(<float complex*>ip1)[0])
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(<float complex *>op0)[0] = <float complex>ov0
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ip0 += steps[0]
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ip1 += steps[1]
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op0 += steps[2]
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sf_error.check_fpe(func_name)
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cdef void loop_D_ddD__As_ddD_D(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
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cdef np.npy_intp i, n = dims[0]
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cdef void *func = (<void**>data)[0]
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cdef char *func_name = <char*>(<void**>data)[1]
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cdef char *ip0 = args[0]
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cdef char *ip1 = args[1]
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cdef char *ip2 = args[2]
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cdef char *op0 = args[3]
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cdef double complex ov0
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for i in range(n):
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ov0 = (<double complex(*)(double, double, double complex) noexcept nogil>func)(<double>(<double*>ip0)[0], <double>(<double*>ip1)[0], <double complex>(<double complex*>ip2)[0])
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(<double complex *>op0)[0] = <double complex>ov0
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ip0 += steps[0]
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ip1 += steps[1]
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ip2 += steps[2]
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op0 += steps[3]
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sf_error.check_fpe(func_name)
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cdef void loop_D_ddD__As_ffF_F(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
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cdef np.npy_intp i, n = dims[0]
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cdef void *func = (<void**>data)[0]
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cdef char *func_name = <char*>(<void**>data)[1]
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cdef char *ip0 = args[0]
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cdef char *ip1 = args[1]
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cdef char *ip2 = args[2]
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cdef char *op0 = args[3]
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cdef double complex ov0
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for i in range(n):
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ov0 = (<double complex(*)(double, double, double complex) noexcept nogil>func)(<double>(<float*>ip0)[0], <double>(<float*>ip1)[0], <double complex>(<float complex*>ip2)[0])
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(<float complex *>op0)[0] = <float complex>ov0
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ip0 += steps[0]
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ip1 += steps[1]
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ip2 += steps[2]
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op0 += steps[3]
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sf_error.check_fpe(func_name)
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cdef void loop_D_dddD__As_dddD_D(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
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cdef np.npy_intp i, n = dims[0]
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cdef void *func = (<void**>data)[0]
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cdef char *func_name = <char*>(<void**>data)[1]
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cdef char *ip0 = args[0]
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cdef char *ip1 = args[1]
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cdef char *ip2 = args[2]
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cdef char *ip3 = args[3]
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cdef char *op0 = args[4]
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cdef double complex ov0
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for i in range(n):
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ov0 = (<double complex(*)(double, double, double, double complex) noexcept nogil>func)(<double>(<double*>ip0)[0], <double>(<double*>ip1)[0], <double>(<double*>ip2)[0], <double complex>(<double complex*>ip3)[0])
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(<double complex *>op0)[0] = <double complex>ov0
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ip0 += steps[0]
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ip1 += steps[1]
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ip2 += steps[2]
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ip3 += steps[3]
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op0 += steps[4]
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sf_error.check_fpe(func_name)
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cdef void loop_D_dddD__As_fffF_F(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
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cdef np.npy_intp i, n = dims[0]
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cdef void *func = (<void**>data)[0]
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cdef char *func_name = <char*>(<void**>data)[1]
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cdef char *ip0 = args[0]
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cdef char *ip1 = args[1]
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cdef char *ip2 = args[2]
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cdef char *ip3 = args[3]
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cdef char *op0 = args[4]
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cdef double complex ov0
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for i in range(n):
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ov0 = (<double complex(*)(double, double, double, double complex) noexcept nogil>func)(<double>(<float*>ip0)[0], <double>(<float*>ip1)[0], <double>(<float*>ip2)[0], <double complex>(<float complex*>ip3)[0])
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(<float complex *>op0)[0] = <float complex>ov0
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ip0 += steps[0]
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ip1 += steps[1]
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ip2 += steps[2]
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ip3 += steps[3]
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op0 += steps[4]
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sf_error.check_fpe(func_name)
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cdef void loop_d_d__As_d_d(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
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cdef np.npy_intp i, n = dims[0]
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cdef void *func = (<void**>data)[0]
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cdef char *func_name = <char*>(<void**>data)[1]
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cdef char *ip0 = args[0]
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cdef char *op0 = args[1]
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cdef double ov0
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for i in range(n):
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ov0 = (<double(*)(double) noexcept nogil>func)(<double>(<double*>ip0)[0])
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(<double *>op0)[0] = <double>ov0
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ip0 += steps[0]
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op0 += steps[1]
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sf_error.check_fpe(func_name)
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cdef void loop_d_d__As_f_f(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
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cdef np.npy_intp i, n = dims[0]
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cdef void *func = (<void**>data)[0]
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cdef char *func_name = <char*>(<void**>data)[1]
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cdef char *ip0 = args[0]
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cdef char *op0 = args[1]
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cdef double ov0
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for i in range(n):
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ov0 = (<double(*)(double) noexcept nogil>func)(<double>(<float*>ip0)[0])
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(<float *>op0)[0] = <float>ov0
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ip0 += steps[0]
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op0 += steps[1]
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sf_error.check_fpe(func_name)
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cdef void loop_d_dd__As_dd_d(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
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cdef np.npy_intp i, n = dims[0]
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cdef void *func = (<void**>data)[0]
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cdef char *func_name = <char*>(<void**>data)[1]
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cdef char *ip0 = args[0]
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cdef char *ip1 = args[1]
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cdef char *op0 = args[2]
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cdef double ov0
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for i in range(n):
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ov0 = (<double(*)(double, double) noexcept nogil>func)(<double>(<double*>ip0)[0], <double>(<double*>ip1)[0])
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(<double *>op0)[0] = <double>ov0
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ip0 += steps[0]
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ip1 += steps[1]
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op0 += steps[2]
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sf_error.check_fpe(func_name)
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cdef void loop_d_dd__As_ff_f(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
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cdef np.npy_intp i, n = dims[0]
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cdef void *func = (<void**>data)[0]
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cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *ip1 = args[1]
|
|
cdef char *op0 = args[2]
|
|
cdef double ov0
|
|
for i in range(n):
|
|
ov0 = (<double(*)(double, double) noexcept nogil>func)(<double>(<float*>ip0)[0], <double>(<float*>ip1)[0])
|
|
(<float *>op0)[0] = <float>ov0
|
|
ip0 += steps[0]
|
|
ip1 += steps[1]
|
|
op0 += steps[2]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef void loop_d_ddd__As_ddd_d(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
|
|
cdef np.npy_intp i, n = dims[0]
|
|
cdef void *func = (<void**>data)[0]
|
|
cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *ip1 = args[1]
|
|
cdef char *ip2 = args[2]
|
|
cdef char *op0 = args[3]
|
|
cdef double ov0
|
|
for i in range(n):
|
|
ov0 = (<double(*)(double, double, double) noexcept nogil>func)(<double>(<double*>ip0)[0], <double>(<double*>ip1)[0], <double>(<double*>ip2)[0])
|
|
(<double *>op0)[0] = <double>ov0
|
|
ip0 += steps[0]
|
|
ip1 += steps[1]
|
|
ip2 += steps[2]
|
|
op0 += steps[3]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef void loop_d_ddd__As_fff_f(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
|
|
cdef np.npy_intp i, n = dims[0]
|
|
cdef void *func = (<void**>data)[0]
|
|
cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *ip1 = args[1]
|
|
cdef char *ip2 = args[2]
|
|
cdef char *op0 = args[3]
|
|
cdef double ov0
|
|
for i in range(n):
|
|
ov0 = (<double(*)(double, double, double) noexcept nogil>func)(<double>(<float*>ip0)[0], <double>(<float*>ip1)[0], <double>(<float*>ip2)[0])
|
|
(<float *>op0)[0] = <float>ov0
|
|
ip0 += steps[0]
|
|
ip1 += steps[1]
|
|
ip2 += steps[2]
|
|
op0 += steps[3]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef void loop_d_dddd__As_dddd_d(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
|
|
cdef np.npy_intp i, n = dims[0]
|
|
cdef void *func = (<void**>data)[0]
|
|
cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *ip1 = args[1]
|
|
cdef char *ip2 = args[2]
|
|
cdef char *ip3 = args[3]
|
|
cdef char *op0 = args[4]
|
|
cdef double ov0
|
|
for i in range(n):
|
|
ov0 = (<double(*)(double, double, double, double) noexcept nogil>func)(<double>(<double*>ip0)[0], <double>(<double*>ip1)[0], <double>(<double*>ip2)[0], <double>(<double*>ip3)[0])
|
|
(<double *>op0)[0] = <double>ov0
|
|
ip0 += steps[0]
|
|
ip1 += steps[1]
|
|
ip2 += steps[2]
|
|
ip3 += steps[3]
|
|
op0 += steps[4]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef void loop_d_dddd__As_ffff_f(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
|
|
cdef np.npy_intp i, n = dims[0]
|
|
cdef void *func = (<void**>data)[0]
|
|
cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *ip1 = args[1]
|
|
cdef char *ip2 = args[2]
|
|
cdef char *ip3 = args[3]
|
|
cdef char *op0 = args[4]
|
|
cdef double ov0
|
|
for i in range(n):
|
|
ov0 = (<double(*)(double, double, double, double) noexcept nogil>func)(<double>(<float*>ip0)[0], <double>(<float*>ip1)[0], <double>(<float*>ip2)[0], <double>(<float*>ip3)[0])
|
|
(<float *>op0)[0] = <float>ov0
|
|
ip0 += steps[0]
|
|
ip1 += steps[1]
|
|
ip2 += steps[2]
|
|
ip3 += steps[3]
|
|
op0 += steps[4]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef void loop_d_ddddddd__As_ddddddd_d(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
|
|
cdef np.npy_intp i, n = dims[0]
|
|
cdef void *func = (<void**>data)[0]
|
|
cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *ip1 = args[1]
|
|
cdef char *ip2 = args[2]
|
|
cdef char *ip3 = args[3]
|
|
cdef char *ip4 = args[4]
|
|
cdef char *ip5 = args[5]
|
|
cdef char *ip6 = args[6]
|
|
cdef char *op0 = args[7]
|
|
cdef double ov0
|
|
for i in range(n):
|
|
ov0 = (<double(*)(double, double, double, double, double, double, double) noexcept nogil>func)(<double>(<double*>ip0)[0], <double>(<double*>ip1)[0], <double>(<double*>ip2)[0], <double>(<double*>ip3)[0], <double>(<double*>ip4)[0], <double>(<double*>ip5)[0], <double>(<double*>ip6)[0])
|
|
(<double *>op0)[0] = <double>ov0
|
|
ip0 += steps[0]
|
|
ip1 += steps[1]
|
|
ip2 += steps[2]
|
|
ip3 += steps[3]
|
|
ip4 += steps[4]
|
|
ip5 += steps[5]
|
|
ip6 += steps[6]
|
|
op0 += steps[7]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef void loop_d_ddddddd__As_fffffff_f(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
|
|
cdef np.npy_intp i, n = dims[0]
|
|
cdef void *func = (<void**>data)[0]
|
|
cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *ip1 = args[1]
|
|
cdef char *ip2 = args[2]
|
|
cdef char *ip3 = args[3]
|
|
cdef char *ip4 = args[4]
|
|
cdef char *ip5 = args[5]
|
|
cdef char *ip6 = args[6]
|
|
cdef char *op0 = args[7]
|
|
cdef double ov0
|
|
for i in range(n):
|
|
ov0 = (<double(*)(double, double, double, double, double, double, double) noexcept nogil>func)(<double>(<float*>ip0)[0], <double>(<float*>ip1)[0], <double>(<float*>ip2)[0], <double>(<float*>ip3)[0], <double>(<float*>ip4)[0], <double>(<float*>ip5)[0], <double>(<float*>ip6)[0])
|
|
(<float *>op0)[0] = <float>ov0
|
|
ip0 += steps[0]
|
|
ip1 += steps[1]
|
|
ip2 += steps[2]
|
|
ip3 += steps[3]
|
|
ip4 += steps[4]
|
|
ip5 += steps[5]
|
|
ip6 += steps[6]
|
|
op0 += steps[7]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef void loop_d_ddiiddd__As_ddllddd_d(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
|
|
cdef np.npy_intp i, n = dims[0]
|
|
cdef void *func = (<void**>data)[0]
|
|
cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *ip1 = args[1]
|
|
cdef char *ip2 = args[2]
|
|
cdef char *ip3 = args[3]
|
|
cdef char *ip4 = args[4]
|
|
cdef char *ip5 = args[5]
|
|
cdef char *ip6 = args[6]
|
|
cdef char *op0 = args[7]
|
|
cdef double ov0
|
|
for i in range(n):
|
|
if <int>(<long*>ip2)[0] == (<long*>ip2)[0] and <int>(<long*>ip3)[0] == (<long*>ip3)[0]:
|
|
ov0 = (<double(*)(double, double, int, int, double, double, double) noexcept nogil>func)(<double>(<double*>ip0)[0], <double>(<double*>ip1)[0], <int>(<long*>ip2)[0], <int>(<long*>ip3)[0], <double>(<double*>ip4)[0], <double>(<double*>ip5)[0], <double>(<double*>ip6)[0])
|
|
else:
|
|
sf_error.error(func_name, sf_error.DOMAIN, "invalid input argument")
|
|
ov0 = <double>NAN
|
|
(<double *>op0)[0] = <double>ov0
|
|
ip0 += steps[0]
|
|
ip1 += steps[1]
|
|
ip2 += steps[2]
|
|
ip3 += steps[3]
|
|
ip4 += steps[4]
|
|
ip5 += steps[5]
|
|
ip6 += steps[6]
|
|
op0 += steps[7]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef void loop_d_ddp_d_As_ddp_dd(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
|
|
cdef np.npy_intp i, n = dims[0]
|
|
cdef void *func = (<void**>data)[0]
|
|
cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *ip1 = args[1]
|
|
cdef char *ip2 = args[2]
|
|
cdef char *op0 = args[3]
|
|
cdef char *op1 = args[4]
|
|
cdef double ov0
|
|
cdef double ov1
|
|
for i in range(n):
|
|
ov0 = (<double(*)(double, double, Py_ssize_t, double *) noexcept nogil>func)(<double>(<double*>ip0)[0], <double>(<double*>ip1)[0], <Py_ssize_t>(<Py_ssize_t*>ip2)[0], &ov1)
|
|
(<double *>op0)[0] = <double>ov0
|
|
(<double *>op1)[0] = <double>ov1
|
|
ip0 += steps[0]
|
|
ip1 += steps[1]
|
|
ip2 += steps[2]
|
|
op0 += steps[3]
|
|
op1 += steps[4]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef void loop_d_dpd__As_dpd_d(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
|
|
cdef np.npy_intp i, n = dims[0]
|
|
cdef void *func = (<void**>data)[0]
|
|
cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *ip1 = args[1]
|
|
cdef char *ip2 = args[2]
|
|
cdef char *op0 = args[3]
|
|
cdef double ov0
|
|
for i in range(n):
|
|
ov0 = (<double(*)(double, Py_ssize_t, double) noexcept nogil>func)(<double>(<double*>ip0)[0], <Py_ssize_t>(<Py_ssize_t*>ip1)[0], <double>(<double*>ip2)[0])
|
|
(<double *>op0)[0] = <double>ov0
|
|
ip0 += steps[0]
|
|
ip1 += steps[1]
|
|
ip2 += steps[2]
|
|
op0 += steps[3]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef void loop_d_pd__As_pd_d(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
|
|
cdef np.npy_intp i, n = dims[0]
|
|
cdef void *func = (<void**>data)[0]
|
|
cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *ip1 = args[1]
|
|
cdef char *op0 = args[2]
|
|
cdef double ov0
|
|
for i in range(n):
|
|
ov0 = (<double(*)(Py_ssize_t, double) noexcept nogil>func)(<Py_ssize_t>(<Py_ssize_t*>ip0)[0], <double>(<double*>ip1)[0])
|
|
(<double *>op0)[0] = <double>ov0
|
|
ip0 += steps[0]
|
|
ip1 += steps[1]
|
|
op0 += steps[2]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef void loop_d_pdd__As_pdd_d(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
|
|
cdef np.npy_intp i, n = dims[0]
|
|
cdef void *func = (<void**>data)[0]
|
|
cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *ip1 = args[1]
|
|
cdef char *ip2 = args[2]
|
|
cdef char *op0 = args[3]
|
|
cdef double ov0
|
|
for i in range(n):
|
|
ov0 = (<double(*)(Py_ssize_t, double, double) noexcept nogil>func)(<Py_ssize_t>(<Py_ssize_t*>ip0)[0], <double>(<double*>ip1)[0], <double>(<double*>ip2)[0])
|
|
(<double *>op0)[0] = <double>ov0
|
|
ip0 += steps[0]
|
|
ip1 += steps[1]
|
|
ip2 += steps[2]
|
|
op0 += steps[3]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef void loop_d_pddd__As_pddd_d(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
|
|
cdef np.npy_intp i, n = dims[0]
|
|
cdef void *func = (<void**>data)[0]
|
|
cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *ip1 = args[1]
|
|
cdef char *ip2 = args[2]
|
|
cdef char *ip3 = args[3]
|
|
cdef char *op0 = args[4]
|
|
cdef double ov0
|
|
for i in range(n):
|
|
ov0 = (<double(*)(Py_ssize_t, double, double, double) noexcept nogil>func)(<Py_ssize_t>(<Py_ssize_t*>ip0)[0], <double>(<double*>ip1)[0], <double>(<double*>ip2)[0], <double>(<double*>ip3)[0])
|
|
(<double *>op0)[0] = <double>ov0
|
|
ip0 += steps[0]
|
|
ip1 += steps[1]
|
|
ip2 += steps[2]
|
|
ip3 += steps[3]
|
|
op0 += steps[4]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef void loop_d_ppd__As_ppd_d(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
|
|
cdef np.npy_intp i, n = dims[0]
|
|
cdef void *func = (<void**>data)[0]
|
|
cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *ip1 = args[1]
|
|
cdef char *ip2 = args[2]
|
|
cdef char *op0 = args[3]
|
|
cdef double ov0
|
|
for i in range(n):
|
|
ov0 = (<double(*)(Py_ssize_t, Py_ssize_t, double) noexcept nogil>func)(<Py_ssize_t>(<Py_ssize_t*>ip0)[0], <Py_ssize_t>(<Py_ssize_t*>ip1)[0], <double>(<double*>ip2)[0])
|
|
(<double *>op0)[0] = <double>ov0
|
|
ip0 += steps[0]
|
|
ip1 += steps[1]
|
|
ip2 += steps[2]
|
|
op0 += steps[3]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef void loop_f_f__As_f_f(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
|
|
cdef np.npy_intp i, n = dims[0]
|
|
cdef void *func = (<void**>data)[0]
|
|
cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *op0 = args[1]
|
|
cdef float ov0
|
|
for i in range(n):
|
|
ov0 = (<float(*)(float) noexcept nogil>func)(<float>(<float*>ip0)[0])
|
|
(<float *>op0)[0] = <float>ov0
|
|
ip0 += steps[0]
|
|
op0 += steps[1]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef void loop_f_ff__As_ff_f(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
|
|
cdef np.npy_intp i, n = dims[0]
|
|
cdef void *func = (<void**>data)[0]
|
|
cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *ip1 = args[1]
|
|
cdef char *op0 = args[2]
|
|
cdef float ov0
|
|
for i in range(n):
|
|
ov0 = (<float(*)(float, float) noexcept nogil>func)(<float>(<float*>ip0)[0], <float>(<float*>ip1)[0])
|
|
(<float *>op0)[0] = <float>ov0
|
|
ip0 += steps[0]
|
|
ip1 += steps[1]
|
|
op0 += steps[2]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef void loop_f_fff__As_fff_f(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
|
|
cdef np.npy_intp i, n = dims[0]
|
|
cdef void *func = (<void**>data)[0]
|
|
cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *ip1 = args[1]
|
|
cdef char *ip2 = args[2]
|
|
cdef char *op0 = args[3]
|
|
cdef float ov0
|
|
for i in range(n):
|
|
ov0 = (<float(*)(float, float, float) noexcept nogil>func)(<float>(<float*>ip0)[0], <float>(<float*>ip1)[0], <float>(<float*>ip2)[0])
|
|
(<float *>op0)[0] = <float>ov0
|
|
ip0 += steps[0]
|
|
ip1 += steps[1]
|
|
ip2 += steps[2]
|
|
op0 += steps[3]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef void loop_f_ffff__As_ffff_f(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
|
|
cdef np.npy_intp i, n = dims[0]
|
|
cdef void *func = (<void**>data)[0]
|
|
cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *ip1 = args[1]
|
|
cdef char *ip2 = args[2]
|
|
cdef char *ip3 = args[3]
|
|
cdef char *op0 = args[4]
|
|
cdef float ov0
|
|
for i in range(n):
|
|
ov0 = (<float(*)(float, float, float, float) noexcept nogil>func)(<float>(<float*>ip0)[0], <float>(<float*>ip1)[0], <float>(<float*>ip2)[0], <float>(<float*>ip3)[0])
|
|
(<float *>op0)[0] = <float>ov0
|
|
ip0 += steps[0]
|
|
ip1 += steps[1]
|
|
ip2 += steps[2]
|
|
ip3 += steps[3]
|
|
op0 += steps[4]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef void loop_i_D_DD_As_D_DD(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
|
|
cdef np.npy_intp i, n = dims[0]
|
|
cdef void *func = (<void**>data)[0]
|
|
cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *op0 = args[1]
|
|
cdef char *op1 = args[2]
|
|
cdef double complex ov0
|
|
cdef double complex ov1
|
|
for i in range(n):
|
|
(<int(*)(double complex, double complex *, double complex *) noexcept nogil>func)(<double complex>(<double complex*>ip0)[0], &ov0, &ov1)
|
|
(<double complex *>op0)[0] = <double complex>ov0
|
|
(<double complex *>op1)[0] = <double complex>ov1
|
|
ip0 += steps[0]
|
|
op0 += steps[1]
|
|
op1 += steps[2]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef void loop_i_D_DD_As_F_FF(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
|
|
cdef np.npy_intp i, n = dims[0]
|
|
cdef void *func = (<void**>data)[0]
|
|
cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *op0 = args[1]
|
|
cdef char *op1 = args[2]
|
|
cdef double complex ov0
|
|
cdef double complex ov1
|
|
for i in range(n):
|
|
(<int(*)(double complex, double complex *, double complex *) noexcept nogil>func)(<double complex>(<float complex*>ip0)[0], &ov0, &ov1)
|
|
(<float complex *>op0)[0] = <float complex>ov0
|
|
(<float complex *>op1)[0] = <float complex>ov1
|
|
ip0 += steps[0]
|
|
op0 += steps[1]
|
|
op1 += steps[2]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef void loop_i_d_dd_As_d_dd(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
|
|
cdef np.npy_intp i, n = dims[0]
|
|
cdef void *func = (<void**>data)[0]
|
|
cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *op0 = args[1]
|
|
cdef char *op1 = args[2]
|
|
cdef double ov0
|
|
cdef double ov1
|
|
for i in range(n):
|
|
(<int(*)(double, double *, double *) noexcept nogil>func)(<double>(<double*>ip0)[0], &ov0, &ov1)
|
|
(<double *>op0)[0] = <double>ov0
|
|
(<double *>op1)[0] = <double>ov1
|
|
ip0 += steps[0]
|
|
op0 += steps[1]
|
|
op1 += steps[2]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef void loop_i_d_dd_As_f_ff(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
|
|
cdef np.npy_intp i, n = dims[0]
|
|
cdef void *func = (<void**>data)[0]
|
|
cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *op0 = args[1]
|
|
cdef char *op1 = args[2]
|
|
cdef double ov0
|
|
cdef double ov1
|
|
for i in range(n):
|
|
(<int(*)(double, double *, double *) noexcept nogil>func)(<double>(<float*>ip0)[0], &ov0, &ov1)
|
|
(<float *>op0)[0] = <float>ov0
|
|
(<float *>op1)[0] = <float>ov1
|
|
ip0 += steps[0]
|
|
op0 += steps[1]
|
|
op1 += steps[2]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef void loop_i_i__As_l_l(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
|
|
cdef np.npy_intp i, n = dims[0]
|
|
cdef void *func = (<void**>data)[0]
|
|
cdef char *func_name = <char*>(<void**>data)[1]
|
|
cdef char *ip0 = args[0]
|
|
cdef char *op0 = args[1]
|
|
cdef int ov0
|
|
for i in range(n):
|
|
if <int>(<long*>ip0)[0] == (<long*>ip0)[0]:
|
|
ov0 = (<int(*)(int) noexcept nogil>func)(<int>(<long*>ip0)[0])
|
|
else:
|
|
sf_error.error(func_name, sf_error.DOMAIN, "invalid input argument")
|
|
ov0 = <int>0xbad0bad0
|
|
(<long *>op0)[0] = <long>ov0
|
|
ip0 += steps[0]
|
|
op0 += steps[1]
|
|
sf_error.check_fpe(func_name)
|
|
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cosine_cdf "cosine_cdf"(double) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cosine_invcdf "cosine_invcdf"(double) noexcept nogil
|
|
from ._ellip_harm cimport ellip_harmonic as _func_ellip_harmonic
|
|
ctypedef double _proto_ellip_harmonic_t(double, double, int, int, double, double, double) noexcept nogil
|
|
cdef _proto_ellip_harmonic_t *_proto_ellip_harmonic_t_var = &_func_ellip_harmonic
|
|
from ._legacy cimport ellip_harmonic_unsafe as _func_ellip_harmonic_unsafe
|
|
ctypedef double _proto_ellip_harmonic_unsafe_t(double, double, double, double, double, double, double) noexcept nogil
|
|
cdef _proto_ellip_harmonic_unsafe_t *_proto_ellip_harmonic_unsafe_t_var = &_func_ellip_harmonic_unsafe
|
|
from ._factorial cimport _factorial as _func__factorial
|
|
ctypedef double _proto__factorial_t(double) noexcept nogil
|
|
cdef _proto__factorial_t *_proto__factorial_t_var = &_func__factorial
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes_igam_fac "cephes_igam_fac"(double, double) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_xsf_kolmogc "xsf_kolmogc"(double) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_xsf_kolmogci "xsf_kolmogci"(double) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_xsf_kolmogp "xsf_kolmogp"(double) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes_lanczos_sum_expg_scaled "cephes_lanczos_sum_expg_scaled"(double) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes_lgam1p "cephes_lgam1p"(double) noexcept nogil
|
|
from .sf_error cimport _sf_error_test_function as _func__sf_error_test_function
|
|
ctypedef int _proto__sf_error_test_function_t(int) noexcept nogil
|
|
cdef _proto__sf_error_test_function_t *_proto__sf_error_test_function_t_var = &_func__sf_error_test_function
|
|
from ._legacy cimport smirnovc_unsafe as _func_smirnovc_unsafe
|
|
ctypedef double _proto_smirnovc_unsafe_t(double, double) noexcept nogil
|
|
cdef _proto_smirnovc_unsafe_t *_proto_smirnovc_unsafe_t_var = &_func_smirnovc_unsafe
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes_smirnovc_wrap "cephes_smirnovc_wrap"(Py_ssize_t, double) noexcept nogil
|
|
from ._legacy cimport smirnovci_unsafe as _func_smirnovci_unsafe
|
|
ctypedef double _proto_smirnovci_unsafe_t(double, double) noexcept nogil
|
|
cdef _proto_smirnovci_unsafe_t *_proto_smirnovci_unsafe_t_var = &_func_smirnovci_unsafe
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes_smirnovci_wrap "cephes_smirnovci_wrap"(Py_ssize_t, double) noexcept nogil
|
|
from ._legacy cimport smirnovp_unsafe as _func_smirnovp_unsafe
|
|
ctypedef double _proto_smirnovp_unsafe_t(double, double) noexcept nogil
|
|
cdef _proto_smirnovp_unsafe_t *_proto_smirnovp_unsafe_t_var = &_func_smirnovp_unsafe
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes_smirnovp_wrap "cephes_smirnovp_wrap"(Py_ssize_t, double) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes__struve_asymp_large_z "cephes__struve_asymp_large_z"(double, double, Py_ssize_t, double *) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes__struve_bessel_series "cephes__struve_bessel_series"(double, double, Py_ssize_t, double *) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes__struve_power_series "cephes__struve_power_series"(double, double, Py_ssize_t, double *) noexcept nogil
|
|
from ._agm cimport agm as _func_agm
|
|
ctypedef double _proto_agm_t(double, double) noexcept nogil
|
|
cdef _proto_agm_t *_proto_agm_t_var = &_func_agm
|
|
from ._legacy cimport bdtr_unsafe as _func_bdtr_unsafe
|
|
ctypedef double _proto_bdtr_unsafe_t(double, double, double) noexcept nogil
|
|
cdef _proto_bdtr_unsafe_t *_proto_bdtr_unsafe_t_var = &_func_bdtr_unsafe
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes_bdtr_wrap "cephes_bdtr_wrap"(double, Py_ssize_t, double) noexcept nogil
|
|
from ._legacy cimport bdtrc_unsafe as _func_bdtrc_unsafe
|
|
ctypedef double _proto_bdtrc_unsafe_t(double, double, double) noexcept nogil
|
|
cdef _proto_bdtrc_unsafe_t *_proto_bdtrc_unsafe_t_var = &_func_bdtrc_unsafe
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes_bdtrc_wrap "cephes_bdtrc_wrap"(double, Py_ssize_t, double) noexcept nogil
|
|
from ._legacy cimport bdtri_unsafe as _func_bdtri_unsafe
|
|
ctypedef double _proto_bdtri_unsafe_t(double, double, double) noexcept nogil
|
|
cdef _proto_bdtri_unsafe_t *_proto_bdtri_unsafe_t_var = &_func_bdtri_unsafe
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes_bdtri_wrap "cephes_bdtri_wrap"(double, Py_ssize_t, double) noexcept nogil
|
|
from ._cdflib_wrappers cimport bdtrik as _func_bdtrik
|
|
ctypedef double _proto_bdtrik_t(double, double, double) noexcept nogil
|
|
cdef _proto_bdtrik_t *_proto_bdtrik_t_var = &_func_bdtrik
|
|
from ._cdflib_wrappers cimport bdtrin as _func_bdtrin
|
|
ctypedef double _proto_bdtrin_t(double, double, double) noexcept nogil
|
|
cdef _proto_bdtrin_t *_proto_bdtrin_t_var = &_func_bdtrin
|
|
from ._boxcox cimport boxcox as _func_boxcox
|
|
ctypedef double _proto_boxcox_t(double, double) noexcept nogil
|
|
cdef _proto_boxcox_t *_proto_boxcox_t_var = &_func_boxcox
|
|
from ._boxcox cimport boxcox1p as _func_boxcox1p
|
|
ctypedef double _proto_boxcox1p_t(double, double) noexcept nogil
|
|
cdef _proto_boxcox1p_t *_proto_boxcox1p_t_var = &_func_boxcox1p
|
|
from ._cdflib_wrappers cimport btdtria as _func_btdtria
|
|
ctypedef double _proto_btdtria_t(double, double, double) noexcept nogil
|
|
cdef _proto_btdtria_t *_proto_btdtria_t_var = &_func_btdtria
|
|
from ._cdflib_wrappers cimport btdtrib as _func_btdtrib
|
|
ctypedef double _proto_btdtrib_t(double, double, double) noexcept nogil
|
|
cdef _proto_btdtrib_t *_proto_btdtrib_t_var = &_func_btdtrib
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_xsf_chdtr "xsf_chdtr"(double, double) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_xsf_chdtrc "xsf_chdtrc"(double, double) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_xsf_chdtri "xsf_chdtri"(double, double) noexcept nogil
|
|
from ._cdflib_wrappers cimport chdtriv as _func_chdtriv
|
|
ctypedef double _proto_chdtriv_t(double, double) noexcept nogil
|
|
cdef _proto_chdtriv_t *_proto_chdtriv_t_var = &_func_chdtriv
|
|
from ._cdflib_wrappers cimport chndtr as _func_chndtr
|
|
ctypedef double _proto_chndtr_t(double, double, double) noexcept nogil
|
|
cdef _proto_chndtr_t *_proto_chndtr_t_var = &_func_chndtr
|
|
from ._cdflib_wrappers cimport chndtridf as _func_chndtridf
|
|
ctypedef double _proto_chndtridf_t(double, double, double) noexcept nogil
|
|
cdef _proto_chndtridf_t *_proto_chndtridf_t_var = &_func_chndtridf
|
|
from ._cdflib_wrappers cimport chndtrinc as _func_chndtrinc
|
|
ctypedef double _proto_chndtrinc_t(double, double, double) noexcept nogil
|
|
cdef _proto_chndtrinc_t *_proto_chndtrinc_t_var = &_func_chndtrinc
|
|
from ._cdflib_wrappers cimport chndtrix as _func_chndtrix
|
|
ctypedef double _proto_chndtrix_t(double, double, double) noexcept nogil
|
|
cdef _proto_chndtrix_t *_proto_chndtrix_t_var = &_func_chndtrix
|
|
from ._convex_analysis cimport entr as _func_entr
|
|
ctypedef double _proto_entr_t(double) noexcept nogil
|
|
cdef _proto_entr_t *_proto_entr_t_var = &_func_entr
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes_erfcinv "cephes_erfcinv"(double) noexcept nogil
|
|
from .orthogonal_eval cimport eval_chebyc as _func_eval_chebyc
|
|
ctypedef double complex _proto_eval_chebyc_double_complex__t(double, double complex) noexcept nogil
|
|
cdef _proto_eval_chebyc_double_complex__t *_proto_eval_chebyc_double_complex__t_var = &_func_eval_chebyc[double_complex]
|
|
from .orthogonal_eval cimport eval_chebyc as _func_eval_chebyc
|
|
ctypedef double _proto_eval_chebyc_double__t(double, double) noexcept nogil
|
|
cdef _proto_eval_chebyc_double__t *_proto_eval_chebyc_double__t_var = &_func_eval_chebyc[double]
|
|
from .orthogonal_eval cimport eval_chebyc_l as _func_eval_chebyc_l
|
|
ctypedef double _proto_eval_chebyc_l_t(Py_ssize_t, double) noexcept nogil
|
|
cdef _proto_eval_chebyc_l_t *_proto_eval_chebyc_l_t_var = &_func_eval_chebyc_l
|
|
from .orthogonal_eval cimport eval_chebys as _func_eval_chebys
|
|
ctypedef double complex _proto_eval_chebys_double_complex__t(double, double complex) noexcept nogil
|
|
cdef _proto_eval_chebys_double_complex__t *_proto_eval_chebys_double_complex__t_var = &_func_eval_chebys[double_complex]
|
|
from .orthogonal_eval cimport eval_chebys as _func_eval_chebys
|
|
ctypedef double _proto_eval_chebys_double__t(double, double) noexcept nogil
|
|
cdef _proto_eval_chebys_double__t *_proto_eval_chebys_double__t_var = &_func_eval_chebys[double]
|
|
from .orthogonal_eval cimport eval_chebys_l as _func_eval_chebys_l
|
|
ctypedef double _proto_eval_chebys_l_t(Py_ssize_t, double) noexcept nogil
|
|
cdef _proto_eval_chebys_l_t *_proto_eval_chebys_l_t_var = &_func_eval_chebys_l
|
|
from .orthogonal_eval cimport eval_chebyt as _func_eval_chebyt
|
|
ctypedef double complex _proto_eval_chebyt_double_complex__t(double, double complex) noexcept nogil
|
|
cdef _proto_eval_chebyt_double_complex__t *_proto_eval_chebyt_double_complex__t_var = &_func_eval_chebyt[double_complex]
|
|
from .orthogonal_eval cimport eval_chebyt as _func_eval_chebyt
|
|
ctypedef double _proto_eval_chebyt_double__t(double, double) noexcept nogil
|
|
cdef _proto_eval_chebyt_double__t *_proto_eval_chebyt_double__t_var = &_func_eval_chebyt[double]
|
|
from .orthogonal_eval cimport eval_chebyt_l as _func_eval_chebyt_l
|
|
ctypedef double _proto_eval_chebyt_l_t(Py_ssize_t, double) noexcept nogil
|
|
cdef _proto_eval_chebyt_l_t *_proto_eval_chebyt_l_t_var = &_func_eval_chebyt_l
|
|
from .orthogonal_eval cimport eval_chebyu as _func_eval_chebyu
|
|
ctypedef double complex _proto_eval_chebyu_double_complex__t(double, double complex) noexcept nogil
|
|
cdef _proto_eval_chebyu_double_complex__t *_proto_eval_chebyu_double_complex__t_var = &_func_eval_chebyu[double_complex]
|
|
from .orthogonal_eval cimport eval_chebyu as _func_eval_chebyu
|
|
ctypedef double _proto_eval_chebyu_double__t(double, double) noexcept nogil
|
|
cdef _proto_eval_chebyu_double__t *_proto_eval_chebyu_double__t_var = &_func_eval_chebyu[double]
|
|
from .orthogonal_eval cimport eval_chebyu_l as _func_eval_chebyu_l
|
|
ctypedef double _proto_eval_chebyu_l_t(Py_ssize_t, double) noexcept nogil
|
|
cdef _proto_eval_chebyu_l_t *_proto_eval_chebyu_l_t_var = &_func_eval_chebyu_l
|
|
from .orthogonal_eval cimport eval_gegenbauer as _func_eval_gegenbauer
|
|
ctypedef double complex _proto_eval_gegenbauer_double_complex__t(double, double, double complex) noexcept nogil
|
|
cdef _proto_eval_gegenbauer_double_complex__t *_proto_eval_gegenbauer_double_complex__t_var = &_func_eval_gegenbauer[double_complex]
|
|
from .orthogonal_eval cimport eval_gegenbauer as _func_eval_gegenbauer
|
|
ctypedef double _proto_eval_gegenbauer_double__t(double, double, double) noexcept nogil
|
|
cdef _proto_eval_gegenbauer_double__t *_proto_eval_gegenbauer_double__t_var = &_func_eval_gegenbauer[double]
|
|
from .orthogonal_eval cimport eval_gegenbauer_l as _func_eval_gegenbauer_l
|
|
ctypedef double _proto_eval_gegenbauer_l_t(Py_ssize_t, double, double) noexcept nogil
|
|
cdef _proto_eval_gegenbauer_l_t *_proto_eval_gegenbauer_l_t_var = &_func_eval_gegenbauer_l
|
|
from .orthogonal_eval cimport eval_genlaguerre as _func_eval_genlaguerre
|
|
ctypedef double complex _proto_eval_genlaguerre_double_complex__t(double, double, double complex) noexcept nogil
|
|
cdef _proto_eval_genlaguerre_double_complex__t *_proto_eval_genlaguerre_double_complex__t_var = &_func_eval_genlaguerre[double_complex]
|
|
from .orthogonal_eval cimport eval_genlaguerre as _func_eval_genlaguerre
|
|
ctypedef double _proto_eval_genlaguerre_double__t(double, double, double) noexcept nogil
|
|
cdef _proto_eval_genlaguerre_double__t *_proto_eval_genlaguerre_double__t_var = &_func_eval_genlaguerre[double]
|
|
from .orthogonal_eval cimport eval_genlaguerre_l as _func_eval_genlaguerre_l
|
|
ctypedef double _proto_eval_genlaguerre_l_t(Py_ssize_t, double, double) noexcept nogil
|
|
cdef _proto_eval_genlaguerre_l_t *_proto_eval_genlaguerre_l_t_var = &_func_eval_genlaguerre_l
|
|
from .orthogonal_eval cimport eval_hermite as _func_eval_hermite
|
|
ctypedef double _proto_eval_hermite_t(Py_ssize_t, double) noexcept nogil
|
|
cdef _proto_eval_hermite_t *_proto_eval_hermite_t_var = &_func_eval_hermite
|
|
from .orthogonal_eval cimport eval_hermitenorm as _func_eval_hermitenorm
|
|
ctypedef double _proto_eval_hermitenorm_t(Py_ssize_t, double) noexcept nogil
|
|
cdef _proto_eval_hermitenorm_t *_proto_eval_hermitenorm_t_var = &_func_eval_hermitenorm
|
|
from .orthogonal_eval cimport eval_jacobi as _func_eval_jacobi
|
|
ctypedef double complex _proto_eval_jacobi_double_complex__t(double, double, double, double complex) noexcept nogil
|
|
cdef _proto_eval_jacobi_double_complex__t *_proto_eval_jacobi_double_complex__t_var = &_func_eval_jacobi[double_complex]
|
|
from .orthogonal_eval cimport eval_jacobi as _func_eval_jacobi
|
|
ctypedef double _proto_eval_jacobi_double__t(double, double, double, double) noexcept nogil
|
|
cdef _proto_eval_jacobi_double__t *_proto_eval_jacobi_double__t_var = &_func_eval_jacobi[double]
|
|
from .orthogonal_eval cimport eval_jacobi_l as _func_eval_jacobi_l
|
|
ctypedef double _proto_eval_jacobi_l_t(Py_ssize_t, double, double, double) noexcept nogil
|
|
cdef _proto_eval_jacobi_l_t *_proto_eval_jacobi_l_t_var = &_func_eval_jacobi_l
|
|
from .orthogonal_eval cimport eval_laguerre as _func_eval_laguerre
|
|
ctypedef double complex _proto_eval_laguerre_double_complex__t(double, double complex) noexcept nogil
|
|
cdef _proto_eval_laguerre_double_complex__t *_proto_eval_laguerre_double_complex__t_var = &_func_eval_laguerre[double_complex]
|
|
from .orthogonal_eval cimport eval_laguerre as _func_eval_laguerre
|
|
ctypedef double _proto_eval_laguerre_double__t(double, double) noexcept nogil
|
|
cdef _proto_eval_laguerre_double__t *_proto_eval_laguerre_double__t_var = &_func_eval_laguerre[double]
|
|
from .orthogonal_eval cimport eval_laguerre_l as _func_eval_laguerre_l
|
|
ctypedef double _proto_eval_laguerre_l_t(Py_ssize_t, double) noexcept nogil
|
|
cdef _proto_eval_laguerre_l_t *_proto_eval_laguerre_l_t_var = &_func_eval_laguerre_l
|
|
from .orthogonal_eval cimport eval_legendre as _func_eval_legendre
|
|
ctypedef double complex _proto_eval_legendre_double_complex__t(double, double complex) noexcept nogil
|
|
cdef _proto_eval_legendre_double_complex__t *_proto_eval_legendre_double_complex__t_var = &_func_eval_legendre[double_complex]
|
|
from .orthogonal_eval cimport eval_legendre as _func_eval_legendre
|
|
ctypedef double _proto_eval_legendre_double__t(double, double) noexcept nogil
|
|
cdef _proto_eval_legendre_double__t *_proto_eval_legendre_double__t_var = &_func_eval_legendre[double]
|
|
from .orthogonal_eval cimport eval_legendre_l as _func_eval_legendre_l
|
|
ctypedef double _proto_eval_legendre_l_t(Py_ssize_t, double) noexcept nogil
|
|
cdef _proto_eval_legendre_l_t *_proto_eval_legendre_l_t_var = &_func_eval_legendre_l
|
|
from .orthogonal_eval cimport eval_sh_chebyt as _func_eval_sh_chebyt
|
|
ctypedef double complex _proto_eval_sh_chebyt_double_complex__t(double, double complex) noexcept nogil
|
|
cdef _proto_eval_sh_chebyt_double_complex__t *_proto_eval_sh_chebyt_double_complex__t_var = &_func_eval_sh_chebyt[double_complex]
|
|
from .orthogonal_eval cimport eval_sh_chebyt as _func_eval_sh_chebyt
|
|
ctypedef double _proto_eval_sh_chebyt_double__t(double, double) noexcept nogil
|
|
cdef _proto_eval_sh_chebyt_double__t *_proto_eval_sh_chebyt_double__t_var = &_func_eval_sh_chebyt[double]
|
|
from .orthogonal_eval cimport eval_sh_chebyt_l as _func_eval_sh_chebyt_l
|
|
ctypedef double _proto_eval_sh_chebyt_l_t(Py_ssize_t, double) noexcept nogil
|
|
cdef _proto_eval_sh_chebyt_l_t *_proto_eval_sh_chebyt_l_t_var = &_func_eval_sh_chebyt_l
|
|
from .orthogonal_eval cimport eval_sh_chebyu as _func_eval_sh_chebyu
|
|
ctypedef double complex _proto_eval_sh_chebyu_double_complex__t(double, double complex) noexcept nogil
|
|
cdef _proto_eval_sh_chebyu_double_complex__t *_proto_eval_sh_chebyu_double_complex__t_var = &_func_eval_sh_chebyu[double_complex]
|
|
from .orthogonal_eval cimport eval_sh_chebyu as _func_eval_sh_chebyu
|
|
ctypedef double _proto_eval_sh_chebyu_double__t(double, double) noexcept nogil
|
|
cdef _proto_eval_sh_chebyu_double__t *_proto_eval_sh_chebyu_double__t_var = &_func_eval_sh_chebyu[double]
|
|
from .orthogonal_eval cimport eval_sh_chebyu_l as _func_eval_sh_chebyu_l
|
|
ctypedef double _proto_eval_sh_chebyu_l_t(Py_ssize_t, double) noexcept nogil
|
|
cdef _proto_eval_sh_chebyu_l_t *_proto_eval_sh_chebyu_l_t_var = &_func_eval_sh_chebyu_l
|
|
from .orthogonal_eval cimport eval_sh_jacobi as _func_eval_sh_jacobi
|
|
ctypedef double complex _proto_eval_sh_jacobi_double_complex__t(double, double, double, double complex) noexcept nogil
|
|
cdef _proto_eval_sh_jacobi_double_complex__t *_proto_eval_sh_jacobi_double_complex__t_var = &_func_eval_sh_jacobi[double_complex]
|
|
from .orthogonal_eval cimport eval_sh_jacobi as _func_eval_sh_jacobi
|
|
ctypedef double _proto_eval_sh_jacobi_double__t(double, double, double, double) noexcept nogil
|
|
cdef _proto_eval_sh_jacobi_double__t *_proto_eval_sh_jacobi_double__t_var = &_func_eval_sh_jacobi[double]
|
|
from .orthogonal_eval cimport eval_sh_jacobi_l as _func_eval_sh_jacobi_l
|
|
ctypedef double _proto_eval_sh_jacobi_l_t(Py_ssize_t, double, double, double) noexcept nogil
|
|
cdef _proto_eval_sh_jacobi_l_t *_proto_eval_sh_jacobi_l_t_var = &_func_eval_sh_jacobi_l
|
|
from .orthogonal_eval cimport eval_sh_legendre as _func_eval_sh_legendre
|
|
ctypedef double complex _proto_eval_sh_legendre_double_complex__t(double, double complex) noexcept nogil
|
|
cdef _proto_eval_sh_legendre_double_complex__t *_proto_eval_sh_legendre_double_complex__t_var = &_func_eval_sh_legendre[double_complex]
|
|
from .orthogonal_eval cimport eval_sh_legendre as _func_eval_sh_legendre
|
|
ctypedef double _proto_eval_sh_legendre_double__t(double, double) noexcept nogil
|
|
cdef _proto_eval_sh_legendre_double__t *_proto_eval_sh_legendre_double__t_var = &_func_eval_sh_legendre[double]
|
|
from .orthogonal_eval cimport eval_sh_legendre_l as _func_eval_sh_legendre_l
|
|
ctypedef double _proto_eval_sh_legendre_l_t(Py_ssize_t, double) noexcept nogil
|
|
cdef _proto_eval_sh_legendre_l_t *_proto_eval_sh_legendre_l_t_var = &_func_eval_sh_legendre_l
|
|
from ._legacy cimport expn_unsafe as _func_expn_unsafe
|
|
ctypedef double _proto_expn_unsafe_t(double, double) noexcept nogil
|
|
cdef _proto_expn_unsafe_t *_proto_expn_unsafe_t_var = &_func_expn_unsafe
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes_expn_wrap "cephes_expn_wrap"(Py_ssize_t, double) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_xsf_fdtr "xsf_fdtr"(double, double, double) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_xsf_fdtrc "xsf_fdtrc"(double, double, double) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_xsf_fdtri "xsf_fdtri"(double, double, double) noexcept nogil
|
|
from ._cdflib_wrappers cimport fdtridfd as _func_fdtridfd
|
|
ctypedef double _proto_fdtridfd_t(double, double, double) noexcept nogil
|
|
cdef _proto_fdtridfd_t *_proto_fdtridfd_t_var = &_func_fdtridfd
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_xsf_gdtr "xsf_gdtr"(double, double, double) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_xsf_gdtrc "xsf_gdtrc"(double, double, double) noexcept nogil
|
|
from ._cdflib_wrappers cimport gdtria as _func_gdtria
|
|
ctypedef double _proto_gdtria_t(double, double, double) noexcept nogil
|
|
cdef _proto_gdtria_t *_proto_gdtria_t_var = &_func_gdtria
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_xsf_gdtrib "xsf_gdtrib"(double, double, double) noexcept nogil
|
|
from ._cdflib_wrappers cimport gdtrix as _func_gdtrix
|
|
ctypedef double _proto_gdtrix_t(double, double, double) noexcept nogil
|
|
cdef _proto_gdtrix_t *_proto_gdtrix_t_var = &_func_gdtrix
|
|
from ._convex_analysis cimport huber as _func_huber
|
|
ctypedef double _proto_huber_t(double, double) noexcept nogil
|
|
cdef _proto_huber_t *_proto_huber_t_var = &_func_huber
|
|
from ._hyp0f1 cimport _hyp0f1_cmplx as _func__hyp0f1_cmplx
|
|
ctypedef double complex _proto__hyp0f1_cmplx_t(double, double complex) noexcept nogil
|
|
cdef _proto__hyp0f1_cmplx_t *_proto__hyp0f1_cmplx_t_var = &_func__hyp0f1_cmplx
|
|
from ._hyp0f1 cimport _hyp0f1_real as _func__hyp0f1_real
|
|
ctypedef double _proto__hyp0f1_real_t(double, double) noexcept nogil
|
|
cdef _proto__hyp0f1_real_t *_proto__hyp0f1_real_t_var = &_func__hyp0f1_real
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double complex _func_chyp1f1_wrap "chyp1f1_wrap"(double, double, double complex) noexcept nogil
|
|
from ._hypergeometric cimport hyperu as _func_hyperu
|
|
ctypedef double _proto_hyperu_t(double, double, double) noexcept nogil
|
|
cdef _proto_hyperu_t *_proto_hyperu_t_var = &_func_hyperu
|
|
from ._boxcox cimport inv_boxcox as _func_inv_boxcox
|
|
ctypedef double _proto_inv_boxcox_t(double, double) noexcept nogil
|
|
cdef _proto_inv_boxcox_t *_proto_inv_boxcox_t_var = &_func_inv_boxcox
|
|
from ._boxcox cimport inv_boxcox1p as _func_inv_boxcox1p
|
|
ctypedef double _proto_inv_boxcox1p_t(double, double) noexcept nogil
|
|
cdef _proto_inv_boxcox1p_t *_proto_inv_boxcox1p_t_var = &_func_inv_boxcox1p
|
|
from ._convex_analysis cimport kl_div as _func_kl_div
|
|
ctypedef double _proto_kl_div_t(double, double) noexcept nogil
|
|
cdef _proto_kl_div_t *_proto_kl_div_t_var = &_func_kl_div
|
|
from ._legacy cimport kn_unsafe as _func_kn_unsafe
|
|
ctypedef double _proto_kn_unsafe_t(double, double) noexcept nogil
|
|
cdef _proto_kn_unsafe_t *_proto_kn_unsafe_t_var = &_func_kn_unsafe
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_special_cyl_bessel_k_int "special_cyl_bessel_k_int"(Py_ssize_t, double) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_xsf_kolmogi "xsf_kolmogi"(double) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_xsf_kolmogorov "xsf_kolmogorov"(double) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_pmv_wrap "pmv_wrap"(double, double, double) noexcept nogil
|
|
from ._legacy cimport nbdtr_unsafe as _func_nbdtr_unsafe
|
|
ctypedef double _proto_nbdtr_unsafe_t(double, double, double) noexcept nogil
|
|
cdef _proto_nbdtr_unsafe_t *_proto_nbdtr_unsafe_t_var = &_func_nbdtr_unsafe
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes_nbdtr_wrap "cephes_nbdtr_wrap"(Py_ssize_t, Py_ssize_t, double) noexcept nogil
|
|
from ._legacy cimport nbdtrc_unsafe as _func_nbdtrc_unsafe
|
|
ctypedef double _proto_nbdtrc_unsafe_t(double, double, double) noexcept nogil
|
|
cdef _proto_nbdtrc_unsafe_t *_proto_nbdtrc_unsafe_t_var = &_func_nbdtrc_unsafe
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes_nbdtrc_wrap "cephes_nbdtrc_wrap"(Py_ssize_t, Py_ssize_t, double) noexcept nogil
|
|
from ._legacy cimport nbdtri_unsafe as _func_nbdtri_unsafe
|
|
ctypedef double _proto_nbdtri_unsafe_t(double, double, double) noexcept nogil
|
|
cdef _proto_nbdtri_unsafe_t *_proto_nbdtri_unsafe_t_var = &_func_nbdtri_unsafe
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes_nbdtri_wrap "cephes_nbdtri_wrap"(Py_ssize_t, Py_ssize_t, double) noexcept nogil
|
|
from ._cdflib_wrappers cimport nbdtrik as _func_nbdtrik
|
|
ctypedef double _proto_nbdtrik_t(double, double, double) noexcept nogil
|
|
cdef _proto_nbdtrik_t *_proto_nbdtrik_t_var = &_func_nbdtrik
|
|
from ._cdflib_wrappers cimport nbdtrin as _func_nbdtrin
|
|
ctypedef double _proto_nbdtrin_t(double, double, double) noexcept nogil
|
|
cdef _proto_nbdtrin_t *_proto_nbdtrin_t_var = &_func_nbdtrin
|
|
from ._cdflib_wrappers cimport ncfdtridfd as _func_ncfdtridfd
|
|
ctypedef double _proto_ncfdtridfd_t(double, double, double, double) noexcept nogil
|
|
cdef _proto_ncfdtridfd_t *_proto_ncfdtridfd_t_var = &_func_ncfdtridfd
|
|
from ._cdflib_wrappers cimport ncfdtridfn as _func_ncfdtridfn
|
|
ctypedef double _proto_ncfdtridfn_t(double, double, double, double) noexcept nogil
|
|
cdef _proto_ncfdtridfn_t *_proto_ncfdtridfn_t_var = &_func_ncfdtridfn
|
|
from ._cdflib_wrappers cimport ncfdtrinc as _func_ncfdtrinc
|
|
ctypedef double _proto_ncfdtrinc_t(double, double, double, double) noexcept nogil
|
|
cdef _proto_ncfdtrinc_t *_proto_ncfdtrinc_t_var = &_func_ncfdtrinc
|
|
from ._cdflib_wrappers cimport nctdtridf as _func_nctdtridf
|
|
ctypedef double _proto_nctdtridf_t(double, double, double) noexcept nogil
|
|
cdef _proto_nctdtridf_t *_proto_nctdtridf_t_var = &_func_nctdtridf
|
|
from ._cdflib_wrappers cimport nctdtrinc as _func_nctdtrinc
|
|
ctypedef double _proto_nctdtrinc_t(double, double, double) noexcept nogil
|
|
cdef _proto_nctdtrinc_t *_proto_nctdtrinc_t_var = &_func_nctdtrinc
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_xsf_ndtri "xsf_ndtri"(double) noexcept nogil
|
|
from ._ndtri_exp cimport ndtri_exp as _func_ndtri_exp
|
|
ctypedef double _proto_ndtri_exp_t(double) noexcept nogil
|
|
cdef _proto_ndtri_exp_t *_proto_ndtri_exp_t_var = &_func_ndtri_exp
|
|
from ._cdflib_wrappers cimport nrdtrimn as _func_nrdtrimn
|
|
ctypedef double _proto_nrdtrimn_t(double, double, double) noexcept nogil
|
|
cdef _proto_nrdtrimn_t *_proto_nrdtrimn_t_var = &_func_nrdtrimn
|
|
from ._cdflib_wrappers cimport nrdtrisd as _func_nrdtrisd
|
|
ctypedef double _proto_nrdtrisd_t(double, double, double) noexcept nogil
|
|
cdef _proto_nrdtrisd_t *_proto_nrdtrisd_t_var = &_func_nrdtrisd
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_xsf_owens_t "xsf_owens_t"(double, double) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_xsf_pdtr "xsf_pdtr"(double, double) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_xsf_pdtrc "xsf_pdtrc"(double, double) noexcept nogil
|
|
from ._legacy cimport pdtri_unsafe as _func_pdtri_unsafe
|
|
ctypedef double _proto_pdtri_unsafe_t(double, double) noexcept nogil
|
|
cdef _proto_pdtri_unsafe_t *_proto_pdtri_unsafe_t_var = &_func_pdtri_unsafe
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes_pdtri_wrap "cephes_pdtri_wrap"(Py_ssize_t, double) noexcept nogil
|
|
from ._cdflib_wrappers cimport pdtrik as _func_pdtrik
|
|
ctypedef double _proto_pdtrik_t(double, double) noexcept nogil
|
|
cdef _proto_pdtrik_t *_proto_pdtrik_t_var = &_func_pdtrik
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes_poch "cephes_poch"(double, double) noexcept nogil
|
|
from ._convex_analysis cimport pseudo_huber as _func_pseudo_huber
|
|
ctypedef double _proto_pseudo_huber_t(double, double) noexcept nogil
|
|
cdef _proto_pseudo_huber_t *_proto_pseudo_huber_t_var = &_func_pseudo_huber
|
|
from ._convex_analysis cimport rel_entr as _func_rel_entr
|
|
ctypedef double _proto_rel_entr_t(double, double) noexcept nogil
|
|
cdef _proto_rel_entr_t *_proto_rel_entr_t_var = &_func_rel_entr
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes_round "cephes_round"(double) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef int _func_xsf_cshichi "xsf_cshichi"(double complex, double complex *, double complex *) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef int _func_xsf_shichi "xsf_shichi"(double, double *, double *) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef int _func_xsf_csici "xsf_csici"(double complex, double complex *, double complex *) noexcept nogil
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef int _func_xsf_sici "xsf_sici"(double, double *, double *) noexcept nogil
|
|
from ._legacy cimport smirnov_unsafe as _func_smirnov_unsafe
|
|
ctypedef double _proto_smirnov_unsafe_t(double, double) noexcept nogil
|
|
cdef _proto_smirnov_unsafe_t *_proto_smirnov_unsafe_t_var = &_func_smirnov_unsafe
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes_smirnov_wrap "cephes_smirnov_wrap"(Py_ssize_t, double) noexcept nogil
|
|
from ._legacy cimport smirnovi_unsafe as _func_smirnovi_unsafe
|
|
ctypedef double _proto_smirnovi_unsafe_t(double, double) noexcept nogil
|
|
cdef _proto_smirnovi_unsafe_t *_proto_smirnovi_unsafe_t_var = &_func_smirnovi_unsafe
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes_smirnovi_wrap "cephes_smirnovi_wrap"(Py_ssize_t, double) noexcept nogil
|
|
from ._spence cimport cspence as _func_cspence
|
|
ctypedef double complex _proto_cspence_t(double complex) noexcept nogil
|
|
cdef _proto_cspence_t *_proto_cspence_t_var = &_func_cspence
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes_spence "cephes_spence"(double) noexcept nogil
|
|
from ._cdflib_wrappers cimport stdtr as _func_stdtr
|
|
ctypedef double _proto_stdtr_t(double, double) noexcept nogil
|
|
cdef _proto_stdtr_t *_proto_stdtr_t_var = &_func_stdtr
|
|
from ._cdflib_wrappers cimport stdtridf as _func_stdtridf
|
|
ctypedef double _proto_stdtridf_t(double, double) noexcept nogil
|
|
cdef _proto_stdtridf_t *_proto_stdtridf_t_var = &_func_stdtridf
|
|
from ._cdflib_wrappers cimport stdtrit as _func_stdtrit
|
|
ctypedef double _proto_stdtrit_t(double, double) noexcept nogil
|
|
cdef _proto_stdtrit_t *_proto_stdtrit_t_var = &_func_stdtrit
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_xsf_tukeylambdacdf "xsf_tukeylambdacdf"(double, double) noexcept nogil
|
|
from ._legacy cimport yn_unsafe as _func_yn_unsafe
|
|
ctypedef double _proto_yn_unsafe_t(double, double) noexcept nogil
|
|
cdef _proto_yn_unsafe_t *_proto_yn_unsafe_t_var = &_func_yn_unsafe
|
|
cdef extern from r"_ufuncs_defs.h":
|
|
cdef double _func_cephes_yn_wrap "cephes_yn_wrap"(Py_ssize_t, double) noexcept nogil
|
|
cdef np.PyUFuncGenericFunction ufunc__beta_pdf_loops[2]
|
|
cdef void *ufunc__beta_pdf_ptr[4]
|
|
cdef void *ufunc__beta_pdf_data[2]
|
|
cdef char ufunc__beta_pdf_types[8]
|
|
cdef char *ufunc__beta_pdf_doc = (
|
|
"_beta_pdf(x, a, b)\n"
|
|
"\n"
|
|
"Probability density function of beta distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued such that :math:`0 \\leq x \\leq 1`,\n"
|
|
" the upper limit of integration\n"
|
|
"a, b : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__beta_pdf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__beta_pdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__beta_pdf_types[0] = <char>NPY_FLOAT
|
|
ufunc__beta_pdf_types[1] = <char>NPY_FLOAT
|
|
ufunc__beta_pdf_types[2] = <char>NPY_FLOAT
|
|
ufunc__beta_pdf_types[3] = <char>NPY_FLOAT
|
|
ufunc__beta_pdf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__beta_pdf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__beta_pdf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__beta_pdf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__beta_pdf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_beta_pdf_float
|
|
ufunc__beta_pdf_ptr[2*0+1] = <void*>(<char*>"_beta_pdf")
|
|
ufunc__beta_pdf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_beta_pdf_double
|
|
ufunc__beta_pdf_ptr[2*1+1] = <void*>(<char*>"_beta_pdf")
|
|
ufunc__beta_pdf_data[0] = &ufunc__beta_pdf_ptr[2*0]
|
|
ufunc__beta_pdf_data[1] = &ufunc__beta_pdf_ptr[2*1]
|
|
_beta_pdf = np.PyUFunc_FromFuncAndData(ufunc__beta_pdf_loops, ufunc__beta_pdf_data, ufunc__beta_pdf_types, 2, 3, 1, 0, '_beta_pdf', ufunc__beta_pdf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__beta_ppf_loops[2]
|
|
cdef void *ufunc__beta_ppf_ptr[4]
|
|
cdef void *ufunc__beta_ppf_data[2]
|
|
cdef char ufunc__beta_ppf_types[8]
|
|
cdef char *ufunc__beta_ppf_doc = (
|
|
"_beta_ppf(x, a, b)\n"
|
|
"\n"
|
|
"Percent point function of beta distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued such that :math:`0 \\leq x \\leq 1`,\n"
|
|
" the upper limit of integration\n"
|
|
"a, b : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__beta_ppf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__beta_ppf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__beta_ppf_types[0] = <char>NPY_FLOAT
|
|
ufunc__beta_ppf_types[1] = <char>NPY_FLOAT
|
|
ufunc__beta_ppf_types[2] = <char>NPY_FLOAT
|
|
ufunc__beta_ppf_types[3] = <char>NPY_FLOAT
|
|
ufunc__beta_ppf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__beta_ppf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__beta_ppf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__beta_ppf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__beta_ppf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_beta_ppf_float
|
|
ufunc__beta_ppf_ptr[2*0+1] = <void*>(<char*>"_beta_ppf")
|
|
ufunc__beta_ppf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_beta_ppf_double
|
|
ufunc__beta_ppf_ptr[2*1+1] = <void*>(<char*>"_beta_ppf")
|
|
ufunc__beta_ppf_data[0] = &ufunc__beta_ppf_ptr[2*0]
|
|
ufunc__beta_ppf_data[1] = &ufunc__beta_ppf_ptr[2*1]
|
|
_beta_ppf = np.PyUFunc_FromFuncAndData(ufunc__beta_ppf_loops, ufunc__beta_ppf_data, ufunc__beta_ppf_types, 2, 3, 1, 0, '_beta_ppf', ufunc__beta_ppf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__binom_cdf_loops[2]
|
|
cdef void *ufunc__binom_cdf_ptr[4]
|
|
cdef void *ufunc__binom_cdf_data[2]
|
|
cdef char ufunc__binom_cdf_types[8]
|
|
cdef char *ufunc__binom_cdf_doc = (
|
|
"_binom_cdf(x, n, p)\n"
|
|
"\n"
|
|
"Cumulative density function of binomial distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued\n"
|
|
"n : array_like\n"
|
|
" Positive, integer-valued parameter\n"
|
|
"p : array_like\n"
|
|
" Positive, real-valued parameter\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__binom_cdf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__binom_cdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__binom_cdf_types[0] = <char>NPY_FLOAT
|
|
ufunc__binom_cdf_types[1] = <char>NPY_FLOAT
|
|
ufunc__binom_cdf_types[2] = <char>NPY_FLOAT
|
|
ufunc__binom_cdf_types[3] = <char>NPY_FLOAT
|
|
ufunc__binom_cdf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__binom_cdf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__binom_cdf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__binom_cdf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__binom_cdf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_binom_cdf_float
|
|
ufunc__binom_cdf_ptr[2*0+1] = <void*>(<char*>"_binom_cdf")
|
|
ufunc__binom_cdf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_binom_cdf_double
|
|
ufunc__binom_cdf_ptr[2*1+1] = <void*>(<char*>"_binom_cdf")
|
|
ufunc__binom_cdf_data[0] = &ufunc__binom_cdf_ptr[2*0]
|
|
ufunc__binom_cdf_data[1] = &ufunc__binom_cdf_ptr[2*1]
|
|
_binom_cdf = np.PyUFunc_FromFuncAndData(ufunc__binom_cdf_loops, ufunc__binom_cdf_data, ufunc__binom_cdf_types, 2, 3, 1, 0, '_binom_cdf', ufunc__binom_cdf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__binom_isf_loops[2]
|
|
cdef void *ufunc__binom_isf_ptr[4]
|
|
cdef void *ufunc__binom_isf_data[2]
|
|
cdef char ufunc__binom_isf_types[8]
|
|
cdef char *ufunc__binom_isf_doc = (
|
|
"_binom_isf(x, n, p)\n"
|
|
"\n"
|
|
"Inverse survival function of binomial distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued\n"
|
|
"n : array_like\n"
|
|
" Positive, integer-valued parameter\n"
|
|
"p : array_like\n"
|
|
" Positive, real-valued parameter\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__binom_isf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__binom_isf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__binom_isf_types[0] = <char>NPY_FLOAT
|
|
ufunc__binom_isf_types[1] = <char>NPY_FLOAT
|
|
ufunc__binom_isf_types[2] = <char>NPY_FLOAT
|
|
ufunc__binom_isf_types[3] = <char>NPY_FLOAT
|
|
ufunc__binom_isf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__binom_isf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__binom_isf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__binom_isf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__binom_isf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_binom_isf_float
|
|
ufunc__binom_isf_ptr[2*0+1] = <void*>(<char*>"_binom_isf")
|
|
ufunc__binom_isf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_binom_isf_double
|
|
ufunc__binom_isf_ptr[2*1+1] = <void*>(<char*>"_binom_isf")
|
|
ufunc__binom_isf_data[0] = &ufunc__binom_isf_ptr[2*0]
|
|
ufunc__binom_isf_data[1] = &ufunc__binom_isf_ptr[2*1]
|
|
_binom_isf = np.PyUFunc_FromFuncAndData(ufunc__binom_isf_loops, ufunc__binom_isf_data, ufunc__binom_isf_types, 2, 3, 1, 0, '_binom_isf', ufunc__binom_isf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__binom_pmf_loops[2]
|
|
cdef void *ufunc__binom_pmf_ptr[4]
|
|
cdef void *ufunc__binom_pmf_data[2]
|
|
cdef char ufunc__binom_pmf_types[8]
|
|
cdef char *ufunc__binom_pmf_doc = (
|
|
"_binom_pmf(x, n, p)\n"
|
|
"\n"
|
|
"Probability mass function of binomial distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued\n"
|
|
"n : array_like\n"
|
|
" Positive, integer-valued parameter\n"
|
|
"p : array_like\n"
|
|
" Positive, real-valued parameter\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__binom_pmf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__binom_pmf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__binom_pmf_types[0] = <char>NPY_FLOAT
|
|
ufunc__binom_pmf_types[1] = <char>NPY_FLOAT
|
|
ufunc__binom_pmf_types[2] = <char>NPY_FLOAT
|
|
ufunc__binom_pmf_types[3] = <char>NPY_FLOAT
|
|
ufunc__binom_pmf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__binom_pmf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__binom_pmf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__binom_pmf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__binom_pmf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_binom_pmf_float
|
|
ufunc__binom_pmf_ptr[2*0+1] = <void*>(<char*>"_binom_pmf")
|
|
ufunc__binom_pmf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_binom_pmf_double
|
|
ufunc__binom_pmf_ptr[2*1+1] = <void*>(<char*>"_binom_pmf")
|
|
ufunc__binom_pmf_data[0] = &ufunc__binom_pmf_ptr[2*0]
|
|
ufunc__binom_pmf_data[1] = &ufunc__binom_pmf_ptr[2*1]
|
|
_binom_pmf = np.PyUFunc_FromFuncAndData(ufunc__binom_pmf_loops, ufunc__binom_pmf_data, ufunc__binom_pmf_types, 2, 3, 1, 0, '_binom_pmf', ufunc__binom_pmf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__binom_ppf_loops[2]
|
|
cdef void *ufunc__binom_ppf_ptr[4]
|
|
cdef void *ufunc__binom_ppf_data[2]
|
|
cdef char ufunc__binom_ppf_types[8]
|
|
cdef char *ufunc__binom_ppf_doc = (
|
|
"_binom_ppf(x, n, p)\n"
|
|
"\n"
|
|
"Percent point function of binomial distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued\n"
|
|
"n : array_like\n"
|
|
" Positive, integer-valued parameter\n"
|
|
"p : array_like\n"
|
|
" Positive, real-valued parameter\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__binom_ppf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__binom_ppf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__binom_ppf_types[0] = <char>NPY_FLOAT
|
|
ufunc__binom_ppf_types[1] = <char>NPY_FLOAT
|
|
ufunc__binom_ppf_types[2] = <char>NPY_FLOAT
|
|
ufunc__binom_ppf_types[3] = <char>NPY_FLOAT
|
|
ufunc__binom_ppf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__binom_ppf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__binom_ppf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__binom_ppf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__binom_ppf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_binom_ppf_float
|
|
ufunc__binom_ppf_ptr[2*0+1] = <void*>(<char*>"_binom_ppf")
|
|
ufunc__binom_ppf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_binom_ppf_double
|
|
ufunc__binom_ppf_ptr[2*1+1] = <void*>(<char*>"_binom_ppf")
|
|
ufunc__binom_ppf_data[0] = &ufunc__binom_ppf_ptr[2*0]
|
|
ufunc__binom_ppf_data[1] = &ufunc__binom_ppf_ptr[2*1]
|
|
_binom_ppf = np.PyUFunc_FromFuncAndData(ufunc__binom_ppf_loops, ufunc__binom_ppf_data, ufunc__binom_ppf_types, 2, 3, 1, 0, '_binom_ppf', ufunc__binom_ppf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__binom_sf_loops[2]
|
|
cdef void *ufunc__binom_sf_ptr[4]
|
|
cdef void *ufunc__binom_sf_data[2]
|
|
cdef char ufunc__binom_sf_types[8]
|
|
cdef char *ufunc__binom_sf_doc = (
|
|
"_binom_sf(x, n, p)\n"
|
|
"\n"
|
|
"Survival function of binomial distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued\n"
|
|
"n : array_like\n"
|
|
" Positive, integer-valued parameter\n"
|
|
"p : array_like\n"
|
|
" Positive, real-valued parameter\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__binom_sf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__binom_sf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__binom_sf_types[0] = <char>NPY_FLOAT
|
|
ufunc__binom_sf_types[1] = <char>NPY_FLOAT
|
|
ufunc__binom_sf_types[2] = <char>NPY_FLOAT
|
|
ufunc__binom_sf_types[3] = <char>NPY_FLOAT
|
|
ufunc__binom_sf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__binom_sf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__binom_sf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__binom_sf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__binom_sf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_binom_sf_float
|
|
ufunc__binom_sf_ptr[2*0+1] = <void*>(<char*>"_binom_sf")
|
|
ufunc__binom_sf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_binom_sf_double
|
|
ufunc__binom_sf_ptr[2*1+1] = <void*>(<char*>"_binom_sf")
|
|
ufunc__binom_sf_data[0] = &ufunc__binom_sf_ptr[2*0]
|
|
ufunc__binom_sf_data[1] = &ufunc__binom_sf_ptr[2*1]
|
|
_binom_sf = np.PyUFunc_FromFuncAndData(ufunc__binom_sf_loops, ufunc__binom_sf_data, ufunc__binom_sf_types, 2, 3, 1, 0, '_binom_sf', ufunc__binom_sf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__cauchy_isf_loops[2]
|
|
cdef void *ufunc__cauchy_isf_ptr[4]
|
|
cdef void *ufunc__cauchy_isf_data[2]
|
|
cdef char ufunc__cauchy_isf_types[8]
|
|
cdef char *ufunc__cauchy_isf_doc = (
|
|
"_cauchy_isf(p, loc, scale)\n"
|
|
"\n"
|
|
"Inverse survival function of the Cauchy distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"p : array_like\n"
|
|
" Probabilities\n"
|
|
"loc : array_like\n"
|
|
" Location parameter of the distribution.\n"
|
|
"scale : array_like\n"
|
|
" Scale parameter of the distribution.\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__cauchy_isf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__cauchy_isf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__cauchy_isf_types[0] = <char>NPY_FLOAT
|
|
ufunc__cauchy_isf_types[1] = <char>NPY_FLOAT
|
|
ufunc__cauchy_isf_types[2] = <char>NPY_FLOAT
|
|
ufunc__cauchy_isf_types[3] = <char>NPY_FLOAT
|
|
ufunc__cauchy_isf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__cauchy_isf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__cauchy_isf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__cauchy_isf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__cauchy_isf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_cauchy_isf_float
|
|
ufunc__cauchy_isf_ptr[2*0+1] = <void*>(<char*>"_cauchy_isf")
|
|
ufunc__cauchy_isf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_cauchy_isf_double
|
|
ufunc__cauchy_isf_ptr[2*1+1] = <void*>(<char*>"_cauchy_isf")
|
|
ufunc__cauchy_isf_data[0] = &ufunc__cauchy_isf_ptr[2*0]
|
|
ufunc__cauchy_isf_data[1] = &ufunc__cauchy_isf_ptr[2*1]
|
|
_cauchy_isf = np.PyUFunc_FromFuncAndData(ufunc__cauchy_isf_loops, ufunc__cauchy_isf_data, ufunc__cauchy_isf_types, 2, 3, 1, 0, '_cauchy_isf', ufunc__cauchy_isf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__cauchy_ppf_loops[2]
|
|
cdef void *ufunc__cauchy_ppf_ptr[4]
|
|
cdef void *ufunc__cauchy_ppf_data[2]
|
|
cdef char ufunc__cauchy_ppf_types[8]
|
|
cdef char *ufunc__cauchy_ppf_doc = (
|
|
"_cauchy_ppf(p, loc, scale)\n"
|
|
"\n"
|
|
"Percent point function (i.e. quantile) of the Cauchy distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"p : array_like\n"
|
|
" Probabilities\n"
|
|
"loc : array_like\n"
|
|
" Location parameter of the distribution.\n"
|
|
"scale : array_like\n"
|
|
" Scale parameter of the distribution.\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__cauchy_ppf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__cauchy_ppf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__cauchy_ppf_types[0] = <char>NPY_FLOAT
|
|
ufunc__cauchy_ppf_types[1] = <char>NPY_FLOAT
|
|
ufunc__cauchy_ppf_types[2] = <char>NPY_FLOAT
|
|
ufunc__cauchy_ppf_types[3] = <char>NPY_FLOAT
|
|
ufunc__cauchy_ppf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__cauchy_ppf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__cauchy_ppf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__cauchy_ppf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__cauchy_ppf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_cauchy_ppf_float
|
|
ufunc__cauchy_ppf_ptr[2*0+1] = <void*>(<char*>"_cauchy_ppf")
|
|
ufunc__cauchy_ppf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_cauchy_ppf_double
|
|
ufunc__cauchy_ppf_ptr[2*1+1] = <void*>(<char*>"_cauchy_ppf")
|
|
ufunc__cauchy_ppf_data[0] = &ufunc__cauchy_ppf_ptr[2*0]
|
|
ufunc__cauchy_ppf_data[1] = &ufunc__cauchy_ppf_ptr[2*1]
|
|
_cauchy_ppf = np.PyUFunc_FromFuncAndData(ufunc__cauchy_ppf_loops, ufunc__cauchy_ppf_data, ufunc__cauchy_ppf_types, 2, 3, 1, 0, '_cauchy_ppf', ufunc__cauchy_ppf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__cosine_cdf_loops[2]
|
|
cdef void *ufunc__cosine_cdf_ptr[4]
|
|
cdef void *ufunc__cosine_cdf_data[2]
|
|
cdef char ufunc__cosine_cdf_types[4]
|
|
cdef char *ufunc__cosine_cdf_doc = (
|
|
"_cosine_cdf(x)\n"
|
|
"\n"
|
|
"Cumulative distribution function (CDF) of the cosine distribution::\n"
|
|
"\n"
|
|
" { 0, x < -pi\n"
|
|
" cdf(x) = { (pi + x + sin(x))/(2*pi), -pi <= x <= pi\n"
|
|
" { 1, x > pi\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" `x` must contain real numbers.\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" The cosine distribution CDF evaluated at `x`.")
|
|
ufunc__cosine_cdf_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
|
|
ufunc__cosine_cdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
|
|
ufunc__cosine_cdf_types[0] = <char>NPY_FLOAT
|
|
ufunc__cosine_cdf_types[1] = <char>NPY_FLOAT
|
|
ufunc__cosine_cdf_types[2] = <char>NPY_DOUBLE
|
|
ufunc__cosine_cdf_types[3] = <char>NPY_DOUBLE
|
|
ufunc__cosine_cdf_ptr[2*0] = <void*>_func_cosine_cdf
|
|
ufunc__cosine_cdf_ptr[2*0+1] = <void*>(<char*>"_cosine_cdf")
|
|
ufunc__cosine_cdf_ptr[2*1] = <void*>_func_cosine_cdf
|
|
ufunc__cosine_cdf_ptr[2*1+1] = <void*>(<char*>"_cosine_cdf")
|
|
ufunc__cosine_cdf_data[0] = &ufunc__cosine_cdf_ptr[2*0]
|
|
ufunc__cosine_cdf_data[1] = &ufunc__cosine_cdf_ptr[2*1]
|
|
_cosine_cdf = np.PyUFunc_FromFuncAndData(ufunc__cosine_cdf_loops, ufunc__cosine_cdf_data, ufunc__cosine_cdf_types, 2, 1, 1, 0, '_cosine_cdf', ufunc__cosine_cdf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__cosine_invcdf_loops[2]
|
|
cdef void *ufunc__cosine_invcdf_ptr[4]
|
|
cdef void *ufunc__cosine_invcdf_data[2]
|
|
cdef char ufunc__cosine_invcdf_types[4]
|
|
cdef char *ufunc__cosine_invcdf_doc = (
|
|
"_cosine_invcdf(p)\n"
|
|
"\n"
|
|
"Inverse of the cumulative distribution function (CDF) of the cosine\n"
|
|
"distribution.\n"
|
|
"\n"
|
|
"The CDF of the cosine distribution is::\n"
|
|
"\n"
|
|
" cdf(x) = (pi + x + sin(x))/(2*pi)\n"
|
|
"\n"
|
|
"This function computes the inverse of cdf(x).\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"p : array_like\n"
|
|
" `p` must contain real numbers in the interval ``0 <= p <= 1``.\n"
|
|
" `nan` is returned for values of `p` outside the interval [0, 1].\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" The inverse of the cosine distribution CDF evaluated at `p`.")
|
|
ufunc__cosine_invcdf_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
|
|
ufunc__cosine_invcdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
|
|
ufunc__cosine_invcdf_types[0] = <char>NPY_FLOAT
|
|
ufunc__cosine_invcdf_types[1] = <char>NPY_FLOAT
|
|
ufunc__cosine_invcdf_types[2] = <char>NPY_DOUBLE
|
|
ufunc__cosine_invcdf_types[3] = <char>NPY_DOUBLE
|
|
ufunc__cosine_invcdf_ptr[2*0] = <void*>_func_cosine_invcdf
|
|
ufunc__cosine_invcdf_ptr[2*0+1] = <void*>(<char*>"_cosine_invcdf")
|
|
ufunc__cosine_invcdf_ptr[2*1] = <void*>_func_cosine_invcdf
|
|
ufunc__cosine_invcdf_ptr[2*1+1] = <void*>(<char*>"_cosine_invcdf")
|
|
ufunc__cosine_invcdf_data[0] = &ufunc__cosine_invcdf_ptr[2*0]
|
|
ufunc__cosine_invcdf_data[1] = &ufunc__cosine_invcdf_ptr[2*1]
|
|
_cosine_invcdf = np.PyUFunc_FromFuncAndData(ufunc__cosine_invcdf_loops, ufunc__cosine_invcdf_data, ufunc__cosine_invcdf_types, 2, 1, 1, 0, '_cosine_invcdf', ufunc__cosine_invcdf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__ellip_harm_loops[3]
|
|
cdef void *ufunc__ellip_harm_ptr[6]
|
|
cdef void *ufunc__ellip_harm_data[3]
|
|
cdef char ufunc__ellip_harm_types[24]
|
|
cdef char *ufunc__ellip_harm_doc = (
|
|
"Internal function, use `ellip_harm` instead.")
|
|
ufunc__ellip_harm_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddddddd__As_fffffff_f
|
|
ufunc__ellip_harm_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddiiddd__As_ddllddd_d
|
|
ufunc__ellip_harm_loops[2] = <np.PyUFuncGenericFunction>loop_d_ddddddd__As_ddddddd_d
|
|
ufunc__ellip_harm_types[0] = <char>NPY_FLOAT
|
|
ufunc__ellip_harm_types[1] = <char>NPY_FLOAT
|
|
ufunc__ellip_harm_types[2] = <char>NPY_FLOAT
|
|
ufunc__ellip_harm_types[3] = <char>NPY_FLOAT
|
|
ufunc__ellip_harm_types[4] = <char>NPY_FLOAT
|
|
ufunc__ellip_harm_types[5] = <char>NPY_FLOAT
|
|
ufunc__ellip_harm_types[6] = <char>NPY_FLOAT
|
|
ufunc__ellip_harm_types[7] = <char>NPY_FLOAT
|
|
ufunc__ellip_harm_types[8] = <char>NPY_DOUBLE
|
|
ufunc__ellip_harm_types[9] = <char>NPY_DOUBLE
|
|
ufunc__ellip_harm_types[10] = <char>NPY_LONG
|
|
ufunc__ellip_harm_types[11] = <char>NPY_LONG
|
|
ufunc__ellip_harm_types[12] = <char>NPY_DOUBLE
|
|
ufunc__ellip_harm_types[13] = <char>NPY_DOUBLE
|
|
ufunc__ellip_harm_types[14] = <char>NPY_DOUBLE
|
|
ufunc__ellip_harm_types[15] = <char>NPY_DOUBLE
|
|
ufunc__ellip_harm_types[16] = <char>NPY_DOUBLE
|
|
ufunc__ellip_harm_types[17] = <char>NPY_DOUBLE
|
|
ufunc__ellip_harm_types[18] = <char>NPY_DOUBLE
|
|
ufunc__ellip_harm_types[19] = <char>NPY_DOUBLE
|
|
ufunc__ellip_harm_types[20] = <char>NPY_DOUBLE
|
|
ufunc__ellip_harm_types[21] = <char>NPY_DOUBLE
|
|
ufunc__ellip_harm_types[22] = <char>NPY_DOUBLE
|
|
ufunc__ellip_harm_types[23] = <char>NPY_DOUBLE
|
|
ufunc__ellip_harm_ptr[2*0] = <void*>_func_ellip_harmonic_unsafe
|
|
ufunc__ellip_harm_ptr[2*0+1] = <void*>(<char*>"_ellip_harm")
|
|
ufunc__ellip_harm_ptr[2*1] = <void*>_func_ellip_harmonic
|
|
ufunc__ellip_harm_ptr[2*1+1] = <void*>(<char*>"_ellip_harm")
|
|
ufunc__ellip_harm_ptr[2*2] = <void*>_func_ellip_harmonic_unsafe
|
|
ufunc__ellip_harm_ptr[2*2+1] = <void*>(<char*>"_ellip_harm")
|
|
ufunc__ellip_harm_data[0] = &ufunc__ellip_harm_ptr[2*0]
|
|
ufunc__ellip_harm_data[1] = &ufunc__ellip_harm_ptr[2*1]
|
|
ufunc__ellip_harm_data[2] = &ufunc__ellip_harm_ptr[2*2]
|
|
_ellip_harm = np.PyUFunc_FromFuncAndData(ufunc__ellip_harm_loops, ufunc__ellip_harm_data, ufunc__ellip_harm_types, 3, 7, 1, 0, '_ellip_harm', ufunc__ellip_harm_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__factorial_loops[2]
|
|
cdef void *ufunc__factorial_ptr[4]
|
|
cdef void *ufunc__factorial_data[2]
|
|
cdef char ufunc__factorial_types[4]
|
|
cdef char *ufunc__factorial_doc = (
|
|
"Internal function, do not use.")
|
|
ufunc__factorial_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
|
|
ufunc__factorial_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
|
|
ufunc__factorial_types[0] = <char>NPY_FLOAT
|
|
ufunc__factorial_types[1] = <char>NPY_FLOAT
|
|
ufunc__factorial_types[2] = <char>NPY_DOUBLE
|
|
ufunc__factorial_types[3] = <char>NPY_DOUBLE
|
|
ufunc__factorial_ptr[2*0] = <void*>_func__factorial
|
|
ufunc__factorial_ptr[2*0+1] = <void*>(<char*>"_factorial")
|
|
ufunc__factorial_ptr[2*1] = <void*>_func__factorial
|
|
ufunc__factorial_ptr[2*1+1] = <void*>(<char*>"_factorial")
|
|
ufunc__factorial_data[0] = &ufunc__factorial_ptr[2*0]
|
|
ufunc__factorial_data[1] = &ufunc__factorial_ptr[2*1]
|
|
_factorial = np.PyUFunc_FromFuncAndData(ufunc__factorial_loops, ufunc__factorial_data, ufunc__factorial_types, 2, 1, 1, 0, '_factorial', ufunc__factorial_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__hypergeom_cdf_loops[2]
|
|
cdef void *ufunc__hypergeom_cdf_ptr[4]
|
|
cdef void *ufunc__hypergeom_cdf_data[2]
|
|
cdef char ufunc__hypergeom_cdf_types[10]
|
|
cdef char *ufunc__hypergeom_cdf_doc = (
|
|
"_hypergeom_cdf(x, r, N, M)\n"
|
|
"\n"
|
|
"Cumulative density function of hypergeometric distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued\n"
|
|
"r, N, M : array_like\n"
|
|
" Positive, integer-valued parameter\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__hypergeom_cdf_loops[0] = <np.PyUFuncGenericFunction>loop_f_ffff__As_ffff_f
|
|
ufunc__hypergeom_cdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
|
|
ufunc__hypergeom_cdf_types[0] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_cdf_types[1] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_cdf_types[2] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_cdf_types[3] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_cdf_types[4] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_cdf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_cdf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_cdf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_cdf_types[8] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_cdf_types[9] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_cdf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_cdf_float
|
|
ufunc__hypergeom_cdf_ptr[2*0+1] = <void*>(<char*>"_hypergeom_cdf")
|
|
ufunc__hypergeom_cdf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_cdf_double
|
|
ufunc__hypergeom_cdf_ptr[2*1+1] = <void*>(<char*>"_hypergeom_cdf")
|
|
ufunc__hypergeom_cdf_data[0] = &ufunc__hypergeom_cdf_ptr[2*0]
|
|
ufunc__hypergeom_cdf_data[1] = &ufunc__hypergeom_cdf_ptr[2*1]
|
|
_hypergeom_cdf = np.PyUFunc_FromFuncAndData(ufunc__hypergeom_cdf_loops, ufunc__hypergeom_cdf_data, ufunc__hypergeom_cdf_types, 2, 4, 1, 0, '_hypergeom_cdf', ufunc__hypergeom_cdf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__hypergeom_mean_loops[2]
|
|
cdef void *ufunc__hypergeom_mean_ptr[4]
|
|
cdef void *ufunc__hypergeom_mean_data[2]
|
|
cdef char ufunc__hypergeom_mean_types[8]
|
|
cdef char *ufunc__hypergeom_mean_doc = (
|
|
"_hypergeom_mean(r, N, M)\n"
|
|
"\n"
|
|
"Mean of hypergeometric distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"r, N, M : array_like\n"
|
|
" Positive, integer-valued parameter\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__hypergeom_mean_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__hypergeom_mean_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__hypergeom_mean_types[0] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_mean_types[1] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_mean_types[2] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_mean_types[3] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_mean_types[4] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_mean_types[5] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_mean_types[6] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_mean_types[7] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_mean_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_mean_float
|
|
ufunc__hypergeom_mean_ptr[2*0+1] = <void*>(<char*>"_hypergeom_mean")
|
|
ufunc__hypergeom_mean_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_mean_double
|
|
ufunc__hypergeom_mean_ptr[2*1+1] = <void*>(<char*>"_hypergeom_mean")
|
|
ufunc__hypergeom_mean_data[0] = &ufunc__hypergeom_mean_ptr[2*0]
|
|
ufunc__hypergeom_mean_data[1] = &ufunc__hypergeom_mean_ptr[2*1]
|
|
_hypergeom_mean = np.PyUFunc_FromFuncAndData(ufunc__hypergeom_mean_loops, ufunc__hypergeom_mean_data, ufunc__hypergeom_mean_types, 2, 3, 1, 0, '_hypergeom_mean', ufunc__hypergeom_mean_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__hypergeom_pmf_loops[2]
|
|
cdef void *ufunc__hypergeom_pmf_ptr[4]
|
|
cdef void *ufunc__hypergeom_pmf_data[2]
|
|
cdef char ufunc__hypergeom_pmf_types[10]
|
|
cdef char *ufunc__hypergeom_pmf_doc = (
|
|
"_hypergeom_pmf(x, r, N, M)\n"
|
|
"\n"
|
|
"Probability mass function of hypergeometric distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued\n"
|
|
"r, N, M : array_like\n"
|
|
" Positive, integer-valued parameter\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__hypergeom_pmf_loops[0] = <np.PyUFuncGenericFunction>loop_f_ffff__As_ffff_f
|
|
ufunc__hypergeom_pmf_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
|
|
ufunc__hypergeom_pmf_types[0] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_pmf_types[1] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_pmf_types[2] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_pmf_types[3] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_pmf_types[4] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_pmf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_pmf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_pmf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_pmf_types[8] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_pmf_types[9] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_pmf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_pmf_float
|
|
ufunc__hypergeom_pmf_ptr[2*0+1] = <void*>(<char*>"_hypergeom_pmf")
|
|
ufunc__hypergeom_pmf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_pmf_double
|
|
ufunc__hypergeom_pmf_ptr[2*1+1] = <void*>(<char*>"_hypergeom_pmf")
|
|
ufunc__hypergeom_pmf_data[0] = &ufunc__hypergeom_pmf_ptr[2*0]
|
|
ufunc__hypergeom_pmf_data[1] = &ufunc__hypergeom_pmf_ptr[2*1]
|
|
_hypergeom_pmf = np.PyUFunc_FromFuncAndData(ufunc__hypergeom_pmf_loops, ufunc__hypergeom_pmf_data, ufunc__hypergeom_pmf_types, 2, 4, 1, 0, '_hypergeom_pmf', ufunc__hypergeom_pmf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__hypergeom_sf_loops[2]
|
|
cdef void *ufunc__hypergeom_sf_ptr[4]
|
|
cdef void *ufunc__hypergeom_sf_data[2]
|
|
cdef char ufunc__hypergeom_sf_types[10]
|
|
cdef char *ufunc__hypergeom_sf_doc = (
|
|
"_hypergeom_sf(x, r, N, M)\n"
|
|
"\n"
|
|
"Survival function of hypergeometric distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued\n"
|
|
"r, N, M : array_like\n"
|
|
" Positive, integer-valued parameter\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__hypergeom_sf_loops[0] = <np.PyUFuncGenericFunction>loop_f_ffff__As_ffff_f
|
|
ufunc__hypergeom_sf_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
|
|
ufunc__hypergeom_sf_types[0] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_sf_types[1] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_sf_types[2] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_sf_types[3] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_sf_types[4] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_sf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_sf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_sf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_sf_types[8] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_sf_types[9] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_sf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_sf_float
|
|
ufunc__hypergeom_sf_ptr[2*0+1] = <void*>(<char*>"_hypergeom_sf")
|
|
ufunc__hypergeom_sf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_sf_double
|
|
ufunc__hypergeom_sf_ptr[2*1+1] = <void*>(<char*>"_hypergeom_sf")
|
|
ufunc__hypergeom_sf_data[0] = &ufunc__hypergeom_sf_ptr[2*0]
|
|
ufunc__hypergeom_sf_data[1] = &ufunc__hypergeom_sf_ptr[2*1]
|
|
_hypergeom_sf = np.PyUFunc_FromFuncAndData(ufunc__hypergeom_sf_loops, ufunc__hypergeom_sf_data, ufunc__hypergeom_sf_types, 2, 4, 1, 0, '_hypergeom_sf', ufunc__hypergeom_sf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__hypergeom_skewness_loops[2]
|
|
cdef void *ufunc__hypergeom_skewness_ptr[4]
|
|
cdef void *ufunc__hypergeom_skewness_data[2]
|
|
cdef char ufunc__hypergeom_skewness_types[8]
|
|
cdef char *ufunc__hypergeom_skewness_doc = (
|
|
"_hypergeom_skewness(r, N, M)\n"
|
|
"\n"
|
|
"Skewness of hypergeometric distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"r, N, M : array_like\n"
|
|
" Positive, integer-valued parameter\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__hypergeom_skewness_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__hypergeom_skewness_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__hypergeom_skewness_types[0] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_skewness_types[1] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_skewness_types[2] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_skewness_types[3] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_skewness_types[4] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_skewness_types[5] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_skewness_types[6] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_skewness_types[7] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_skewness_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_skewness_float
|
|
ufunc__hypergeom_skewness_ptr[2*0+1] = <void*>(<char*>"_hypergeom_skewness")
|
|
ufunc__hypergeom_skewness_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_skewness_double
|
|
ufunc__hypergeom_skewness_ptr[2*1+1] = <void*>(<char*>"_hypergeom_skewness")
|
|
ufunc__hypergeom_skewness_data[0] = &ufunc__hypergeom_skewness_ptr[2*0]
|
|
ufunc__hypergeom_skewness_data[1] = &ufunc__hypergeom_skewness_ptr[2*1]
|
|
_hypergeom_skewness = np.PyUFunc_FromFuncAndData(ufunc__hypergeom_skewness_loops, ufunc__hypergeom_skewness_data, ufunc__hypergeom_skewness_types, 2, 3, 1, 0, '_hypergeom_skewness', ufunc__hypergeom_skewness_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__hypergeom_variance_loops[2]
|
|
cdef void *ufunc__hypergeom_variance_ptr[4]
|
|
cdef void *ufunc__hypergeom_variance_data[2]
|
|
cdef char ufunc__hypergeom_variance_types[8]
|
|
cdef char *ufunc__hypergeom_variance_doc = (
|
|
"_hypergeom_variance(r, N, M)\n"
|
|
"\n"
|
|
"Mean of hypergeometric distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"r, N, M : array_like\n"
|
|
" Positive, integer-valued parameter\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__hypergeom_variance_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__hypergeom_variance_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__hypergeom_variance_types[0] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_variance_types[1] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_variance_types[2] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_variance_types[3] = <char>NPY_FLOAT
|
|
ufunc__hypergeom_variance_types[4] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_variance_types[5] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_variance_types[6] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_variance_types[7] = <char>NPY_DOUBLE
|
|
ufunc__hypergeom_variance_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_variance_float
|
|
ufunc__hypergeom_variance_ptr[2*0+1] = <void*>(<char*>"_hypergeom_variance")
|
|
ufunc__hypergeom_variance_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_variance_double
|
|
ufunc__hypergeom_variance_ptr[2*1+1] = <void*>(<char*>"_hypergeom_variance")
|
|
ufunc__hypergeom_variance_data[0] = &ufunc__hypergeom_variance_ptr[2*0]
|
|
ufunc__hypergeom_variance_data[1] = &ufunc__hypergeom_variance_ptr[2*1]
|
|
_hypergeom_variance = np.PyUFunc_FromFuncAndData(ufunc__hypergeom_variance_loops, ufunc__hypergeom_variance_data, ufunc__hypergeom_variance_types, 2, 3, 1, 0, '_hypergeom_variance', ufunc__hypergeom_variance_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__igam_fac_loops[2]
|
|
cdef void *ufunc__igam_fac_ptr[4]
|
|
cdef void *ufunc__igam_fac_data[2]
|
|
cdef char ufunc__igam_fac_types[6]
|
|
cdef char *ufunc__igam_fac_doc = (
|
|
"Internal function, do not use.")
|
|
ufunc__igam_fac_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc__igam_fac_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc__igam_fac_types[0] = <char>NPY_FLOAT
|
|
ufunc__igam_fac_types[1] = <char>NPY_FLOAT
|
|
ufunc__igam_fac_types[2] = <char>NPY_FLOAT
|
|
ufunc__igam_fac_types[3] = <char>NPY_DOUBLE
|
|
ufunc__igam_fac_types[4] = <char>NPY_DOUBLE
|
|
ufunc__igam_fac_types[5] = <char>NPY_DOUBLE
|
|
ufunc__igam_fac_ptr[2*0] = <void*>_func_cephes_igam_fac
|
|
ufunc__igam_fac_ptr[2*0+1] = <void*>(<char*>"_igam_fac")
|
|
ufunc__igam_fac_ptr[2*1] = <void*>_func_cephes_igam_fac
|
|
ufunc__igam_fac_ptr[2*1+1] = <void*>(<char*>"_igam_fac")
|
|
ufunc__igam_fac_data[0] = &ufunc__igam_fac_ptr[2*0]
|
|
ufunc__igam_fac_data[1] = &ufunc__igam_fac_ptr[2*1]
|
|
_igam_fac = np.PyUFunc_FromFuncAndData(ufunc__igam_fac_loops, ufunc__igam_fac_data, ufunc__igam_fac_types, 2, 2, 1, 0, '_igam_fac', ufunc__igam_fac_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__invgauss_isf_loops[2]
|
|
cdef void *ufunc__invgauss_isf_ptr[4]
|
|
cdef void *ufunc__invgauss_isf_data[2]
|
|
cdef char ufunc__invgauss_isf_types[8]
|
|
cdef char *ufunc__invgauss_isf_doc = (
|
|
"_invgauss_isf(x, mu, s)\n"
|
|
"\n"
|
|
"Inverse survival function of inverse gaussian distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Positive real-valued\n"
|
|
"mu : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"s : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__invgauss_isf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__invgauss_isf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__invgauss_isf_types[0] = <char>NPY_FLOAT
|
|
ufunc__invgauss_isf_types[1] = <char>NPY_FLOAT
|
|
ufunc__invgauss_isf_types[2] = <char>NPY_FLOAT
|
|
ufunc__invgauss_isf_types[3] = <char>NPY_FLOAT
|
|
ufunc__invgauss_isf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__invgauss_isf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__invgauss_isf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__invgauss_isf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__invgauss_isf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_invgauss_isf_float
|
|
ufunc__invgauss_isf_ptr[2*0+1] = <void*>(<char*>"_invgauss_isf")
|
|
ufunc__invgauss_isf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_invgauss_isf_double
|
|
ufunc__invgauss_isf_ptr[2*1+1] = <void*>(<char*>"_invgauss_isf")
|
|
ufunc__invgauss_isf_data[0] = &ufunc__invgauss_isf_ptr[2*0]
|
|
ufunc__invgauss_isf_data[1] = &ufunc__invgauss_isf_ptr[2*1]
|
|
_invgauss_isf = np.PyUFunc_FromFuncAndData(ufunc__invgauss_isf_loops, ufunc__invgauss_isf_data, ufunc__invgauss_isf_types, 2, 3, 1, 0, '_invgauss_isf', ufunc__invgauss_isf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__invgauss_ppf_loops[2]
|
|
cdef void *ufunc__invgauss_ppf_ptr[4]
|
|
cdef void *ufunc__invgauss_ppf_data[2]
|
|
cdef char ufunc__invgauss_ppf_types[8]
|
|
cdef char *ufunc__invgauss_ppf_doc = (
|
|
"_invgauss_ppf(x, mu)\n"
|
|
"\n"
|
|
"Percent point function of inverse gaussian distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Positive real-valued\n"
|
|
"mu : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__invgauss_ppf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__invgauss_ppf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__invgauss_ppf_types[0] = <char>NPY_FLOAT
|
|
ufunc__invgauss_ppf_types[1] = <char>NPY_FLOAT
|
|
ufunc__invgauss_ppf_types[2] = <char>NPY_FLOAT
|
|
ufunc__invgauss_ppf_types[3] = <char>NPY_FLOAT
|
|
ufunc__invgauss_ppf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__invgauss_ppf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__invgauss_ppf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__invgauss_ppf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__invgauss_ppf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_invgauss_ppf_float
|
|
ufunc__invgauss_ppf_ptr[2*0+1] = <void*>(<char*>"_invgauss_ppf")
|
|
ufunc__invgauss_ppf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_invgauss_ppf_double
|
|
ufunc__invgauss_ppf_ptr[2*1+1] = <void*>(<char*>"_invgauss_ppf")
|
|
ufunc__invgauss_ppf_data[0] = &ufunc__invgauss_ppf_ptr[2*0]
|
|
ufunc__invgauss_ppf_data[1] = &ufunc__invgauss_ppf_ptr[2*1]
|
|
_invgauss_ppf = np.PyUFunc_FromFuncAndData(ufunc__invgauss_ppf_loops, ufunc__invgauss_ppf_data, ufunc__invgauss_ppf_types, 2, 3, 1, 0, '_invgauss_ppf', ufunc__invgauss_ppf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__kolmogc_loops[2]
|
|
cdef void *ufunc__kolmogc_ptr[4]
|
|
cdef void *ufunc__kolmogc_data[2]
|
|
cdef char ufunc__kolmogc_types[4]
|
|
cdef char *ufunc__kolmogc_doc = (
|
|
"Internal function, do not use.")
|
|
ufunc__kolmogc_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
|
|
ufunc__kolmogc_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
|
|
ufunc__kolmogc_types[0] = <char>NPY_FLOAT
|
|
ufunc__kolmogc_types[1] = <char>NPY_FLOAT
|
|
ufunc__kolmogc_types[2] = <char>NPY_DOUBLE
|
|
ufunc__kolmogc_types[3] = <char>NPY_DOUBLE
|
|
ufunc__kolmogc_ptr[2*0] = <void*>_func_xsf_kolmogc
|
|
ufunc__kolmogc_ptr[2*0+1] = <void*>(<char*>"_kolmogc")
|
|
ufunc__kolmogc_ptr[2*1] = <void*>_func_xsf_kolmogc
|
|
ufunc__kolmogc_ptr[2*1+1] = <void*>(<char*>"_kolmogc")
|
|
ufunc__kolmogc_data[0] = &ufunc__kolmogc_ptr[2*0]
|
|
ufunc__kolmogc_data[1] = &ufunc__kolmogc_ptr[2*1]
|
|
_kolmogc = np.PyUFunc_FromFuncAndData(ufunc__kolmogc_loops, ufunc__kolmogc_data, ufunc__kolmogc_types, 2, 1, 1, 0, '_kolmogc', ufunc__kolmogc_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__kolmogci_loops[2]
|
|
cdef void *ufunc__kolmogci_ptr[4]
|
|
cdef void *ufunc__kolmogci_data[2]
|
|
cdef char ufunc__kolmogci_types[4]
|
|
cdef char *ufunc__kolmogci_doc = (
|
|
"Internal function, do not use.")
|
|
ufunc__kolmogci_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
|
|
ufunc__kolmogci_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
|
|
ufunc__kolmogci_types[0] = <char>NPY_FLOAT
|
|
ufunc__kolmogci_types[1] = <char>NPY_FLOAT
|
|
ufunc__kolmogci_types[2] = <char>NPY_DOUBLE
|
|
ufunc__kolmogci_types[3] = <char>NPY_DOUBLE
|
|
ufunc__kolmogci_ptr[2*0] = <void*>_func_xsf_kolmogci
|
|
ufunc__kolmogci_ptr[2*0+1] = <void*>(<char*>"_kolmogci")
|
|
ufunc__kolmogci_ptr[2*1] = <void*>_func_xsf_kolmogci
|
|
ufunc__kolmogci_ptr[2*1+1] = <void*>(<char*>"_kolmogci")
|
|
ufunc__kolmogci_data[0] = &ufunc__kolmogci_ptr[2*0]
|
|
ufunc__kolmogci_data[1] = &ufunc__kolmogci_ptr[2*1]
|
|
_kolmogci = np.PyUFunc_FromFuncAndData(ufunc__kolmogci_loops, ufunc__kolmogci_data, ufunc__kolmogci_types, 2, 1, 1, 0, '_kolmogci', ufunc__kolmogci_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__kolmogp_loops[2]
|
|
cdef void *ufunc__kolmogp_ptr[4]
|
|
cdef void *ufunc__kolmogp_data[2]
|
|
cdef char ufunc__kolmogp_types[4]
|
|
cdef char *ufunc__kolmogp_doc = (
|
|
"Internal function, do not use.")
|
|
ufunc__kolmogp_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
|
|
ufunc__kolmogp_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
|
|
ufunc__kolmogp_types[0] = <char>NPY_FLOAT
|
|
ufunc__kolmogp_types[1] = <char>NPY_FLOAT
|
|
ufunc__kolmogp_types[2] = <char>NPY_DOUBLE
|
|
ufunc__kolmogp_types[3] = <char>NPY_DOUBLE
|
|
ufunc__kolmogp_ptr[2*0] = <void*>_func_xsf_kolmogp
|
|
ufunc__kolmogp_ptr[2*0+1] = <void*>(<char*>"_kolmogp")
|
|
ufunc__kolmogp_ptr[2*1] = <void*>_func_xsf_kolmogp
|
|
ufunc__kolmogp_ptr[2*1+1] = <void*>(<char*>"_kolmogp")
|
|
ufunc__kolmogp_data[0] = &ufunc__kolmogp_ptr[2*0]
|
|
ufunc__kolmogp_data[1] = &ufunc__kolmogp_ptr[2*1]
|
|
_kolmogp = np.PyUFunc_FromFuncAndData(ufunc__kolmogp_loops, ufunc__kolmogp_data, ufunc__kolmogp_types, 2, 1, 1, 0, '_kolmogp', ufunc__kolmogp_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__lanczos_sum_expg_scaled_loops[2]
|
|
cdef void *ufunc__lanczos_sum_expg_scaled_ptr[4]
|
|
cdef void *ufunc__lanczos_sum_expg_scaled_data[2]
|
|
cdef char ufunc__lanczos_sum_expg_scaled_types[4]
|
|
cdef char *ufunc__lanczos_sum_expg_scaled_doc = (
|
|
"Internal function, do not use.")
|
|
ufunc__lanczos_sum_expg_scaled_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
|
|
ufunc__lanczos_sum_expg_scaled_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
|
|
ufunc__lanczos_sum_expg_scaled_types[0] = <char>NPY_FLOAT
|
|
ufunc__lanczos_sum_expg_scaled_types[1] = <char>NPY_FLOAT
|
|
ufunc__lanczos_sum_expg_scaled_types[2] = <char>NPY_DOUBLE
|
|
ufunc__lanczos_sum_expg_scaled_types[3] = <char>NPY_DOUBLE
|
|
ufunc__lanczos_sum_expg_scaled_ptr[2*0] = <void*>_func_cephes_lanczos_sum_expg_scaled
|
|
ufunc__lanczos_sum_expg_scaled_ptr[2*0+1] = <void*>(<char*>"_lanczos_sum_expg_scaled")
|
|
ufunc__lanczos_sum_expg_scaled_ptr[2*1] = <void*>_func_cephes_lanczos_sum_expg_scaled
|
|
ufunc__lanczos_sum_expg_scaled_ptr[2*1+1] = <void*>(<char*>"_lanczos_sum_expg_scaled")
|
|
ufunc__lanczos_sum_expg_scaled_data[0] = &ufunc__lanczos_sum_expg_scaled_ptr[2*0]
|
|
ufunc__lanczos_sum_expg_scaled_data[1] = &ufunc__lanczos_sum_expg_scaled_ptr[2*1]
|
|
_lanczos_sum_expg_scaled = np.PyUFunc_FromFuncAndData(ufunc__lanczos_sum_expg_scaled_loops, ufunc__lanczos_sum_expg_scaled_data, ufunc__lanczos_sum_expg_scaled_types, 2, 1, 1, 0, '_lanczos_sum_expg_scaled', ufunc__lanczos_sum_expg_scaled_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__landau_cdf_loops[2]
|
|
cdef void *ufunc__landau_cdf_ptr[4]
|
|
cdef void *ufunc__landau_cdf_data[2]
|
|
cdef char ufunc__landau_cdf_types[8]
|
|
cdef char *ufunc__landau_cdf_doc = (
|
|
"_landau_cdf(x, loc, scale)\n"
|
|
"\n"
|
|
"Cumulative distribution function of the Landau distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued argument\n"
|
|
"loc : array_like\n"
|
|
" Real-valued distribution location\n"
|
|
"scale : array_like\n"
|
|
" Positive, real-valued distribution scale\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__landau_cdf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__landau_cdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__landau_cdf_types[0] = <char>NPY_FLOAT
|
|
ufunc__landau_cdf_types[1] = <char>NPY_FLOAT
|
|
ufunc__landau_cdf_types[2] = <char>NPY_FLOAT
|
|
ufunc__landau_cdf_types[3] = <char>NPY_FLOAT
|
|
ufunc__landau_cdf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__landau_cdf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__landau_cdf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__landau_cdf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__landau_cdf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_landau_cdf_float
|
|
ufunc__landau_cdf_ptr[2*0+1] = <void*>(<char*>"_landau_cdf")
|
|
ufunc__landau_cdf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_landau_cdf_double
|
|
ufunc__landau_cdf_ptr[2*1+1] = <void*>(<char*>"_landau_cdf")
|
|
ufunc__landau_cdf_data[0] = &ufunc__landau_cdf_ptr[2*0]
|
|
ufunc__landau_cdf_data[1] = &ufunc__landau_cdf_ptr[2*1]
|
|
_landau_cdf = np.PyUFunc_FromFuncAndData(ufunc__landau_cdf_loops, ufunc__landau_cdf_data, ufunc__landau_cdf_types, 2, 3, 1, 0, '_landau_cdf', ufunc__landau_cdf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__landau_isf_loops[2]
|
|
cdef void *ufunc__landau_isf_ptr[4]
|
|
cdef void *ufunc__landau_isf_data[2]
|
|
cdef char ufunc__landau_isf_types[8]
|
|
cdef char *ufunc__landau_isf_doc = (
|
|
"_landau_isf(p, loc, scale)\n"
|
|
"\n"
|
|
"Inverse survival function of the Landau distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"p : array_like\n"
|
|
" Real-valued argument between 0 and 1\n"
|
|
"loc : array_like\n"
|
|
" Real-valued distribution location\n"
|
|
"scale : array_like\n"
|
|
" Positive, real-valued distribution scale\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__landau_isf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__landau_isf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__landau_isf_types[0] = <char>NPY_FLOAT
|
|
ufunc__landau_isf_types[1] = <char>NPY_FLOAT
|
|
ufunc__landau_isf_types[2] = <char>NPY_FLOAT
|
|
ufunc__landau_isf_types[3] = <char>NPY_FLOAT
|
|
ufunc__landau_isf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__landau_isf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__landau_isf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__landau_isf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__landau_isf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_landau_isf_float
|
|
ufunc__landau_isf_ptr[2*0+1] = <void*>(<char*>"_landau_isf")
|
|
ufunc__landau_isf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_landau_isf_double
|
|
ufunc__landau_isf_ptr[2*1+1] = <void*>(<char*>"_landau_isf")
|
|
ufunc__landau_isf_data[0] = &ufunc__landau_isf_ptr[2*0]
|
|
ufunc__landau_isf_data[1] = &ufunc__landau_isf_ptr[2*1]
|
|
_landau_isf = np.PyUFunc_FromFuncAndData(ufunc__landau_isf_loops, ufunc__landau_isf_data, ufunc__landau_isf_types, 2, 3, 1, 0, '_landau_isf', ufunc__landau_isf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__landau_pdf_loops[2]
|
|
cdef void *ufunc__landau_pdf_ptr[4]
|
|
cdef void *ufunc__landau_pdf_data[2]
|
|
cdef char ufunc__landau_pdf_types[8]
|
|
cdef char *ufunc__landau_pdf_doc = (
|
|
"_landau_pdf(x, loc, scale)\n"
|
|
"\n"
|
|
"Probability density function of the Landau distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued argument\n"
|
|
"loc : array_like\n"
|
|
" Real-valued distribution location\n"
|
|
"scale : array_like\n"
|
|
" Positive, real-valued distribution scale\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__landau_pdf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__landau_pdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__landau_pdf_types[0] = <char>NPY_FLOAT
|
|
ufunc__landau_pdf_types[1] = <char>NPY_FLOAT
|
|
ufunc__landau_pdf_types[2] = <char>NPY_FLOAT
|
|
ufunc__landau_pdf_types[3] = <char>NPY_FLOAT
|
|
ufunc__landau_pdf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__landau_pdf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__landau_pdf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__landau_pdf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__landau_pdf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_landau_pdf_float
|
|
ufunc__landau_pdf_ptr[2*0+1] = <void*>(<char*>"_landau_pdf")
|
|
ufunc__landau_pdf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_landau_pdf_double
|
|
ufunc__landau_pdf_ptr[2*1+1] = <void*>(<char*>"_landau_pdf")
|
|
ufunc__landau_pdf_data[0] = &ufunc__landau_pdf_ptr[2*0]
|
|
ufunc__landau_pdf_data[1] = &ufunc__landau_pdf_ptr[2*1]
|
|
_landau_pdf = np.PyUFunc_FromFuncAndData(ufunc__landau_pdf_loops, ufunc__landau_pdf_data, ufunc__landau_pdf_types, 2, 3, 1, 0, '_landau_pdf', ufunc__landau_pdf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__landau_ppf_loops[2]
|
|
cdef void *ufunc__landau_ppf_ptr[4]
|
|
cdef void *ufunc__landau_ppf_data[2]
|
|
cdef char ufunc__landau_ppf_types[8]
|
|
cdef char *ufunc__landau_ppf_doc = (
|
|
"_landau_ppf(p, loc, scale)\n"
|
|
"\n"
|
|
"Percent point function of the Landau distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"p : array_like\n"
|
|
" Real-valued argument between 0 and 1\n"
|
|
"loc : array_like\n"
|
|
" Real-valued distribution location\n"
|
|
"scale : array_like\n"
|
|
" Positive, real-valued distribution scale\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__landau_ppf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__landau_ppf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__landau_ppf_types[0] = <char>NPY_FLOAT
|
|
ufunc__landau_ppf_types[1] = <char>NPY_FLOAT
|
|
ufunc__landau_ppf_types[2] = <char>NPY_FLOAT
|
|
ufunc__landau_ppf_types[3] = <char>NPY_FLOAT
|
|
ufunc__landau_ppf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__landau_ppf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__landau_ppf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__landau_ppf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__landau_ppf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_landau_ppf_float
|
|
ufunc__landau_ppf_ptr[2*0+1] = <void*>(<char*>"_landau_ppf")
|
|
ufunc__landau_ppf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_landau_ppf_double
|
|
ufunc__landau_ppf_ptr[2*1+1] = <void*>(<char*>"_landau_ppf")
|
|
ufunc__landau_ppf_data[0] = &ufunc__landau_ppf_ptr[2*0]
|
|
ufunc__landau_ppf_data[1] = &ufunc__landau_ppf_ptr[2*1]
|
|
_landau_ppf = np.PyUFunc_FromFuncAndData(ufunc__landau_ppf_loops, ufunc__landau_ppf_data, ufunc__landau_ppf_types, 2, 3, 1, 0, '_landau_ppf', ufunc__landau_ppf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__landau_sf_loops[2]
|
|
cdef void *ufunc__landau_sf_ptr[4]
|
|
cdef void *ufunc__landau_sf_data[2]
|
|
cdef char ufunc__landau_sf_types[8]
|
|
cdef char *ufunc__landau_sf_doc = (
|
|
"_landau_sf(x, loc, scale)\n"
|
|
"\n"
|
|
"Survival function of the Landau distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued argument\n"
|
|
"loc : array_like\n"
|
|
" Real-valued distribution location\n"
|
|
"scale : array_like\n"
|
|
" Positive, real-valued distribution scale\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__landau_sf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__landau_sf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__landau_sf_types[0] = <char>NPY_FLOAT
|
|
ufunc__landau_sf_types[1] = <char>NPY_FLOAT
|
|
ufunc__landau_sf_types[2] = <char>NPY_FLOAT
|
|
ufunc__landau_sf_types[3] = <char>NPY_FLOAT
|
|
ufunc__landau_sf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__landau_sf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__landau_sf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__landau_sf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__landau_sf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_landau_sf_float
|
|
ufunc__landau_sf_ptr[2*0+1] = <void*>(<char*>"_landau_sf")
|
|
ufunc__landau_sf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_landau_sf_double
|
|
ufunc__landau_sf_ptr[2*1+1] = <void*>(<char*>"_landau_sf")
|
|
ufunc__landau_sf_data[0] = &ufunc__landau_sf_ptr[2*0]
|
|
ufunc__landau_sf_data[1] = &ufunc__landau_sf_ptr[2*1]
|
|
_landau_sf = np.PyUFunc_FromFuncAndData(ufunc__landau_sf_loops, ufunc__landau_sf_data, ufunc__landau_sf_types, 2, 3, 1, 0, '_landau_sf', ufunc__landau_sf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__lgam1p_loops[2]
|
|
cdef void *ufunc__lgam1p_ptr[4]
|
|
cdef void *ufunc__lgam1p_data[2]
|
|
cdef char ufunc__lgam1p_types[4]
|
|
cdef char *ufunc__lgam1p_doc = (
|
|
"Internal function, do not use.")
|
|
ufunc__lgam1p_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
|
|
ufunc__lgam1p_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
|
|
ufunc__lgam1p_types[0] = <char>NPY_FLOAT
|
|
ufunc__lgam1p_types[1] = <char>NPY_FLOAT
|
|
ufunc__lgam1p_types[2] = <char>NPY_DOUBLE
|
|
ufunc__lgam1p_types[3] = <char>NPY_DOUBLE
|
|
ufunc__lgam1p_ptr[2*0] = <void*>_func_cephes_lgam1p
|
|
ufunc__lgam1p_ptr[2*0+1] = <void*>(<char*>"_lgam1p")
|
|
ufunc__lgam1p_ptr[2*1] = <void*>_func_cephes_lgam1p
|
|
ufunc__lgam1p_ptr[2*1+1] = <void*>(<char*>"_lgam1p")
|
|
ufunc__lgam1p_data[0] = &ufunc__lgam1p_ptr[2*0]
|
|
ufunc__lgam1p_data[1] = &ufunc__lgam1p_ptr[2*1]
|
|
_lgam1p = np.PyUFunc_FromFuncAndData(ufunc__lgam1p_loops, ufunc__lgam1p_data, ufunc__lgam1p_types, 2, 1, 1, 0, '_lgam1p', ufunc__lgam1p_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__nbinom_cdf_loops[2]
|
|
cdef void *ufunc__nbinom_cdf_ptr[4]
|
|
cdef void *ufunc__nbinom_cdf_data[2]
|
|
cdef char ufunc__nbinom_cdf_types[8]
|
|
cdef char *ufunc__nbinom_cdf_doc = (
|
|
"_nbinom_cdf(x, r, p)\n"
|
|
"\n"
|
|
"Cumulative density function of negative binomial distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued\n"
|
|
"r : array_like\n"
|
|
" Positive, integer-valued parameter\n"
|
|
"p : array_like\n"
|
|
" Positive, real-valued parameter\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__nbinom_cdf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__nbinom_cdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__nbinom_cdf_types[0] = <char>NPY_FLOAT
|
|
ufunc__nbinom_cdf_types[1] = <char>NPY_FLOAT
|
|
ufunc__nbinom_cdf_types[2] = <char>NPY_FLOAT
|
|
ufunc__nbinom_cdf_types[3] = <char>NPY_FLOAT
|
|
ufunc__nbinom_cdf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_cdf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_cdf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_cdf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_cdf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nbinom_cdf_float
|
|
ufunc__nbinom_cdf_ptr[2*0+1] = <void*>(<char*>"_nbinom_cdf")
|
|
ufunc__nbinom_cdf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nbinom_cdf_double
|
|
ufunc__nbinom_cdf_ptr[2*1+1] = <void*>(<char*>"_nbinom_cdf")
|
|
ufunc__nbinom_cdf_data[0] = &ufunc__nbinom_cdf_ptr[2*0]
|
|
ufunc__nbinom_cdf_data[1] = &ufunc__nbinom_cdf_ptr[2*1]
|
|
_nbinom_cdf = np.PyUFunc_FromFuncAndData(ufunc__nbinom_cdf_loops, ufunc__nbinom_cdf_data, ufunc__nbinom_cdf_types, 2, 3, 1, 0, '_nbinom_cdf', ufunc__nbinom_cdf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__nbinom_isf_loops[2]
|
|
cdef void *ufunc__nbinom_isf_ptr[4]
|
|
cdef void *ufunc__nbinom_isf_data[2]
|
|
cdef char ufunc__nbinom_isf_types[8]
|
|
cdef char *ufunc__nbinom_isf_doc = (
|
|
"_nbinom_isf(x, r, p)\n"
|
|
"\n"
|
|
"Inverse survival function of negative binomial distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued\n"
|
|
"r : array_like\n"
|
|
" Positive, integer-valued parameter\n"
|
|
"p : array_like\n"
|
|
" Positive, real-valued parameter\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__nbinom_isf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__nbinom_isf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__nbinom_isf_types[0] = <char>NPY_FLOAT
|
|
ufunc__nbinom_isf_types[1] = <char>NPY_FLOAT
|
|
ufunc__nbinom_isf_types[2] = <char>NPY_FLOAT
|
|
ufunc__nbinom_isf_types[3] = <char>NPY_FLOAT
|
|
ufunc__nbinom_isf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_isf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_isf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_isf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_isf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nbinom_isf_float
|
|
ufunc__nbinom_isf_ptr[2*0+1] = <void*>(<char*>"_nbinom_isf")
|
|
ufunc__nbinom_isf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nbinom_isf_double
|
|
ufunc__nbinom_isf_ptr[2*1+1] = <void*>(<char*>"_nbinom_isf")
|
|
ufunc__nbinom_isf_data[0] = &ufunc__nbinom_isf_ptr[2*0]
|
|
ufunc__nbinom_isf_data[1] = &ufunc__nbinom_isf_ptr[2*1]
|
|
_nbinom_isf = np.PyUFunc_FromFuncAndData(ufunc__nbinom_isf_loops, ufunc__nbinom_isf_data, ufunc__nbinom_isf_types, 2, 3, 1, 0, '_nbinom_isf', ufunc__nbinom_isf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__nbinom_kurtosis_excess_loops[2]
|
|
cdef void *ufunc__nbinom_kurtosis_excess_ptr[4]
|
|
cdef void *ufunc__nbinom_kurtosis_excess_data[2]
|
|
cdef char ufunc__nbinom_kurtosis_excess_types[6]
|
|
cdef char *ufunc__nbinom_kurtosis_excess_doc = (
|
|
"_nbinom_kurtosis_excess(r, p)\n"
|
|
"\n"
|
|
"Kurtosis excess of negative binomial distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"r : array_like\n"
|
|
" Positive, integer-valued parameter\n"
|
|
"p : array_like\n"
|
|
" Positive, real-valued parameter\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__nbinom_kurtosis_excess_loops[0] = <np.PyUFuncGenericFunction>loop_f_ff__As_ff_f
|
|
ufunc__nbinom_kurtosis_excess_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc__nbinom_kurtosis_excess_types[0] = <char>NPY_FLOAT
|
|
ufunc__nbinom_kurtosis_excess_types[1] = <char>NPY_FLOAT
|
|
ufunc__nbinom_kurtosis_excess_types[2] = <char>NPY_FLOAT
|
|
ufunc__nbinom_kurtosis_excess_types[3] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_kurtosis_excess_types[4] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_kurtosis_excess_types[5] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_kurtosis_excess_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nbinom_kurtosis_excess_float
|
|
ufunc__nbinom_kurtosis_excess_ptr[2*0+1] = <void*>(<char*>"_nbinom_kurtosis_excess")
|
|
ufunc__nbinom_kurtosis_excess_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nbinom_kurtosis_excess_double
|
|
ufunc__nbinom_kurtosis_excess_ptr[2*1+1] = <void*>(<char*>"_nbinom_kurtosis_excess")
|
|
ufunc__nbinom_kurtosis_excess_data[0] = &ufunc__nbinom_kurtosis_excess_ptr[2*0]
|
|
ufunc__nbinom_kurtosis_excess_data[1] = &ufunc__nbinom_kurtosis_excess_ptr[2*1]
|
|
_nbinom_kurtosis_excess = np.PyUFunc_FromFuncAndData(ufunc__nbinom_kurtosis_excess_loops, ufunc__nbinom_kurtosis_excess_data, ufunc__nbinom_kurtosis_excess_types, 2, 2, 1, 0, '_nbinom_kurtosis_excess', ufunc__nbinom_kurtosis_excess_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__nbinom_mean_loops[2]
|
|
cdef void *ufunc__nbinom_mean_ptr[4]
|
|
cdef void *ufunc__nbinom_mean_data[2]
|
|
cdef char ufunc__nbinom_mean_types[6]
|
|
cdef char *ufunc__nbinom_mean_doc = (
|
|
"_nbinom_mean(r, p)\n"
|
|
"\n"
|
|
"Mean of negative binomial distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"r : array_like\n"
|
|
" Positive, integer-valued parameter\n"
|
|
"p : array_like\n"
|
|
" Positive, real-valued parameter\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__nbinom_mean_loops[0] = <np.PyUFuncGenericFunction>loop_f_ff__As_ff_f
|
|
ufunc__nbinom_mean_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc__nbinom_mean_types[0] = <char>NPY_FLOAT
|
|
ufunc__nbinom_mean_types[1] = <char>NPY_FLOAT
|
|
ufunc__nbinom_mean_types[2] = <char>NPY_FLOAT
|
|
ufunc__nbinom_mean_types[3] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_mean_types[4] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_mean_types[5] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_mean_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nbinom_mean_float
|
|
ufunc__nbinom_mean_ptr[2*0+1] = <void*>(<char*>"_nbinom_mean")
|
|
ufunc__nbinom_mean_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nbinom_mean_double
|
|
ufunc__nbinom_mean_ptr[2*1+1] = <void*>(<char*>"_nbinom_mean")
|
|
ufunc__nbinom_mean_data[0] = &ufunc__nbinom_mean_ptr[2*0]
|
|
ufunc__nbinom_mean_data[1] = &ufunc__nbinom_mean_ptr[2*1]
|
|
_nbinom_mean = np.PyUFunc_FromFuncAndData(ufunc__nbinom_mean_loops, ufunc__nbinom_mean_data, ufunc__nbinom_mean_types, 2, 2, 1, 0, '_nbinom_mean', ufunc__nbinom_mean_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__nbinom_pmf_loops[2]
|
|
cdef void *ufunc__nbinom_pmf_ptr[4]
|
|
cdef void *ufunc__nbinom_pmf_data[2]
|
|
cdef char ufunc__nbinom_pmf_types[8]
|
|
cdef char *ufunc__nbinom_pmf_doc = (
|
|
"_nbinom_pmf(x, r, p)\n"
|
|
"\n"
|
|
"Probability mass function of negative binomial distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued\n"
|
|
"r : array_like\n"
|
|
" Positive, integer-valued parameter\n"
|
|
"p : array_like\n"
|
|
" Positive, real-valued parameter\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__nbinom_pmf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__nbinom_pmf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__nbinom_pmf_types[0] = <char>NPY_FLOAT
|
|
ufunc__nbinom_pmf_types[1] = <char>NPY_FLOAT
|
|
ufunc__nbinom_pmf_types[2] = <char>NPY_FLOAT
|
|
ufunc__nbinom_pmf_types[3] = <char>NPY_FLOAT
|
|
ufunc__nbinom_pmf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_pmf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_pmf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_pmf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_pmf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nbinom_pmf_float
|
|
ufunc__nbinom_pmf_ptr[2*0+1] = <void*>(<char*>"_nbinom_pmf")
|
|
ufunc__nbinom_pmf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nbinom_pmf_double
|
|
ufunc__nbinom_pmf_ptr[2*1+1] = <void*>(<char*>"_nbinom_pmf")
|
|
ufunc__nbinom_pmf_data[0] = &ufunc__nbinom_pmf_ptr[2*0]
|
|
ufunc__nbinom_pmf_data[1] = &ufunc__nbinom_pmf_ptr[2*1]
|
|
_nbinom_pmf = np.PyUFunc_FromFuncAndData(ufunc__nbinom_pmf_loops, ufunc__nbinom_pmf_data, ufunc__nbinom_pmf_types, 2, 3, 1, 0, '_nbinom_pmf', ufunc__nbinom_pmf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__nbinom_ppf_loops[2]
|
|
cdef void *ufunc__nbinom_ppf_ptr[4]
|
|
cdef void *ufunc__nbinom_ppf_data[2]
|
|
cdef char ufunc__nbinom_ppf_types[8]
|
|
cdef char *ufunc__nbinom_ppf_doc = (
|
|
"_nbinom_ppf(x, r, p)\n"
|
|
"\n"
|
|
"Percent point function of negative binomial distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued\n"
|
|
"r : array_like\n"
|
|
" Positive, integer-valued parameter\n"
|
|
"p : array_like\n"
|
|
" Positive, real-valued parameter\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__nbinom_ppf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__nbinom_ppf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__nbinom_ppf_types[0] = <char>NPY_FLOAT
|
|
ufunc__nbinom_ppf_types[1] = <char>NPY_FLOAT
|
|
ufunc__nbinom_ppf_types[2] = <char>NPY_FLOAT
|
|
ufunc__nbinom_ppf_types[3] = <char>NPY_FLOAT
|
|
ufunc__nbinom_ppf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_ppf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_ppf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_ppf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_ppf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nbinom_ppf_float
|
|
ufunc__nbinom_ppf_ptr[2*0+1] = <void*>(<char*>"_nbinom_ppf")
|
|
ufunc__nbinom_ppf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nbinom_ppf_double
|
|
ufunc__nbinom_ppf_ptr[2*1+1] = <void*>(<char*>"_nbinom_ppf")
|
|
ufunc__nbinom_ppf_data[0] = &ufunc__nbinom_ppf_ptr[2*0]
|
|
ufunc__nbinom_ppf_data[1] = &ufunc__nbinom_ppf_ptr[2*1]
|
|
_nbinom_ppf = np.PyUFunc_FromFuncAndData(ufunc__nbinom_ppf_loops, ufunc__nbinom_ppf_data, ufunc__nbinom_ppf_types, 2, 3, 1, 0, '_nbinom_ppf', ufunc__nbinom_ppf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__nbinom_sf_loops[2]
|
|
cdef void *ufunc__nbinom_sf_ptr[4]
|
|
cdef void *ufunc__nbinom_sf_data[2]
|
|
cdef char ufunc__nbinom_sf_types[8]
|
|
cdef char *ufunc__nbinom_sf_doc = (
|
|
"_nbinom_sf(x, r, p)\n"
|
|
"\n"
|
|
"Survival function of negative binomial distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued\n"
|
|
"r : array_like\n"
|
|
" Positive, integer-valued parameter\n"
|
|
"p : array_like\n"
|
|
" Positive, real-valued parameter\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__nbinom_sf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__nbinom_sf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__nbinom_sf_types[0] = <char>NPY_FLOAT
|
|
ufunc__nbinom_sf_types[1] = <char>NPY_FLOAT
|
|
ufunc__nbinom_sf_types[2] = <char>NPY_FLOAT
|
|
ufunc__nbinom_sf_types[3] = <char>NPY_FLOAT
|
|
ufunc__nbinom_sf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_sf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_sf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_sf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_sf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nbinom_sf_float
|
|
ufunc__nbinom_sf_ptr[2*0+1] = <void*>(<char*>"_nbinom_sf")
|
|
ufunc__nbinom_sf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nbinom_sf_double
|
|
ufunc__nbinom_sf_ptr[2*1+1] = <void*>(<char*>"_nbinom_sf")
|
|
ufunc__nbinom_sf_data[0] = &ufunc__nbinom_sf_ptr[2*0]
|
|
ufunc__nbinom_sf_data[1] = &ufunc__nbinom_sf_ptr[2*1]
|
|
_nbinom_sf = np.PyUFunc_FromFuncAndData(ufunc__nbinom_sf_loops, ufunc__nbinom_sf_data, ufunc__nbinom_sf_types, 2, 3, 1, 0, '_nbinom_sf', ufunc__nbinom_sf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__nbinom_skewness_loops[2]
|
|
cdef void *ufunc__nbinom_skewness_ptr[4]
|
|
cdef void *ufunc__nbinom_skewness_data[2]
|
|
cdef char ufunc__nbinom_skewness_types[6]
|
|
cdef char *ufunc__nbinom_skewness_doc = (
|
|
"_nbinom_skewness(r, p)\n"
|
|
"\n"
|
|
"Skewness of negative binomial distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"r : array_like\n"
|
|
" Positive, integer-valued parameter\n"
|
|
"p : array_like\n"
|
|
" Positive, real-valued parameter\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__nbinom_skewness_loops[0] = <np.PyUFuncGenericFunction>loop_f_ff__As_ff_f
|
|
ufunc__nbinom_skewness_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc__nbinom_skewness_types[0] = <char>NPY_FLOAT
|
|
ufunc__nbinom_skewness_types[1] = <char>NPY_FLOAT
|
|
ufunc__nbinom_skewness_types[2] = <char>NPY_FLOAT
|
|
ufunc__nbinom_skewness_types[3] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_skewness_types[4] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_skewness_types[5] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_skewness_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nbinom_skewness_float
|
|
ufunc__nbinom_skewness_ptr[2*0+1] = <void*>(<char*>"_nbinom_skewness")
|
|
ufunc__nbinom_skewness_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nbinom_skewness_double
|
|
ufunc__nbinom_skewness_ptr[2*1+1] = <void*>(<char*>"_nbinom_skewness")
|
|
ufunc__nbinom_skewness_data[0] = &ufunc__nbinom_skewness_ptr[2*0]
|
|
ufunc__nbinom_skewness_data[1] = &ufunc__nbinom_skewness_ptr[2*1]
|
|
_nbinom_skewness = np.PyUFunc_FromFuncAndData(ufunc__nbinom_skewness_loops, ufunc__nbinom_skewness_data, ufunc__nbinom_skewness_types, 2, 2, 1, 0, '_nbinom_skewness', ufunc__nbinom_skewness_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__nbinom_variance_loops[2]
|
|
cdef void *ufunc__nbinom_variance_ptr[4]
|
|
cdef void *ufunc__nbinom_variance_data[2]
|
|
cdef char ufunc__nbinom_variance_types[6]
|
|
cdef char *ufunc__nbinom_variance_doc = (
|
|
"_nbinom_variance(r, p)\n"
|
|
"\n"
|
|
"Variance of negative binomial distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"r : array_like\n"
|
|
" Positive, integer-valued parameter\n"
|
|
"p : array_like\n"
|
|
" Positive, real-valued parameter\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__nbinom_variance_loops[0] = <np.PyUFuncGenericFunction>loop_f_ff__As_ff_f
|
|
ufunc__nbinom_variance_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc__nbinom_variance_types[0] = <char>NPY_FLOAT
|
|
ufunc__nbinom_variance_types[1] = <char>NPY_FLOAT
|
|
ufunc__nbinom_variance_types[2] = <char>NPY_FLOAT
|
|
ufunc__nbinom_variance_types[3] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_variance_types[4] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_variance_types[5] = <char>NPY_DOUBLE
|
|
ufunc__nbinom_variance_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nbinom_variance_float
|
|
ufunc__nbinom_variance_ptr[2*0+1] = <void*>(<char*>"_nbinom_variance")
|
|
ufunc__nbinom_variance_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nbinom_variance_double
|
|
ufunc__nbinom_variance_ptr[2*1+1] = <void*>(<char*>"_nbinom_variance")
|
|
ufunc__nbinom_variance_data[0] = &ufunc__nbinom_variance_ptr[2*0]
|
|
ufunc__nbinom_variance_data[1] = &ufunc__nbinom_variance_ptr[2*1]
|
|
_nbinom_variance = np.PyUFunc_FromFuncAndData(ufunc__nbinom_variance_loops, ufunc__nbinom_variance_data, ufunc__nbinom_variance_types, 2, 2, 1, 0, '_nbinom_variance', ufunc__nbinom_variance_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__ncf_isf_loops[2]
|
|
cdef void *ufunc__ncf_isf_ptr[4]
|
|
cdef void *ufunc__ncf_isf_data[2]
|
|
cdef char ufunc__ncf_isf_types[10]
|
|
cdef char *ufunc__ncf_isf_doc = (
|
|
"_ncf_isf(x, v1, v2, l)\n"
|
|
"\n"
|
|
"Inverse survival function of noncentral F-distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Positive real-valued\n"
|
|
"v1, v2, l : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__ncf_isf_loops[0] = <np.PyUFuncGenericFunction>loop_f_ffff__As_ffff_f
|
|
ufunc__ncf_isf_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
|
|
ufunc__ncf_isf_types[0] = <char>NPY_FLOAT
|
|
ufunc__ncf_isf_types[1] = <char>NPY_FLOAT
|
|
ufunc__ncf_isf_types[2] = <char>NPY_FLOAT
|
|
ufunc__ncf_isf_types[3] = <char>NPY_FLOAT
|
|
ufunc__ncf_isf_types[4] = <char>NPY_FLOAT
|
|
ufunc__ncf_isf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__ncf_isf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__ncf_isf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__ncf_isf_types[8] = <char>NPY_DOUBLE
|
|
ufunc__ncf_isf_types[9] = <char>NPY_DOUBLE
|
|
ufunc__ncf_isf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncf_isf_float
|
|
ufunc__ncf_isf_ptr[2*0+1] = <void*>(<char*>"_ncf_isf")
|
|
ufunc__ncf_isf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncf_isf_double
|
|
ufunc__ncf_isf_ptr[2*1+1] = <void*>(<char*>"_ncf_isf")
|
|
ufunc__ncf_isf_data[0] = &ufunc__ncf_isf_ptr[2*0]
|
|
ufunc__ncf_isf_data[1] = &ufunc__ncf_isf_ptr[2*1]
|
|
_ncf_isf = np.PyUFunc_FromFuncAndData(ufunc__ncf_isf_loops, ufunc__ncf_isf_data, ufunc__ncf_isf_types, 2, 4, 1, 0, '_ncf_isf', ufunc__ncf_isf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__ncf_kurtosis_excess_loops[2]
|
|
cdef void *ufunc__ncf_kurtosis_excess_ptr[4]
|
|
cdef void *ufunc__ncf_kurtosis_excess_data[2]
|
|
cdef char ufunc__ncf_kurtosis_excess_types[8]
|
|
cdef char *ufunc__ncf_kurtosis_excess_doc = (
|
|
"_ncf_kurtosis_excess(v1, v2, l)\n"
|
|
"\n"
|
|
"Kurtosis excess of noncentral F-distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"v1, v2, l : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__ncf_kurtosis_excess_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__ncf_kurtosis_excess_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__ncf_kurtosis_excess_types[0] = <char>NPY_FLOAT
|
|
ufunc__ncf_kurtosis_excess_types[1] = <char>NPY_FLOAT
|
|
ufunc__ncf_kurtosis_excess_types[2] = <char>NPY_FLOAT
|
|
ufunc__ncf_kurtosis_excess_types[3] = <char>NPY_FLOAT
|
|
ufunc__ncf_kurtosis_excess_types[4] = <char>NPY_DOUBLE
|
|
ufunc__ncf_kurtosis_excess_types[5] = <char>NPY_DOUBLE
|
|
ufunc__ncf_kurtosis_excess_types[6] = <char>NPY_DOUBLE
|
|
ufunc__ncf_kurtosis_excess_types[7] = <char>NPY_DOUBLE
|
|
ufunc__ncf_kurtosis_excess_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncf_kurtosis_excess_float
|
|
ufunc__ncf_kurtosis_excess_ptr[2*0+1] = <void*>(<char*>"_ncf_kurtosis_excess")
|
|
ufunc__ncf_kurtosis_excess_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncf_kurtosis_excess_double
|
|
ufunc__ncf_kurtosis_excess_ptr[2*1+1] = <void*>(<char*>"_ncf_kurtosis_excess")
|
|
ufunc__ncf_kurtosis_excess_data[0] = &ufunc__ncf_kurtosis_excess_ptr[2*0]
|
|
ufunc__ncf_kurtosis_excess_data[1] = &ufunc__ncf_kurtosis_excess_ptr[2*1]
|
|
_ncf_kurtosis_excess = np.PyUFunc_FromFuncAndData(ufunc__ncf_kurtosis_excess_loops, ufunc__ncf_kurtosis_excess_data, ufunc__ncf_kurtosis_excess_types, 2, 3, 1, 0, '_ncf_kurtosis_excess', ufunc__ncf_kurtosis_excess_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__ncf_mean_loops[2]
|
|
cdef void *ufunc__ncf_mean_ptr[4]
|
|
cdef void *ufunc__ncf_mean_data[2]
|
|
cdef char ufunc__ncf_mean_types[8]
|
|
cdef char *ufunc__ncf_mean_doc = (
|
|
"_ncf_mean(v1, v2, l)\n"
|
|
"\n"
|
|
"Mean of noncentral F-distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"v1, v2, l : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__ncf_mean_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__ncf_mean_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__ncf_mean_types[0] = <char>NPY_FLOAT
|
|
ufunc__ncf_mean_types[1] = <char>NPY_FLOAT
|
|
ufunc__ncf_mean_types[2] = <char>NPY_FLOAT
|
|
ufunc__ncf_mean_types[3] = <char>NPY_FLOAT
|
|
ufunc__ncf_mean_types[4] = <char>NPY_DOUBLE
|
|
ufunc__ncf_mean_types[5] = <char>NPY_DOUBLE
|
|
ufunc__ncf_mean_types[6] = <char>NPY_DOUBLE
|
|
ufunc__ncf_mean_types[7] = <char>NPY_DOUBLE
|
|
ufunc__ncf_mean_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncf_mean_float
|
|
ufunc__ncf_mean_ptr[2*0+1] = <void*>(<char*>"_ncf_mean")
|
|
ufunc__ncf_mean_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncf_mean_double
|
|
ufunc__ncf_mean_ptr[2*1+1] = <void*>(<char*>"_ncf_mean")
|
|
ufunc__ncf_mean_data[0] = &ufunc__ncf_mean_ptr[2*0]
|
|
ufunc__ncf_mean_data[1] = &ufunc__ncf_mean_ptr[2*1]
|
|
_ncf_mean = np.PyUFunc_FromFuncAndData(ufunc__ncf_mean_loops, ufunc__ncf_mean_data, ufunc__ncf_mean_types, 2, 3, 1, 0, '_ncf_mean', ufunc__ncf_mean_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__ncf_pdf_loops[2]
|
|
cdef void *ufunc__ncf_pdf_ptr[4]
|
|
cdef void *ufunc__ncf_pdf_data[2]
|
|
cdef char ufunc__ncf_pdf_types[10]
|
|
cdef char *ufunc__ncf_pdf_doc = (
|
|
"_ncf_pdf(x, v1, v2, l)\n"
|
|
"\n"
|
|
"Probability density function of noncentral F-distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Positive real-valued\n"
|
|
"v1, v2, l : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__ncf_pdf_loops[0] = <np.PyUFuncGenericFunction>loop_f_ffff__As_ffff_f
|
|
ufunc__ncf_pdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
|
|
ufunc__ncf_pdf_types[0] = <char>NPY_FLOAT
|
|
ufunc__ncf_pdf_types[1] = <char>NPY_FLOAT
|
|
ufunc__ncf_pdf_types[2] = <char>NPY_FLOAT
|
|
ufunc__ncf_pdf_types[3] = <char>NPY_FLOAT
|
|
ufunc__ncf_pdf_types[4] = <char>NPY_FLOAT
|
|
ufunc__ncf_pdf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__ncf_pdf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__ncf_pdf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__ncf_pdf_types[8] = <char>NPY_DOUBLE
|
|
ufunc__ncf_pdf_types[9] = <char>NPY_DOUBLE
|
|
ufunc__ncf_pdf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncf_pdf_float
|
|
ufunc__ncf_pdf_ptr[2*0+1] = <void*>(<char*>"_ncf_pdf")
|
|
ufunc__ncf_pdf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncf_pdf_double
|
|
ufunc__ncf_pdf_ptr[2*1+1] = <void*>(<char*>"_ncf_pdf")
|
|
ufunc__ncf_pdf_data[0] = &ufunc__ncf_pdf_ptr[2*0]
|
|
ufunc__ncf_pdf_data[1] = &ufunc__ncf_pdf_ptr[2*1]
|
|
_ncf_pdf = np.PyUFunc_FromFuncAndData(ufunc__ncf_pdf_loops, ufunc__ncf_pdf_data, ufunc__ncf_pdf_types, 2, 4, 1, 0, '_ncf_pdf', ufunc__ncf_pdf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__ncf_sf_loops[2]
|
|
cdef void *ufunc__ncf_sf_ptr[4]
|
|
cdef void *ufunc__ncf_sf_data[2]
|
|
cdef char ufunc__ncf_sf_types[10]
|
|
cdef char *ufunc__ncf_sf_doc = (
|
|
"_ncf_sf(x, v1, v2, l)\n"
|
|
"\n"
|
|
"Survival function of noncentral F-distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Positive real-valued\n"
|
|
"v1, v2, l : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__ncf_sf_loops[0] = <np.PyUFuncGenericFunction>loop_f_ffff__As_ffff_f
|
|
ufunc__ncf_sf_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
|
|
ufunc__ncf_sf_types[0] = <char>NPY_FLOAT
|
|
ufunc__ncf_sf_types[1] = <char>NPY_FLOAT
|
|
ufunc__ncf_sf_types[2] = <char>NPY_FLOAT
|
|
ufunc__ncf_sf_types[3] = <char>NPY_FLOAT
|
|
ufunc__ncf_sf_types[4] = <char>NPY_FLOAT
|
|
ufunc__ncf_sf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__ncf_sf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__ncf_sf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__ncf_sf_types[8] = <char>NPY_DOUBLE
|
|
ufunc__ncf_sf_types[9] = <char>NPY_DOUBLE
|
|
ufunc__ncf_sf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncf_sf_float
|
|
ufunc__ncf_sf_ptr[2*0+1] = <void*>(<char*>"_ncf_sf")
|
|
ufunc__ncf_sf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncf_sf_double
|
|
ufunc__ncf_sf_ptr[2*1+1] = <void*>(<char*>"_ncf_sf")
|
|
ufunc__ncf_sf_data[0] = &ufunc__ncf_sf_ptr[2*0]
|
|
ufunc__ncf_sf_data[1] = &ufunc__ncf_sf_ptr[2*1]
|
|
_ncf_sf = np.PyUFunc_FromFuncAndData(ufunc__ncf_sf_loops, ufunc__ncf_sf_data, ufunc__ncf_sf_types, 2, 4, 1, 0, '_ncf_sf', ufunc__ncf_sf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__ncf_skewness_loops[2]
|
|
cdef void *ufunc__ncf_skewness_ptr[4]
|
|
cdef void *ufunc__ncf_skewness_data[2]
|
|
cdef char ufunc__ncf_skewness_types[8]
|
|
cdef char *ufunc__ncf_skewness_doc = (
|
|
"_ncf_skewness(v1, v2, l)\n"
|
|
"\n"
|
|
"Skewness of noncentral F-distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"v1, v2, l : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__ncf_skewness_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__ncf_skewness_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__ncf_skewness_types[0] = <char>NPY_FLOAT
|
|
ufunc__ncf_skewness_types[1] = <char>NPY_FLOAT
|
|
ufunc__ncf_skewness_types[2] = <char>NPY_FLOAT
|
|
ufunc__ncf_skewness_types[3] = <char>NPY_FLOAT
|
|
ufunc__ncf_skewness_types[4] = <char>NPY_DOUBLE
|
|
ufunc__ncf_skewness_types[5] = <char>NPY_DOUBLE
|
|
ufunc__ncf_skewness_types[6] = <char>NPY_DOUBLE
|
|
ufunc__ncf_skewness_types[7] = <char>NPY_DOUBLE
|
|
ufunc__ncf_skewness_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncf_skewness_float
|
|
ufunc__ncf_skewness_ptr[2*0+1] = <void*>(<char*>"_ncf_skewness")
|
|
ufunc__ncf_skewness_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncf_skewness_double
|
|
ufunc__ncf_skewness_ptr[2*1+1] = <void*>(<char*>"_ncf_skewness")
|
|
ufunc__ncf_skewness_data[0] = &ufunc__ncf_skewness_ptr[2*0]
|
|
ufunc__ncf_skewness_data[1] = &ufunc__ncf_skewness_ptr[2*1]
|
|
_ncf_skewness = np.PyUFunc_FromFuncAndData(ufunc__ncf_skewness_loops, ufunc__ncf_skewness_data, ufunc__ncf_skewness_types, 2, 3, 1, 0, '_ncf_skewness', ufunc__ncf_skewness_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__ncf_variance_loops[2]
|
|
cdef void *ufunc__ncf_variance_ptr[4]
|
|
cdef void *ufunc__ncf_variance_data[2]
|
|
cdef char ufunc__ncf_variance_types[8]
|
|
cdef char *ufunc__ncf_variance_doc = (
|
|
"_ncf_variance(v1, v2, l)\n"
|
|
"\n"
|
|
"Variance of noncentral F-distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"v1, v2, l : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__ncf_variance_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__ncf_variance_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__ncf_variance_types[0] = <char>NPY_FLOAT
|
|
ufunc__ncf_variance_types[1] = <char>NPY_FLOAT
|
|
ufunc__ncf_variance_types[2] = <char>NPY_FLOAT
|
|
ufunc__ncf_variance_types[3] = <char>NPY_FLOAT
|
|
ufunc__ncf_variance_types[4] = <char>NPY_DOUBLE
|
|
ufunc__ncf_variance_types[5] = <char>NPY_DOUBLE
|
|
ufunc__ncf_variance_types[6] = <char>NPY_DOUBLE
|
|
ufunc__ncf_variance_types[7] = <char>NPY_DOUBLE
|
|
ufunc__ncf_variance_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncf_variance_float
|
|
ufunc__ncf_variance_ptr[2*0+1] = <void*>(<char*>"_ncf_variance")
|
|
ufunc__ncf_variance_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncf_variance_double
|
|
ufunc__ncf_variance_ptr[2*1+1] = <void*>(<char*>"_ncf_variance")
|
|
ufunc__ncf_variance_data[0] = &ufunc__ncf_variance_ptr[2*0]
|
|
ufunc__ncf_variance_data[1] = &ufunc__ncf_variance_ptr[2*1]
|
|
_ncf_variance = np.PyUFunc_FromFuncAndData(ufunc__ncf_variance_loops, ufunc__ncf_variance_data, ufunc__ncf_variance_types, 2, 3, 1, 0, '_ncf_variance', ufunc__ncf_variance_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__nct_isf_loops[2]
|
|
cdef void *ufunc__nct_isf_ptr[4]
|
|
cdef void *ufunc__nct_isf_data[2]
|
|
cdef char ufunc__nct_isf_types[8]
|
|
cdef char *ufunc__nct_isf_doc = (
|
|
"_nct_isf(x, v, l)\n"
|
|
"\n"
|
|
"Inverse survival function of noncentral t-distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued\n"
|
|
"v : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"l : array_like\n"
|
|
" Real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__nct_isf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__nct_isf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__nct_isf_types[0] = <char>NPY_FLOAT
|
|
ufunc__nct_isf_types[1] = <char>NPY_FLOAT
|
|
ufunc__nct_isf_types[2] = <char>NPY_FLOAT
|
|
ufunc__nct_isf_types[3] = <char>NPY_FLOAT
|
|
ufunc__nct_isf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__nct_isf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__nct_isf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__nct_isf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__nct_isf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nct_isf_float
|
|
ufunc__nct_isf_ptr[2*0+1] = <void*>(<char*>"_nct_isf")
|
|
ufunc__nct_isf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nct_isf_double
|
|
ufunc__nct_isf_ptr[2*1+1] = <void*>(<char*>"_nct_isf")
|
|
ufunc__nct_isf_data[0] = &ufunc__nct_isf_ptr[2*0]
|
|
ufunc__nct_isf_data[1] = &ufunc__nct_isf_ptr[2*1]
|
|
_nct_isf = np.PyUFunc_FromFuncAndData(ufunc__nct_isf_loops, ufunc__nct_isf_data, ufunc__nct_isf_types, 2, 3, 1, 0, '_nct_isf', ufunc__nct_isf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__nct_kurtosis_excess_loops[2]
|
|
cdef void *ufunc__nct_kurtosis_excess_ptr[4]
|
|
cdef void *ufunc__nct_kurtosis_excess_data[2]
|
|
cdef char ufunc__nct_kurtosis_excess_types[6]
|
|
cdef char *ufunc__nct_kurtosis_excess_doc = (
|
|
"_nct_kurtosis_excess(v, l)\n"
|
|
"\n"
|
|
"Kurtosis excess of noncentral t-distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"v : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"l : array_like\n"
|
|
" Real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__nct_kurtosis_excess_loops[0] = <np.PyUFuncGenericFunction>loop_f_ff__As_ff_f
|
|
ufunc__nct_kurtosis_excess_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc__nct_kurtosis_excess_types[0] = <char>NPY_FLOAT
|
|
ufunc__nct_kurtosis_excess_types[1] = <char>NPY_FLOAT
|
|
ufunc__nct_kurtosis_excess_types[2] = <char>NPY_FLOAT
|
|
ufunc__nct_kurtosis_excess_types[3] = <char>NPY_DOUBLE
|
|
ufunc__nct_kurtosis_excess_types[4] = <char>NPY_DOUBLE
|
|
ufunc__nct_kurtosis_excess_types[5] = <char>NPY_DOUBLE
|
|
ufunc__nct_kurtosis_excess_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nct_kurtosis_excess_float
|
|
ufunc__nct_kurtosis_excess_ptr[2*0+1] = <void*>(<char*>"_nct_kurtosis_excess")
|
|
ufunc__nct_kurtosis_excess_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nct_kurtosis_excess_double
|
|
ufunc__nct_kurtosis_excess_ptr[2*1+1] = <void*>(<char*>"_nct_kurtosis_excess")
|
|
ufunc__nct_kurtosis_excess_data[0] = &ufunc__nct_kurtosis_excess_ptr[2*0]
|
|
ufunc__nct_kurtosis_excess_data[1] = &ufunc__nct_kurtosis_excess_ptr[2*1]
|
|
_nct_kurtosis_excess = np.PyUFunc_FromFuncAndData(ufunc__nct_kurtosis_excess_loops, ufunc__nct_kurtosis_excess_data, ufunc__nct_kurtosis_excess_types, 2, 2, 1, 0, '_nct_kurtosis_excess', ufunc__nct_kurtosis_excess_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__nct_mean_loops[2]
|
|
cdef void *ufunc__nct_mean_ptr[4]
|
|
cdef void *ufunc__nct_mean_data[2]
|
|
cdef char ufunc__nct_mean_types[6]
|
|
cdef char *ufunc__nct_mean_doc = (
|
|
"_nct_mean(v, l)\n"
|
|
"\n"
|
|
"Mean of noncentral t-distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"v : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"l : array_like\n"
|
|
" Real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__nct_mean_loops[0] = <np.PyUFuncGenericFunction>loop_f_ff__As_ff_f
|
|
ufunc__nct_mean_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc__nct_mean_types[0] = <char>NPY_FLOAT
|
|
ufunc__nct_mean_types[1] = <char>NPY_FLOAT
|
|
ufunc__nct_mean_types[2] = <char>NPY_FLOAT
|
|
ufunc__nct_mean_types[3] = <char>NPY_DOUBLE
|
|
ufunc__nct_mean_types[4] = <char>NPY_DOUBLE
|
|
ufunc__nct_mean_types[5] = <char>NPY_DOUBLE
|
|
ufunc__nct_mean_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nct_mean_float
|
|
ufunc__nct_mean_ptr[2*0+1] = <void*>(<char*>"_nct_mean")
|
|
ufunc__nct_mean_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nct_mean_double
|
|
ufunc__nct_mean_ptr[2*1+1] = <void*>(<char*>"_nct_mean")
|
|
ufunc__nct_mean_data[0] = &ufunc__nct_mean_ptr[2*0]
|
|
ufunc__nct_mean_data[1] = &ufunc__nct_mean_ptr[2*1]
|
|
_nct_mean = np.PyUFunc_FromFuncAndData(ufunc__nct_mean_loops, ufunc__nct_mean_data, ufunc__nct_mean_types, 2, 2, 1, 0, '_nct_mean', ufunc__nct_mean_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__nct_pdf_loops[2]
|
|
cdef void *ufunc__nct_pdf_ptr[4]
|
|
cdef void *ufunc__nct_pdf_data[2]
|
|
cdef char ufunc__nct_pdf_types[8]
|
|
cdef char *ufunc__nct_pdf_doc = (
|
|
"_nct_pdf(x, v, l)\n"
|
|
"\n"
|
|
"Probability density function of noncentral t-distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued\n"
|
|
"v : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"l : array_like\n"
|
|
" Real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__nct_pdf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__nct_pdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__nct_pdf_types[0] = <char>NPY_FLOAT
|
|
ufunc__nct_pdf_types[1] = <char>NPY_FLOAT
|
|
ufunc__nct_pdf_types[2] = <char>NPY_FLOAT
|
|
ufunc__nct_pdf_types[3] = <char>NPY_FLOAT
|
|
ufunc__nct_pdf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__nct_pdf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__nct_pdf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__nct_pdf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__nct_pdf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nct_pdf_float
|
|
ufunc__nct_pdf_ptr[2*0+1] = <void*>(<char*>"_nct_pdf")
|
|
ufunc__nct_pdf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nct_pdf_double
|
|
ufunc__nct_pdf_ptr[2*1+1] = <void*>(<char*>"_nct_pdf")
|
|
ufunc__nct_pdf_data[0] = &ufunc__nct_pdf_ptr[2*0]
|
|
ufunc__nct_pdf_data[1] = &ufunc__nct_pdf_ptr[2*1]
|
|
_nct_pdf = np.PyUFunc_FromFuncAndData(ufunc__nct_pdf_loops, ufunc__nct_pdf_data, ufunc__nct_pdf_types, 2, 3, 1, 0, '_nct_pdf', ufunc__nct_pdf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__nct_sf_loops[2]
|
|
cdef void *ufunc__nct_sf_ptr[4]
|
|
cdef void *ufunc__nct_sf_data[2]
|
|
cdef char ufunc__nct_sf_types[8]
|
|
cdef char *ufunc__nct_sf_doc = (
|
|
"_nct_sf(x, v, l)\n"
|
|
"\n"
|
|
"Survival function of noncentral t-distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued\n"
|
|
"v : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"l : array_like\n"
|
|
" Real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__nct_sf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__nct_sf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__nct_sf_types[0] = <char>NPY_FLOAT
|
|
ufunc__nct_sf_types[1] = <char>NPY_FLOAT
|
|
ufunc__nct_sf_types[2] = <char>NPY_FLOAT
|
|
ufunc__nct_sf_types[3] = <char>NPY_FLOAT
|
|
ufunc__nct_sf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__nct_sf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__nct_sf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__nct_sf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__nct_sf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nct_sf_float
|
|
ufunc__nct_sf_ptr[2*0+1] = <void*>(<char*>"_nct_sf")
|
|
ufunc__nct_sf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nct_sf_double
|
|
ufunc__nct_sf_ptr[2*1+1] = <void*>(<char*>"_nct_sf")
|
|
ufunc__nct_sf_data[0] = &ufunc__nct_sf_ptr[2*0]
|
|
ufunc__nct_sf_data[1] = &ufunc__nct_sf_ptr[2*1]
|
|
_nct_sf = np.PyUFunc_FromFuncAndData(ufunc__nct_sf_loops, ufunc__nct_sf_data, ufunc__nct_sf_types, 2, 3, 1, 0, '_nct_sf', ufunc__nct_sf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__nct_skewness_loops[2]
|
|
cdef void *ufunc__nct_skewness_ptr[4]
|
|
cdef void *ufunc__nct_skewness_data[2]
|
|
cdef char ufunc__nct_skewness_types[6]
|
|
cdef char *ufunc__nct_skewness_doc = (
|
|
"_nct_skewness(v, l)\n"
|
|
"\n"
|
|
"Skewness of noncentral t-distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"v : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"l : array_like\n"
|
|
" Real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__nct_skewness_loops[0] = <np.PyUFuncGenericFunction>loop_f_ff__As_ff_f
|
|
ufunc__nct_skewness_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc__nct_skewness_types[0] = <char>NPY_FLOAT
|
|
ufunc__nct_skewness_types[1] = <char>NPY_FLOAT
|
|
ufunc__nct_skewness_types[2] = <char>NPY_FLOAT
|
|
ufunc__nct_skewness_types[3] = <char>NPY_DOUBLE
|
|
ufunc__nct_skewness_types[4] = <char>NPY_DOUBLE
|
|
ufunc__nct_skewness_types[5] = <char>NPY_DOUBLE
|
|
ufunc__nct_skewness_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nct_skewness_float
|
|
ufunc__nct_skewness_ptr[2*0+1] = <void*>(<char*>"_nct_skewness")
|
|
ufunc__nct_skewness_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nct_skewness_double
|
|
ufunc__nct_skewness_ptr[2*1+1] = <void*>(<char*>"_nct_skewness")
|
|
ufunc__nct_skewness_data[0] = &ufunc__nct_skewness_ptr[2*0]
|
|
ufunc__nct_skewness_data[1] = &ufunc__nct_skewness_ptr[2*1]
|
|
_nct_skewness = np.PyUFunc_FromFuncAndData(ufunc__nct_skewness_loops, ufunc__nct_skewness_data, ufunc__nct_skewness_types, 2, 2, 1, 0, '_nct_skewness', ufunc__nct_skewness_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__nct_variance_loops[2]
|
|
cdef void *ufunc__nct_variance_ptr[4]
|
|
cdef void *ufunc__nct_variance_data[2]
|
|
cdef char ufunc__nct_variance_types[6]
|
|
cdef char *ufunc__nct_variance_doc = (
|
|
"_nct_variance(v, l)\n"
|
|
"\n"
|
|
"Variance of noncentral t-distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"v : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"l : array_like\n"
|
|
" Real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__nct_variance_loops[0] = <np.PyUFuncGenericFunction>loop_f_ff__As_ff_f
|
|
ufunc__nct_variance_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc__nct_variance_types[0] = <char>NPY_FLOAT
|
|
ufunc__nct_variance_types[1] = <char>NPY_FLOAT
|
|
ufunc__nct_variance_types[2] = <char>NPY_FLOAT
|
|
ufunc__nct_variance_types[3] = <char>NPY_DOUBLE
|
|
ufunc__nct_variance_types[4] = <char>NPY_DOUBLE
|
|
ufunc__nct_variance_types[5] = <char>NPY_DOUBLE
|
|
ufunc__nct_variance_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nct_variance_float
|
|
ufunc__nct_variance_ptr[2*0+1] = <void*>(<char*>"_nct_variance")
|
|
ufunc__nct_variance_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nct_variance_double
|
|
ufunc__nct_variance_ptr[2*1+1] = <void*>(<char*>"_nct_variance")
|
|
ufunc__nct_variance_data[0] = &ufunc__nct_variance_ptr[2*0]
|
|
ufunc__nct_variance_data[1] = &ufunc__nct_variance_ptr[2*1]
|
|
_nct_variance = np.PyUFunc_FromFuncAndData(ufunc__nct_variance_loops, ufunc__nct_variance_data, ufunc__nct_variance_types, 2, 2, 1, 0, '_nct_variance', ufunc__nct_variance_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__ncx2_cdf_loops[2]
|
|
cdef void *ufunc__ncx2_cdf_ptr[4]
|
|
cdef void *ufunc__ncx2_cdf_data[2]
|
|
cdef char ufunc__ncx2_cdf_types[8]
|
|
cdef char *ufunc__ncx2_cdf_doc = (
|
|
"_ncx2_cdf(x, k, l)\n"
|
|
"\n"
|
|
"Cumulative density function of Non-central chi-squared distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Positive real-valued\n"
|
|
"k, l : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__ncx2_cdf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__ncx2_cdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__ncx2_cdf_types[0] = <char>NPY_FLOAT
|
|
ufunc__ncx2_cdf_types[1] = <char>NPY_FLOAT
|
|
ufunc__ncx2_cdf_types[2] = <char>NPY_FLOAT
|
|
ufunc__ncx2_cdf_types[3] = <char>NPY_FLOAT
|
|
ufunc__ncx2_cdf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__ncx2_cdf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__ncx2_cdf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__ncx2_cdf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__ncx2_cdf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncx2_cdf_float
|
|
ufunc__ncx2_cdf_ptr[2*0+1] = <void*>(<char*>"_ncx2_cdf")
|
|
ufunc__ncx2_cdf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncx2_cdf_double
|
|
ufunc__ncx2_cdf_ptr[2*1+1] = <void*>(<char*>"_ncx2_cdf")
|
|
ufunc__ncx2_cdf_data[0] = &ufunc__ncx2_cdf_ptr[2*0]
|
|
ufunc__ncx2_cdf_data[1] = &ufunc__ncx2_cdf_ptr[2*1]
|
|
_ncx2_cdf = np.PyUFunc_FromFuncAndData(ufunc__ncx2_cdf_loops, ufunc__ncx2_cdf_data, ufunc__ncx2_cdf_types, 2, 3, 1, 0, '_ncx2_cdf', ufunc__ncx2_cdf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__ncx2_isf_loops[2]
|
|
cdef void *ufunc__ncx2_isf_ptr[4]
|
|
cdef void *ufunc__ncx2_isf_data[2]
|
|
cdef char ufunc__ncx2_isf_types[8]
|
|
cdef char *ufunc__ncx2_isf_doc = (
|
|
"_ncx2_isf(x, k, l)\n"
|
|
"\n"
|
|
"Inverse survival function of Non-central chi-squared distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Positive real-valued\n"
|
|
"k, l : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__ncx2_isf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__ncx2_isf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__ncx2_isf_types[0] = <char>NPY_FLOAT
|
|
ufunc__ncx2_isf_types[1] = <char>NPY_FLOAT
|
|
ufunc__ncx2_isf_types[2] = <char>NPY_FLOAT
|
|
ufunc__ncx2_isf_types[3] = <char>NPY_FLOAT
|
|
ufunc__ncx2_isf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__ncx2_isf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__ncx2_isf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__ncx2_isf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__ncx2_isf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncx2_isf_float
|
|
ufunc__ncx2_isf_ptr[2*0+1] = <void*>(<char*>"_ncx2_isf")
|
|
ufunc__ncx2_isf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncx2_isf_double
|
|
ufunc__ncx2_isf_ptr[2*1+1] = <void*>(<char*>"_ncx2_isf")
|
|
ufunc__ncx2_isf_data[0] = &ufunc__ncx2_isf_ptr[2*0]
|
|
ufunc__ncx2_isf_data[1] = &ufunc__ncx2_isf_ptr[2*1]
|
|
_ncx2_isf = np.PyUFunc_FromFuncAndData(ufunc__ncx2_isf_loops, ufunc__ncx2_isf_data, ufunc__ncx2_isf_types, 2, 3, 1, 0, '_ncx2_isf', ufunc__ncx2_isf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__ncx2_pdf_loops[2]
|
|
cdef void *ufunc__ncx2_pdf_ptr[4]
|
|
cdef void *ufunc__ncx2_pdf_data[2]
|
|
cdef char ufunc__ncx2_pdf_types[8]
|
|
cdef char *ufunc__ncx2_pdf_doc = (
|
|
"_ncx2_pdf(x, k, l)\n"
|
|
"\n"
|
|
"Probability density function of Non-central chi-squared distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Positive real-valued\n"
|
|
"k, l : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__ncx2_pdf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__ncx2_pdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__ncx2_pdf_types[0] = <char>NPY_FLOAT
|
|
ufunc__ncx2_pdf_types[1] = <char>NPY_FLOAT
|
|
ufunc__ncx2_pdf_types[2] = <char>NPY_FLOAT
|
|
ufunc__ncx2_pdf_types[3] = <char>NPY_FLOAT
|
|
ufunc__ncx2_pdf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__ncx2_pdf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__ncx2_pdf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__ncx2_pdf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__ncx2_pdf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncx2_pdf_float
|
|
ufunc__ncx2_pdf_ptr[2*0+1] = <void*>(<char*>"_ncx2_pdf")
|
|
ufunc__ncx2_pdf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncx2_pdf_double
|
|
ufunc__ncx2_pdf_ptr[2*1+1] = <void*>(<char*>"_ncx2_pdf")
|
|
ufunc__ncx2_pdf_data[0] = &ufunc__ncx2_pdf_ptr[2*0]
|
|
ufunc__ncx2_pdf_data[1] = &ufunc__ncx2_pdf_ptr[2*1]
|
|
_ncx2_pdf = np.PyUFunc_FromFuncAndData(ufunc__ncx2_pdf_loops, ufunc__ncx2_pdf_data, ufunc__ncx2_pdf_types, 2, 3, 1, 0, '_ncx2_pdf', ufunc__ncx2_pdf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__ncx2_ppf_loops[2]
|
|
cdef void *ufunc__ncx2_ppf_ptr[4]
|
|
cdef void *ufunc__ncx2_ppf_data[2]
|
|
cdef char ufunc__ncx2_ppf_types[8]
|
|
cdef char *ufunc__ncx2_ppf_doc = (
|
|
"_ncx2_ppf(x, k, l)\n"
|
|
"\n"
|
|
"Percent point function of Non-central chi-squared distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Positive real-valued\n"
|
|
"k, l : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__ncx2_ppf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__ncx2_ppf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__ncx2_ppf_types[0] = <char>NPY_FLOAT
|
|
ufunc__ncx2_ppf_types[1] = <char>NPY_FLOAT
|
|
ufunc__ncx2_ppf_types[2] = <char>NPY_FLOAT
|
|
ufunc__ncx2_ppf_types[3] = <char>NPY_FLOAT
|
|
ufunc__ncx2_ppf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__ncx2_ppf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__ncx2_ppf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__ncx2_ppf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__ncx2_ppf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncx2_ppf_float
|
|
ufunc__ncx2_ppf_ptr[2*0+1] = <void*>(<char*>"_ncx2_ppf")
|
|
ufunc__ncx2_ppf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncx2_ppf_double
|
|
ufunc__ncx2_ppf_ptr[2*1+1] = <void*>(<char*>"_ncx2_ppf")
|
|
ufunc__ncx2_ppf_data[0] = &ufunc__ncx2_ppf_ptr[2*0]
|
|
ufunc__ncx2_ppf_data[1] = &ufunc__ncx2_ppf_ptr[2*1]
|
|
_ncx2_ppf = np.PyUFunc_FromFuncAndData(ufunc__ncx2_ppf_loops, ufunc__ncx2_ppf_data, ufunc__ncx2_ppf_types, 2, 3, 1, 0, '_ncx2_ppf', ufunc__ncx2_ppf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__ncx2_sf_loops[2]
|
|
cdef void *ufunc__ncx2_sf_ptr[4]
|
|
cdef void *ufunc__ncx2_sf_data[2]
|
|
cdef char ufunc__ncx2_sf_types[8]
|
|
cdef char *ufunc__ncx2_sf_doc = (
|
|
"_ncx2_sf(x, k, l)\n"
|
|
"\n"
|
|
"Survival function of Non-central chi-squared distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Positive real-valued\n"
|
|
"k, l : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__ncx2_sf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc__ncx2_sf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc__ncx2_sf_types[0] = <char>NPY_FLOAT
|
|
ufunc__ncx2_sf_types[1] = <char>NPY_FLOAT
|
|
ufunc__ncx2_sf_types[2] = <char>NPY_FLOAT
|
|
ufunc__ncx2_sf_types[3] = <char>NPY_FLOAT
|
|
ufunc__ncx2_sf_types[4] = <char>NPY_DOUBLE
|
|
ufunc__ncx2_sf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__ncx2_sf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__ncx2_sf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__ncx2_sf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncx2_sf_float
|
|
ufunc__ncx2_sf_ptr[2*0+1] = <void*>(<char*>"_ncx2_sf")
|
|
ufunc__ncx2_sf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncx2_sf_double
|
|
ufunc__ncx2_sf_ptr[2*1+1] = <void*>(<char*>"_ncx2_sf")
|
|
ufunc__ncx2_sf_data[0] = &ufunc__ncx2_sf_ptr[2*0]
|
|
ufunc__ncx2_sf_data[1] = &ufunc__ncx2_sf_ptr[2*1]
|
|
_ncx2_sf = np.PyUFunc_FromFuncAndData(ufunc__ncx2_sf_loops, ufunc__ncx2_sf_data, ufunc__ncx2_sf_types, 2, 3, 1, 0, '_ncx2_sf', ufunc__ncx2_sf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__sf_error_test_function_loops[1]
|
|
cdef void *ufunc__sf_error_test_function_ptr[2]
|
|
cdef void *ufunc__sf_error_test_function_data[1]
|
|
cdef char ufunc__sf_error_test_function_types[2]
|
|
cdef char *ufunc__sf_error_test_function_doc = (
|
|
"Private function; do not use.")
|
|
ufunc__sf_error_test_function_loops[0] = <np.PyUFuncGenericFunction>loop_i_i__As_l_l
|
|
ufunc__sf_error_test_function_types[0] = <char>NPY_LONG
|
|
ufunc__sf_error_test_function_types[1] = <char>NPY_LONG
|
|
ufunc__sf_error_test_function_ptr[2*0] = <void*>_func__sf_error_test_function
|
|
ufunc__sf_error_test_function_ptr[2*0+1] = <void*>(<char*>"_sf_error_test_function")
|
|
ufunc__sf_error_test_function_data[0] = &ufunc__sf_error_test_function_ptr[2*0]
|
|
_sf_error_test_function = np.PyUFunc_FromFuncAndData(ufunc__sf_error_test_function_loops, ufunc__sf_error_test_function_data, ufunc__sf_error_test_function_types, 1, 1, 1, 0, '_sf_error_test_function', ufunc__sf_error_test_function_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__skewnorm_cdf_loops[2]
|
|
cdef void *ufunc__skewnorm_cdf_ptr[4]
|
|
cdef void *ufunc__skewnorm_cdf_data[2]
|
|
cdef char ufunc__skewnorm_cdf_types[10]
|
|
cdef char *ufunc__skewnorm_cdf_doc = (
|
|
"_skewnorm_cdf(x, l, sc, sh)\n"
|
|
"\n"
|
|
"Cumulative density function of skewnorm distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued\n"
|
|
"l : array_like\n"
|
|
" Real-valued parameters\n"
|
|
"sc : array_like\n"
|
|
" Positive, Real-valued parameters\n"
|
|
"sh : array_like\n"
|
|
" Real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__skewnorm_cdf_loops[0] = <np.PyUFuncGenericFunction>loop_f_ffff__As_ffff_f
|
|
ufunc__skewnorm_cdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
|
|
ufunc__skewnorm_cdf_types[0] = <char>NPY_FLOAT
|
|
ufunc__skewnorm_cdf_types[1] = <char>NPY_FLOAT
|
|
ufunc__skewnorm_cdf_types[2] = <char>NPY_FLOAT
|
|
ufunc__skewnorm_cdf_types[3] = <char>NPY_FLOAT
|
|
ufunc__skewnorm_cdf_types[4] = <char>NPY_FLOAT
|
|
ufunc__skewnorm_cdf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__skewnorm_cdf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__skewnorm_cdf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__skewnorm_cdf_types[8] = <char>NPY_DOUBLE
|
|
ufunc__skewnorm_cdf_types[9] = <char>NPY_DOUBLE
|
|
ufunc__skewnorm_cdf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_skewnorm_cdf_float
|
|
ufunc__skewnorm_cdf_ptr[2*0+1] = <void*>(<char*>"_skewnorm_cdf")
|
|
ufunc__skewnorm_cdf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_skewnorm_cdf_double
|
|
ufunc__skewnorm_cdf_ptr[2*1+1] = <void*>(<char*>"_skewnorm_cdf")
|
|
ufunc__skewnorm_cdf_data[0] = &ufunc__skewnorm_cdf_ptr[2*0]
|
|
ufunc__skewnorm_cdf_data[1] = &ufunc__skewnorm_cdf_ptr[2*1]
|
|
_skewnorm_cdf = np.PyUFunc_FromFuncAndData(ufunc__skewnorm_cdf_loops, ufunc__skewnorm_cdf_data, ufunc__skewnorm_cdf_types, 2, 4, 1, 0, '_skewnorm_cdf', ufunc__skewnorm_cdf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__skewnorm_isf_loops[2]
|
|
cdef void *ufunc__skewnorm_isf_ptr[4]
|
|
cdef void *ufunc__skewnorm_isf_data[2]
|
|
cdef char ufunc__skewnorm_isf_types[10]
|
|
cdef char *ufunc__skewnorm_isf_doc = (
|
|
"_skewnorm_isf(x, l, sc, sh)\n"
|
|
"\n"
|
|
"Inverse survival function of skewnorm distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued\n"
|
|
"l : array_like\n"
|
|
" Real-valued parameters\n"
|
|
"sc : array_like\n"
|
|
" Positive, Real-valued parameters\n"
|
|
"sh : array_like\n"
|
|
" Real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__skewnorm_isf_loops[0] = <np.PyUFuncGenericFunction>loop_f_ffff__As_ffff_f
|
|
ufunc__skewnorm_isf_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
|
|
ufunc__skewnorm_isf_types[0] = <char>NPY_FLOAT
|
|
ufunc__skewnorm_isf_types[1] = <char>NPY_FLOAT
|
|
ufunc__skewnorm_isf_types[2] = <char>NPY_FLOAT
|
|
ufunc__skewnorm_isf_types[3] = <char>NPY_FLOAT
|
|
ufunc__skewnorm_isf_types[4] = <char>NPY_FLOAT
|
|
ufunc__skewnorm_isf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__skewnorm_isf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__skewnorm_isf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__skewnorm_isf_types[8] = <char>NPY_DOUBLE
|
|
ufunc__skewnorm_isf_types[9] = <char>NPY_DOUBLE
|
|
ufunc__skewnorm_isf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_skewnorm_isf_float
|
|
ufunc__skewnorm_isf_ptr[2*0+1] = <void*>(<char*>"_skewnorm_isf")
|
|
ufunc__skewnorm_isf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_skewnorm_isf_double
|
|
ufunc__skewnorm_isf_ptr[2*1+1] = <void*>(<char*>"_skewnorm_isf")
|
|
ufunc__skewnorm_isf_data[0] = &ufunc__skewnorm_isf_ptr[2*0]
|
|
ufunc__skewnorm_isf_data[1] = &ufunc__skewnorm_isf_ptr[2*1]
|
|
_skewnorm_isf = np.PyUFunc_FromFuncAndData(ufunc__skewnorm_isf_loops, ufunc__skewnorm_isf_data, ufunc__skewnorm_isf_types, 2, 4, 1, 0, '_skewnorm_isf', ufunc__skewnorm_isf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__skewnorm_ppf_loops[2]
|
|
cdef void *ufunc__skewnorm_ppf_ptr[4]
|
|
cdef void *ufunc__skewnorm_ppf_data[2]
|
|
cdef char ufunc__skewnorm_ppf_types[10]
|
|
cdef char *ufunc__skewnorm_ppf_doc = (
|
|
"_skewnorm_ppf(x, l, sc, sh)\n"
|
|
"\n"
|
|
"Percent point function of skewnorm distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real-valued\n"
|
|
"l : array_like\n"
|
|
" Real-valued parameters\n"
|
|
"sc : array_like\n"
|
|
" Positive, Real-valued parameters\n"
|
|
"sh : array_like\n"
|
|
" Real-valued parameters\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray")
|
|
ufunc__skewnorm_ppf_loops[0] = <np.PyUFuncGenericFunction>loop_f_ffff__As_ffff_f
|
|
ufunc__skewnorm_ppf_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
|
|
ufunc__skewnorm_ppf_types[0] = <char>NPY_FLOAT
|
|
ufunc__skewnorm_ppf_types[1] = <char>NPY_FLOAT
|
|
ufunc__skewnorm_ppf_types[2] = <char>NPY_FLOAT
|
|
ufunc__skewnorm_ppf_types[3] = <char>NPY_FLOAT
|
|
ufunc__skewnorm_ppf_types[4] = <char>NPY_FLOAT
|
|
ufunc__skewnorm_ppf_types[5] = <char>NPY_DOUBLE
|
|
ufunc__skewnorm_ppf_types[6] = <char>NPY_DOUBLE
|
|
ufunc__skewnorm_ppf_types[7] = <char>NPY_DOUBLE
|
|
ufunc__skewnorm_ppf_types[8] = <char>NPY_DOUBLE
|
|
ufunc__skewnorm_ppf_types[9] = <char>NPY_DOUBLE
|
|
ufunc__skewnorm_ppf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_skewnorm_ppf_float
|
|
ufunc__skewnorm_ppf_ptr[2*0+1] = <void*>(<char*>"_skewnorm_ppf")
|
|
ufunc__skewnorm_ppf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_skewnorm_ppf_double
|
|
ufunc__skewnorm_ppf_ptr[2*1+1] = <void*>(<char*>"_skewnorm_ppf")
|
|
ufunc__skewnorm_ppf_data[0] = &ufunc__skewnorm_ppf_ptr[2*0]
|
|
ufunc__skewnorm_ppf_data[1] = &ufunc__skewnorm_ppf_ptr[2*1]
|
|
_skewnorm_ppf = np.PyUFunc_FromFuncAndData(ufunc__skewnorm_ppf_loops, ufunc__skewnorm_ppf_data, ufunc__skewnorm_ppf_types, 2, 4, 1, 0, '_skewnorm_ppf', ufunc__skewnorm_ppf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__smirnovc_loops[3]
|
|
cdef void *ufunc__smirnovc_ptr[6]
|
|
cdef void *ufunc__smirnovc_data[3]
|
|
cdef char ufunc__smirnovc_types[9]
|
|
cdef char *ufunc__smirnovc_doc = (
|
|
"_smirnovc(n, d)\n"
|
|
" Internal function, do not use.")
|
|
ufunc__smirnovc_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
|
|
ufunc__smirnovc_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc__smirnovc_loops[2] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc__smirnovc_types[0] = <char>NPY_INTP
|
|
ufunc__smirnovc_types[1] = <char>NPY_DOUBLE
|
|
ufunc__smirnovc_types[2] = <char>NPY_DOUBLE
|
|
ufunc__smirnovc_types[3] = <char>NPY_FLOAT
|
|
ufunc__smirnovc_types[4] = <char>NPY_FLOAT
|
|
ufunc__smirnovc_types[5] = <char>NPY_FLOAT
|
|
ufunc__smirnovc_types[6] = <char>NPY_DOUBLE
|
|
ufunc__smirnovc_types[7] = <char>NPY_DOUBLE
|
|
ufunc__smirnovc_types[8] = <char>NPY_DOUBLE
|
|
ufunc__smirnovc_ptr[2*0] = <void*>_func_cephes_smirnovc_wrap
|
|
ufunc__smirnovc_ptr[2*0+1] = <void*>(<char*>"_smirnovc")
|
|
ufunc__smirnovc_ptr[2*1] = <void*>_func_smirnovc_unsafe
|
|
ufunc__smirnovc_ptr[2*1+1] = <void*>(<char*>"_smirnovc")
|
|
ufunc__smirnovc_ptr[2*2] = <void*>_func_smirnovc_unsafe
|
|
ufunc__smirnovc_ptr[2*2+1] = <void*>(<char*>"_smirnovc")
|
|
ufunc__smirnovc_data[0] = &ufunc__smirnovc_ptr[2*0]
|
|
ufunc__smirnovc_data[1] = &ufunc__smirnovc_ptr[2*1]
|
|
ufunc__smirnovc_data[2] = &ufunc__smirnovc_ptr[2*2]
|
|
_smirnovc = np.PyUFunc_FromFuncAndData(ufunc__smirnovc_loops, ufunc__smirnovc_data, ufunc__smirnovc_types, 3, 2, 1, 0, '_smirnovc', ufunc__smirnovc_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__smirnovci_loops[3]
|
|
cdef void *ufunc__smirnovci_ptr[6]
|
|
cdef void *ufunc__smirnovci_data[3]
|
|
cdef char ufunc__smirnovci_types[9]
|
|
cdef char *ufunc__smirnovci_doc = (
|
|
"Internal function, do not use.")
|
|
ufunc__smirnovci_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
|
|
ufunc__smirnovci_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc__smirnovci_loops[2] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc__smirnovci_types[0] = <char>NPY_INTP
|
|
ufunc__smirnovci_types[1] = <char>NPY_DOUBLE
|
|
ufunc__smirnovci_types[2] = <char>NPY_DOUBLE
|
|
ufunc__smirnovci_types[3] = <char>NPY_FLOAT
|
|
ufunc__smirnovci_types[4] = <char>NPY_FLOAT
|
|
ufunc__smirnovci_types[5] = <char>NPY_FLOAT
|
|
ufunc__smirnovci_types[6] = <char>NPY_DOUBLE
|
|
ufunc__smirnovci_types[7] = <char>NPY_DOUBLE
|
|
ufunc__smirnovci_types[8] = <char>NPY_DOUBLE
|
|
ufunc__smirnovci_ptr[2*0] = <void*>_func_cephes_smirnovci_wrap
|
|
ufunc__smirnovci_ptr[2*0+1] = <void*>(<char*>"_smirnovci")
|
|
ufunc__smirnovci_ptr[2*1] = <void*>_func_smirnovci_unsafe
|
|
ufunc__smirnovci_ptr[2*1+1] = <void*>(<char*>"_smirnovci")
|
|
ufunc__smirnovci_ptr[2*2] = <void*>_func_smirnovci_unsafe
|
|
ufunc__smirnovci_ptr[2*2+1] = <void*>(<char*>"_smirnovci")
|
|
ufunc__smirnovci_data[0] = &ufunc__smirnovci_ptr[2*0]
|
|
ufunc__smirnovci_data[1] = &ufunc__smirnovci_ptr[2*1]
|
|
ufunc__smirnovci_data[2] = &ufunc__smirnovci_ptr[2*2]
|
|
_smirnovci = np.PyUFunc_FromFuncAndData(ufunc__smirnovci_loops, ufunc__smirnovci_data, ufunc__smirnovci_types, 3, 2, 1, 0, '_smirnovci', ufunc__smirnovci_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__smirnovp_loops[3]
|
|
cdef void *ufunc__smirnovp_ptr[6]
|
|
cdef void *ufunc__smirnovp_data[3]
|
|
cdef char ufunc__smirnovp_types[9]
|
|
cdef char *ufunc__smirnovp_doc = (
|
|
"_smirnovp(n, p)\n"
|
|
" Internal function, do not use.")
|
|
ufunc__smirnovp_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
|
|
ufunc__smirnovp_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc__smirnovp_loops[2] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc__smirnovp_types[0] = <char>NPY_INTP
|
|
ufunc__smirnovp_types[1] = <char>NPY_DOUBLE
|
|
ufunc__smirnovp_types[2] = <char>NPY_DOUBLE
|
|
ufunc__smirnovp_types[3] = <char>NPY_FLOAT
|
|
ufunc__smirnovp_types[4] = <char>NPY_FLOAT
|
|
ufunc__smirnovp_types[5] = <char>NPY_FLOAT
|
|
ufunc__smirnovp_types[6] = <char>NPY_DOUBLE
|
|
ufunc__smirnovp_types[7] = <char>NPY_DOUBLE
|
|
ufunc__smirnovp_types[8] = <char>NPY_DOUBLE
|
|
ufunc__smirnovp_ptr[2*0] = <void*>_func_cephes_smirnovp_wrap
|
|
ufunc__smirnovp_ptr[2*0+1] = <void*>(<char*>"_smirnovp")
|
|
ufunc__smirnovp_ptr[2*1] = <void*>_func_smirnovp_unsafe
|
|
ufunc__smirnovp_ptr[2*1+1] = <void*>(<char*>"_smirnovp")
|
|
ufunc__smirnovp_ptr[2*2] = <void*>_func_smirnovp_unsafe
|
|
ufunc__smirnovp_ptr[2*2+1] = <void*>(<char*>"_smirnovp")
|
|
ufunc__smirnovp_data[0] = &ufunc__smirnovp_ptr[2*0]
|
|
ufunc__smirnovp_data[1] = &ufunc__smirnovp_ptr[2*1]
|
|
ufunc__smirnovp_data[2] = &ufunc__smirnovp_ptr[2*2]
|
|
_smirnovp = np.PyUFunc_FromFuncAndData(ufunc__smirnovp_loops, ufunc__smirnovp_data, ufunc__smirnovp_types, 3, 2, 1, 0, '_smirnovp', ufunc__smirnovp_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__stirling2_inexact_loops[2]
|
|
cdef void *ufunc__stirling2_inexact_ptr[4]
|
|
cdef void *ufunc__stirling2_inexact_data[2]
|
|
cdef char ufunc__stirling2_inexact_types[6]
|
|
cdef char *ufunc__stirling2_inexact_doc = (
|
|
"Internal function, do not use.")
|
|
ufunc__stirling2_inexact_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc__stirling2_inexact_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc__stirling2_inexact_types[0] = <char>NPY_FLOAT
|
|
ufunc__stirling2_inexact_types[1] = <char>NPY_FLOAT
|
|
ufunc__stirling2_inexact_types[2] = <char>NPY_FLOAT
|
|
ufunc__stirling2_inexact_types[3] = <char>NPY_DOUBLE
|
|
ufunc__stirling2_inexact_types[4] = <char>NPY_DOUBLE
|
|
ufunc__stirling2_inexact_types[5] = <char>NPY_DOUBLE
|
|
ufunc__stirling2_inexact_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export__stirling2_inexact
|
|
ufunc__stirling2_inexact_ptr[2*0+1] = <void*>(<char*>"_stirling2_inexact")
|
|
ufunc__stirling2_inexact_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export__stirling2_inexact
|
|
ufunc__stirling2_inexact_ptr[2*1+1] = <void*>(<char*>"_stirling2_inexact")
|
|
ufunc__stirling2_inexact_data[0] = &ufunc__stirling2_inexact_ptr[2*0]
|
|
ufunc__stirling2_inexact_data[1] = &ufunc__stirling2_inexact_ptr[2*1]
|
|
_stirling2_inexact = np.PyUFunc_FromFuncAndData(ufunc__stirling2_inexact_loops, ufunc__stirling2_inexact_data, ufunc__stirling2_inexact_types, 2, 2, 1, 0, '_stirling2_inexact', ufunc__stirling2_inexact_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__struve_asymp_large_z_loops[1]
|
|
cdef void *ufunc__struve_asymp_large_z_ptr[2]
|
|
cdef void *ufunc__struve_asymp_large_z_data[1]
|
|
cdef char ufunc__struve_asymp_large_z_types[5]
|
|
cdef char *ufunc__struve_asymp_large_z_doc = (
|
|
"_struve_asymp_large_z(v, z, is_h)\n"
|
|
"\n"
|
|
"Internal function for testing `struve` & `modstruve`\n"
|
|
"\n"
|
|
"Evaluates using asymptotic expansion\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"v, err")
|
|
ufunc__struve_asymp_large_z_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddp_d_As_ddp_dd
|
|
ufunc__struve_asymp_large_z_types[0] = <char>NPY_DOUBLE
|
|
ufunc__struve_asymp_large_z_types[1] = <char>NPY_DOUBLE
|
|
ufunc__struve_asymp_large_z_types[2] = <char>NPY_INTP
|
|
ufunc__struve_asymp_large_z_types[3] = <char>NPY_DOUBLE
|
|
ufunc__struve_asymp_large_z_types[4] = <char>NPY_DOUBLE
|
|
ufunc__struve_asymp_large_z_ptr[2*0] = <void*>_func_cephes__struve_asymp_large_z
|
|
ufunc__struve_asymp_large_z_ptr[2*0+1] = <void*>(<char*>"_struve_asymp_large_z")
|
|
ufunc__struve_asymp_large_z_data[0] = &ufunc__struve_asymp_large_z_ptr[2*0]
|
|
_struve_asymp_large_z = np.PyUFunc_FromFuncAndData(ufunc__struve_asymp_large_z_loops, ufunc__struve_asymp_large_z_data, ufunc__struve_asymp_large_z_types, 1, 3, 2, 0, '_struve_asymp_large_z', ufunc__struve_asymp_large_z_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__struve_bessel_series_loops[1]
|
|
cdef void *ufunc__struve_bessel_series_ptr[2]
|
|
cdef void *ufunc__struve_bessel_series_data[1]
|
|
cdef char ufunc__struve_bessel_series_types[5]
|
|
cdef char *ufunc__struve_bessel_series_doc = (
|
|
"_struve_bessel_series(v, z, is_h)\n"
|
|
"\n"
|
|
"Internal function for testing `struve` & `modstruve`\n"
|
|
"\n"
|
|
"Evaluates using Bessel function series\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"v, err")
|
|
ufunc__struve_bessel_series_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddp_d_As_ddp_dd
|
|
ufunc__struve_bessel_series_types[0] = <char>NPY_DOUBLE
|
|
ufunc__struve_bessel_series_types[1] = <char>NPY_DOUBLE
|
|
ufunc__struve_bessel_series_types[2] = <char>NPY_INTP
|
|
ufunc__struve_bessel_series_types[3] = <char>NPY_DOUBLE
|
|
ufunc__struve_bessel_series_types[4] = <char>NPY_DOUBLE
|
|
ufunc__struve_bessel_series_ptr[2*0] = <void*>_func_cephes__struve_bessel_series
|
|
ufunc__struve_bessel_series_ptr[2*0+1] = <void*>(<char*>"_struve_bessel_series")
|
|
ufunc__struve_bessel_series_data[0] = &ufunc__struve_bessel_series_ptr[2*0]
|
|
_struve_bessel_series = np.PyUFunc_FromFuncAndData(ufunc__struve_bessel_series_loops, ufunc__struve_bessel_series_data, ufunc__struve_bessel_series_types, 1, 3, 2, 0, '_struve_bessel_series', ufunc__struve_bessel_series_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc__struve_power_series_loops[1]
|
|
cdef void *ufunc__struve_power_series_ptr[2]
|
|
cdef void *ufunc__struve_power_series_data[1]
|
|
cdef char ufunc__struve_power_series_types[5]
|
|
cdef char *ufunc__struve_power_series_doc = (
|
|
"_struve_power_series(v, z, is_h)\n"
|
|
"\n"
|
|
"Internal function for testing `struve` & `modstruve`\n"
|
|
"\n"
|
|
"Evaluates using power series\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"v, err")
|
|
ufunc__struve_power_series_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddp_d_As_ddp_dd
|
|
ufunc__struve_power_series_types[0] = <char>NPY_DOUBLE
|
|
ufunc__struve_power_series_types[1] = <char>NPY_DOUBLE
|
|
ufunc__struve_power_series_types[2] = <char>NPY_INTP
|
|
ufunc__struve_power_series_types[3] = <char>NPY_DOUBLE
|
|
ufunc__struve_power_series_types[4] = <char>NPY_DOUBLE
|
|
ufunc__struve_power_series_ptr[2*0] = <void*>_func_cephes__struve_power_series
|
|
ufunc__struve_power_series_ptr[2*0+1] = <void*>(<char*>"_struve_power_series")
|
|
ufunc__struve_power_series_data[0] = &ufunc__struve_power_series_ptr[2*0]
|
|
_struve_power_series = np.PyUFunc_FromFuncAndData(ufunc__struve_power_series_loops, ufunc__struve_power_series_data, ufunc__struve_power_series_types, 1, 3, 2, 0, '_struve_power_series', ufunc__struve_power_series_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_agm_loops[2]
|
|
cdef void *ufunc_agm_ptr[4]
|
|
cdef void *ufunc_agm_data[2]
|
|
cdef char ufunc_agm_types[6]
|
|
cdef char *ufunc_agm_doc = (
|
|
"agm(a, b, out=None)\n"
|
|
"\n"
|
|
"Compute the arithmetic-geometric mean of `a` and `b`.\n"
|
|
"\n"
|
|
"Start with a_0 = a and b_0 = b and iteratively compute::\n"
|
|
"\n"
|
|
" a_{n+1} = (a_n + b_n)/2\n"
|
|
" b_{n+1} = sqrt(a_n*b_n)\n"
|
|
"\n"
|
|
"a_n and b_n converge to the same limit as n increases; their common\n"
|
|
"limit is agm(a, b).\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"a, b : array_like\n"
|
|
" Real values only. If the values are both negative, the result\n"
|
|
" is negative. If one value is negative and the other is positive,\n"
|
|
" `nan` is returned.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" The arithmetic-geometric mean of `a` and `b`.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import agm\n"
|
|
">>> a, b = 24.0, 6.0\n"
|
|
">>> agm(a, b)\n"
|
|
"13.458171481725614\n"
|
|
"\n"
|
|
"Compare that result to the iteration:\n"
|
|
"\n"
|
|
">>> while a != b:\n"
|
|
"... a, b = (a + b)/2, np.sqrt(a*b)\n"
|
|
"... print(\"a = %19.16f b=%19.16f\" % (a, b))\n"
|
|
"...\n"
|
|
"a = 15.0000000000000000 b=12.0000000000000000\n"
|
|
"a = 13.5000000000000000 b=13.4164078649987388\n"
|
|
"a = 13.4582039324993694 b=13.4581390309909850\n"
|
|
"a = 13.4581714817451772 b=13.4581714817060547\n"
|
|
"a = 13.4581714817256159 b=13.4581714817256159\n"
|
|
"\n"
|
|
"When array-like arguments are given, broadcasting applies:\n"
|
|
"\n"
|
|
">>> a = np.array([[1.5], [3], [6]]) # a has shape (3, 1).\n"
|
|
">>> b = np.array([6, 12, 24, 48]) # b has shape (4,).\n"
|
|
">>> agm(a, b)\n"
|
|
"array([[ 3.36454287, 5.42363427, 9.05798751, 15.53650756],\n"
|
|
" [ 4.37037309, 6.72908574, 10.84726853, 18.11597502],\n"
|
|
" [ 6. , 8.74074619, 13.45817148, 21.69453707]])")
|
|
ufunc_agm_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_agm_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_agm_types[0] = <char>NPY_FLOAT
|
|
ufunc_agm_types[1] = <char>NPY_FLOAT
|
|
ufunc_agm_types[2] = <char>NPY_FLOAT
|
|
ufunc_agm_types[3] = <char>NPY_DOUBLE
|
|
ufunc_agm_types[4] = <char>NPY_DOUBLE
|
|
ufunc_agm_types[5] = <char>NPY_DOUBLE
|
|
ufunc_agm_ptr[2*0] = <void*>_func_agm
|
|
ufunc_agm_ptr[2*0+1] = <void*>(<char*>"agm")
|
|
ufunc_agm_ptr[2*1] = <void*>_func_agm
|
|
ufunc_agm_ptr[2*1+1] = <void*>(<char*>"agm")
|
|
ufunc_agm_data[0] = &ufunc_agm_ptr[2*0]
|
|
ufunc_agm_data[1] = &ufunc_agm_ptr[2*1]
|
|
agm = np.PyUFunc_FromFuncAndData(ufunc_agm_loops, ufunc_agm_data, ufunc_agm_types, 2, 2, 1, 0, 'agm', ufunc_agm_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_bdtr_loops[3]
|
|
cdef void *ufunc_bdtr_ptr[6]
|
|
cdef void *ufunc_bdtr_data[3]
|
|
cdef char ufunc_bdtr_types[12]
|
|
cdef char *ufunc_bdtr_doc = (
|
|
"bdtr(k, n, p, out=None)\n"
|
|
"\n"
|
|
"Binomial distribution cumulative distribution function.\n"
|
|
"\n"
|
|
"Sum of the terms 0 through `floor(k)` of the Binomial probability density.\n"
|
|
"\n"
|
|
".. math::\n"
|
|
" \\mathrm{bdtr}(k, n, p) =\n"
|
|
" \\sum_{j=0}^{\\lfloor k \\rfloor} {{n}\\choose{j}} p^j (1-p)^{n-j}\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"k : array_like\n"
|
|
" Number of successes (double), rounded down to the nearest integer.\n"
|
|
"n : array_like\n"
|
|
" Number of events (int).\n"
|
|
"p : array_like\n"
|
|
" Probability of success in a single event (float).\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"y : scalar or ndarray\n"
|
|
" Probability of `floor(k)` or fewer successes in `n` independent events with\n"
|
|
" success probabilities of `p`.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"The terms are not summed directly; instead the regularized incomplete beta\n"
|
|
"function is employed, according to the formula,\n"
|
|
"\n"
|
|
".. math::\n"
|
|
" \\mathrm{bdtr}(k, n, p) =\n"
|
|
" I_{1 - p}(n - \\lfloor k \\rfloor, \\lfloor k \\rfloor + 1).\n"
|
|
"\n"
|
|
"Wrapper for the Cephes [1]_ routine `bdtr`.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Cephes Mathematical Functions Library,\n"
|
|
" http://www.netlib.org/cephes/")
|
|
ufunc_bdtr_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_bdtr_loops[1] = <np.PyUFuncGenericFunction>loop_d_dpd__As_dpd_d
|
|
ufunc_bdtr_loops[2] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_bdtr_types[0] = <char>NPY_FLOAT
|
|
ufunc_bdtr_types[1] = <char>NPY_FLOAT
|
|
ufunc_bdtr_types[2] = <char>NPY_FLOAT
|
|
ufunc_bdtr_types[3] = <char>NPY_FLOAT
|
|
ufunc_bdtr_types[4] = <char>NPY_DOUBLE
|
|
ufunc_bdtr_types[5] = <char>NPY_INTP
|
|
ufunc_bdtr_types[6] = <char>NPY_DOUBLE
|
|
ufunc_bdtr_types[7] = <char>NPY_DOUBLE
|
|
ufunc_bdtr_types[8] = <char>NPY_DOUBLE
|
|
ufunc_bdtr_types[9] = <char>NPY_DOUBLE
|
|
ufunc_bdtr_types[10] = <char>NPY_DOUBLE
|
|
ufunc_bdtr_types[11] = <char>NPY_DOUBLE
|
|
ufunc_bdtr_ptr[2*0] = <void*>_func_bdtr_unsafe
|
|
ufunc_bdtr_ptr[2*0+1] = <void*>(<char*>"bdtr")
|
|
ufunc_bdtr_ptr[2*1] = <void*>_func_cephes_bdtr_wrap
|
|
ufunc_bdtr_ptr[2*1+1] = <void*>(<char*>"bdtr")
|
|
ufunc_bdtr_ptr[2*2] = <void*>_func_bdtr_unsafe
|
|
ufunc_bdtr_ptr[2*2+1] = <void*>(<char*>"bdtr")
|
|
ufunc_bdtr_data[0] = &ufunc_bdtr_ptr[2*0]
|
|
ufunc_bdtr_data[1] = &ufunc_bdtr_ptr[2*1]
|
|
ufunc_bdtr_data[2] = &ufunc_bdtr_ptr[2*2]
|
|
bdtr = np.PyUFunc_FromFuncAndData(ufunc_bdtr_loops, ufunc_bdtr_data, ufunc_bdtr_types, 3, 3, 1, 0, 'bdtr', ufunc_bdtr_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_bdtrc_loops[3]
|
|
cdef void *ufunc_bdtrc_ptr[6]
|
|
cdef void *ufunc_bdtrc_data[3]
|
|
cdef char ufunc_bdtrc_types[12]
|
|
cdef char *ufunc_bdtrc_doc = (
|
|
"bdtrc(k, n, p, out=None)\n"
|
|
"\n"
|
|
"Binomial distribution survival function.\n"
|
|
"\n"
|
|
"Sum of the terms `floor(k) + 1` through `n` of the binomial probability\n"
|
|
"density,\n"
|
|
"\n"
|
|
".. math::\n"
|
|
" \\mathrm{bdtrc}(k, n, p) =\n"
|
|
" \\sum_{j=\\lfloor k \\rfloor +1}^n {{n}\\choose{j}} p^j (1-p)^{n-j}\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"k : array_like\n"
|
|
" Number of successes (double), rounded down to nearest integer.\n"
|
|
"n : array_like\n"
|
|
" Number of events (int)\n"
|
|
"p : array_like\n"
|
|
" Probability of success in a single event.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"y : scalar or ndarray\n"
|
|
" Probability of `floor(k) + 1` or more successes in `n` independent\n"
|
|
" events with success probabilities of `p`.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"bdtr\n"
|
|
"betainc\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"The terms are not summed directly; instead the regularized incomplete beta\n"
|
|
"function is employed, according to the formula,\n"
|
|
"\n"
|
|
".. math::\n"
|
|
" \\mathrm{bdtrc}(k, n, p) = I_{p}(\\lfloor k \\rfloor + 1, n - \\lfloor k \\rfloor).\n"
|
|
"\n"
|
|
"Wrapper for the Cephes [1]_ routine `bdtrc`.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Cephes Mathematical Functions Library,\n"
|
|
" http://www.netlib.org/cephes/")
|
|
ufunc_bdtrc_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_bdtrc_loops[1] = <np.PyUFuncGenericFunction>loop_d_dpd__As_dpd_d
|
|
ufunc_bdtrc_loops[2] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_bdtrc_types[0] = <char>NPY_FLOAT
|
|
ufunc_bdtrc_types[1] = <char>NPY_FLOAT
|
|
ufunc_bdtrc_types[2] = <char>NPY_FLOAT
|
|
ufunc_bdtrc_types[3] = <char>NPY_FLOAT
|
|
ufunc_bdtrc_types[4] = <char>NPY_DOUBLE
|
|
ufunc_bdtrc_types[5] = <char>NPY_INTP
|
|
ufunc_bdtrc_types[6] = <char>NPY_DOUBLE
|
|
ufunc_bdtrc_types[7] = <char>NPY_DOUBLE
|
|
ufunc_bdtrc_types[8] = <char>NPY_DOUBLE
|
|
ufunc_bdtrc_types[9] = <char>NPY_DOUBLE
|
|
ufunc_bdtrc_types[10] = <char>NPY_DOUBLE
|
|
ufunc_bdtrc_types[11] = <char>NPY_DOUBLE
|
|
ufunc_bdtrc_ptr[2*0] = <void*>_func_bdtrc_unsafe
|
|
ufunc_bdtrc_ptr[2*0+1] = <void*>(<char*>"bdtrc")
|
|
ufunc_bdtrc_ptr[2*1] = <void*>_func_cephes_bdtrc_wrap
|
|
ufunc_bdtrc_ptr[2*1+1] = <void*>(<char*>"bdtrc")
|
|
ufunc_bdtrc_ptr[2*2] = <void*>_func_bdtrc_unsafe
|
|
ufunc_bdtrc_ptr[2*2+1] = <void*>(<char*>"bdtrc")
|
|
ufunc_bdtrc_data[0] = &ufunc_bdtrc_ptr[2*0]
|
|
ufunc_bdtrc_data[1] = &ufunc_bdtrc_ptr[2*1]
|
|
ufunc_bdtrc_data[2] = &ufunc_bdtrc_ptr[2*2]
|
|
bdtrc = np.PyUFunc_FromFuncAndData(ufunc_bdtrc_loops, ufunc_bdtrc_data, ufunc_bdtrc_types, 3, 3, 1, 0, 'bdtrc', ufunc_bdtrc_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_bdtri_loops[3]
|
|
cdef void *ufunc_bdtri_ptr[6]
|
|
cdef void *ufunc_bdtri_data[3]
|
|
cdef char ufunc_bdtri_types[12]
|
|
cdef char *ufunc_bdtri_doc = (
|
|
"bdtri(k, n, y, out=None)\n"
|
|
"\n"
|
|
"Inverse function to `bdtr` with respect to `p`.\n"
|
|
"\n"
|
|
"Finds the event probability `p` such that the sum of the terms 0 through\n"
|
|
"`k` of the binomial probability density is equal to the given cumulative\n"
|
|
"probability `y`.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"k : array_like\n"
|
|
" Number of successes (float), rounded down to the nearest integer.\n"
|
|
"n : array_like\n"
|
|
" Number of events (float)\n"
|
|
"y : array_like\n"
|
|
" Cumulative probability (probability of `k` or fewer successes in `n`\n"
|
|
" events).\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"p : scalar or ndarray\n"
|
|
" The event probability such that `bdtr(\\lfloor k \\rfloor, n, p) = y`.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"bdtr\n"
|
|
"betaincinv\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"The computation is carried out using the inverse beta integral function\n"
|
|
"and the relation,::\n"
|
|
"\n"
|
|
" 1 - p = betaincinv(n - k, k + 1, y).\n"
|
|
"\n"
|
|
"Wrapper for the Cephes [1]_ routine `bdtri`.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Cephes Mathematical Functions Library,\n"
|
|
" http://www.netlib.org/cephes/")
|
|
ufunc_bdtri_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_bdtri_loops[1] = <np.PyUFuncGenericFunction>loop_d_dpd__As_dpd_d
|
|
ufunc_bdtri_loops[2] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_bdtri_types[0] = <char>NPY_FLOAT
|
|
ufunc_bdtri_types[1] = <char>NPY_FLOAT
|
|
ufunc_bdtri_types[2] = <char>NPY_FLOAT
|
|
ufunc_bdtri_types[3] = <char>NPY_FLOAT
|
|
ufunc_bdtri_types[4] = <char>NPY_DOUBLE
|
|
ufunc_bdtri_types[5] = <char>NPY_INTP
|
|
ufunc_bdtri_types[6] = <char>NPY_DOUBLE
|
|
ufunc_bdtri_types[7] = <char>NPY_DOUBLE
|
|
ufunc_bdtri_types[8] = <char>NPY_DOUBLE
|
|
ufunc_bdtri_types[9] = <char>NPY_DOUBLE
|
|
ufunc_bdtri_types[10] = <char>NPY_DOUBLE
|
|
ufunc_bdtri_types[11] = <char>NPY_DOUBLE
|
|
ufunc_bdtri_ptr[2*0] = <void*>_func_bdtri_unsafe
|
|
ufunc_bdtri_ptr[2*0+1] = <void*>(<char*>"bdtri")
|
|
ufunc_bdtri_ptr[2*1] = <void*>_func_cephes_bdtri_wrap
|
|
ufunc_bdtri_ptr[2*1+1] = <void*>(<char*>"bdtri")
|
|
ufunc_bdtri_ptr[2*2] = <void*>_func_bdtri_unsafe
|
|
ufunc_bdtri_ptr[2*2+1] = <void*>(<char*>"bdtri")
|
|
ufunc_bdtri_data[0] = &ufunc_bdtri_ptr[2*0]
|
|
ufunc_bdtri_data[1] = &ufunc_bdtri_ptr[2*1]
|
|
ufunc_bdtri_data[2] = &ufunc_bdtri_ptr[2*2]
|
|
bdtri = np.PyUFunc_FromFuncAndData(ufunc_bdtri_loops, ufunc_bdtri_data, ufunc_bdtri_types, 3, 3, 1, 0, 'bdtri', ufunc_bdtri_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_bdtrik_loops[2]
|
|
cdef void *ufunc_bdtrik_ptr[4]
|
|
cdef void *ufunc_bdtrik_data[2]
|
|
cdef char ufunc_bdtrik_types[8]
|
|
cdef char *ufunc_bdtrik_doc = (
|
|
"bdtrik(y, n, p, out=None)\n"
|
|
"\n"
|
|
"Inverse function to `bdtr` with respect to `k`.\n"
|
|
"\n"
|
|
"Finds the number of successes `k` such that the sum of the terms 0 through\n"
|
|
"`k` of the Binomial probability density for `n` events with probability\n"
|
|
"`p` is equal to the given cumulative probability `y`.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"y : array_like\n"
|
|
" Cumulative probability (probability of `k` or fewer successes in `n`\n"
|
|
" events).\n"
|
|
"n : array_like\n"
|
|
" Number of events (float).\n"
|
|
"p : array_like\n"
|
|
" Success probability (float).\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"k : scalar or ndarray\n"
|
|
" The number of successes `k` such that `bdtr(k, n, p) = y`.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"bdtr\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"Formula 26.5.24 of [1]_ is used to reduce the binomial distribution to the\n"
|
|
"cumulative incomplete beta distribution.\n"
|
|
"\n"
|
|
"Computation of `k` involves a search for a value that produces the desired\n"
|
|
"value of `y`. The search relies on the monotonicity of `y` with `k`.\n"
|
|
"\n"
|
|
"Wrapper for the CDFLIB [2]_ Fortran routine `cdfbin`.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Milton Abramowitz and Irene A. Stegun, eds.\n"
|
|
" Handbook of Mathematical Functions with Formulas,\n"
|
|
" Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
|
|
".. [2] Barry Brown, James Lovato, and Kathy Russell,\n"
|
|
" CDFLIB: Library of Fortran Routines for Cumulative Distribution\n"
|
|
" Functions, Inverses, and Other Parameters.")
|
|
ufunc_bdtrik_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_bdtrik_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_bdtrik_types[0] = <char>NPY_FLOAT
|
|
ufunc_bdtrik_types[1] = <char>NPY_FLOAT
|
|
ufunc_bdtrik_types[2] = <char>NPY_FLOAT
|
|
ufunc_bdtrik_types[3] = <char>NPY_FLOAT
|
|
ufunc_bdtrik_types[4] = <char>NPY_DOUBLE
|
|
ufunc_bdtrik_types[5] = <char>NPY_DOUBLE
|
|
ufunc_bdtrik_types[6] = <char>NPY_DOUBLE
|
|
ufunc_bdtrik_types[7] = <char>NPY_DOUBLE
|
|
ufunc_bdtrik_ptr[2*0] = <void*>_func_bdtrik
|
|
ufunc_bdtrik_ptr[2*0+1] = <void*>(<char*>"bdtrik")
|
|
ufunc_bdtrik_ptr[2*1] = <void*>_func_bdtrik
|
|
ufunc_bdtrik_ptr[2*1+1] = <void*>(<char*>"bdtrik")
|
|
ufunc_bdtrik_data[0] = &ufunc_bdtrik_ptr[2*0]
|
|
ufunc_bdtrik_data[1] = &ufunc_bdtrik_ptr[2*1]
|
|
bdtrik = np.PyUFunc_FromFuncAndData(ufunc_bdtrik_loops, ufunc_bdtrik_data, ufunc_bdtrik_types, 2, 3, 1, 0, 'bdtrik', ufunc_bdtrik_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_bdtrin_loops[2]
|
|
cdef void *ufunc_bdtrin_ptr[4]
|
|
cdef void *ufunc_bdtrin_data[2]
|
|
cdef char ufunc_bdtrin_types[8]
|
|
cdef char *ufunc_bdtrin_doc = (
|
|
"bdtrin(k, y, p, out=None)\n"
|
|
"\n"
|
|
"Inverse function to `bdtr` with respect to `n`.\n"
|
|
"\n"
|
|
"Finds the number of events `n` such that the sum of the terms 0 through\n"
|
|
"`k` of the Binomial probability density for events with probability `p` is\n"
|
|
"equal to the given cumulative probability `y`.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"k : array_like\n"
|
|
" Number of successes (float).\n"
|
|
"y : array_like\n"
|
|
" Cumulative probability (probability of `k` or fewer successes in `n`\n"
|
|
" events).\n"
|
|
"p : array_like\n"
|
|
" Success probability (float).\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"n : scalar or ndarray\n"
|
|
" The number of events `n` such that `bdtr(k, n, p) = y`.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"bdtr\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"Formula 26.5.24 of [1]_ is used to reduce the binomial distribution to the\n"
|
|
"cumulative incomplete beta distribution.\n"
|
|
"\n"
|
|
"Computation of `n` involves a search for a value that produces the desired\n"
|
|
"value of `y`. The search relies on the monotonicity of `y` with `n`.\n"
|
|
"\n"
|
|
"Wrapper for the CDFLIB [2]_ Fortran routine `cdfbin`.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Milton Abramowitz and Irene A. Stegun, eds.\n"
|
|
" Handbook of Mathematical Functions with Formulas,\n"
|
|
" Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
|
|
".. [2] Barry Brown, James Lovato, and Kathy Russell,\n"
|
|
" CDFLIB: Library of Fortran Routines for Cumulative Distribution\n"
|
|
" Functions, Inverses, and Other Parameters.")
|
|
ufunc_bdtrin_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_bdtrin_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_bdtrin_types[0] = <char>NPY_FLOAT
|
|
ufunc_bdtrin_types[1] = <char>NPY_FLOAT
|
|
ufunc_bdtrin_types[2] = <char>NPY_FLOAT
|
|
ufunc_bdtrin_types[3] = <char>NPY_FLOAT
|
|
ufunc_bdtrin_types[4] = <char>NPY_DOUBLE
|
|
ufunc_bdtrin_types[5] = <char>NPY_DOUBLE
|
|
ufunc_bdtrin_types[6] = <char>NPY_DOUBLE
|
|
ufunc_bdtrin_types[7] = <char>NPY_DOUBLE
|
|
ufunc_bdtrin_ptr[2*0] = <void*>_func_bdtrin
|
|
ufunc_bdtrin_ptr[2*0+1] = <void*>(<char*>"bdtrin")
|
|
ufunc_bdtrin_ptr[2*1] = <void*>_func_bdtrin
|
|
ufunc_bdtrin_ptr[2*1+1] = <void*>(<char*>"bdtrin")
|
|
ufunc_bdtrin_data[0] = &ufunc_bdtrin_ptr[2*0]
|
|
ufunc_bdtrin_data[1] = &ufunc_bdtrin_ptr[2*1]
|
|
bdtrin = np.PyUFunc_FromFuncAndData(ufunc_bdtrin_loops, ufunc_bdtrin_data, ufunc_bdtrin_types, 2, 3, 1, 0, 'bdtrin', ufunc_bdtrin_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_betainc_loops[2]
|
|
cdef void *ufunc_betainc_ptr[4]
|
|
cdef void *ufunc_betainc_data[2]
|
|
cdef char ufunc_betainc_types[8]
|
|
cdef char *ufunc_betainc_doc = (
|
|
"betainc(a, b, x, out=None)\n"
|
|
"\n"
|
|
"Regularized incomplete beta function.\n"
|
|
"\n"
|
|
"Computes the regularized incomplete beta function, defined as [1]_:\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" I_x(a, b) = \\frac{\\Gamma(a+b)}{\\Gamma(a)\\Gamma(b)} \\int_0^x\n"
|
|
" t^{a-1}(1-t)^{b-1}dt,\n"
|
|
"\n"
|
|
"for :math:`0 \\leq x \\leq 1`.\n"
|
|
"\n"
|
|
"This function is the cumulative distribution function for the beta\n"
|
|
"distribution; its range is [0, 1].\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"a, b : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"x : array_like\n"
|
|
" Real-valued such that :math:`0 \\leq x \\leq 1`,\n"
|
|
" the upper limit of integration\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" Value of the regularized incomplete beta function\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"beta : beta function\n"
|
|
"betaincinv : inverse of the regularized incomplete beta function\n"
|
|
"betaincc : complement of the regularized incomplete beta function\n"
|
|
"scipy.stats.beta : beta distribution\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"The term *regularized* in the name of this function refers to the\n"
|
|
"scaling of the function by the gamma function terms shown in the\n"
|
|
"formula. When not qualified as *regularized*, the name *incomplete\n"
|
|
"beta function* often refers to just the integral expression,\n"
|
|
"without the gamma terms. One can use the function `beta` from\n"
|
|
"`scipy.special` to get this \"nonregularized\" incomplete beta\n"
|
|
"function by multiplying the result of ``betainc(a, b, x)`` by\n"
|
|
"``beta(a, b)``.\n"
|
|
"\n"
|
|
"``betainc(a, b, x)`` is treated as a two parameter family of functions\n"
|
|
"of a single variable `x`, rather than as a function of three variables.\n"
|
|
"This impacts only the limiting cases ``a = 0``, ``b = 0``, ``a = inf``,\n"
|
|
"``b = inf``.\n"
|
|
"\n"
|
|
"In general\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" \\lim_{(a, b) \\rightarrow (a_0, b_0)} \\mathrm{betainc}(a, b, x)\n"
|
|
"\n"
|
|
"is treated as a pointwise limit in ``x``. Thus for example,\n"
|
|
"``betainc(0, b, 0)`` equals ``0`` for ``b > 0``, although it would be\n"
|
|
"indeterminate when considering the simultaneous limit ``(a, x) -> (0+, 0+)``.\n"
|
|
"\n"
|
|
"This function wraps the ``ibeta`` routine from the\n"
|
|
"Boost Math C++ library [2]_.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] NIST Digital Library of Mathematical Functions\n"
|
|
" https://dlmf.nist.gov/8.17\n"
|
|
".. [2] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"\n"
|
|
"Let :math:`B(a, b)` be the `beta` function.\n"
|
|
"\n"
|
|
">>> import scipy.special as sc\n"
|
|
"\n"
|
|
"The coefficient in terms of `gamma` is equal to\n"
|
|
":math:`1/B(a, b)`. Also, when :math:`x=1`\n"
|
|
"the integral is equal to :math:`B(a, b)`.\n"
|
|
"Therefore, :math:`I_{x=1}(a, b) = 1` for any :math:`a, b`.\n"
|
|
"\n"
|
|
">>> sc.betainc(0.2, 3.5, 1.0)\n"
|
|
"1.0\n"
|
|
"\n"
|
|
"It satisfies\n"
|
|
":math:`I_x(a, b) = x^a F(a, 1-b, a+1, x)/ (aB(a, b))`,\n"
|
|
"where :math:`F` is the hypergeometric function `hyp2f1`:\n"
|
|
"\n"
|
|
">>> a, b, x = 1.4, 3.1, 0.5\n"
|
|
">>> x**a * sc.hyp2f1(a, 1 - b, a + 1, x)/(a * sc.beta(a, b))\n"
|
|
"0.8148904036225295\n"
|
|
">>> sc.betainc(a, b, x)\n"
|
|
"0.8148904036225296\n"
|
|
"\n"
|
|
"This functions satisfies the relationship\n"
|
|
":math:`I_x(a, b) = 1 - I_{1-x}(b, a)`:\n"
|
|
"\n"
|
|
">>> sc.betainc(2.2, 3.1, 0.4)\n"
|
|
"0.49339638807619446\n"
|
|
">>> 1 - sc.betainc(3.1, 2.2, 1 - 0.4)\n"
|
|
"0.49339638807619446")
|
|
ufunc_betainc_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc_betainc_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_betainc_types[0] = <char>NPY_FLOAT
|
|
ufunc_betainc_types[1] = <char>NPY_FLOAT
|
|
ufunc_betainc_types[2] = <char>NPY_FLOAT
|
|
ufunc_betainc_types[3] = <char>NPY_FLOAT
|
|
ufunc_betainc_types[4] = <char>NPY_DOUBLE
|
|
ufunc_betainc_types[5] = <char>NPY_DOUBLE
|
|
ufunc_betainc_types[6] = <char>NPY_DOUBLE
|
|
ufunc_betainc_types[7] = <char>NPY_DOUBLE
|
|
ufunc_betainc_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ibeta_float
|
|
ufunc_betainc_ptr[2*0+1] = <void*>(<char*>"betainc")
|
|
ufunc_betainc_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ibeta_double
|
|
ufunc_betainc_ptr[2*1+1] = <void*>(<char*>"betainc")
|
|
ufunc_betainc_data[0] = &ufunc_betainc_ptr[2*0]
|
|
ufunc_betainc_data[1] = &ufunc_betainc_ptr[2*1]
|
|
betainc = np.PyUFunc_FromFuncAndData(ufunc_betainc_loops, ufunc_betainc_data, ufunc_betainc_types, 2, 3, 1, 0, 'betainc', ufunc_betainc_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_betaincc_loops[2]
|
|
cdef void *ufunc_betaincc_ptr[4]
|
|
cdef void *ufunc_betaincc_data[2]
|
|
cdef char ufunc_betaincc_types[8]
|
|
cdef char *ufunc_betaincc_doc = (
|
|
"betaincc(a, b, x, out=None)\n"
|
|
"\n"
|
|
"Complement of the regularized incomplete beta function.\n"
|
|
"\n"
|
|
"Computes the complement of the regularized incomplete beta function,\n"
|
|
"defined as [1]_:\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" \\bar{I}_x(a, b) = 1 - I_x(a, b)\n"
|
|
" = 1 - \\frac{\\Gamma(a+b)}{\\Gamma(a)\\Gamma(b)} \\int_0^x\n"
|
|
" t^{a-1}(1-t)^{b-1}dt,\n"
|
|
"\n"
|
|
"for :math:`0 \\leq x \\leq 1`.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"a, b : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"x : array_like\n"
|
|
" Real-valued such that :math:`0 \\leq x \\leq 1`,\n"
|
|
" the upper limit of integration\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" Value of the regularized incomplete beta function\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"betainc : regularized incomplete beta function\n"
|
|
"betaincinv : inverse of the regularized incomplete beta function\n"
|
|
"betainccinv :\n"
|
|
" inverse of the complement of the regularized incomplete beta function\n"
|
|
"beta : beta function\n"
|
|
"scipy.stats.beta : beta distribution\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
".. versionadded:: 1.11.0\n"
|
|
"\n"
|
|
"Like `betainc`, ``betaincc(a, b, x)`` is treated as a two parameter\n"
|
|
"family of functions of a single variable `x`, rather than as a function of\n"
|
|
"three variables. See the `betainc` docstring for more info on how this\n"
|
|
"impacts limiting cases.\n"
|
|
"\n"
|
|
"This function wraps the ``ibetac`` routine from the\n"
|
|
"Boost Math C++ library [2]_.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] NIST Digital Library of Mathematical Functions\n"
|
|
" https://dlmf.nist.gov/8.17\n"
|
|
".. [2] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> from scipy.special import betaincc, betainc\n"
|
|
"\n"
|
|
"The naive calculation ``1 - betainc(a, b, x)`` loses precision when\n"
|
|
"the values of ``betainc(a, b, x)`` are close to 1:\n"
|
|
"\n"
|
|
">>> 1 - betainc(0.5, 8, [0.9, 0.99, 0.999])\n"
|
|
"array([2.0574632e-09, 0.0000000e+00, 0.0000000e+00])\n"
|
|
"\n"
|
|
"By using ``betaincc``, we get the correct values:\n"
|
|
"\n"
|
|
">>> betaincc(0.5, 8, [0.9, 0.99, 0.999])\n"
|
|
"array([2.05746321e-09, 1.97259354e-17, 1.96467954e-25])")
|
|
ufunc_betaincc_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc_betaincc_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_betaincc_types[0] = <char>NPY_FLOAT
|
|
ufunc_betaincc_types[1] = <char>NPY_FLOAT
|
|
ufunc_betaincc_types[2] = <char>NPY_FLOAT
|
|
ufunc_betaincc_types[3] = <char>NPY_FLOAT
|
|
ufunc_betaincc_types[4] = <char>NPY_DOUBLE
|
|
ufunc_betaincc_types[5] = <char>NPY_DOUBLE
|
|
ufunc_betaincc_types[6] = <char>NPY_DOUBLE
|
|
ufunc_betaincc_types[7] = <char>NPY_DOUBLE
|
|
ufunc_betaincc_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ibetac_float
|
|
ufunc_betaincc_ptr[2*0+1] = <void*>(<char*>"betaincc")
|
|
ufunc_betaincc_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ibetac_double
|
|
ufunc_betaincc_ptr[2*1+1] = <void*>(<char*>"betaincc")
|
|
ufunc_betaincc_data[0] = &ufunc_betaincc_ptr[2*0]
|
|
ufunc_betaincc_data[1] = &ufunc_betaincc_ptr[2*1]
|
|
betaincc = np.PyUFunc_FromFuncAndData(ufunc_betaincc_loops, ufunc_betaincc_data, ufunc_betaincc_types, 2, 3, 1, 0, 'betaincc', ufunc_betaincc_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_betainccinv_loops[2]
|
|
cdef void *ufunc_betainccinv_ptr[4]
|
|
cdef void *ufunc_betainccinv_data[2]
|
|
cdef char ufunc_betainccinv_types[8]
|
|
cdef char *ufunc_betainccinv_doc = (
|
|
"betainccinv(a, b, y, out=None)\n"
|
|
"\n"
|
|
"Inverse of the complemented regularized incomplete beta function.\n"
|
|
"\n"
|
|
"Computes :math:`x` such that:\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" y = 1 - I_x(a, b) = 1 - \\frac{\\Gamma(a+b)}{\\Gamma(a)\\Gamma(b)}\n"
|
|
" \\int_0^x t^{a-1}(1-t)^{b-1}dt,\n"
|
|
"\n"
|
|
"where :math:`I_x` is the normalized incomplete beta function `betainc`\n"
|
|
"and :math:`\\Gamma` is the `gamma` function [1]_.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"a, b : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"y : array_like\n"
|
|
" Real-valued input\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" Value of the inverse of the regularized incomplete beta function\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"betainc : regularized incomplete beta function\n"
|
|
"betaincc : complement of the regularized incomplete beta function\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
".. versionadded:: 1.11.0\n"
|
|
"\n"
|
|
"This function wraps the ``ibetac_inv`` routine from the\n"
|
|
"Boost Math C++ library [2]_.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] NIST Digital Library of Mathematical Functions\n"
|
|
" https://dlmf.nist.gov/8.17\n"
|
|
".. [2] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> from scipy.special import betainccinv, betaincc\n"
|
|
"\n"
|
|
"This function is the inverse of `betaincc` for fixed\n"
|
|
"values of :math:`a` and :math:`b`.\n"
|
|
"\n"
|
|
">>> a, b = 1.2, 3.1\n"
|
|
">>> y = betaincc(a, b, 0.2)\n"
|
|
">>> betainccinv(a, b, y)\n"
|
|
"0.2\n"
|
|
"\n"
|
|
">>> a, b = 7, 2.5\n"
|
|
">>> x = betainccinv(a, b, 0.875)\n"
|
|
">>> betaincc(a, b, x)\n"
|
|
"0.875")
|
|
ufunc_betainccinv_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc_betainccinv_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_betainccinv_types[0] = <char>NPY_FLOAT
|
|
ufunc_betainccinv_types[1] = <char>NPY_FLOAT
|
|
ufunc_betainccinv_types[2] = <char>NPY_FLOAT
|
|
ufunc_betainccinv_types[3] = <char>NPY_FLOAT
|
|
ufunc_betainccinv_types[4] = <char>NPY_DOUBLE
|
|
ufunc_betainccinv_types[5] = <char>NPY_DOUBLE
|
|
ufunc_betainccinv_types[6] = <char>NPY_DOUBLE
|
|
ufunc_betainccinv_types[7] = <char>NPY_DOUBLE
|
|
ufunc_betainccinv_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ibetac_inv_float
|
|
ufunc_betainccinv_ptr[2*0+1] = <void*>(<char*>"betainccinv")
|
|
ufunc_betainccinv_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ibetac_inv_double
|
|
ufunc_betainccinv_ptr[2*1+1] = <void*>(<char*>"betainccinv")
|
|
ufunc_betainccinv_data[0] = &ufunc_betainccinv_ptr[2*0]
|
|
ufunc_betainccinv_data[1] = &ufunc_betainccinv_ptr[2*1]
|
|
betainccinv = np.PyUFunc_FromFuncAndData(ufunc_betainccinv_loops, ufunc_betainccinv_data, ufunc_betainccinv_types, 2, 3, 1, 0, 'betainccinv', ufunc_betainccinv_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_betaincinv_loops[2]
|
|
cdef void *ufunc_betaincinv_ptr[4]
|
|
cdef void *ufunc_betaincinv_data[2]
|
|
cdef char ufunc_betaincinv_types[8]
|
|
cdef char *ufunc_betaincinv_doc = (
|
|
"betaincinv(a, b, y, out=None)\n"
|
|
"\n"
|
|
"Inverse of the regularized incomplete beta function.\n"
|
|
"\n"
|
|
"Computes :math:`x` such that:\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" y = I_x(a, b) = \\frac{\\Gamma(a+b)}{\\Gamma(a)\\Gamma(b)}\n"
|
|
" \\int_0^x t^{a-1}(1-t)^{b-1}dt,\n"
|
|
"\n"
|
|
"where :math:`I_x` is the normalized incomplete beta function `betainc`\n"
|
|
"and :math:`\\Gamma` is the `gamma` function [1]_.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"a, b : array_like\n"
|
|
" Positive, real-valued parameters\n"
|
|
"y : array_like\n"
|
|
" Real-valued input\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" Value of the inverse of the regularized incomplete beta function\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"betainc : regularized incomplete beta function\n"
|
|
"gamma : gamma function\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"This function wraps the ``ibeta_inv`` routine from the\n"
|
|
"Boost Math C++ library [2]_.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] NIST Digital Library of Mathematical Functions\n"
|
|
" https://dlmf.nist.gov/8.17\n"
|
|
".. [2] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import scipy.special as sc\n"
|
|
"\n"
|
|
"This function is the inverse of `betainc` for fixed\n"
|
|
"values of :math:`a` and :math:`b`.\n"
|
|
"\n"
|
|
">>> a, b = 1.2, 3.1\n"
|
|
">>> y = sc.betainc(a, b, 0.2)\n"
|
|
">>> sc.betaincinv(a, b, y)\n"
|
|
"0.2\n"
|
|
">>>\n"
|
|
">>> a, b = 7.5, 0.4\n"
|
|
">>> x = sc.betaincinv(a, b, 0.5)\n"
|
|
">>> sc.betainc(a, b, x)\n"
|
|
"0.5")
|
|
ufunc_betaincinv_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc_betaincinv_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_betaincinv_types[0] = <char>NPY_FLOAT
|
|
ufunc_betaincinv_types[1] = <char>NPY_FLOAT
|
|
ufunc_betaincinv_types[2] = <char>NPY_FLOAT
|
|
ufunc_betaincinv_types[3] = <char>NPY_FLOAT
|
|
ufunc_betaincinv_types[4] = <char>NPY_DOUBLE
|
|
ufunc_betaincinv_types[5] = <char>NPY_DOUBLE
|
|
ufunc_betaincinv_types[6] = <char>NPY_DOUBLE
|
|
ufunc_betaincinv_types[7] = <char>NPY_DOUBLE
|
|
ufunc_betaincinv_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ibeta_inv_float
|
|
ufunc_betaincinv_ptr[2*0+1] = <void*>(<char*>"betaincinv")
|
|
ufunc_betaincinv_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ibeta_inv_double
|
|
ufunc_betaincinv_ptr[2*1+1] = <void*>(<char*>"betaincinv")
|
|
ufunc_betaincinv_data[0] = &ufunc_betaincinv_ptr[2*0]
|
|
ufunc_betaincinv_data[1] = &ufunc_betaincinv_ptr[2*1]
|
|
betaincinv = np.PyUFunc_FromFuncAndData(ufunc_betaincinv_loops, ufunc_betaincinv_data, ufunc_betaincinv_types, 2, 3, 1, 0, 'betaincinv', ufunc_betaincinv_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_boxcox_loops[2]
|
|
cdef void *ufunc_boxcox_ptr[4]
|
|
cdef void *ufunc_boxcox_data[2]
|
|
cdef char ufunc_boxcox_types[6]
|
|
cdef char *ufunc_boxcox_doc = (
|
|
"boxcox(x, lmbda, out=None)\n"
|
|
"\n"
|
|
"Compute the Box-Cox transformation.\n"
|
|
"\n"
|
|
"The Box-Cox transformation is::\n"
|
|
"\n"
|
|
" y = (x**lmbda - 1) / lmbda if lmbda != 0\n"
|
|
" log(x) if lmbda == 0\n"
|
|
"\n"
|
|
"Returns `nan` if ``x < 0``.\n"
|
|
"Returns `-inf` if ``x == 0`` and ``lmbda < 0``.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Data to be transformed.\n"
|
|
"lmbda : array_like\n"
|
|
" Power parameter of the Box-Cox transform.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"y : scalar or ndarray\n"
|
|
" Transformed data.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"\n"
|
|
".. versionadded:: 0.14.0\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> from scipy.special import boxcox\n"
|
|
">>> boxcox([1, 4, 10], 2.5)\n"
|
|
"array([ 0. , 12.4 , 126.09110641])\n"
|
|
">>> boxcox(2, [0, 1, 2])\n"
|
|
"array([ 0.69314718, 1. , 1.5 ])")
|
|
ufunc_boxcox_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_boxcox_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_boxcox_types[0] = <char>NPY_FLOAT
|
|
ufunc_boxcox_types[1] = <char>NPY_FLOAT
|
|
ufunc_boxcox_types[2] = <char>NPY_FLOAT
|
|
ufunc_boxcox_types[3] = <char>NPY_DOUBLE
|
|
ufunc_boxcox_types[4] = <char>NPY_DOUBLE
|
|
ufunc_boxcox_types[5] = <char>NPY_DOUBLE
|
|
ufunc_boxcox_ptr[2*0] = <void*>_func_boxcox
|
|
ufunc_boxcox_ptr[2*0+1] = <void*>(<char*>"boxcox")
|
|
ufunc_boxcox_ptr[2*1] = <void*>_func_boxcox
|
|
ufunc_boxcox_ptr[2*1+1] = <void*>(<char*>"boxcox")
|
|
ufunc_boxcox_data[0] = &ufunc_boxcox_ptr[2*0]
|
|
ufunc_boxcox_data[1] = &ufunc_boxcox_ptr[2*1]
|
|
boxcox = np.PyUFunc_FromFuncAndData(ufunc_boxcox_loops, ufunc_boxcox_data, ufunc_boxcox_types, 2, 2, 1, 0, 'boxcox', ufunc_boxcox_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_boxcox1p_loops[2]
|
|
cdef void *ufunc_boxcox1p_ptr[4]
|
|
cdef void *ufunc_boxcox1p_data[2]
|
|
cdef char ufunc_boxcox1p_types[6]
|
|
cdef char *ufunc_boxcox1p_doc = (
|
|
"boxcox1p(x, lmbda, out=None)\n"
|
|
"\n"
|
|
"Compute the Box-Cox transformation of 1 + `x`.\n"
|
|
"\n"
|
|
"The Box-Cox transformation computed by `boxcox1p` is::\n"
|
|
"\n"
|
|
" y = ((1+x)**lmbda - 1) / lmbda if lmbda != 0\n"
|
|
" log(1+x) if lmbda == 0\n"
|
|
"\n"
|
|
"Returns `nan` if ``x < -1``.\n"
|
|
"Returns `-inf` if ``x == -1`` and ``lmbda < 0``.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Data to be transformed.\n"
|
|
"lmbda : array_like\n"
|
|
" Power parameter of the Box-Cox transform.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"y : scalar or ndarray\n"
|
|
" Transformed data.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"\n"
|
|
".. versionadded:: 0.14.0\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> from scipy.special import boxcox1p\n"
|
|
">>> boxcox1p(1e-4, [0, 0.5, 1])\n"
|
|
"array([ 9.99950003e-05, 9.99975001e-05, 1.00000000e-04])\n"
|
|
">>> boxcox1p([0.01, 0.1], 0.25)\n"
|
|
"array([ 0.00996272, 0.09645476])")
|
|
ufunc_boxcox1p_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_boxcox1p_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_boxcox1p_types[0] = <char>NPY_FLOAT
|
|
ufunc_boxcox1p_types[1] = <char>NPY_FLOAT
|
|
ufunc_boxcox1p_types[2] = <char>NPY_FLOAT
|
|
ufunc_boxcox1p_types[3] = <char>NPY_DOUBLE
|
|
ufunc_boxcox1p_types[4] = <char>NPY_DOUBLE
|
|
ufunc_boxcox1p_types[5] = <char>NPY_DOUBLE
|
|
ufunc_boxcox1p_ptr[2*0] = <void*>_func_boxcox1p
|
|
ufunc_boxcox1p_ptr[2*0+1] = <void*>(<char*>"boxcox1p")
|
|
ufunc_boxcox1p_ptr[2*1] = <void*>_func_boxcox1p
|
|
ufunc_boxcox1p_ptr[2*1+1] = <void*>(<char*>"boxcox1p")
|
|
ufunc_boxcox1p_data[0] = &ufunc_boxcox1p_ptr[2*0]
|
|
ufunc_boxcox1p_data[1] = &ufunc_boxcox1p_ptr[2*1]
|
|
boxcox1p = np.PyUFunc_FromFuncAndData(ufunc_boxcox1p_loops, ufunc_boxcox1p_data, ufunc_boxcox1p_types, 2, 2, 1, 0, 'boxcox1p', ufunc_boxcox1p_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_btdtria_loops[2]
|
|
cdef void *ufunc_btdtria_ptr[4]
|
|
cdef void *ufunc_btdtria_data[2]
|
|
cdef char ufunc_btdtria_types[8]
|
|
cdef char *ufunc_btdtria_doc = (
|
|
"btdtria(p, b, x, out=None)\n"
|
|
"\n"
|
|
"Inverse of `betainc` with respect to `a`.\n"
|
|
"\n"
|
|
"This is the inverse of the beta cumulative distribution function, `betainc`,\n"
|
|
"considered as a function of `a`, returning the value of `a` for which\n"
|
|
"`betainc(a, b, x) = p`, or\n"
|
|
"\n"
|
|
".. math::\n"
|
|
" p = \\int_0^x \\frac{\\Gamma(a + b)}{\\Gamma(a)\\Gamma(b)} t^{a-1} (1-t)^{b-1}\\,dt\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"p : array_like\n"
|
|
" Cumulative probability, in [0, 1].\n"
|
|
"b : array_like\n"
|
|
" Shape parameter (`b` > 0).\n"
|
|
"x : array_like\n"
|
|
" The quantile, in [0, 1].\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"a : scalar or ndarray\n"
|
|
" The value of the shape parameter `a` such that `betainc(a, b, x) = p`.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"btdtrib : Inverse of the beta cumulative distribution function, with respect to `b`.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"Wrapper for the CDFLIB [1]_ Fortran routine `cdfbet`.\n"
|
|
"\n"
|
|
"The cumulative distribution function `p` is computed using a routine by\n"
|
|
"DiDinato and Morris [2]_. Computation of `a` involves a search for a value\n"
|
|
"that produces the desired value of `p`. The search relies on the\n"
|
|
"monotonicity of `p` with `a`.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Barry Brown, James Lovato, and Kathy Russell,\n"
|
|
" CDFLIB: Library of Fortran Routines for Cumulative Distribution\n"
|
|
" Functions, Inverses, and Other Parameters.\n"
|
|
".. [2] DiDinato, A. R. and Morris, A. H.,\n"
|
|
" Algorithm 708: Significant Digit Computation of the Incomplete Beta\n"
|
|
" Function Ratios. ACM Trans. Math. Softw. 18 (1993), 360-373.")
|
|
ufunc_btdtria_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_btdtria_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_btdtria_types[0] = <char>NPY_FLOAT
|
|
ufunc_btdtria_types[1] = <char>NPY_FLOAT
|
|
ufunc_btdtria_types[2] = <char>NPY_FLOAT
|
|
ufunc_btdtria_types[3] = <char>NPY_FLOAT
|
|
ufunc_btdtria_types[4] = <char>NPY_DOUBLE
|
|
ufunc_btdtria_types[5] = <char>NPY_DOUBLE
|
|
ufunc_btdtria_types[6] = <char>NPY_DOUBLE
|
|
ufunc_btdtria_types[7] = <char>NPY_DOUBLE
|
|
ufunc_btdtria_ptr[2*0] = <void*>_func_btdtria
|
|
ufunc_btdtria_ptr[2*0+1] = <void*>(<char*>"btdtria")
|
|
ufunc_btdtria_ptr[2*1] = <void*>_func_btdtria
|
|
ufunc_btdtria_ptr[2*1+1] = <void*>(<char*>"btdtria")
|
|
ufunc_btdtria_data[0] = &ufunc_btdtria_ptr[2*0]
|
|
ufunc_btdtria_data[1] = &ufunc_btdtria_ptr[2*1]
|
|
btdtria = np.PyUFunc_FromFuncAndData(ufunc_btdtria_loops, ufunc_btdtria_data, ufunc_btdtria_types, 2, 3, 1, 0, 'btdtria', ufunc_btdtria_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_btdtrib_loops[2]
|
|
cdef void *ufunc_btdtrib_ptr[4]
|
|
cdef void *ufunc_btdtrib_data[2]
|
|
cdef char ufunc_btdtrib_types[8]
|
|
cdef char *ufunc_btdtrib_doc = (
|
|
"btdtria(a, p, x, out=None)\n"
|
|
"\n"
|
|
"Inverse of `betainc` with respect to `b`.\n"
|
|
"\n"
|
|
"This is the inverse of the beta cumulative distribution function, `betainc`,\n"
|
|
"considered as a function of `b`, returning the value of `b` for which\n"
|
|
"`betainc(a, b, x) = p`, or\n"
|
|
"\n"
|
|
".. math::\n"
|
|
" p = \\int_0^x \\frac{\\Gamma(a + b)}{\\Gamma(a)\\Gamma(b)} t^{a-1} (1-t)^{b-1}\\,dt\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"a : array_like\n"
|
|
" Shape parameter (`a` > 0).\n"
|
|
"p : array_like\n"
|
|
" Cumulative probability, in [0, 1].\n"
|
|
"x : array_like\n"
|
|
" The quantile, in [0, 1].\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"b : scalar or ndarray\n"
|
|
" The value of the shape parameter `b` such that `betainc(a, b, x) = p`.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"btdtria : Inverse of the beta cumulative distribution function, with respect to `a`.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"Wrapper for the CDFLIB [1]_ Fortran routine `cdfbet`.\n"
|
|
"\n"
|
|
"The cumulative distribution function `p` is computed using a routine by\n"
|
|
"DiDinato and Morris [2]_. Computation of `b` involves a search for a value\n"
|
|
"that produces the desired value of `p`. The search relies on the\n"
|
|
"monotonicity of `p` with `b`.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Barry Brown, James Lovato, and Kathy Russell,\n"
|
|
" CDFLIB: Library of Fortran Routines for Cumulative Distribution\n"
|
|
" Functions, Inverses, and Other Parameters.\n"
|
|
".. [2] DiDinato, A. R. and Morris, A. H.,\n"
|
|
" Algorithm 708: Significant Digit Computation of the Incomplete Beta\n"
|
|
" Function Ratios. ACM Trans. Math. Softw. 18 (1993), 360-373.")
|
|
ufunc_btdtrib_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_btdtrib_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_btdtrib_types[0] = <char>NPY_FLOAT
|
|
ufunc_btdtrib_types[1] = <char>NPY_FLOAT
|
|
ufunc_btdtrib_types[2] = <char>NPY_FLOAT
|
|
ufunc_btdtrib_types[3] = <char>NPY_FLOAT
|
|
ufunc_btdtrib_types[4] = <char>NPY_DOUBLE
|
|
ufunc_btdtrib_types[5] = <char>NPY_DOUBLE
|
|
ufunc_btdtrib_types[6] = <char>NPY_DOUBLE
|
|
ufunc_btdtrib_types[7] = <char>NPY_DOUBLE
|
|
ufunc_btdtrib_ptr[2*0] = <void*>_func_btdtrib
|
|
ufunc_btdtrib_ptr[2*0+1] = <void*>(<char*>"btdtrib")
|
|
ufunc_btdtrib_ptr[2*1] = <void*>_func_btdtrib
|
|
ufunc_btdtrib_ptr[2*1+1] = <void*>(<char*>"btdtrib")
|
|
ufunc_btdtrib_data[0] = &ufunc_btdtrib_ptr[2*0]
|
|
ufunc_btdtrib_data[1] = &ufunc_btdtrib_ptr[2*1]
|
|
btdtrib = np.PyUFunc_FromFuncAndData(ufunc_btdtrib_loops, ufunc_btdtrib_data, ufunc_btdtrib_types, 2, 3, 1, 0, 'btdtrib', ufunc_btdtrib_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_chdtr_loops[2]
|
|
cdef void *ufunc_chdtr_ptr[4]
|
|
cdef void *ufunc_chdtr_data[2]
|
|
cdef char ufunc_chdtr_types[6]
|
|
cdef char *ufunc_chdtr_doc = (
|
|
"chdtr(v, x, out=None)\n"
|
|
"\n"
|
|
"Chi square cumulative distribution function.\n"
|
|
"\n"
|
|
"Returns the area under the left tail (from 0 to `x`) of the Chi\n"
|
|
"square probability density function with `v` degrees of freedom:\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" \\frac{1}{2^{v/2} \\Gamma(v/2)} \\int_0^x t^{v/2 - 1} e^{-t/2} dt\n"
|
|
"\n"
|
|
"Here :math:`\\Gamma` is the Gamma function; see `gamma`. This\n"
|
|
"integral can be expressed in terms of the regularized lower\n"
|
|
"incomplete gamma function `gammainc` as\n"
|
|
"``gammainc(v / 2, x / 2)``. [1]_\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"v : array_like\n"
|
|
" Degrees of freedom.\n"
|
|
"x : array_like\n"
|
|
" Upper bound of the integral.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results.\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" Values of the cumulative distribution function.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"chdtrc, chdtri, chdtriv, gammainc\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Chi-Square distribution,\n"
|
|
" https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> import scipy.special as sc\n"
|
|
"\n"
|
|
"It can be expressed in terms of the regularized lower incomplete\n"
|
|
"gamma function.\n"
|
|
"\n"
|
|
">>> v = 1\n"
|
|
">>> x = np.arange(4)\n"
|
|
">>> sc.chdtr(v, x)\n"
|
|
"array([0. , 0.68268949, 0.84270079, 0.91673548])\n"
|
|
">>> sc.gammainc(v / 2, x / 2)\n"
|
|
"array([0. , 0.68268949, 0.84270079, 0.91673548])")
|
|
ufunc_chdtr_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_chdtr_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_chdtr_types[0] = <char>NPY_FLOAT
|
|
ufunc_chdtr_types[1] = <char>NPY_FLOAT
|
|
ufunc_chdtr_types[2] = <char>NPY_FLOAT
|
|
ufunc_chdtr_types[3] = <char>NPY_DOUBLE
|
|
ufunc_chdtr_types[4] = <char>NPY_DOUBLE
|
|
ufunc_chdtr_types[5] = <char>NPY_DOUBLE
|
|
ufunc_chdtr_ptr[2*0] = <void*>_func_xsf_chdtr
|
|
ufunc_chdtr_ptr[2*0+1] = <void*>(<char*>"chdtr")
|
|
ufunc_chdtr_ptr[2*1] = <void*>_func_xsf_chdtr
|
|
ufunc_chdtr_ptr[2*1+1] = <void*>(<char*>"chdtr")
|
|
ufunc_chdtr_data[0] = &ufunc_chdtr_ptr[2*0]
|
|
ufunc_chdtr_data[1] = &ufunc_chdtr_ptr[2*1]
|
|
chdtr = np.PyUFunc_FromFuncAndData(ufunc_chdtr_loops, ufunc_chdtr_data, ufunc_chdtr_types, 2, 2, 1, 0, 'chdtr', ufunc_chdtr_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_chdtrc_loops[2]
|
|
cdef void *ufunc_chdtrc_ptr[4]
|
|
cdef void *ufunc_chdtrc_data[2]
|
|
cdef char ufunc_chdtrc_types[6]
|
|
cdef char *ufunc_chdtrc_doc = (
|
|
"chdtrc(v, x, out=None)\n"
|
|
"\n"
|
|
"Chi square survival function.\n"
|
|
"\n"
|
|
"Returns the area under the right hand tail (from `x` to infinity)\n"
|
|
"of the Chi square probability density function with `v` degrees of\n"
|
|
"freedom:\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" \\frac{1}{2^{v/2} \\Gamma(v/2)} \\int_x^\\infty t^{v/2 - 1} e^{-t/2} dt\n"
|
|
"\n"
|
|
"Here :math:`\\Gamma` is the Gamma function; see `gamma`. This\n"
|
|
"integral can be expressed in terms of the regularized upper\n"
|
|
"incomplete gamma function `gammaincc` as\n"
|
|
"``gammaincc(v / 2, x / 2)``. [1]_\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"v : array_like\n"
|
|
" Degrees of freedom.\n"
|
|
"x : array_like\n"
|
|
" Lower bound of the integral.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results.\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" Values of the survival function.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"chdtr, chdtri, chdtriv, gammaincc\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Chi-Square distribution,\n"
|
|
" https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> import scipy.special as sc\n"
|
|
"\n"
|
|
"It can be expressed in terms of the regularized upper incomplete\n"
|
|
"gamma function.\n"
|
|
"\n"
|
|
">>> v = 1\n"
|
|
">>> x = np.arange(4)\n"
|
|
">>> sc.chdtrc(v, x)\n"
|
|
"array([1. , 0.31731051, 0.15729921, 0.08326452])\n"
|
|
">>> sc.gammaincc(v / 2, x / 2)\n"
|
|
"array([1. , 0.31731051, 0.15729921, 0.08326452])")
|
|
ufunc_chdtrc_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_chdtrc_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_chdtrc_types[0] = <char>NPY_FLOAT
|
|
ufunc_chdtrc_types[1] = <char>NPY_FLOAT
|
|
ufunc_chdtrc_types[2] = <char>NPY_FLOAT
|
|
ufunc_chdtrc_types[3] = <char>NPY_DOUBLE
|
|
ufunc_chdtrc_types[4] = <char>NPY_DOUBLE
|
|
ufunc_chdtrc_types[5] = <char>NPY_DOUBLE
|
|
ufunc_chdtrc_ptr[2*0] = <void*>_func_xsf_chdtrc
|
|
ufunc_chdtrc_ptr[2*0+1] = <void*>(<char*>"chdtrc")
|
|
ufunc_chdtrc_ptr[2*1] = <void*>_func_xsf_chdtrc
|
|
ufunc_chdtrc_ptr[2*1+1] = <void*>(<char*>"chdtrc")
|
|
ufunc_chdtrc_data[0] = &ufunc_chdtrc_ptr[2*0]
|
|
ufunc_chdtrc_data[1] = &ufunc_chdtrc_ptr[2*1]
|
|
chdtrc = np.PyUFunc_FromFuncAndData(ufunc_chdtrc_loops, ufunc_chdtrc_data, ufunc_chdtrc_types, 2, 2, 1, 0, 'chdtrc', ufunc_chdtrc_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_chdtri_loops[2]
|
|
cdef void *ufunc_chdtri_ptr[4]
|
|
cdef void *ufunc_chdtri_data[2]
|
|
cdef char ufunc_chdtri_types[6]
|
|
cdef char *ufunc_chdtri_doc = (
|
|
"chdtri(v, p, out=None)\n"
|
|
"\n"
|
|
"Inverse to `chdtrc` with respect to `x`.\n"
|
|
"\n"
|
|
"Returns `x` such that ``chdtrc(v, x) == p``.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"v : array_like\n"
|
|
" Degrees of freedom.\n"
|
|
"p : array_like\n"
|
|
" Probability.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results.\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"x : scalar or ndarray\n"
|
|
" Value so that the probability a Chi square random variable\n"
|
|
" with `v` degrees of freedom is greater than `x` equals `p`.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"chdtrc, chdtr, chdtriv\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Chi-Square distribution,\n"
|
|
" https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import scipy.special as sc\n"
|
|
"\n"
|
|
"It inverts `chdtrc`.\n"
|
|
"\n"
|
|
">>> v, p = 1, 0.3\n"
|
|
">>> sc.chdtrc(v, sc.chdtri(v, p))\n"
|
|
"0.3\n"
|
|
">>> x = 1\n"
|
|
">>> sc.chdtri(v, sc.chdtrc(v, x))\n"
|
|
"1.0")
|
|
ufunc_chdtri_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_chdtri_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_chdtri_types[0] = <char>NPY_FLOAT
|
|
ufunc_chdtri_types[1] = <char>NPY_FLOAT
|
|
ufunc_chdtri_types[2] = <char>NPY_FLOAT
|
|
ufunc_chdtri_types[3] = <char>NPY_DOUBLE
|
|
ufunc_chdtri_types[4] = <char>NPY_DOUBLE
|
|
ufunc_chdtri_types[5] = <char>NPY_DOUBLE
|
|
ufunc_chdtri_ptr[2*0] = <void*>_func_xsf_chdtri
|
|
ufunc_chdtri_ptr[2*0+1] = <void*>(<char*>"chdtri")
|
|
ufunc_chdtri_ptr[2*1] = <void*>_func_xsf_chdtri
|
|
ufunc_chdtri_ptr[2*1+1] = <void*>(<char*>"chdtri")
|
|
ufunc_chdtri_data[0] = &ufunc_chdtri_ptr[2*0]
|
|
ufunc_chdtri_data[1] = &ufunc_chdtri_ptr[2*1]
|
|
chdtri = np.PyUFunc_FromFuncAndData(ufunc_chdtri_loops, ufunc_chdtri_data, ufunc_chdtri_types, 2, 2, 1, 0, 'chdtri', ufunc_chdtri_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_chdtriv_loops[2]
|
|
cdef void *ufunc_chdtriv_ptr[4]
|
|
cdef void *ufunc_chdtriv_data[2]
|
|
cdef char ufunc_chdtriv_types[6]
|
|
cdef char *ufunc_chdtriv_doc = (
|
|
"chdtriv(p, x, out=None)\n"
|
|
"\n"
|
|
"Inverse to `chdtr` with respect to `v`.\n"
|
|
"\n"
|
|
"Returns `v` such that ``chdtr(v, x) == p``.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"p : array_like\n"
|
|
" Probability that the Chi square random variable is less than\n"
|
|
" or equal to `x`.\n"
|
|
"x : array_like\n"
|
|
" Nonnegative input.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results.\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" Degrees of freedom.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"chdtr, chdtrc, chdtri\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Chi-Square distribution,\n"
|
|
" https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import scipy.special as sc\n"
|
|
"\n"
|
|
"It inverts `chdtr`.\n"
|
|
"\n"
|
|
">>> p, x = 0.5, 1\n"
|
|
">>> sc.chdtr(sc.chdtriv(p, x), x)\n"
|
|
"0.5000000000202172\n"
|
|
">>> v = 1\n"
|
|
">>> sc.chdtriv(sc.chdtr(v, x), v)\n"
|
|
"1.0000000000000013")
|
|
ufunc_chdtriv_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_chdtriv_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_chdtriv_types[0] = <char>NPY_FLOAT
|
|
ufunc_chdtriv_types[1] = <char>NPY_FLOAT
|
|
ufunc_chdtriv_types[2] = <char>NPY_FLOAT
|
|
ufunc_chdtriv_types[3] = <char>NPY_DOUBLE
|
|
ufunc_chdtriv_types[4] = <char>NPY_DOUBLE
|
|
ufunc_chdtriv_types[5] = <char>NPY_DOUBLE
|
|
ufunc_chdtriv_ptr[2*0] = <void*>_func_chdtriv
|
|
ufunc_chdtriv_ptr[2*0+1] = <void*>(<char*>"chdtriv")
|
|
ufunc_chdtriv_ptr[2*1] = <void*>_func_chdtriv
|
|
ufunc_chdtriv_ptr[2*1+1] = <void*>(<char*>"chdtriv")
|
|
ufunc_chdtriv_data[0] = &ufunc_chdtriv_ptr[2*0]
|
|
ufunc_chdtriv_data[1] = &ufunc_chdtriv_ptr[2*1]
|
|
chdtriv = np.PyUFunc_FromFuncAndData(ufunc_chdtriv_loops, ufunc_chdtriv_data, ufunc_chdtriv_types, 2, 2, 1, 0, 'chdtriv', ufunc_chdtriv_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_chndtr_loops[2]
|
|
cdef void *ufunc_chndtr_ptr[4]
|
|
cdef void *ufunc_chndtr_data[2]
|
|
cdef char ufunc_chndtr_types[8]
|
|
cdef char *ufunc_chndtr_doc = (
|
|
"chndtr(x, df, nc, out=None)\n"
|
|
"\n"
|
|
"Non-central chi square cumulative distribution function\n"
|
|
"\n"
|
|
"The cumulative distribution function is given by:\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" P(\\chi^{\\prime 2} \\vert \\nu, \\lambda) =\\sum_{j=0}^{\\infty}\n"
|
|
" e^{-\\lambda /2}\n"
|
|
" \\frac{(\\lambda /2)^j}{j!} P(\\chi^{\\prime 2} \\vert \\nu + 2j),\n"
|
|
"\n"
|
|
"where :math:`\\nu > 0` is the degrees of freedom (``df``) and\n"
|
|
":math:`\\lambda \\geq 0` is the non-centrality parameter (``nc``).\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Upper bound of the integral; must satisfy ``x >= 0``\n"
|
|
"df : array_like\n"
|
|
" Degrees of freedom; must satisfy ``df > 0``\n"
|
|
"nc : array_like\n"
|
|
" Non-centrality parameter; must satisfy ``nc >= 0``\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"x : scalar or ndarray\n"
|
|
" Value of the non-central chi square cumulative distribution function.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"chndtrix, chndtridf, chndtrinc")
|
|
ufunc_chndtr_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_chndtr_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_chndtr_types[0] = <char>NPY_FLOAT
|
|
ufunc_chndtr_types[1] = <char>NPY_FLOAT
|
|
ufunc_chndtr_types[2] = <char>NPY_FLOAT
|
|
ufunc_chndtr_types[3] = <char>NPY_FLOAT
|
|
ufunc_chndtr_types[4] = <char>NPY_DOUBLE
|
|
ufunc_chndtr_types[5] = <char>NPY_DOUBLE
|
|
ufunc_chndtr_types[6] = <char>NPY_DOUBLE
|
|
ufunc_chndtr_types[7] = <char>NPY_DOUBLE
|
|
ufunc_chndtr_ptr[2*0] = <void*>_func_chndtr
|
|
ufunc_chndtr_ptr[2*0+1] = <void*>(<char*>"chndtr")
|
|
ufunc_chndtr_ptr[2*1] = <void*>_func_chndtr
|
|
ufunc_chndtr_ptr[2*1+1] = <void*>(<char*>"chndtr")
|
|
ufunc_chndtr_data[0] = &ufunc_chndtr_ptr[2*0]
|
|
ufunc_chndtr_data[1] = &ufunc_chndtr_ptr[2*1]
|
|
chndtr = np.PyUFunc_FromFuncAndData(ufunc_chndtr_loops, ufunc_chndtr_data, ufunc_chndtr_types, 2, 3, 1, 0, 'chndtr', ufunc_chndtr_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_chndtridf_loops[2]
|
|
cdef void *ufunc_chndtridf_ptr[4]
|
|
cdef void *ufunc_chndtridf_data[2]
|
|
cdef char ufunc_chndtridf_types[8]
|
|
cdef char *ufunc_chndtridf_doc = (
|
|
"chndtridf(x, p, nc, out=None)\n"
|
|
"\n"
|
|
"Inverse to `chndtr` vs `df`\n"
|
|
"\n"
|
|
"Calculated using a search to find a value for `df` that produces the\n"
|
|
"desired value of `p`.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Upper bound of the integral; must satisfy ``x >= 0``\n"
|
|
"p : array_like\n"
|
|
" Probability; must satisfy ``0 <= p < 1``\n"
|
|
"nc : array_like\n"
|
|
" Non-centrality parameter; must satisfy ``nc >= 0``\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"df : scalar or ndarray\n"
|
|
" Degrees of freedom\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"chndtr, chndtrix, chndtrinc")
|
|
ufunc_chndtridf_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_chndtridf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_chndtridf_types[0] = <char>NPY_FLOAT
|
|
ufunc_chndtridf_types[1] = <char>NPY_FLOAT
|
|
ufunc_chndtridf_types[2] = <char>NPY_FLOAT
|
|
ufunc_chndtridf_types[3] = <char>NPY_FLOAT
|
|
ufunc_chndtridf_types[4] = <char>NPY_DOUBLE
|
|
ufunc_chndtridf_types[5] = <char>NPY_DOUBLE
|
|
ufunc_chndtridf_types[6] = <char>NPY_DOUBLE
|
|
ufunc_chndtridf_types[7] = <char>NPY_DOUBLE
|
|
ufunc_chndtridf_ptr[2*0] = <void*>_func_chndtridf
|
|
ufunc_chndtridf_ptr[2*0+1] = <void*>(<char*>"chndtridf")
|
|
ufunc_chndtridf_ptr[2*1] = <void*>_func_chndtridf
|
|
ufunc_chndtridf_ptr[2*1+1] = <void*>(<char*>"chndtridf")
|
|
ufunc_chndtridf_data[0] = &ufunc_chndtridf_ptr[2*0]
|
|
ufunc_chndtridf_data[1] = &ufunc_chndtridf_ptr[2*1]
|
|
chndtridf = np.PyUFunc_FromFuncAndData(ufunc_chndtridf_loops, ufunc_chndtridf_data, ufunc_chndtridf_types, 2, 3, 1, 0, 'chndtridf', ufunc_chndtridf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_chndtrinc_loops[2]
|
|
cdef void *ufunc_chndtrinc_ptr[4]
|
|
cdef void *ufunc_chndtrinc_data[2]
|
|
cdef char ufunc_chndtrinc_types[8]
|
|
cdef char *ufunc_chndtrinc_doc = (
|
|
"chndtrinc(x, df, p, out=None)\n"
|
|
"\n"
|
|
"Inverse to `chndtr` vs `nc`\n"
|
|
"\n"
|
|
"Calculated using a search to find a value for `df` that produces the\n"
|
|
"desired value of `p`.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Upper bound of the integral; must satisfy ``x >= 0``\n"
|
|
"df : array_like\n"
|
|
" Degrees of freedom; must satisfy ``df > 0``\n"
|
|
"p : array_like\n"
|
|
" Probability; must satisfy ``0 <= p < 1``\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"nc : scalar or ndarray\n"
|
|
" Non-centrality\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"chndtr, chndtrix, chndtrinc")
|
|
ufunc_chndtrinc_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_chndtrinc_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_chndtrinc_types[0] = <char>NPY_FLOAT
|
|
ufunc_chndtrinc_types[1] = <char>NPY_FLOAT
|
|
ufunc_chndtrinc_types[2] = <char>NPY_FLOAT
|
|
ufunc_chndtrinc_types[3] = <char>NPY_FLOAT
|
|
ufunc_chndtrinc_types[4] = <char>NPY_DOUBLE
|
|
ufunc_chndtrinc_types[5] = <char>NPY_DOUBLE
|
|
ufunc_chndtrinc_types[6] = <char>NPY_DOUBLE
|
|
ufunc_chndtrinc_types[7] = <char>NPY_DOUBLE
|
|
ufunc_chndtrinc_ptr[2*0] = <void*>_func_chndtrinc
|
|
ufunc_chndtrinc_ptr[2*0+1] = <void*>(<char*>"chndtrinc")
|
|
ufunc_chndtrinc_ptr[2*1] = <void*>_func_chndtrinc
|
|
ufunc_chndtrinc_ptr[2*1+1] = <void*>(<char*>"chndtrinc")
|
|
ufunc_chndtrinc_data[0] = &ufunc_chndtrinc_ptr[2*0]
|
|
ufunc_chndtrinc_data[1] = &ufunc_chndtrinc_ptr[2*1]
|
|
chndtrinc = np.PyUFunc_FromFuncAndData(ufunc_chndtrinc_loops, ufunc_chndtrinc_data, ufunc_chndtrinc_types, 2, 3, 1, 0, 'chndtrinc', ufunc_chndtrinc_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_chndtrix_loops[2]
|
|
cdef void *ufunc_chndtrix_ptr[4]
|
|
cdef void *ufunc_chndtrix_data[2]
|
|
cdef char ufunc_chndtrix_types[8]
|
|
cdef char *ufunc_chndtrix_doc = (
|
|
"chndtrix(p, df, nc, out=None)\n"
|
|
"\n"
|
|
"Inverse to `chndtr` vs `x`\n"
|
|
"\n"
|
|
"Calculated using a search to find a value for `x` that produces the\n"
|
|
"desired value of `p`.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"p : array_like\n"
|
|
" Probability; must satisfy ``0 <= p < 1``\n"
|
|
"df : array_like\n"
|
|
" Degrees of freedom; must satisfy ``df > 0``\n"
|
|
"nc : array_like\n"
|
|
" Non-centrality parameter; must satisfy ``nc >= 0``\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"x : scalar or ndarray\n"
|
|
" Value so that the probability a non-central Chi square random variable\n"
|
|
" with `df` degrees of freedom and non-centrality, `nc`, is greater than\n"
|
|
" `x` equals `p`.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"chndtr, chndtridf, chndtrinc")
|
|
ufunc_chndtrix_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_chndtrix_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_chndtrix_types[0] = <char>NPY_FLOAT
|
|
ufunc_chndtrix_types[1] = <char>NPY_FLOAT
|
|
ufunc_chndtrix_types[2] = <char>NPY_FLOAT
|
|
ufunc_chndtrix_types[3] = <char>NPY_FLOAT
|
|
ufunc_chndtrix_types[4] = <char>NPY_DOUBLE
|
|
ufunc_chndtrix_types[5] = <char>NPY_DOUBLE
|
|
ufunc_chndtrix_types[6] = <char>NPY_DOUBLE
|
|
ufunc_chndtrix_types[7] = <char>NPY_DOUBLE
|
|
ufunc_chndtrix_ptr[2*0] = <void*>_func_chndtrix
|
|
ufunc_chndtrix_ptr[2*0+1] = <void*>(<char*>"chndtrix")
|
|
ufunc_chndtrix_ptr[2*1] = <void*>_func_chndtrix
|
|
ufunc_chndtrix_ptr[2*1+1] = <void*>(<char*>"chndtrix")
|
|
ufunc_chndtrix_data[0] = &ufunc_chndtrix_ptr[2*0]
|
|
ufunc_chndtrix_data[1] = &ufunc_chndtrix_ptr[2*1]
|
|
chndtrix = np.PyUFunc_FromFuncAndData(ufunc_chndtrix_loops, ufunc_chndtrix_data, ufunc_chndtrix_types, 2, 3, 1, 0, 'chndtrix', ufunc_chndtrix_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_elliprc_loops[4]
|
|
cdef void *ufunc_elliprc_ptr[8]
|
|
cdef void *ufunc_elliprc_data[4]
|
|
cdef char ufunc_elliprc_types[12]
|
|
cdef char *ufunc_elliprc_doc = (
|
|
"elliprc(x, y, out=None)\n"
|
|
"\n"
|
|
"Degenerate symmetric elliptic integral.\n"
|
|
"\n"
|
|
"The function RC is defined as [1]_\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" R_{\\mathrm{C}}(x, y) =\n"
|
|
" \\frac{1}{2} \\int_0^{+\\infty} (t + x)^{-1/2} (t + y)^{-1} dt\n"
|
|
" = R_{\\mathrm{F}}(x, y, y)\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x, y : array_like\n"
|
|
" Real or complex input parameters. `x` can be any number in the\n"
|
|
" complex plane cut along the negative real axis. `y` must be non-zero.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"R : scalar or ndarray\n"
|
|
" Value of the integral. If `y` is real and negative, the Cauchy\n"
|
|
" principal value is returned. If both of `x` and `y` are real, the\n"
|
|
" return value is real. Otherwise, the return value is complex.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"elliprf : Completely-symmetric elliptic integral of the first kind.\n"
|
|
"elliprd : Symmetric elliptic integral of the second kind.\n"
|
|
"elliprg : Completely-symmetric elliptic integral of the second kind.\n"
|
|
"elliprj : Symmetric elliptic integral of the third kind.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"RC is a degenerate case of the symmetric integral RF: ``elliprc(x, y) ==\n"
|
|
"elliprf(x, y, y)``. It is an elementary function rather than an elliptic\n"
|
|
"integral.\n"
|
|
"\n"
|
|
"The code implements Carlson's algorithm based on the duplication theorems\n"
|
|
"and series expansion up to the 7th order. [2]_\n"
|
|
"\n"
|
|
".. versionadded:: 1.8.0\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] B. C. Carlson, ed., Chapter 19 in \"Digital Library of Mathematical\n"
|
|
" Functions,\" NIST, US Dept. of Commerce.\n"
|
|
" https://dlmf.nist.gov/19.16.E6\n"
|
|
".. [2] B. C. Carlson, \"Numerical computation of real or complex elliptic\n"
|
|
" integrals,\" Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.\n"
|
|
" https://arxiv.org/abs/math/9409227\n"
|
|
" https://doi.org/10.1007/BF02198293\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"Basic homogeneity property:\n"
|
|
"\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import elliprc\n"
|
|
"\n"
|
|
">>> x = 1.2 + 3.4j\n"
|
|
">>> y = 5.\n"
|
|
">>> scale = 0.3 + 0.4j\n"
|
|
">>> elliprc(scale*x, scale*y)\n"
|
|
"(0.5484493976710874-0.4169557678995833j)\n"
|
|
"\n"
|
|
">>> elliprc(x, y)/np.sqrt(scale)\n"
|
|
"(0.5484493976710874-0.41695576789958333j)\n"
|
|
"\n"
|
|
"When the two arguments coincide, the integral is particularly\n"
|
|
"simple:\n"
|
|
"\n"
|
|
">>> x = 1.2 + 3.4j\n"
|
|
">>> elliprc(x, x)\n"
|
|
"(0.4299173120614631-0.3041729818745595j)\n"
|
|
"\n"
|
|
">>> 1/np.sqrt(x)\n"
|
|
"(0.4299173120614631-0.30417298187455954j)\n"
|
|
"\n"
|
|
"Another simple case: the first argument vanishes:\n"
|
|
"\n"
|
|
">>> y = 1.2 + 3.4j\n"
|
|
">>> elliprc(0, y)\n"
|
|
"(0.6753125346116815-0.47779380263880866j)\n"
|
|
"\n"
|
|
">>> np.pi/2/np.sqrt(y)\n"
|
|
"(0.6753125346116815-0.4777938026388088j)\n"
|
|
"\n"
|
|
"When `x` and `y` are both positive, we can express\n"
|
|
":math:`R_C(x,y)` in terms of more elementary functions. For the\n"
|
|
"case :math:`0 \\le x < y`,\n"
|
|
"\n"
|
|
">>> x = 3.2\n"
|
|
">>> y = 6.\n"
|
|
">>> elliprc(x, y)\n"
|
|
"0.44942991498453444\n"
|
|
"\n"
|
|
">>> np.arctan(np.sqrt((y-x)/x))/np.sqrt(y-x)\n"
|
|
"0.44942991498453433\n"
|
|
"\n"
|
|
"And for the case :math:`0 \\le y < x`,\n"
|
|
"\n"
|
|
">>> x = 6.\n"
|
|
">>> y = 3.2\n"
|
|
">>> elliprc(x,y)\n"
|
|
"0.4989837501576147\n"
|
|
"\n"
|
|
">>> np.log((np.sqrt(x)+np.sqrt(x-y))/np.sqrt(y))/np.sqrt(x-y)\n"
|
|
"0.49898375015761476")
|
|
ufunc_elliprc_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_elliprc_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_elliprc_loops[2] = <np.PyUFuncGenericFunction>loop_D_DD__As_FF_F
|
|
ufunc_elliprc_loops[3] = <np.PyUFuncGenericFunction>loop_D_DD__As_DD_D
|
|
ufunc_elliprc_types[0] = <char>NPY_FLOAT
|
|
ufunc_elliprc_types[1] = <char>NPY_FLOAT
|
|
ufunc_elliprc_types[2] = <char>NPY_FLOAT
|
|
ufunc_elliprc_types[3] = <char>NPY_DOUBLE
|
|
ufunc_elliprc_types[4] = <char>NPY_DOUBLE
|
|
ufunc_elliprc_types[5] = <char>NPY_DOUBLE
|
|
ufunc_elliprc_types[6] = <char>NPY_CFLOAT
|
|
ufunc_elliprc_types[7] = <char>NPY_CFLOAT
|
|
ufunc_elliprc_types[8] = <char>NPY_CFLOAT
|
|
ufunc_elliprc_types[9] = <char>NPY_CDOUBLE
|
|
ufunc_elliprc_types[10] = <char>NPY_CDOUBLE
|
|
ufunc_elliprc_types[11] = <char>NPY_CDOUBLE
|
|
ufunc_elliprc_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_fellint_RC
|
|
ufunc_elliprc_ptr[2*0+1] = <void*>(<char*>"elliprc")
|
|
ufunc_elliprc_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_fellint_RC
|
|
ufunc_elliprc_ptr[2*1+1] = <void*>(<char*>"elliprc")
|
|
ufunc_elliprc_ptr[2*2] = <void*>scipy.special._ufuncs_cxx._export_cellint_RC
|
|
ufunc_elliprc_ptr[2*2+1] = <void*>(<char*>"elliprc")
|
|
ufunc_elliprc_ptr[2*3] = <void*>scipy.special._ufuncs_cxx._export_cellint_RC
|
|
ufunc_elliprc_ptr[2*3+1] = <void*>(<char*>"elliprc")
|
|
ufunc_elliprc_data[0] = &ufunc_elliprc_ptr[2*0]
|
|
ufunc_elliprc_data[1] = &ufunc_elliprc_ptr[2*1]
|
|
ufunc_elliprc_data[2] = &ufunc_elliprc_ptr[2*2]
|
|
ufunc_elliprc_data[3] = &ufunc_elliprc_ptr[2*3]
|
|
elliprc = np.PyUFunc_FromFuncAndData(ufunc_elliprc_loops, ufunc_elliprc_data, ufunc_elliprc_types, 4, 2, 1, 0, 'elliprc', ufunc_elliprc_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_elliprd_loops[4]
|
|
cdef void *ufunc_elliprd_ptr[8]
|
|
cdef void *ufunc_elliprd_data[4]
|
|
cdef char ufunc_elliprd_types[16]
|
|
cdef char *ufunc_elliprd_doc = (
|
|
"elliprd(x, y, z, out=None)\n"
|
|
"\n"
|
|
"Symmetric elliptic integral of the second kind.\n"
|
|
"\n"
|
|
"The function RD is defined as [1]_\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" R_{\\mathrm{D}}(x, y, z) =\n"
|
|
" \\frac{3}{2} \\int_0^{+\\infty} [(t + x) (t + y)]^{-1/2} (t + z)^{-3/2}\n"
|
|
" dt\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x, y, z : array_like\n"
|
|
" Real or complex input parameters. `x` or `y` can be any number in the\n"
|
|
" complex plane cut along the negative real axis, but at most one of them\n"
|
|
" can be zero, while `z` must be non-zero.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"R : scalar or ndarray\n"
|
|
" Value of the integral. If all of `x`, `y`, and `z` are real, the\n"
|
|
" return value is real. Otherwise, the return value is complex.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"elliprc : Degenerate symmetric elliptic integral.\n"
|
|
"elliprf : Completely-symmetric elliptic integral of the first kind.\n"
|
|
"elliprg : Completely-symmetric elliptic integral of the second kind.\n"
|
|
"elliprj : Symmetric elliptic integral of the third kind.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"RD is a degenerate case of the elliptic integral RJ: ``elliprd(x, y, z) ==\n"
|
|
"elliprj(x, y, z, z)``.\n"
|
|
"\n"
|
|
"The code implements Carlson's algorithm based on the duplication theorems\n"
|
|
"and series expansion up to the 7th order. [2]_\n"
|
|
"\n"
|
|
".. versionadded:: 1.8.0\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] B. C. Carlson, ed., Chapter 19 in \"Digital Library of Mathematical\n"
|
|
" Functions,\" NIST, US Dept. of Commerce.\n"
|
|
" https://dlmf.nist.gov/19.16.E5\n"
|
|
".. [2] B. C. Carlson, \"Numerical computation of real or complex elliptic\n"
|
|
" integrals,\" Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.\n"
|
|
" https://arxiv.org/abs/math/9409227\n"
|
|
" https://doi.org/10.1007/BF02198293\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"Basic homogeneity property:\n"
|
|
"\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import elliprd\n"
|
|
"\n"
|
|
">>> x = 1.2 + 3.4j\n"
|
|
">>> y = 5.\n"
|
|
">>> z = 6.\n"
|
|
">>> scale = 0.3 + 0.4j\n"
|
|
">>> elliprd(scale*x, scale*y, scale*z)\n"
|
|
"(-0.03703043835680379-0.24500934665683802j)\n"
|
|
"\n"
|
|
">>> elliprd(x, y, z)*np.power(scale, -1.5)\n"
|
|
"(-0.0370304383568038-0.24500934665683805j)\n"
|
|
"\n"
|
|
"All three arguments coincide:\n"
|
|
"\n"
|
|
">>> x = 1.2 + 3.4j\n"
|
|
">>> elliprd(x, x, x)\n"
|
|
"(-0.03986825876151896-0.14051741840449586j)\n"
|
|
"\n"
|
|
">>> np.power(x, -1.5)\n"
|
|
"(-0.03986825876151894-0.14051741840449583j)\n"
|
|
"\n"
|
|
"The so-called \"second lemniscate constant\":\n"
|
|
"\n"
|
|
">>> elliprd(0, 2, 1)/3\n"
|
|
"0.5990701173677961\n"
|
|
"\n"
|
|
">>> from scipy.special import gamma\n"
|
|
">>> gamma(0.75)**2/np.sqrt(2*np.pi)\n"
|
|
"0.5990701173677959")
|
|
ufunc_elliprd_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_elliprd_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_elliprd_loops[2] = <np.PyUFuncGenericFunction>loop_D_DDD__As_FFF_F
|
|
ufunc_elliprd_loops[3] = <np.PyUFuncGenericFunction>loop_D_DDD__As_DDD_D
|
|
ufunc_elliprd_types[0] = <char>NPY_FLOAT
|
|
ufunc_elliprd_types[1] = <char>NPY_FLOAT
|
|
ufunc_elliprd_types[2] = <char>NPY_FLOAT
|
|
ufunc_elliprd_types[3] = <char>NPY_FLOAT
|
|
ufunc_elliprd_types[4] = <char>NPY_DOUBLE
|
|
ufunc_elliprd_types[5] = <char>NPY_DOUBLE
|
|
ufunc_elliprd_types[6] = <char>NPY_DOUBLE
|
|
ufunc_elliprd_types[7] = <char>NPY_DOUBLE
|
|
ufunc_elliprd_types[8] = <char>NPY_CFLOAT
|
|
ufunc_elliprd_types[9] = <char>NPY_CFLOAT
|
|
ufunc_elliprd_types[10] = <char>NPY_CFLOAT
|
|
ufunc_elliprd_types[11] = <char>NPY_CFLOAT
|
|
ufunc_elliprd_types[12] = <char>NPY_CDOUBLE
|
|
ufunc_elliprd_types[13] = <char>NPY_CDOUBLE
|
|
ufunc_elliprd_types[14] = <char>NPY_CDOUBLE
|
|
ufunc_elliprd_types[15] = <char>NPY_CDOUBLE
|
|
ufunc_elliprd_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_fellint_RD
|
|
ufunc_elliprd_ptr[2*0+1] = <void*>(<char*>"elliprd")
|
|
ufunc_elliprd_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_fellint_RD
|
|
ufunc_elliprd_ptr[2*1+1] = <void*>(<char*>"elliprd")
|
|
ufunc_elliprd_ptr[2*2] = <void*>scipy.special._ufuncs_cxx._export_cellint_RD
|
|
ufunc_elliprd_ptr[2*2+1] = <void*>(<char*>"elliprd")
|
|
ufunc_elliprd_ptr[2*3] = <void*>scipy.special._ufuncs_cxx._export_cellint_RD
|
|
ufunc_elliprd_ptr[2*3+1] = <void*>(<char*>"elliprd")
|
|
ufunc_elliprd_data[0] = &ufunc_elliprd_ptr[2*0]
|
|
ufunc_elliprd_data[1] = &ufunc_elliprd_ptr[2*1]
|
|
ufunc_elliprd_data[2] = &ufunc_elliprd_ptr[2*2]
|
|
ufunc_elliprd_data[3] = &ufunc_elliprd_ptr[2*3]
|
|
elliprd = np.PyUFunc_FromFuncAndData(ufunc_elliprd_loops, ufunc_elliprd_data, ufunc_elliprd_types, 4, 3, 1, 0, 'elliprd', ufunc_elliprd_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_elliprf_loops[4]
|
|
cdef void *ufunc_elliprf_ptr[8]
|
|
cdef void *ufunc_elliprf_data[4]
|
|
cdef char ufunc_elliprf_types[16]
|
|
cdef char *ufunc_elliprf_doc = (
|
|
"elliprf(x, y, z, out=None)\n"
|
|
"\n"
|
|
"Completely-symmetric elliptic integral of the first kind.\n"
|
|
"\n"
|
|
"The function RF is defined as [1]_\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" R_{\\mathrm{F}}(x, y, z) =\n"
|
|
" \\frac{1}{2} \\int_0^{+\\infty} [(t + x) (t + y) (t + z)]^{-1/2} dt\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x, y, z : array_like\n"
|
|
" Real or complex input parameters. `x`, `y`, or `z` can be any number in\n"
|
|
" the complex plane cut along the negative real axis, but at most one of\n"
|
|
" them can be zero.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"R : scalar or ndarray\n"
|
|
" Value of the integral. If all of `x`, `y`, and `z` are real, the return\n"
|
|
" value is real. Otherwise, the return value is complex.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"elliprc : Degenerate symmetric integral.\n"
|
|
"elliprd : Symmetric elliptic integral of the second kind.\n"
|
|
"elliprg : Completely-symmetric elliptic integral of the second kind.\n"
|
|
"elliprj : Symmetric elliptic integral of the third kind.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"The code implements Carlson's algorithm based on the duplication theorems\n"
|
|
"and series expansion up to the 7th order (cf.:\n"
|
|
"https://dlmf.nist.gov/19.36.i) and the AGM algorithm for the complete\n"
|
|
"integral. [2]_\n"
|
|
"\n"
|
|
".. versionadded:: 1.8.0\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] B. C. Carlson, ed., Chapter 19 in \"Digital Library of Mathematical\n"
|
|
" Functions,\" NIST, US Dept. of Commerce.\n"
|
|
" https://dlmf.nist.gov/19.16.E1\n"
|
|
".. [2] B. C. Carlson, \"Numerical computation of real or complex elliptic\n"
|
|
" integrals,\" Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.\n"
|
|
" https://arxiv.org/abs/math/9409227\n"
|
|
" https://doi.org/10.1007/BF02198293\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"Basic homogeneity property:\n"
|
|
"\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import elliprf\n"
|
|
"\n"
|
|
">>> x = 1.2 + 3.4j\n"
|
|
">>> y = 5.\n"
|
|
">>> z = 6.\n"
|
|
">>> scale = 0.3 + 0.4j\n"
|
|
">>> elliprf(scale*x, scale*y, scale*z)\n"
|
|
"(0.5328051227278146-0.4008623567957094j)\n"
|
|
"\n"
|
|
">>> elliprf(x, y, z)/np.sqrt(scale)\n"
|
|
"(0.5328051227278147-0.4008623567957095j)\n"
|
|
"\n"
|
|
"All three arguments coincide:\n"
|
|
"\n"
|
|
">>> x = 1.2 + 3.4j\n"
|
|
">>> elliprf(x, x, x)\n"
|
|
"(0.42991731206146316-0.30417298187455954j)\n"
|
|
"\n"
|
|
">>> 1/np.sqrt(x)\n"
|
|
"(0.4299173120614631-0.30417298187455954j)\n"
|
|
"\n"
|
|
"The so-called \"first lemniscate constant\":\n"
|
|
"\n"
|
|
">>> elliprf(0, 1, 2)\n"
|
|
"1.3110287771460598\n"
|
|
"\n"
|
|
">>> from scipy.special import gamma\n"
|
|
">>> gamma(0.25)**2/(4*np.sqrt(2*np.pi))\n"
|
|
"1.3110287771460598")
|
|
ufunc_elliprf_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_elliprf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_elliprf_loops[2] = <np.PyUFuncGenericFunction>loop_D_DDD__As_FFF_F
|
|
ufunc_elliprf_loops[3] = <np.PyUFuncGenericFunction>loop_D_DDD__As_DDD_D
|
|
ufunc_elliprf_types[0] = <char>NPY_FLOAT
|
|
ufunc_elliprf_types[1] = <char>NPY_FLOAT
|
|
ufunc_elliprf_types[2] = <char>NPY_FLOAT
|
|
ufunc_elliprf_types[3] = <char>NPY_FLOAT
|
|
ufunc_elliprf_types[4] = <char>NPY_DOUBLE
|
|
ufunc_elliprf_types[5] = <char>NPY_DOUBLE
|
|
ufunc_elliprf_types[6] = <char>NPY_DOUBLE
|
|
ufunc_elliprf_types[7] = <char>NPY_DOUBLE
|
|
ufunc_elliprf_types[8] = <char>NPY_CFLOAT
|
|
ufunc_elliprf_types[9] = <char>NPY_CFLOAT
|
|
ufunc_elliprf_types[10] = <char>NPY_CFLOAT
|
|
ufunc_elliprf_types[11] = <char>NPY_CFLOAT
|
|
ufunc_elliprf_types[12] = <char>NPY_CDOUBLE
|
|
ufunc_elliprf_types[13] = <char>NPY_CDOUBLE
|
|
ufunc_elliprf_types[14] = <char>NPY_CDOUBLE
|
|
ufunc_elliprf_types[15] = <char>NPY_CDOUBLE
|
|
ufunc_elliprf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_fellint_RF
|
|
ufunc_elliprf_ptr[2*0+1] = <void*>(<char*>"elliprf")
|
|
ufunc_elliprf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_fellint_RF
|
|
ufunc_elliprf_ptr[2*1+1] = <void*>(<char*>"elliprf")
|
|
ufunc_elliprf_ptr[2*2] = <void*>scipy.special._ufuncs_cxx._export_cellint_RF
|
|
ufunc_elliprf_ptr[2*2+1] = <void*>(<char*>"elliprf")
|
|
ufunc_elliprf_ptr[2*3] = <void*>scipy.special._ufuncs_cxx._export_cellint_RF
|
|
ufunc_elliprf_ptr[2*3+1] = <void*>(<char*>"elliprf")
|
|
ufunc_elliprf_data[0] = &ufunc_elliprf_ptr[2*0]
|
|
ufunc_elliprf_data[1] = &ufunc_elliprf_ptr[2*1]
|
|
ufunc_elliprf_data[2] = &ufunc_elliprf_ptr[2*2]
|
|
ufunc_elliprf_data[3] = &ufunc_elliprf_ptr[2*3]
|
|
elliprf = np.PyUFunc_FromFuncAndData(ufunc_elliprf_loops, ufunc_elliprf_data, ufunc_elliprf_types, 4, 3, 1, 0, 'elliprf', ufunc_elliprf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_elliprg_loops[4]
|
|
cdef void *ufunc_elliprg_ptr[8]
|
|
cdef void *ufunc_elliprg_data[4]
|
|
cdef char ufunc_elliprg_types[16]
|
|
cdef char *ufunc_elliprg_doc = (
|
|
"elliprg(x, y, z, out=None)\n"
|
|
"\n"
|
|
"Completely-symmetric elliptic integral of the second kind.\n"
|
|
"\n"
|
|
"The function RG is defined as [1]_\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" R_{\\mathrm{G}}(x, y, z) =\n"
|
|
" \\frac{1}{4} \\int_0^{+\\infty} [(t + x) (t + y) (t + z)]^{-1/2}\n"
|
|
" \\left(\\frac{x}{t + x} + \\frac{y}{t + y} + \\frac{z}{t + z}\\right) t\n"
|
|
" dt\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x, y, z : array_like\n"
|
|
" Real or complex input parameters. `x`, `y`, or `z` can be any number in\n"
|
|
" the complex plane cut along the negative real axis.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"R : scalar or ndarray\n"
|
|
" Value of the integral. If all of `x`, `y`, and `z` are real, the return\n"
|
|
" value is real. Otherwise, the return value is complex.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"elliprc : Degenerate symmetric integral.\n"
|
|
"elliprd : Symmetric elliptic integral of the second kind.\n"
|
|
"elliprf : Completely-symmetric elliptic integral of the first kind.\n"
|
|
"elliprj : Symmetric elliptic integral of the third kind.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"The implementation uses the relation [1]_\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" 2 R_{\\mathrm{G}}(x, y, z) =\n"
|
|
" z R_{\\mathrm{F}}(x, y, z) -\n"
|
|
" \\frac{1}{3} (x - z) (y - z) R_{\\mathrm{D}}(x, y, z) +\n"
|
|
" \\sqrt{\\frac{x y}{z}}\n"
|
|
"\n"
|
|
"and the symmetry of `x`, `y`, `z` when at least one non-zero parameter can\n"
|
|
"be chosen as the pivot. When one of the arguments is close to zero, the AGM\n"
|
|
"method is applied instead. Other special cases are computed following Ref.\n"
|
|
"[2]_\n"
|
|
"\n"
|
|
".. versionadded:: 1.8.0\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] B. C. Carlson, \"Numerical computation of real or complex elliptic\n"
|
|
" integrals,\" Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.\n"
|
|
" https://arxiv.org/abs/math/9409227\n"
|
|
" https://doi.org/10.1007/BF02198293\n"
|
|
".. [2] B. C. Carlson, ed., Chapter 19 in \"Digital Library of Mathematical\n"
|
|
" Functions,\" NIST, US Dept. of Commerce.\n"
|
|
" https://dlmf.nist.gov/19.16.E1\n"
|
|
" https://dlmf.nist.gov/19.20.ii\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"Basic homogeneity property:\n"
|
|
"\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import elliprg\n"
|
|
"\n"
|
|
">>> x = 1.2 + 3.4j\n"
|
|
">>> y = 5.\n"
|
|
">>> z = 6.\n"
|
|
">>> scale = 0.3 + 0.4j\n"
|
|
">>> elliprg(scale*x, scale*y, scale*z)\n"
|
|
"(1.195936862005246+0.8470988320464167j)\n"
|
|
"\n"
|
|
">>> elliprg(x, y, z)*np.sqrt(scale)\n"
|
|
"(1.195936862005246+0.8470988320464165j)\n"
|
|
"\n"
|
|
"Simplifications:\n"
|
|
"\n"
|
|
">>> elliprg(0, y, y)\n"
|
|
"1.756203682760182\n"
|
|
"\n"
|
|
">>> 0.25*np.pi*np.sqrt(y)\n"
|
|
"1.7562036827601817\n"
|
|
"\n"
|
|
">>> elliprg(0, 0, z)\n"
|
|
"1.224744871391589\n"
|
|
"\n"
|
|
">>> 0.5*np.sqrt(z)\n"
|
|
"1.224744871391589\n"
|
|
"\n"
|
|
"The surface area of a triaxial ellipsoid with semiaxes ``a``, ``b``, and\n"
|
|
"``c`` is given by\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" S = 4 \\pi a b c R_{\\mathrm{G}}(1 / a^2, 1 / b^2, 1 / c^2).\n"
|
|
"\n"
|
|
">>> def ellipsoid_area(a, b, c):\n"
|
|
"... r = 4.0 * np.pi * a * b * c\n"
|
|
"... return r * elliprg(1.0 / (a * a), 1.0 / (b * b), 1.0 / (c * c))\n"
|
|
">>> print(ellipsoid_area(1, 3, 5))\n"
|
|
"108.62688289491807")
|
|
ufunc_elliprg_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_elliprg_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_elliprg_loops[2] = <np.PyUFuncGenericFunction>loop_D_DDD__As_FFF_F
|
|
ufunc_elliprg_loops[3] = <np.PyUFuncGenericFunction>loop_D_DDD__As_DDD_D
|
|
ufunc_elliprg_types[0] = <char>NPY_FLOAT
|
|
ufunc_elliprg_types[1] = <char>NPY_FLOAT
|
|
ufunc_elliprg_types[2] = <char>NPY_FLOAT
|
|
ufunc_elliprg_types[3] = <char>NPY_FLOAT
|
|
ufunc_elliprg_types[4] = <char>NPY_DOUBLE
|
|
ufunc_elliprg_types[5] = <char>NPY_DOUBLE
|
|
ufunc_elliprg_types[6] = <char>NPY_DOUBLE
|
|
ufunc_elliprg_types[7] = <char>NPY_DOUBLE
|
|
ufunc_elliprg_types[8] = <char>NPY_CFLOAT
|
|
ufunc_elliprg_types[9] = <char>NPY_CFLOAT
|
|
ufunc_elliprg_types[10] = <char>NPY_CFLOAT
|
|
ufunc_elliprg_types[11] = <char>NPY_CFLOAT
|
|
ufunc_elliprg_types[12] = <char>NPY_CDOUBLE
|
|
ufunc_elliprg_types[13] = <char>NPY_CDOUBLE
|
|
ufunc_elliprg_types[14] = <char>NPY_CDOUBLE
|
|
ufunc_elliprg_types[15] = <char>NPY_CDOUBLE
|
|
ufunc_elliprg_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_fellint_RG
|
|
ufunc_elliprg_ptr[2*0+1] = <void*>(<char*>"elliprg")
|
|
ufunc_elliprg_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_fellint_RG
|
|
ufunc_elliprg_ptr[2*1+1] = <void*>(<char*>"elliprg")
|
|
ufunc_elliprg_ptr[2*2] = <void*>scipy.special._ufuncs_cxx._export_cellint_RG
|
|
ufunc_elliprg_ptr[2*2+1] = <void*>(<char*>"elliprg")
|
|
ufunc_elliprg_ptr[2*3] = <void*>scipy.special._ufuncs_cxx._export_cellint_RG
|
|
ufunc_elliprg_ptr[2*3+1] = <void*>(<char*>"elliprg")
|
|
ufunc_elliprg_data[0] = &ufunc_elliprg_ptr[2*0]
|
|
ufunc_elliprg_data[1] = &ufunc_elliprg_ptr[2*1]
|
|
ufunc_elliprg_data[2] = &ufunc_elliprg_ptr[2*2]
|
|
ufunc_elliprg_data[3] = &ufunc_elliprg_ptr[2*3]
|
|
elliprg = np.PyUFunc_FromFuncAndData(ufunc_elliprg_loops, ufunc_elliprg_data, ufunc_elliprg_types, 4, 3, 1, 0, 'elliprg', ufunc_elliprg_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_elliprj_loops[4]
|
|
cdef void *ufunc_elliprj_ptr[8]
|
|
cdef void *ufunc_elliprj_data[4]
|
|
cdef char ufunc_elliprj_types[20]
|
|
cdef char *ufunc_elliprj_doc = (
|
|
"elliprj(x, y, z, p, out=None)\n"
|
|
"\n"
|
|
"Symmetric elliptic integral of the third kind.\n"
|
|
"\n"
|
|
"The function RJ is defined as [1]_\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" R_{\\mathrm{J}}(x, y, z, p) =\n"
|
|
" \\frac{3}{2} \\int_0^{+\\infty} [(t + x) (t + y) (t + z)]^{-1/2}\n"
|
|
" (t + p)^{-1} dt\n"
|
|
"\n"
|
|
".. warning::\n"
|
|
" This function should be considered experimental when the inputs are\n"
|
|
" unbalanced. Check correctness with another independent implementation.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x, y, z, p : array_like\n"
|
|
" Real or complex input parameters. `x`, `y`, or `z` are numbers in\n"
|
|
" the complex plane cut along the negative real axis (subject to further\n"
|
|
" constraints, see Notes), and at most one of them can be zero. `p` must\n"
|
|
" be non-zero.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"R : scalar or ndarray\n"
|
|
" Value of the integral. If all of `x`, `y`, `z`, and `p` are real, the\n"
|
|
" return value is real. Otherwise, the return value is complex.\n"
|
|
"\n"
|
|
" If `p` is real and negative, while `x`, `y`, and `z` are real,\n"
|
|
" non-negative, and at most one of them is zero, the Cauchy principal\n"
|
|
" value is returned. [1]_ [2]_\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"elliprc : Degenerate symmetric integral.\n"
|
|
"elliprd : Symmetric elliptic integral of the second kind.\n"
|
|
"elliprf : Completely-symmetric elliptic integral of the first kind.\n"
|
|
"elliprg : Completely-symmetric elliptic integral of the second kind.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"The code implements Carlson's algorithm based on the duplication theorems\n"
|
|
"and series expansion up to the 7th order. [3]_ The algorithm is slightly\n"
|
|
"different from its earlier incarnation as it appears in [1]_, in that the\n"
|
|
"call to `elliprc` (or ``atan``/``atanh``, see [4]_) is no longer needed in\n"
|
|
"the inner loop. Asymptotic approximations are used where arguments differ\n"
|
|
"widely in the order of magnitude. [5]_\n"
|
|
"\n"
|
|
"The input values are subject to certain sufficient but not necessary\n"
|
|
"constraints when input arguments are complex. Notably, ``x``, ``y``, and\n"
|
|
"``z`` must have non-negative real parts, unless two of them are\n"
|
|
"non-negative and complex-conjugates to each other while the other is a real\n"
|
|
"non-negative number. [1]_ If the inputs do not satisfy the sufficient\n"
|
|
"condition described in Ref. [1]_ they are rejected outright with the output\n"
|
|
"set to NaN.\n"
|
|
"\n"
|
|
"In the case where one of ``x``, ``y``, and ``z`` is equal to ``p``, the\n"
|
|
"function ``elliprd`` should be preferred because of its less restrictive\n"
|
|
"domain.\n"
|
|
"\n"
|
|
".. versionadded:: 1.8.0\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] B. C. Carlson, \"Numerical computation of real or complex elliptic\n"
|
|
" integrals,\" Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.\n"
|
|
" https://arxiv.org/abs/math/9409227\n"
|
|
" https://doi.org/10.1007/BF02198293\n"
|
|
".. [2] B. C. Carlson, ed., Chapter 19 in \"Digital Library of Mathematical\n"
|
|
" Functions,\" NIST, US Dept. of Commerce.\n"
|
|
" https://dlmf.nist.gov/19.20.iii\n"
|
|
".. [3] B. C. Carlson, J. FitzSimmons, \"Reduction Theorems for Elliptic\n"
|
|
" Integrands with the Square Root of Two Quadratic Factors,\" J.\n"
|
|
" Comput. Appl. Math., vol. 118, nos. 1-2, pp. 71-85, 2000.\n"
|
|
" https://doi.org/10.1016/S0377-0427(00)00282-X\n"
|
|
".. [4] F. Johansson, \"Numerical Evaluation of Elliptic Functions, Elliptic\n"
|
|
" Integrals and Modular Forms,\" in J. Blumlein, C. Schneider, P.\n"
|
|
" Paule, eds., \"Elliptic Integrals, Elliptic Functions and Modular\n"
|
|
" Forms in Quantum Field Theory,\" pp. 269-293, 2019 (Cham,\n"
|
|
" Switzerland: Springer Nature Switzerland)\n"
|
|
" https://arxiv.org/abs/1806.06725\n"
|
|
" https://doi.org/10.1007/978-3-030-04480-0\n"
|
|
".. [5] B. C. Carlson, J. L. Gustafson, \"Asymptotic Approximations for\n"
|
|
" Symmetric Elliptic Integrals,\" SIAM J. Math. Anls., vol. 25, no. 2,\n"
|
|
" pp. 288-303, 1994.\n"
|
|
" https://arxiv.org/abs/math/9310223\n"
|
|
" https://doi.org/10.1137/S0036141092228477\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"Basic homogeneity property:\n"
|
|
"\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import elliprj\n"
|
|
"\n"
|
|
">>> x = 1.2 + 3.4j\n"
|
|
">>> y = 5.\n"
|
|
">>> z = 6.\n"
|
|
">>> p = 7.\n"
|
|
">>> scale = 0.3 - 0.4j\n"
|
|
">>> elliprj(scale*x, scale*y, scale*z, scale*p)\n"
|
|
"(0.10834905565679157+0.19694950747103812j)\n"
|
|
"\n"
|
|
">>> elliprj(x, y, z, p)*np.power(scale, -1.5)\n"
|
|
"(0.10834905565679556+0.19694950747103854j)\n"
|
|
"\n"
|
|
"Reduction to simpler elliptic integral:\n"
|
|
"\n"
|
|
">>> elliprj(x, y, z, z)\n"
|
|
"(0.08288462362195129-0.028376809745123258j)\n"
|
|
"\n"
|
|
">>> from scipy.special import elliprd\n"
|
|
">>> elliprd(x, y, z)\n"
|
|
"(0.08288462362195136-0.028376809745123296j)\n"
|
|
"\n"
|
|
"All arguments coincide:\n"
|
|
"\n"
|
|
">>> elliprj(x, x, x, x)\n"
|
|
"(-0.03986825876151896-0.14051741840449586j)\n"
|
|
"\n"
|
|
">>> np.power(x, -1.5)\n"
|
|
"(-0.03986825876151894-0.14051741840449583j)")
|
|
ufunc_elliprj_loops[0] = <np.PyUFuncGenericFunction>loop_d_dddd__As_ffff_f
|
|
ufunc_elliprj_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
|
|
ufunc_elliprj_loops[2] = <np.PyUFuncGenericFunction>loop_D_DDDD__As_FFFF_F
|
|
ufunc_elliprj_loops[3] = <np.PyUFuncGenericFunction>loop_D_DDDD__As_DDDD_D
|
|
ufunc_elliprj_types[0] = <char>NPY_FLOAT
|
|
ufunc_elliprj_types[1] = <char>NPY_FLOAT
|
|
ufunc_elliprj_types[2] = <char>NPY_FLOAT
|
|
ufunc_elliprj_types[3] = <char>NPY_FLOAT
|
|
ufunc_elliprj_types[4] = <char>NPY_FLOAT
|
|
ufunc_elliprj_types[5] = <char>NPY_DOUBLE
|
|
ufunc_elliprj_types[6] = <char>NPY_DOUBLE
|
|
ufunc_elliprj_types[7] = <char>NPY_DOUBLE
|
|
ufunc_elliprj_types[8] = <char>NPY_DOUBLE
|
|
ufunc_elliprj_types[9] = <char>NPY_DOUBLE
|
|
ufunc_elliprj_types[10] = <char>NPY_CFLOAT
|
|
ufunc_elliprj_types[11] = <char>NPY_CFLOAT
|
|
ufunc_elliprj_types[12] = <char>NPY_CFLOAT
|
|
ufunc_elliprj_types[13] = <char>NPY_CFLOAT
|
|
ufunc_elliprj_types[14] = <char>NPY_CFLOAT
|
|
ufunc_elliprj_types[15] = <char>NPY_CDOUBLE
|
|
ufunc_elliprj_types[16] = <char>NPY_CDOUBLE
|
|
ufunc_elliprj_types[17] = <char>NPY_CDOUBLE
|
|
ufunc_elliprj_types[18] = <char>NPY_CDOUBLE
|
|
ufunc_elliprj_types[19] = <char>NPY_CDOUBLE
|
|
ufunc_elliprj_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_fellint_RJ
|
|
ufunc_elliprj_ptr[2*0+1] = <void*>(<char*>"elliprj")
|
|
ufunc_elliprj_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_fellint_RJ
|
|
ufunc_elliprj_ptr[2*1+1] = <void*>(<char*>"elliprj")
|
|
ufunc_elliprj_ptr[2*2] = <void*>scipy.special._ufuncs_cxx._export_cellint_RJ
|
|
ufunc_elliprj_ptr[2*2+1] = <void*>(<char*>"elliprj")
|
|
ufunc_elliprj_ptr[2*3] = <void*>scipy.special._ufuncs_cxx._export_cellint_RJ
|
|
ufunc_elliprj_ptr[2*3+1] = <void*>(<char*>"elliprj")
|
|
ufunc_elliprj_data[0] = &ufunc_elliprj_ptr[2*0]
|
|
ufunc_elliprj_data[1] = &ufunc_elliprj_ptr[2*1]
|
|
ufunc_elliprj_data[2] = &ufunc_elliprj_ptr[2*2]
|
|
ufunc_elliprj_data[3] = &ufunc_elliprj_ptr[2*3]
|
|
elliprj = np.PyUFunc_FromFuncAndData(ufunc_elliprj_loops, ufunc_elliprj_data, ufunc_elliprj_types, 4, 4, 1, 0, 'elliprj', ufunc_elliprj_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_entr_loops[2]
|
|
cdef void *ufunc_entr_ptr[4]
|
|
cdef void *ufunc_entr_data[2]
|
|
cdef char ufunc_entr_types[4]
|
|
cdef char *ufunc_entr_doc = (
|
|
"entr(x, out=None)\n"
|
|
"\n"
|
|
"Elementwise function for computing entropy.\n"
|
|
"\n"
|
|
".. math:: \\text{entr}(x) = \\begin{cases} - x \\log(x) & x > 0 \\\\ 0 & x = 0\n"
|
|
" \\\\ -\\infty & \\text{otherwise} \\end{cases}\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : ndarray\n"
|
|
" Input array.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"res : scalar or ndarray\n"
|
|
" The value of the elementwise entropy function at the given points `x`.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"kl_div, rel_entr, scipy.stats.entropy\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
".. versionadded:: 0.15.0\n"
|
|
"\n"
|
|
"This function is concave.\n"
|
|
"\n"
|
|
"The origin of this function is in convex programming; see [1]_.\n"
|
|
"Given a probability distribution :math:`p_1, \\ldots, p_n`,\n"
|
|
"the definition of entropy in the context of *information theory* is\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" \\sum_{i = 1}^n \\mathrm{entr}(p_i).\n"
|
|
"\n"
|
|
"To compute the latter quantity, use `scipy.stats.entropy`.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Boyd, Stephen and Lieven Vandenberghe. *Convex optimization*.\n"
|
|
" Cambridge University Press, 2004.\n"
|
|
" :doi:`https://doi.org/10.1017/CBO9780511804441`")
|
|
ufunc_entr_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
|
|
ufunc_entr_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
|
|
ufunc_entr_types[0] = <char>NPY_FLOAT
|
|
ufunc_entr_types[1] = <char>NPY_FLOAT
|
|
ufunc_entr_types[2] = <char>NPY_DOUBLE
|
|
ufunc_entr_types[3] = <char>NPY_DOUBLE
|
|
ufunc_entr_ptr[2*0] = <void*>_func_entr
|
|
ufunc_entr_ptr[2*0+1] = <void*>(<char*>"entr")
|
|
ufunc_entr_ptr[2*1] = <void*>_func_entr
|
|
ufunc_entr_ptr[2*1+1] = <void*>(<char*>"entr")
|
|
ufunc_entr_data[0] = &ufunc_entr_ptr[2*0]
|
|
ufunc_entr_data[1] = &ufunc_entr_ptr[2*1]
|
|
entr = np.PyUFunc_FromFuncAndData(ufunc_entr_loops, ufunc_entr_data, ufunc_entr_types, 2, 1, 1, 0, 'entr', ufunc_entr_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_erfcinv_loops[2]
|
|
cdef void *ufunc_erfcinv_ptr[4]
|
|
cdef void *ufunc_erfcinv_data[2]
|
|
cdef char ufunc_erfcinv_types[4]
|
|
cdef char *ufunc_erfcinv_doc = (
|
|
"erfcinv(y, out=None)\n"
|
|
"\n"
|
|
"Inverse of the complementary error function.\n"
|
|
"\n"
|
|
"Computes the inverse of the complementary error function.\n"
|
|
"\n"
|
|
"In the complex domain, there is no unique complex number w satisfying\n"
|
|
"erfc(w)=z. This indicates a true inverse function would be multivalued.\n"
|
|
"When the domain restricts to the real, 0 < x < 2, there is a unique real\n"
|
|
"number satisfying erfc(erfcinv(x)) = erfcinv(erfc(x)).\n"
|
|
"\n"
|
|
"It is related to inverse of the error function by erfcinv(1-x) = erfinv(x)\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"y : ndarray\n"
|
|
" Argument at which to evaluate. Domain: [0, 2]\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"erfcinv : scalar or ndarray\n"
|
|
" The inverse of erfc of y, element-wise\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"erf : Error function of a complex argument\n"
|
|
"erfc : Complementary error function, ``1 - erf(x)``\n"
|
|
"erfinv : Inverse of the error function\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
">>> from scipy.special import erfcinv\n"
|
|
"\n"
|
|
">>> erfcinv(0.5)\n"
|
|
"0.4769362762044699\n"
|
|
"\n"
|
|
">>> y = np.linspace(0.0, 2.0, num=11)\n"
|
|
">>> erfcinv(y)\n"
|
|
"array([ inf, 0.9061938 , 0.59511608, 0.37080716, 0.17914345,\n"
|
|
" -0. , -0.17914345, -0.37080716, -0.59511608, -0.9061938 ,\n"
|
|
" -inf])\n"
|
|
"\n"
|
|
"Plot the function:\n"
|
|
"\n"
|
|
">>> y = np.linspace(0, 2, 200)\n"
|
|
">>> fig, ax = plt.subplots()\n"
|
|
">>> ax.plot(y, erfcinv(y))\n"
|
|
">>> ax.grid(True)\n"
|
|
">>> ax.set_xlabel('y')\n"
|
|
">>> ax.set_title('erfcinv(y)')\n"
|
|
">>> plt.show()")
|
|
ufunc_erfcinv_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
|
|
ufunc_erfcinv_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
|
|
ufunc_erfcinv_types[0] = <char>NPY_FLOAT
|
|
ufunc_erfcinv_types[1] = <char>NPY_FLOAT
|
|
ufunc_erfcinv_types[2] = <char>NPY_DOUBLE
|
|
ufunc_erfcinv_types[3] = <char>NPY_DOUBLE
|
|
ufunc_erfcinv_ptr[2*0] = <void*>_func_cephes_erfcinv
|
|
ufunc_erfcinv_ptr[2*0+1] = <void*>(<char*>"erfcinv")
|
|
ufunc_erfcinv_ptr[2*1] = <void*>_func_cephes_erfcinv
|
|
ufunc_erfcinv_ptr[2*1+1] = <void*>(<char*>"erfcinv")
|
|
ufunc_erfcinv_data[0] = &ufunc_erfcinv_ptr[2*0]
|
|
ufunc_erfcinv_data[1] = &ufunc_erfcinv_ptr[2*1]
|
|
erfcinv = np.PyUFunc_FromFuncAndData(ufunc_erfcinv_loops, ufunc_erfcinv_data, ufunc_erfcinv_types, 2, 1, 1, 0, 'erfcinv', ufunc_erfcinv_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_erfinv_loops[2]
|
|
cdef void *ufunc_erfinv_ptr[4]
|
|
cdef void *ufunc_erfinv_data[2]
|
|
cdef char ufunc_erfinv_types[4]
|
|
cdef char *ufunc_erfinv_doc = (
|
|
"erfinv(y, out=None)\n"
|
|
"\n"
|
|
"Inverse of the error function.\n"
|
|
"\n"
|
|
"Computes the inverse of the error function.\n"
|
|
"\n"
|
|
"In the complex domain, there is no unique complex number w satisfying\n"
|
|
"erf(w)=z. This indicates a true inverse function would be multivalued.\n"
|
|
"When the domain restricts to the real, -1 < x < 1, there is a unique real\n"
|
|
"number satisfying erf(erfinv(x)) = x.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"y : ndarray\n"
|
|
" Argument at which to evaluate. Domain: [-1, 1]\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"erfinv : scalar or ndarray\n"
|
|
" The inverse of erf of y, element-wise\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"erf : Error function of a complex argument\n"
|
|
"erfc : Complementary error function, ``1 - erf(x)``\n"
|
|
"erfcinv : Inverse of the complementary error function\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"This function wraps the ``erf_inv`` routine from the\n"
|
|
"Boost Math C++ library [1]_.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
">>> from scipy.special import erfinv, erf\n"
|
|
"\n"
|
|
">>> erfinv(0.5)\n"
|
|
"0.4769362762044699\n"
|
|
"\n"
|
|
">>> y = np.linspace(-1.0, 1.0, num=9)\n"
|
|
">>> x = erfinv(y)\n"
|
|
">>> x\n"
|
|
"array([ -inf, -0.81341985, -0.47693628, -0.22531206, 0. ,\n"
|
|
" 0.22531206, 0.47693628, 0.81341985, inf])\n"
|
|
"\n"
|
|
"Verify that ``erf(erfinv(y))`` is ``y``.\n"
|
|
"\n"
|
|
">>> erf(x)\n"
|
|
"array([-1. , -0.75, -0.5 , -0.25, 0. , 0.25, 0.5 , 0.75, 1. ])\n"
|
|
"\n"
|
|
"Plot the function:\n"
|
|
"\n"
|
|
">>> y = np.linspace(-1, 1, 200)\n"
|
|
">>> fig, ax = plt.subplots()\n"
|
|
">>> ax.plot(y, erfinv(y))\n"
|
|
">>> ax.grid(True)\n"
|
|
">>> ax.set_xlabel('y')\n"
|
|
">>> ax.set_title('erfinv(y)')\n"
|
|
">>> plt.show()")
|
|
ufunc_erfinv_loops[0] = <np.PyUFuncGenericFunction>loop_f_f__As_f_f
|
|
ufunc_erfinv_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
|
|
ufunc_erfinv_types[0] = <char>NPY_FLOAT
|
|
ufunc_erfinv_types[1] = <char>NPY_FLOAT
|
|
ufunc_erfinv_types[2] = <char>NPY_DOUBLE
|
|
ufunc_erfinv_types[3] = <char>NPY_DOUBLE
|
|
ufunc_erfinv_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_erfinv_float
|
|
ufunc_erfinv_ptr[2*0+1] = <void*>(<char*>"erfinv")
|
|
ufunc_erfinv_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_erfinv_double
|
|
ufunc_erfinv_ptr[2*1+1] = <void*>(<char*>"erfinv")
|
|
ufunc_erfinv_data[0] = &ufunc_erfinv_ptr[2*0]
|
|
ufunc_erfinv_data[1] = &ufunc_erfinv_ptr[2*1]
|
|
erfinv = np.PyUFunc_FromFuncAndData(ufunc_erfinv_loops, ufunc_erfinv_data, ufunc_erfinv_types, 2, 1, 1, 0, 'erfinv', ufunc_erfinv_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_eval_chebyc_loops[5]
|
|
cdef void *ufunc_eval_chebyc_ptr[10]
|
|
cdef void *ufunc_eval_chebyc_data[5]
|
|
cdef char ufunc_eval_chebyc_types[15]
|
|
cdef char *ufunc_eval_chebyc_doc = (
|
|
"eval_chebyc(n, x, out=None)\n"
|
|
"\n"
|
|
"Evaluate Chebyshev polynomial of the first kind on [-2, 2] at a\n"
|
|
"point.\n"
|
|
"\n"
|
|
"These polynomials are defined as\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" C_n(x) = 2 T_n(x/2)\n"
|
|
"\n"
|
|
"where :math:`T_n` is a Chebyshev polynomial of the first kind. See\n"
|
|
"22.5.11 in [AS]_ for details.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"n : array_like\n"
|
|
" Degree of the polynomial. If not an integer, the result is\n"
|
|
" determined via the relation to `eval_chebyt`.\n"
|
|
"x : array_like\n"
|
|
" Points at which to evaluate the Chebyshev polynomial\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"C : scalar or ndarray\n"
|
|
" Values of the Chebyshev polynomial\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"roots_chebyc : roots and quadrature weights of Chebyshev\n"
|
|
" polynomials of the first kind on [-2, 2]\n"
|
|
"chebyc : Chebyshev polynomial object\n"
|
|
"numpy.polynomial.chebyshev.Chebyshev : Chebyshev series\n"
|
|
"eval_chebyt : evaluate Chebycshev polynomials of the first kind\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
|
|
" Handbook of Mathematical Functions with Formulas,\n"
|
|
" Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> import scipy.special as sc\n"
|
|
"\n"
|
|
"They are a scaled version of the Chebyshev polynomials of the\n"
|
|
"first kind.\n"
|
|
"\n"
|
|
">>> x = np.linspace(-2, 2, 6)\n"
|
|
">>> sc.eval_chebyc(3, x)\n"
|
|
"array([-2. , 1.872, 1.136, -1.136, -1.872, 2. ])\n"
|
|
">>> 2 * sc.eval_chebyt(3, x / 2)\n"
|
|
"array([-2. , 1.872, 1.136, -1.136, -1.872, 2. ])")
|
|
ufunc_eval_chebyc_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
|
|
ufunc_eval_chebyc_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_eval_chebyc_loops[2] = <np.PyUFuncGenericFunction>loop_D_dD__As_fF_F
|
|
ufunc_eval_chebyc_loops[3] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_eval_chebyc_loops[4] = <np.PyUFuncGenericFunction>loop_D_dD__As_dD_D
|
|
ufunc_eval_chebyc_types[0] = <char>NPY_INTP
|
|
ufunc_eval_chebyc_types[1] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebyc_types[2] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebyc_types[3] = <char>NPY_FLOAT
|
|
ufunc_eval_chebyc_types[4] = <char>NPY_FLOAT
|
|
ufunc_eval_chebyc_types[5] = <char>NPY_FLOAT
|
|
ufunc_eval_chebyc_types[6] = <char>NPY_FLOAT
|
|
ufunc_eval_chebyc_types[7] = <char>NPY_CFLOAT
|
|
ufunc_eval_chebyc_types[8] = <char>NPY_CFLOAT
|
|
ufunc_eval_chebyc_types[9] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebyc_types[10] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebyc_types[11] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebyc_types[12] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebyc_types[13] = <char>NPY_CDOUBLE
|
|
ufunc_eval_chebyc_types[14] = <char>NPY_CDOUBLE
|
|
ufunc_eval_chebyc_ptr[2*0] = <void*>_func_eval_chebyc_l
|
|
ufunc_eval_chebyc_ptr[2*0+1] = <void*>(<char*>"eval_chebyc")
|
|
ufunc_eval_chebyc_ptr[2*1] = <void*>_func_eval_chebyc[double]
|
|
ufunc_eval_chebyc_ptr[2*1+1] = <void*>(<char*>"eval_chebyc")
|
|
ufunc_eval_chebyc_ptr[2*2] = <void*>_func_eval_chebyc[double_complex]
|
|
ufunc_eval_chebyc_ptr[2*2+1] = <void*>(<char*>"eval_chebyc")
|
|
ufunc_eval_chebyc_ptr[2*3] = <void*>_func_eval_chebyc[double]
|
|
ufunc_eval_chebyc_ptr[2*3+1] = <void*>(<char*>"eval_chebyc")
|
|
ufunc_eval_chebyc_ptr[2*4] = <void*>_func_eval_chebyc[double_complex]
|
|
ufunc_eval_chebyc_ptr[2*4+1] = <void*>(<char*>"eval_chebyc")
|
|
ufunc_eval_chebyc_data[0] = &ufunc_eval_chebyc_ptr[2*0]
|
|
ufunc_eval_chebyc_data[1] = &ufunc_eval_chebyc_ptr[2*1]
|
|
ufunc_eval_chebyc_data[2] = &ufunc_eval_chebyc_ptr[2*2]
|
|
ufunc_eval_chebyc_data[3] = &ufunc_eval_chebyc_ptr[2*3]
|
|
ufunc_eval_chebyc_data[4] = &ufunc_eval_chebyc_ptr[2*4]
|
|
eval_chebyc = np.PyUFunc_FromFuncAndData(ufunc_eval_chebyc_loops, ufunc_eval_chebyc_data, ufunc_eval_chebyc_types, 5, 2, 1, 0, 'eval_chebyc', ufunc_eval_chebyc_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_eval_chebys_loops[5]
|
|
cdef void *ufunc_eval_chebys_ptr[10]
|
|
cdef void *ufunc_eval_chebys_data[5]
|
|
cdef char ufunc_eval_chebys_types[15]
|
|
cdef char *ufunc_eval_chebys_doc = (
|
|
"eval_chebys(n, x, out=None)\n"
|
|
"\n"
|
|
"Evaluate Chebyshev polynomial of the second kind on [-2, 2] at a\n"
|
|
"point.\n"
|
|
"\n"
|
|
"These polynomials are defined as\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" S_n(x) = U_n(x/2)\n"
|
|
"\n"
|
|
"where :math:`U_n` is a Chebyshev polynomial of the second\n"
|
|
"kind. See 22.5.13 in [AS]_ for details.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"n : array_like\n"
|
|
" Degree of the polynomial. If not an integer, the result is\n"
|
|
" determined via the relation to `eval_chebyu`.\n"
|
|
"x : array_like\n"
|
|
" Points at which to evaluate the Chebyshev polynomial\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"S : scalar or ndarray\n"
|
|
" Values of the Chebyshev polynomial\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"roots_chebys : roots and quadrature weights of Chebyshev\n"
|
|
" polynomials of the second kind on [-2, 2]\n"
|
|
"chebys : Chebyshev polynomial object\n"
|
|
"eval_chebyu : evaluate Chebyshev polynomials of the second kind\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
|
|
" Handbook of Mathematical Functions with Formulas,\n"
|
|
" Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> import scipy.special as sc\n"
|
|
"\n"
|
|
"They are a scaled version of the Chebyshev polynomials of the\n"
|
|
"second kind.\n"
|
|
"\n"
|
|
">>> x = np.linspace(-2, 2, 6)\n"
|
|
">>> sc.eval_chebys(3, x)\n"
|
|
"array([-4. , 0.672, 0.736, -0.736, -0.672, 4. ])\n"
|
|
">>> sc.eval_chebyu(3, x / 2)\n"
|
|
"array([-4. , 0.672, 0.736, -0.736, -0.672, 4. ])")
|
|
ufunc_eval_chebys_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
|
|
ufunc_eval_chebys_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_eval_chebys_loops[2] = <np.PyUFuncGenericFunction>loop_D_dD__As_fF_F
|
|
ufunc_eval_chebys_loops[3] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_eval_chebys_loops[4] = <np.PyUFuncGenericFunction>loop_D_dD__As_dD_D
|
|
ufunc_eval_chebys_types[0] = <char>NPY_INTP
|
|
ufunc_eval_chebys_types[1] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebys_types[2] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebys_types[3] = <char>NPY_FLOAT
|
|
ufunc_eval_chebys_types[4] = <char>NPY_FLOAT
|
|
ufunc_eval_chebys_types[5] = <char>NPY_FLOAT
|
|
ufunc_eval_chebys_types[6] = <char>NPY_FLOAT
|
|
ufunc_eval_chebys_types[7] = <char>NPY_CFLOAT
|
|
ufunc_eval_chebys_types[8] = <char>NPY_CFLOAT
|
|
ufunc_eval_chebys_types[9] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebys_types[10] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebys_types[11] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebys_types[12] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebys_types[13] = <char>NPY_CDOUBLE
|
|
ufunc_eval_chebys_types[14] = <char>NPY_CDOUBLE
|
|
ufunc_eval_chebys_ptr[2*0] = <void*>_func_eval_chebys_l
|
|
ufunc_eval_chebys_ptr[2*0+1] = <void*>(<char*>"eval_chebys")
|
|
ufunc_eval_chebys_ptr[2*1] = <void*>_func_eval_chebys[double]
|
|
ufunc_eval_chebys_ptr[2*1+1] = <void*>(<char*>"eval_chebys")
|
|
ufunc_eval_chebys_ptr[2*2] = <void*>_func_eval_chebys[double_complex]
|
|
ufunc_eval_chebys_ptr[2*2+1] = <void*>(<char*>"eval_chebys")
|
|
ufunc_eval_chebys_ptr[2*3] = <void*>_func_eval_chebys[double]
|
|
ufunc_eval_chebys_ptr[2*3+1] = <void*>(<char*>"eval_chebys")
|
|
ufunc_eval_chebys_ptr[2*4] = <void*>_func_eval_chebys[double_complex]
|
|
ufunc_eval_chebys_ptr[2*4+1] = <void*>(<char*>"eval_chebys")
|
|
ufunc_eval_chebys_data[0] = &ufunc_eval_chebys_ptr[2*0]
|
|
ufunc_eval_chebys_data[1] = &ufunc_eval_chebys_ptr[2*1]
|
|
ufunc_eval_chebys_data[2] = &ufunc_eval_chebys_ptr[2*2]
|
|
ufunc_eval_chebys_data[3] = &ufunc_eval_chebys_ptr[2*3]
|
|
ufunc_eval_chebys_data[4] = &ufunc_eval_chebys_ptr[2*4]
|
|
eval_chebys = np.PyUFunc_FromFuncAndData(ufunc_eval_chebys_loops, ufunc_eval_chebys_data, ufunc_eval_chebys_types, 5, 2, 1, 0, 'eval_chebys', ufunc_eval_chebys_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_eval_chebyt_loops[5]
|
|
cdef void *ufunc_eval_chebyt_ptr[10]
|
|
cdef void *ufunc_eval_chebyt_data[5]
|
|
cdef char ufunc_eval_chebyt_types[15]
|
|
cdef char *ufunc_eval_chebyt_doc = (
|
|
"eval_chebyt(n, x, out=None)\n"
|
|
"\n"
|
|
"Evaluate Chebyshev polynomial of the first kind at a point.\n"
|
|
"\n"
|
|
"The Chebyshev polynomials of the first kind can be defined via the\n"
|
|
"Gauss hypergeometric function :math:`{}_2F_1` as\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" T_n(x) = {}_2F_1(n, -n; 1/2; (1 - x)/2).\n"
|
|
"\n"
|
|
"When :math:`n` is an integer the result is a polynomial of degree\n"
|
|
":math:`n`. See 22.5.47 in [AS]_ for details.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"n : array_like\n"
|
|
" Degree of the polynomial. If not an integer, the result is\n"
|
|
" determined via the relation to the Gauss hypergeometric\n"
|
|
" function.\n"
|
|
"x : array_like\n"
|
|
" Points at which to evaluate the Chebyshev polynomial\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"T : scalar or ndarray\n"
|
|
" Values of the Chebyshev polynomial\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"roots_chebyt : roots and quadrature weights of Chebyshev\n"
|
|
" polynomials of the first kind\n"
|
|
"chebyu : Chebychev polynomial object\n"
|
|
"eval_chebyu : evaluate Chebyshev polynomials of the second kind\n"
|
|
"hyp2f1 : Gauss hypergeometric function\n"
|
|
"numpy.polynomial.chebyshev.Chebyshev : Chebyshev series\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"This routine is numerically stable for `x` in ``[-1, 1]`` at least\n"
|
|
"up to order ``10000``.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
|
|
" Handbook of Mathematical Functions with Formulas,\n"
|
|
" Graphs, and Mathematical Tables. New York: Dover, 1972.")
|
|
ufunc_eval_chebyt_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
|
|
ufunc_eval_chebyt_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_eval_chebyt_loops[2] = <np.PyUFuncGenericFunction>loop_D_dD__As_fF_F
|
|
ufunc_eval_chebyt_loops[3] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_eval_chebyt_loops[4] = <np.PyUFuncGenericFunction>loop_D_dD__As_dD_D
|
|
ufunc_eval_chebyt_types[0] = <char>NPY_INTP
|
|
ufunc_eval_chebyt_types[1] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebyt_types[2] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebyt_types[3] = <char>NPY_FLOAT
|
|
ufunc_eval_chebyt_types[4] = <char>NPY_FLOAT
|
|
ufunc_eval_chebyt_types[5] = <char>NPY_FLOAT
|
|
ufunc_eval_chebyt_types[6] = <char>NPY_FLOAT
|
|
ufunc_eval_chebyt_types[7] = <char>NPY_CFLOAT
|
|
ufunc_eval_chebyt_types[8] = <char>NPY_CFLOAT
|
|
ufunc_eval_chebyt_types[9] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebyt_types[10] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebyt_types[11] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebyt_types[12] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebyt_types[13] = <char>NPY_CDOUBLE
|
|
ufunc_eval_chebyt_types[14] = <char>NPY_CDOUBLE
|
|
ufunc_eval_chebyt_ptr[2*0] = <void*>_func_eval_chebyt_l
|
|
ufunc_eval_chebyt_ptr[2*0+1] = <void*>(<char*>"eval_chebyt")
|
|
ufunc_eval_chebyt_ptr[2*1] = <void*>_func_eval_chebyt[double]
|
|
ufunc_eval_chebyt_ptr[2*1+1] = <void*>(<char*>"eval_chebyt")
|
|
ufunc_eval_chebyt_ptr[2*2] = <void*>_func_eval_chebyt[double_complex]
|
|
ufunc_eval_chebyt_ptr[2*2+1] = <void*>(<char*>"eval_chebyt")
|
|
ufunc_eval_chebyt_ptr[2*3] = <void*>_func_eval_chebyt[double]
|
|
ufunc_eval_chebyt_ptr[2*3+1] = <void*>(<char*>"eval_chebyt")
|
|
ufunc_eval_chebyt_ptr[2*4] = <void*>_func_eval_chebyt[double_complex]
|
|
ufunc_eval_chebyt_ptr[2*4+1] = <void*>(<char*>"eval_chebyt")
|
|
ufunc_eval_chebyt_data[0] = &ufunc_eval_chebyt_ptr[2*0]
|
|
ufunc_eval_chebyt_data[1] = &ufunc_eval_chebyt_ptr[2*1]
|
|
ufunc_eval_chebyt_data[2] = &ufunc_eval_chebyt_ptr[2*2]
|
|
ufunc_eval_chebyt_data[3] = &ufunc_eval_chebyt_ptr[2*3]
|
|
ufunc_eval_chebyt_data[4] = &ufunc_eval_chebyt_ptr[2*4]
|
|
eval_chebyt = np.PyUFunc_FromFuncAndData(ufunc_eval_chebyt_loops, ufunc_eval_chebyt_data, ufunc_eval_chebyt_types, 5, 2, 1, 0, 'eval_chebyt', ufunc_eval_chebyt_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_eval_chebyu_loops[5]
|
|
cdef void *ufunc_eval_chebyu_ptr[10]
|
|
cdef void *ufunc_eval_chebyu_data[5]
|
|
cdef char ufunc_eval_chebyu_types[15]
|
|
cdef char *ufunc_eval_chebyu_doc = (
|
|
"eval_chebyu(n, x, out=None)\n"
|
|
"\n"
|
|
"Evaluate Chebyshev polynomial of the second kind at a point.\n"
|
|
"\n"
|
|
"The Chebyshev polynomials of the second kind can be defined via\n"
|
|
"the Gauss hypergeometric function :math:`{}_2F_1` as\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" U_n(x) = (n + 1) {}_2F_1(-n, n + 2; 3/2; (1 - x)/2).\n"
|
|
"\n"
|
|
"When :math:`n` is an integer the result is a polynomial of degree\n"
|
|
":math:`n`. See 22.5.48 in [AS]_ for details.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"n : array_like\n"
|
|
" Degree of the polynomial. If not an integer, the result is\n"
|
|
" determined via the relation to the Gauss hypergeometric\n"
|
|
" function.\n"
|
|
"x : array_like\n"
|
|
" Points at which to evaluate the Chebyshev polynomial\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"U : scalar or ndarray\n"
|
|
" Values of the Chebyshev polynomial\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"roots_chebyu : roots and quadrature weights of Chebyshev\n"
|
|
" polynomials of the second kind\n"
|
|
"chebyu : Chebyshev polynomial object\n"
|
|
"eval_chebyt : evaluate Chebyshev polynomials of the first kind\n"
|
|
"hyp2f1 : Gauss hypergeometric function\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
|
|
" Handbook of Mathematical Functions with Formulas,\n"
|
|
" Graphs, and Mathematical Tables. New York: Dover, 1972.")
|
|
ufunc_eval_chebyu_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
|
|
ufunc_eval_chebyu_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_eval_chebyu_loops[2] = <np.PyUFuncGenericFunction>loop_D_dD__As_fF_F
|
|
ufunc_eval_chebyu_loops[3] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_eval_chebyu_loops[4] = <np.PyUFuncGenericFunction>loop_D_dD__As_dD_D
|
|
ufunc_eval_chebyu_types[0] = <char>NPY_INTP
|
|
ufunc_eval_chebyu_types[1] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebyu_types[2] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebyu_types[3] = <char>NPY_FLOAT
|
|
ufunc_eval_chebyu_types[4] = <char>NPY_FLOAT
|
|
ufunc_eval_chebyu_types[5] = <char>NPY_FLOAT
|
|
ufunc_eval_chebyu_types[6] = <char>NPY_FLOAT
|
|
ufunc_eval_chebyu_types[7] = <char>NPY_CFLOAT
|
|
ufunc_eval_chebyu_types[8] = <char>NPY_CFLOAT
|
|
ufunc_eval_chebyu_types[9] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebyu_types[10] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebyu_types[11] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebyu_types[12] = <char>NPY_DOUBLE
|
|
ufunc_eval_chebyu_types[13] = <char>NPY_CDOUBLE
|
|
ufunc_eval_chebyu_types[14] = <char>NPY_CDOUBLE
|
|
ufunc_eval_chebyu_ptr[2*0] = <void*>_func_eval_chebyu_l
|
|
ufunc_eval_chebyu_ptr[2*0+1] = <void*>(<char*>"eval_chebyu")
|
|
ufunc_eval_chebyu_ptr[2*1] = <void*>_func_eval_chebyu[double]
|
|
ufunc_eval_chebyu_ptr[2*1+1] = <void*>(<char*>"eval_chebyu")
|
|
ufunc_eval_chebyu_ptr[2*2] = <void*>_func_eval_chebyu[double_complex]
|
|
ufunc_eval_chebyu_ptr[2*2+1] = <void*>(<char*>"eval_chebyu")
|
|
ufunc_eval_chebyu_ptr[2*3] = <void*>_func_eval_chebyu[double]
|
|
ufunc_eval_chebyu_ptr[2*3+1] = <void*>(<char*>"eval_chebyu")
|
|
ufunc_eval_chebyu_ptr[2*4] = <void*>_func_eval_chebyu[double_complex]
|
|
ufunc_eval_chebyu_ptr[2*4+1] = <void*>(<char*>"eval_chebyu")
|
|
ufunc_eval_chebyu_data[0] = &ufunc_eval_chebyu_ptr[2*0]
|
|
ufunc_eval_chebyu_data[1] = &ufunc_eval_chebyu_ptr[2*1]
|
|
ufunc_eval_chebyu_data[2] = &ufunc_eval_chebyu_ptr[2*2]
|
|
ufunc_eval_chebyu_data[3] = &ufunc_eval_chebyu_ptr[2*3]
|
|
ufunc_eval_chebyu_data[4] = &ufunc_eval_chebyu_ptr[2*4]
|
|
eval_chebyu = np.PyUFunc_FromFuncAndData(ufunc_eval_chebyu_loops, ufunc_eval_chebyu_data, ufunc_eval_chebyu_types, 5, 2, 1, 0, 'eval_chebyu', ufunc_eval_chebyu_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_eval_gegenbauer_loops[5]
|
|
cdef void *ufunc_eval_gegenbauer_ptr[10]
|
|
cdef void *ufunc_eval_gegenbauer_data[5]
|
|
cdef char ufunc_eval_gegenbauer_types[20]
|
|
cdef char *ufunc_eval_gegenbauer_doc = (
|
|
"eval_gegenbauer(n, alpha, x, out=None)\n"
|
|
"\n"
|
|
"Evaluate Gegenbauer polynomial at a point.\n"
|
|
"\n"
|
|
"The Gegenbauer polynomials can be defined via the Gauss\n"
|
|
"hypergeometric function :math:`{}_2F_1` as\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" C_n^{(\\alpha)} = \\frac{(2\\alpha)_n}{\\Gamma(n + 1)}\n"
|
|
" {}_2F_1(-n, 2\\alpha + n; \\alpha + 1/2; (1 - z)/2).\n"
|
|
"\n"
|
|
"When :math:`n` is an integer the result is a polynomial of degree\n"
|
|
":math:`n`. See 22.5.46 in [AS]_ for details.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"n : array_like\n"
|
|
" Degree of the polynomial. If not an integer, the result is\n"
|
|
" determined via the relation to the Gauss hypergeometric\n"
|
|
" function.\n"
|
|
"alpha : array_like\n"
|
|
" Parameter\n"
|
|
"x : array_like\n"
|
|
" Points at which to evaluate the Gegenbauer polynomial\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"C : scalar or ndarray\n"
|
|
" Values of the Gegenbauer polynomial\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"roots_gegenbauer : roots and quadrature weights of Gegenbauer\n"
|
|
" polynomials\n"
|
|
"gegenbauer : Gegenbauer polynomial object\n"
|
|
"hyp2f1 : Gauss hypergeometric function\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
|
|
" Handbook of Mathematical Functions with Formulas,\n"
|
|
" Graphs, and Mathematical Tables. New York: Dover, 1972.")
|
|
ufunc_eval_gegenbauer_loops[0] = <np.PyUFuncGenericFunction>loop_d_pdd__As_pdd_d
|
|
ufunc_eval_gegenbauer_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_eval_gegenbauer_loops[2] = <np.PyUFuncGenericFunction>loop_D_ddD__As_ffF_F
|
|
ufunc_eval_gegenbauer_loops[3] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_eval_gegenbauer_loops[4] = <np.PyUFuncGenericFunction>loop_D_ddD__As_ddD_D
|
|
ufunc_eval_gegenbauer_types[0] = <char>NPY_INTP
|
|
ufunc_eval_gegenbauer_types[1] = <char>NPY_DOUBLE
|
|
ufunc_eval_gegenbauer_types[2] = <char>NPY_DOUBLE
|
|
ufunc_eval_gegenbauer_types[3] = <char>NPY_DOUBLE
|
|
ufunc_eval_gegenbauer_types[4] = <char>NPY_FLOAT
|
|
ufunc_eval_gegenbauer_types[5] = <char>NPY_FLOAT
|
|
ufunc_eval_gegenbauer_types[6] = <char>NPY_FLOAT
|
|
ufunc_eval_gegenbauer_types[7] = <char>NPY_FLOAT
|
|
ufunc_eval_gegenbauer_types[8] = <char>NPY_FLOAT
|
|
ufunc_eval_gegenbauer_types[9] = <char>NPY_FLOAT
|
|
ufunc_eval_gegenbauer_types[10] = <char>NPY_CFLOAT
|
|
ufunc_eval_gegenbauer_types[11] = <char>NPY_CFLOAT
|
|
ufunc_eval_gegenbauer_types[12] = <char>NPY_DOUBLE
|
|
ufunc_eval_gegenbauer_types[13] = <char>NPY_DOUBLE
|
|
ufunc_eval_gegenbauer_types[14] = <char>NPY_DOUBLE
|
|
ufunc_eval_gegenbauer_types[15] = <char>NPY_DOUBLE
|
|
ufunc_eval_gegenbauer_types[16] = <char>NPY_DOUBLE
|
|
ufunc_eval_gegenbauer_types[17] = <char>NPY_DOUBLE
|
|
ufunc_eval_gegenbauer_types[18] = <char>NPY_CDOUBLE
|
|
ufunc_eval_gegenbauer_types[19] = <char>NPY_CDOUBLE
|
|
ufunc_eval_gegenbauer_ptr[2*0] = <void*>_func_eval_gegenbauer_l
|
|
ufunc_eval_gegenbauer_ptr[2*0+1] = <void*>(<char*>"eval_gegenbauer")
|
|
ufunc_eval_gegenbauer_ptr[2*1] = <void*>_func_eval_gegenbauer[double]
|
|
ufunc_eval_gegenbauer_ptr[2*1+1] = <void*>(<char*>"eval_gegenbauer")
|
|
ufunc_eval_gegenbauer_ptr[2*2] = <void*>_func_eval_gegenbauer[double_complex]
|
|
ufunc_eval_gegenbauer_ptr[2*2+1] = <void*>(<char*>"eval_gegenbauer")
|
|
ufunc_eval_gegenbauer_ptr[2*3] = <void*>_func_eval_gegenbauer[double]
|
|
ufunc_eval_gegenbauer_ptr[2*3+1] = <void*>(<char*>"eval_gegenbauer")
|
|
ufunc_eval_gegenbauer_ptr[2*4] = <void*>_func_eval_gegenbauer[double_complex]
|
|
ufunc_eval_gegenbauer_ptr[2*4+1] = <void*>(<char*>"eval_gegenbauer")
|
|
ufunc_eval_gegenbauer_data[0] = &ufunc_eval_gegenbauer_ptr[2*0]
|
|
ufunc_eval_gegenbauer_data[1] = &ufunc_eval_gegenbauer_ptr[2*1]
|
|
ufunc_eval_gegenbauer_data[2] = &ufunc_eval_gegenbauer_ptr[2*2]
|
|
ufunc_eval_gegenbauer_data[3] = &ufunc_eval_gegenbauer_ptr[2*3]
|
|
ufunc_eval_gegenbauer_data[4] = &ufunc_eval_gegenbauer_ptr[2*4]
|
|
eval_gegenbauer = np.PyUFunc_FromFuncAndData(ufunc_eval_gegenbauer_loops, ufunc_eval_gegenbauer_data, ufunc_eval_gegenbauer_types, 5, 3, 1, 0, 'eval_gegenbauer', ufunc_eval_gegenbauer_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_eval_genlaguerre_loops[5]
|
|
cdef void *ufunc_eval_genlaguerre_ptr[10]
|
|
cdef void *ufunc_eval_genlaguerre_data[5]
|
|
cdef char ufunc_eval_genlaguerre_types[20]
|
|
cdef char *ufunc_eval_genlaguerre_doc = (
|
|
"eval_genlaguerre(n, alpha, x, out=None)\n"
|
|
"\n"
|
|
"Evaluate generalized Laguerre polynomial at a point.\n"
|
|
"\n"
|
|
"The generalized Laguerre polynomials can be defined via the\n"
|
|
"confluent hypergeometric function :math:`{}_1F_1` as\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" L_n^{(\\alpha)}(x) = \\binom{n + \\alpha}{n}\n"
|
|
" {}_1F_1(-n, \\alpha + 1, x).\n"
|
|
"\n"
|
|
"When :math:`n` is an integer the result is a polynomial of degree\n"
|
|
":math:`n`. See 22.5.54 in [AS]_ for details. The Laguerre\n"
|
|
"polynomials are the special case where :math:`\\alpha = 0`.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"n : array_like\n"
|
|
" Degree of the polynomial. If not an integer, the result is\n"
|
|
" determined via the relation to the confluent hypergeometric\n"
|
|
" function.\n"
|
|
"alpha : array_like\n"
|
|
" Parameter; must have ``alpha > -1``\n"
|
|
"x : array_like\n"
|
|
" Points at which to evaluate the generalized Laguerre\n"
|
|
" polynomial\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"L : scalar or ndarray\n"
|
|
" Values of the generalized Laguerre polynomial\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"roots_genlaguerre : roots and quadrature weights of generalized\n"
|
|
" Laguerre polynomials\n"
|
|
"genlaguerre : generalized Laguerre polynomial object\n"
|
|
"hyp1f1 : confluent hypergeometric function\n"
|
|
"eval_laguerre : evaluate Laguerre polynomials\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
|
|
" Handbook of Mathematical Functions with Formulas,\n"
|
|
" Graphs, and Mathematical Tables. New York: Dover, 1972.")
|
|
ufunc_eval_genlaguerre_loops[0] = <np.PyUFuncGenericFunction>loop_d_pdd__As_pdd_d
|
|
ufunc_eval_genlaguerre_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_eval_genlaguerre_loops[2] = <np.PyUFuncGenericFunction>loop_D_ddD__As_ffF_F
|
|
ufunc_eval_genlaguerre_loops[3] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_eval_genlaguerre_loops[4] = <np.PyUFuncGenericFunction>loop_D_ddD__As_ddD_D
|
|
ufunc_eval_genlaguerre_types[0] = <char>NPY_INTP
|
|
ufunc_eval_genlaguerre_types[1] = <char>NPY_DOUBLE
|
|
ufunc_eval_genlaguerre_types[2] = <char>NPY_DOUBLE
|
|
ufunc_eval_genlaguerre_types[3] = <char>NPY_DOUBLE
|
|
ufunc_eval_genlaguerre_types[4] = <char>NPY_FLOAT
|
|
ufunc_eval_genlaguerre_types[5] = <char>NPY_FLOAT
|
|
ufunc_eval_genlaguerre_types[6] = <char>NPY_FLOAT
|
|
ufunc_eval_genlaguerre_types[7] = <char>NPY_FLOAT
|
|
ufunc_eval_genlaguerre_types[8] = <char>NPY_FLOAT
|
|
ufunc_eval_genlaguerre_types[9] = <char>NPY_FLOAT
|
|
ufunc_eval_genlaguerre_types[10] = <char>NPY_CFLOAT
|
|
ufunc_eval_genlaguerre_types[11] = <char>NPY_CFLOAT
|
|
ufunc_eval_genlaguerre_types[12] = <char>NPY_DOUBLE
|
|
ufunc_eval_genlaguerre_types[13] = <char>NPY_DOUBLE
|
|
ufunc_eval_genlaguerre_types[14] = <char>NPY_DOUBLE
|
|
ufunc_eval_genlaguerre_types[15] = <char>NPY_DOUBLE
|
|
ufunc_eval_genlaguerre_types[16] = <char>NPY_DOUBLE
|
|
ufunc_eval_genlaguerre_types[17] = <char>NPY_DOUBLE
|
|
ufunc_eval_genlaguerre_types[18] = <char>NPY_CDOUBLE
|
|
ufunc_eval_genlaguerre_types[19] = <char>NPY_CDOUBLE
|
|
ufunc_eval_genlaguerre_ptr[2*0] = <void*>_func_eval_genlaguerre_l
|
|
ufunc_eval_genlaguerre_ptr[2*0+1] = <void*>(<char*>"eval_genlaguerre")
|
|
ufunc_eval_genlaguerre_ptr[2*1] = <void*>_func_eval_genlaguerre[double]
|
|
ufunc_eval_genlaguerre_ptr[2*1+1] = <void*>(<char*>"eval_genlaguerre")
|
|
ufunc_eval_genlaguerre_ptr[2*2] = <void*>_func_eval_genlaguerre[double_complex]
|
|
ufunc_eval_genlaguerre_ptr[2*2+1] = <void*>(<char*>"eval_genlaguerre")
|
|
ufunc_eval_genlaguerre_ptr[2*3] = <void*>_func_eval_genlaguerre[double]
|
|
ufunc_eval_genlaguerre_ptr[2*3+1] = <void*>(<char*>"eval_genlaguerre")
|
|
ufunc_eval_genlaguerre_ptr[2*4] = <void*>_func_eval_genlaguerre[double_complex]
|
|
ufunc_eval_genlaguerre_ptr[2*4+1] = <void*>(<char*>"eval_genlaguerre")
|
|
ufunc_eval_genlaguerre_data[0] = &ufunc_eval_genlaguerre_ptr[2*0]
|
|
ufunc_eval_genlaguerre_data[1] = &ufunc_eval_genlaguerre_ptr[2*1]
|
|
ufunc_eval_genlaguerre_data[2] = &ufunc_eval_genlaguerre_ptr[2*2]
|
|
ufunc_eval_genlaguerre_data[3] = &ufunc_eval_genlaguerre_ptr[2*3]
|
|
ufunc_eval_genlaguerre_data[4] = &ufunc_eval_genlaguerre_ptr[2*4]
|
|
eval_genlaguerre = np.PyUFunc_FromFuncAndData(ufunc_eval_genlaguerre_loops, ufunc_eval_genlaguerre_data, ufunc_eval_genlaguerre_types, 5, 3, 1, 0, 'eval_genlaguerre', ufunc_eval_genlaguerre_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_eval_hermite_loops[1]
|
|
cdef void *ufunc_eval_hermite_ptr[2]
|
|
cdef void *ufunc_eval_hermite_data[1]
|
|
cdef char ufunc_eval_hermite_types[3]
|
|
cdef char *ufunc_eval_hermite_doc = (
|
|
"eval_hermite(n, x, out=None)\n"
|
|
"\n"
|
|
"Evaluate physicist's Hermite polynomial at a point.\n"
|
|
"\n"
|
|
"Defined by\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" H_n(x) = (-1)^n e^{x^2} \\frac{d^n}{dx^n} e^{-x^2};\n"
|
|
"\n"
|
|
":math:`H_n` is a polynomial of degree :math:`n`. See 22.11.7 in\n"
|
|
"[AS]_ for details.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"n : array_like\n"
|
|
" Degree of the polynomial\n"
|
|
"x : array_like\n"
|
|
" Points at which to evaluate the Hermite polynomial\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"H : scalar or ndarray\n"
|
|
" Values of the Hermite polynomial\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"roots_hermite : roots and quadrature weights of physicist's\n"
|
|
" Hermite polynomials\n"
|
|
"hermite : physicist's Hermite polynomial object\n"
|
|
"numpy.polynomial.hermite.Hermite : Physicist's Hermite series\n"
|
|
"eval_hermitenorm : evaluate Probabilist's Hermite polynomials\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
|
|
" Handbook of Mathematical Functions with Formulas,\n"
|
|
" Graphs, and Mathematical Tables. New York: Dover, 1972.")
|
|
ufunc_eval_hermite_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
|
|
ufunc_eval_hermite_types[0] = <char>NPY_INTP
|
|
ufunc_eval_hermite_types[1] = <char>NPY_DOUBLE
|
|
ufunc_eval_hermite_types[2] = <char>NPY_DOUBLE
|
|
ufunc_eval_hermite_ptr[2*0] = <void*>_func_eval_hermite
|
|
ufunc_eval_hermite_ptr[2*0+1] = <void*>(<char*>"eval_hermite")
|
|
ufunc_eval_hermite_data[0] = &ufunc_eval_hermite_ptr[2*0]
|
|
eval_hermite = np.PyUFunc_FromFuncAndData(ufunc_eval_hermite_loops, ufunc_eval_hermite_data, ufunc_eval_hermite_types, 1, 2, 1, 0, 'eval_hermite', ufunc_eval_hermite_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_eval_hermitenorm_loops[1]
|
|
cdef void *ufunc_eval_hermitenorm_ptr[2]
|
|
cdef void *ufunc_eval_hermitenorm_data[1]
|
|
cdef char ufunc_eval_hermitenorm_types[3]
|
|
cdef char *ufunc_eval_hermitenorm_doc = (
|
|
"eval_hermitenorm(n, x, out=None)\n"
|
|
"\n"
|
|
"Evaluate probabilist's (normalized) Hermite polynomial at a\n"
|
|
"point.\n"
|
|
"\n"
|
|
"Defined by\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" He_n(x) = (-1)^n e^{x^2/2} \\frac{d^n}{dx^n} e^{-x^2/2};\n"
|
|
"\n"
|
|
":math:`He_n` is a polynomial of degree :math:`n`. See 22.11.8 in\n"
|
|
"[AS]_ for details.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"n : array_like\n"
|
|
" Degree of the polynomial\n"
|
|
"x : array_like\n"
|
|
" Points at which to evaluate the Hermite polynomial\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"He : scalar or ndarray\n"
|
|
" Values of the Hermite polynomial\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"roots_hermitenorm : roots and quadrature weights of probabilist's\n"
|
|
" Hermite polynomials\n"
|
|
"hermitenorm : probabilist's Hermite polynomial object\n"
|
|
"numpy.polynomial.hermite_e.HermiteE : Probabilist's Hermite series\n"
|
|
"eval_hermite : evaluate physicist's Hermite polynomials\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
|
|
" Handbook of Mathematical Functions with Formulas,\n"
|
|
" Graphs, and Mathematical Tables. New York: Dover, 1972.")
|
|
ufunc_eval_hermitenorm_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
|
|
ufunc_eval_hermitenorm_types[0] = <char>NPY_INTP
|
|
ufunc_eval_hermitenorm_types[1] = <char>NPY_DOUBLE
|
|
ufunc_eval_hermitenorm_types[2] = <char>NPY_DOUBLE
|
|
ufunc_eval_hermitenorm_ptr[2*0] = <void*>_func_eval_hermitenorm
|
|
ufunc_eval_hermitenorm_ptr[2*0+1] = <void*>(<char*>"eval_hermitenorm")
|
|
ufunc_eval_hermitenorm_data[0] = &ufunc_eval_hermitenorm_ptr[2*0]
|
|
eval_hermitenorm = np.PyUFunc_FromFuncAndData(ufunc_eval_hermitenorm_loops, ufunc_eval_hermitenorm_data, ufunc_eval_hermitenorm_types, 1, 2, 1, 0, 'eval_hermitenorm', ufunc_eval_hermitenorm_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_eval_jacobi_loops[5]
|
|
cdef void *ufunc_eval_jacobi_ptr[10]
|
|
cdef void *ufunc_eval_jacobi_data[5]
|
|
cdef char ufunc_eval_jacobi_types[25]
|
|
cdef char *ufunc_eval_jacobi_doc = (
|
|
"eval_jacobi(n, alpha, beta, x, out=None)\n"
|
|
"\n"
|
|
"Evaluate Jacobi polynomial at a point.\n"
|
|
"\n"
|
|
"The Jacobi polynomials can be defined via the Gauss hypergeometric\n"
|
|
"function :math:`{}_2F_1` as\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" P_n^{(\\alpha, \\beta)}(x) = \\frac{(\\alpha + 1)_n}{\\Gamma(n + 1)}\n"
|
|
" {}_2F_1(-n, 1 + \\alpha + \\beta + n; \\alpha + 1; (1 - z)/2)\n"
|
|
"\n"
|
|
"where :math:`(\\cdot)_n` is the Pochhammer symbol; see `poch`. When\n"
|
|
":math:`n` is an integer the result is a polynomial of degree\n"
|
|
":math:`n`. See 22.5.42 in [AS]_ for details.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"n : array_like\n"
|
|
" Degree of the polynomial. If not an integer the result is\n"
|
|
" determined via the relation to the Gauss hypergeometric\n"
|
|
" function.\n"
|
|
"alpha : array_like\n"
|
|
" Parameter\n"
|
|
"beta : array_like\n"
|
|
" Parameter\n"
|
|
"x : array_like\n"
|
|
" Points at which to evaluate the polynomial\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"P : scalar or ndarray\n"
|
|
" Values of the Jacobi polynomial\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"roots_jacobi : roots and quadrature weights of Jacobi polynomials\n"
|
|
"jacobi : Jacobi polynomial object\n"
|
|
"hyp2f1 : Gauss hypergeometric function\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
|
|
" Handbook of Mathematical Functions with Formulas,\n"
|
|
" Graphs, and Mathematical Tables. New York: Dover, 1972.")
|
|
ufunc_eval_jacobi_loops[0] = <np.PyUFuncGenericFunction>loop_d_pddd__As_pddd_d
|
|
ufunc_eval_jacobi_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_ffff_f
|
|
ufunc_eval_jacobi_loops[2] = <np.PyUFuncGenericFunction>loop_D_dddD__As_fffF_F
|
|
ufunc_eval_jacobi_loops[3] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
|
|
ufunc_eval_jacobi_loops[4] = <np.PyUFuncGenericFunction>loop_D_dddD__As_dddD_D
|
|
ufunc_eval_jacobi_types[0] = <char>NPY_INTP
|
|
ufunc_eval_jacobi_types[1] = <char>NPY_DOUBLE
|
|
ufunc_eval_jacobi_types[2] = <char>NPY_DOUBLE
|
|
ufunc_eval_jacobi_types[3] = <char>NPY_DOUBLE
|
|
ufunc_eval_jacobi_types[4] = <char>NPY_DOUBLE
|
|
ufunc_eval_jacobi_types[5] = <char>NPY_FLOAT
|
|
ufunc_eval_jacobi_types[6] = <char>NPY_FLOAT
|
|
ufunc_eval_jacobi_types[7] = <char>NPY_FLOAT
|
|
ufunc_eval_jacobi_types[8] = <char>NPY_FLOAT
|
|
ufunc_eval_jacobi_types[9] = <char>NPY_FLOAT
|
|
ufunc_eval_jacobi_types[10] = <char>NPY_FLOAT
|
|
ufunc_eval_jacobi_types[11] = <char>NPY_FLOAT
|
|
ufunc_eval_jacobi_types[12] = <char>NPY_FLOAT
|
|
ufunc_eval_jacobi_types[13] = <char>NPY_CFLOAT
|
|
ufunc_eval_jacobi_types[14] = <char>NPY_CFLOAT
|
|
ufunc_eval_jacobi_types[15] = <char>NPY_DOUBLE
|
|
ufunc_eval_jacobi_types[16] = <char>NPY_DOUBLE
|
|
ufunc_eval_jacobi_types[17] = <char>NPY_DOUBLE
|
|
ufunc_eval_jacobi_types[18] = <char>NPY_DOUBLE
|
|
ufunc_eval_jacobi_types[19] = <char>NPY_DOUBLE
|
|
ufunc_eval_jacobi_types[20] = <char>NPY_DOUBLE
|
|
ufunc_eval_jacobi_types[21] = <char>NPY_DOUBLE
|
|
ufunc_eval_jacobi_types[22] = <char>NPY_DOUBLE
|
|
ufunc_eval_jacobi_types[23] = <char>NPY_CDOUBLE
|
|
ufunc_eval_jacobi_types[24] = <char>NPY_CDOUBLE
|
|
ufunc_eval_jacobi_ptr[2*0] = <void*>_func_eval_jacobi_l
|
|
ufunc_eval_jacobi_ptr[2*0+1] = <void*>(<char*>"eval_jacobi")
|
|
ufunc_eval_jacobi_ptr[2*1] = <void*>_func_eval_jacobi[double]
|
|
ufunc_eval_jacobi_ptr[2*1+1] = <void*>(<char*>"eval_jacobi")
|
|
ufunc_eval_jacobi_ptr[2*2] = <void*>_func_eval_jacobi[double_complex]
|
|
ufunc_eval_jacobi_ptr[2*2+1] = <void*>(<char*>"eval_jacobi")
|
|
ufunc_eval_jacobi_ptr[2*3] = <void*>_func_eval_jacobi[double]
|
|
ufunc_eval_jacobi_ptr[2*3+1] = <void*>(<char*>"eval_jacobi")
|
|
ufunc_eval_jacobi_ptr[2*4] = <void*>_func_eval_jacobi[double_complex]
|
|
ufunc_eval_jacobi_ptr[2*4+1] = <void*>(<char*>"eval_jacobi")
|
|
ufunc_eval_jacobi_data[0] = &ufunc_eval_jacobi_ptr[2*0]
|
|
ufunc_eval_jacobi_data[1] = &ufunc_eval_jacobi_ptr[2*1]
|
|
ufunc_eval_jacobi_data[2] = &ufunc_eval_jacobi_ptr[2*2]
|
|
ufunc_eval_jacobi_data[3] = &ufunc_eval_jacobi_ptr[2*3]
|
|
ufunc_eval_jacobi_data[4] = &ufunc_eval_jacobi_ptr[2*4]
|
|
eval_jacobi = np.PyUFunc_FromFuncAndData(ufunc_eval_jacobi_loops, ufunc_eval_jacobi_data, ufunc_eval_jacobi_types, 5, 4, 1, 0, 'eval_jacobi', ufunc_eval_jacobi_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_eval_laguerre_loops[5]
|
|
cdef void *ufunc_eval_laguerre_ptr[10]
|
|
cdef void *ufunc_eval_laguerre_data[5]
|
|
cdef char ufunc_eval_laguerre_types[15]
|
|
cdef char *ufunc_eval_laguerre_doc = (
|
|
"eval_laguerre(n, x, out=None)\n"
|
|
"\n"
|
|
"Evaluate Laguerre polynomial at a point.\n"
|
|
"\n"
|
|
"The Laguerre polynomials can be defined via the confluent\n"
|
|
"hypergeometric function :math:`{}_1F_1` as\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" L_n(x) = {}_1F_1(-n, 1, x).\n"
|
|
"\n"
|
|
"See 22.5.16 and 22.5.54 in [AS]_ for details. When :math:`n` is an\n"
|
|
"integer the result is a polynomial of degree :math:`n`.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"n : array_like\n"
|
|
" Degree of the polynomial. If not an integer the result is\n"
|
|
" determined via the relation to the confluent hypergeometric\n"
|
|
" function.\n"
|
|
"x : array_like\n"
|
|
" Points at which to evaluate the Laguerre polynomial\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"L : scalar or ndarray\n"
|
|
" Values of the Laguerre polynomial\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"roots_laguerre : roots and quadrature weights of Laguerre\n"
|
|
" polynomials\n"
|
|
"laguerre : Laguerre polynomial object\n"
|
|
"numpy.polynomial.laguerre.Laguerre : Laguerre series\n"
|
|
"eval_genlaguerre : evaluate generalized Laguerre polynomials\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
|
|
" Handbook of Mathematical Functions with Formulas,\n"
|
|
" Graphs, and Mathematical Tables. New York: Dover, 1972.")
|
|
ufunc_eval_laguerre_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
|
|
ufunc_eval_laguerre_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_eval_laguerre_loops[2] = <np.PyUFuncGenericFunction>loop_D_dD__As_fF_F
|
|
ufunc_eval_laguerre_loops[3] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_eval_laguerre_loops[4] = <np.PyUFuncGenericFunction>loop_D_dD__As_dD_D
|
|
ufunc_eval_laguerre_types[0] = <char>NPY_INTP
|
|
ufunc_eval_laguerre_types[1] = <char>NPY_DOUBLE
|
|
ufunc_eval_laguerre_types[2] = <char>NPY_DOUBLE
|
|
ufunc_eval_laguerre_types[3] = <char>NPY_FLOAT
|
|
ufunc_eval_laguerre_types[4] = <char>NPY_FLOAT
|
|
ufunc_eval_laguerre_types[5] = <char>NPY_FLOAT
|
|
ufunc_eval_laguerre_types[6] = <char>NPY_FLOAT
|
|
ufunc_eval_laguerre_types[7] = <char>NPY_CFLOAT
|
|
ufunc_eval_laguerre_types[8] = <char>NPY_CFLOAT
|
|
ufunc_eval_laguerre_types[9] = <char>NPY_DOUBLE
|
|
ufunc_eval_laguerre_types[10] = <char>NPY_DOUBLE
|
|
ufunc_eval_laguerre_types[11] = <char>NPY_DOUBLE
|
|
ufunc_eval_laguerre_types[12] = <char>NPY_DOUBLE
|
|
ufunc_eval_laguerre_types[13] = <char>NPY_CDOUBLE
|
|
ufunc_eval_laguerre_types[14] = <char>NPY_CDOUBLE
|
|
ufunc_eval_laguerre_ptr[2*0] = <void*>_func_eval_laguerre_l
|
|
ufunc_eval_laguerre_ptr[2*0+1] = <void*>(<char*>"eval_laguerre")
|
|
ufunc_eval_laguerre_ptr[2*1] = <void*>_func_eval_laguerre[double]
|
|
ufunc_eval_laguerre_ptr[2*1+1] = <void*>(<char*>"eval_laguerre")
|
|
ufunc_eval_laguerre_ptr[2*2] = <void*>_func_eval_laguerre[double_complex]
|
|
ufunc_eval_laguerre_ptr[2*2+1] = <void*>(<char*>"eval_laguerre")
|
|
ufunc_eval_laguerre_ptr[2*3] = <void*>_func_eval_laguerre[double]
|
|
ufunc_eval_laguerre_ptr[2*3+1] = <void*>(<char*>"eval_laguerre")
|
|
ufunc_eval_laguerre_ptr[2*4] = <void*>_func_eval_laguerre[double_complex]
|
|
ufunc_eval_laguerre_ptr[2*4+1] = <void*>(<char*>"eval_laguerre")
|
|
ufunc_eval_laguerre_data[0] = &ufunc_eval_laguerre_ptr[2*0]
|
|
ufunc_eval_laguerre_data[1] = &ufunc_eval_laguerre_ptr[2*1]
|
|
ufunc_eval_laguerre_data[2] = &ufunc_eval_laguerre_ptr[2*2]
|
|
ufunc_eval_laguerre_data[3] = &ufunc_eval_laguerre_ptr[2*3]
|
|
ufunc_eval_laguerre_data[4] = &ufunc_eval_laguerre_ptr[2*4]
|
|
eval_laguerre = np.PyUFunc_FromFuncAndData(ufunc_eval_laguerre_loops, ufunc_eval_laguerre_data, ufunc_eval_laguerre_types, 5, 2, 1, 0, 'eval_laguerre', ufunc_eval_laguerre_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_eval_legendre_loops[5]
|
|
cdef void *ufunc_eval_legendre_ptr[10]
|
|
cdef void *ufunc_eval_legendre_data[5]
|
|
cdef char ufunc_eval_legendre_types[15]
|
|
cdef char *ufunc_eval_legendre_doc = (
|
|
"eval_legendre(n, x, out=None)\n"
|
|
"\n"
|
|
"Evaluate Legendre polynomial at a point.\n"
|
|
"\n"
|
|
"The Legendre polynomials can be defined via the Gauss\n"
|
|
"hypergeometric function :math:`{}_2F_1` as\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" P_n(x) = {}_2F_1(-n, n + 1; 1; (1 - x)/2).\n"
|
|
"\n"
|
|
"When :math:`n` is an integer the result is a polynomial of degree\n"
|
|
":math:`n`. See 22.5.49 in [AS]_ for details.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"n : array_like\n"
|
|
" Degree of the polynomial. If not an integer, the result is\n"
|
|
" determined via the relation to the Gauss hypergeometric\n"
|
|
" function.\n"
|
|
"x : array_like\n"
|
|
" Points at which to evaluate the Legendre polynomial\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"P : scalar or ndarray\n"
|
|
" Values of the Legendre polynomial\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"roots_legendre : roots and quadrature weights of Legendre\n"
|
|
" polynomials\n"
|
|
"legendre : Legendre polynomial object\n"
|
|
"hyp2f1 : Gauss hypergeometric function\n"
|
|
"numpy.polynomial.legendre.Legendre : Legendre series\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
|
|
" Handbook of Mathematical Functions with Formulas,\n"
|
|
" Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import eval_legendre\n"
|
|
"\n"
|
|
"Evaluate the zero-order Legendre polynomial at x = 0\n"
|
|
"\n"
|
|
">>> eval_legendre(0, 0)\n"
|
|
"1.0\n"
|
|
"\n"
|
|
"Evaluate the first-order Legendre polynomial between -1 and 1\n"
|
|
"\n"
|
|
">>> X = np.linspace(-1, 1, 5) # Domain of Legendre polynomials\n"
|
|
">>> eval_legendre(1, X)\n"
|
|
"array([-1. , -0.5, 0. , 0.5, 1. ])\n"
|
|
"\n"
|
|
"Evaluate Legendre polynomials of order 0 through 4 at x = 0\n"
|
|
"\n"
|
|
">>> N = range(0, 5)\n"
|
|
">>> eval_legendre(N, 0)\n"
|
|
"array([ 1. , 0. , -0.5 , 0. , 0.375])\n"
|
|
"\n"
|
|
"Plot Legendre polynomials of order 0 through 4\n"
|
|
"\n"
|
|
">>> X = np.linspace(-1, 1)\n"
|
|
"\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
">>> for n in range(0, 5):\n"
|
|
"... y = eval_legendre(n, X)\n"
|
|
"... plt.plot(X, y, label=r'$P_{}(x)$'.format(n))\n"
|
|
"\n"
|
|
">>> plt.title(\"Legendre Polynomials\")\n"
|
|
">>> plt.xlabel(\"x\")\n"
|
|
">>> plt.ylabel(r'$P_n(x)$')\n"
|
|
">>> plt.legend(loc='lower right')\n"
|
|
">>> plt.show()")
|
|
ufunc_eval_legendre_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
|
|
ufunc_eval_legendre_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_eval_legendre_loops[2] = <np.PyUFuncGenericFunction>loop_D_dD__As_fF_F
|
|
ufunc_eval_legendre_loops[3] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_eval_legendre_loops[4] = <np.PyUFuncGenericFunction>loop_D_dD__As_dD_D
|
|
ufunc_eval_legendre_types[0] = <char>NPY_INTP
|
|
ufunc_eval_legendre_types[1] = <char>NPY_DOUBLE
|
|
ufunc_eval_legendre_types[2] = <char>NPY_DOUBLE
|
|
ufunc_eval_legendre_types[3] = <char>NPY_FLOAT
|
|
ufunc_eval_legendre_types[4] = <char>NPY_FLOAT
|
|
ufunc_eval_legendre_types[5] = <char>NPY_FLOAT
|
|
ufunc_eval_legendre_types[6] = <char>NPY_FLOAT
|
|
ufunc_eval_legendre_types[7] = <char>NPY_CFLOAT
|
|
ufunc_eval_legendre_types[8] = <char>NPY_CFLOAT
|
|
ufunc_eval_legendre_types[9] = <char>NPY_DOUBLE
|
|
ufunc_eval_legendre_types[10] = <char>NPY_DOUBLE
|
|
ufunc_eval_legendre_types[11] = <char>NPY_DOUBLE
|
|
ufunc_eval_legendre_types[12] = <char>NPY_DOUBLE
|
|
ufunc_eval_legendre_types[13] = <char>NPY_CDOUBLE
|
|
ufunc_eval_legendre_types[14] = <char>NPY_CDOUBLE
|
|
ufunc_eval_legendre_ptr[2*0] = <void*>_func_eval_legendre_l
|
|
ufunc_eval_legendre_ptr[2*0+1] = <void*>(<char*>"eval_legendre")
|
|
ufunc_eval_legendre_ptr[2*1] = <void*>_func_eval_legendre[double]
|
|
ufunc_eval_legendre_ptr[2*1+1] = <void*>(<char*>"eval_legendre")
|
|
ufunc_eval_legendre_ptr[2*2] = <void*>_func_eval_legendre[double_complex]
|
|
ufunc_eval_legendre_ptr[2*2+1] = <void*>(<char*>"eval_legendre")
|
|
ufunc_eval_legendre_ptr[2*3] = <void*>_func_eval_legendre[double]
|
|
ufunc_eval_legendre_ptr[2*3+1] = <void*>(<char*>"eval_legendre")
|
|
ufunc_eval_legendre_ptr[2*4] = <void*>_func_eval_legendre[double_complex]
|
|
ufunc_eval_legendre_ptr[2*4+1] = <void*>(<char*>"eval_legendre")
|
|
ufunc_eval_legendre_data[0] = &ufunc_eval_legendre_ptr[2*0]
|
|
ufunc_eval_legendre_data[1] = &ufunc_eval_legendre_ptr[2*1]
|
|
ufunc_eval_legendre_data[2] = &ufunc_eval_legendre_ptr[2*2]
|
|
ufunc_eval_legendre_data[3] = &ufunc_eval_legendre_ptr[2*3]
|
|
ufunc_eval_legendre_data[4] = &ufunc_eval_legendre_ptr[2*4]
|
|
eval_legendre = np.PyUFunc_FromFuncAndData(ufunc_eval_legendre_loops, ufunc_eval_legendre_data, ufunc_eval_legendre_types, 5, 2, 1, 0, 'eval_legendre', ufunc_eval_legendre_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_eval_sh_chebyt_loops[5]
|
|
cdef void *ufunc_eval_sh_chebyt_ptr[10]
|
|
cdef void *ufunc_eval_sh_chebyt_data[5]
|
|
cdef char ufunc_eval_sh_chebyt_types[15]
|
|
cdef char *ufunc_eval_sh_chebyt_doc = (
|
|
"eval_sh_chebyt(n, x, out=None)\n"
|
|
"\n"
|
|
"Evaluate shifted Chebyshev polynomial of the first kind at a\n"
|
|
"point.\n"
|
|
"\n"
|
|
"These polynomials are defined as\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" T_n^*(x) = T_n(2x - 1)\n"
|
|
"\n"
|
|
"where :math:`T_n` is a Chebyshev polynomial of the first kind. See\n"
|
|
"22.5.14 in [AS]_ for details.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"n : array_like\n"
|
|
" Degree of the polynomial. If not an integer, the result is\n"
|
|
" determined via the relation to `eval_chebyt`.\n"
|
|
"x : array_like\n"
|
|
" Points at which to evaluate the shifted Chebyshev polynomial\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"T : scalar or ndarray\n"
|
|
" Values of the shifted Chebyshev polynomial\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"roots_sh_chebyt : roots and quadrature weights of shifted\n"
|
|
" Chebyshev polynomials of the first kind\n"
|
|
"sh_chebyt : shifted Chebyshev polynomial object\n"
|
|
"eval_chebyt : evaluate Chebyshev polynomials of the first kind\n"
|
|
"numpy.polynomial.chebyshev.Chebyshev : Chebyshev series\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
|
|
" Handbook of Mathematical Functions with Formulas,\n"
|
|
" Graphs, and Mathematical Tables. New York: Dover, 1972.")
|
|
ufunc_eval_sh_chebyt_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
|
|
ufunc_eval_sh_chebyt_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_eval_sh_chebyt_loops[2] = <np.PyUFuncGenericFunction>loop_D_dD__As_fF_F
|
|
ufunc_eval_sh_chebyt_loops[3] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_eval_sh_chebyt_loops[4] = <np.PyUFuncGenericFunction>loop_D_dD__As_dD_D
|
|
ufunc_eval_sh_chebyt_types[0] = <char>NPY_INTP
|
|
ufunc_eval_sh_chebyt_types[1] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_chebyt_types[2] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_chebyt_types[3] = <char>NPY_FLOAT
|
|
ufunc_eval_sh_chebyt_types[4] = <char>NPY_FLOAT
|
|
ufunc_eval_sh_chebyt_types[5] = <char>NPY_FLOAT
|
|
ufunc_eval_sh_chebyt_types[6] = <char>NPY_FLOAT
|
|
ufunc_eval_sh_chebyt_types[7] = <char>NPY_CFLOAT
|
|
ufunc_eval_sh_chebyt_types[8] = <char>NPY_CFLOAT
|
|
ufunc_eval_sh_chebyt_types[9] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_chebyt_types[10] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_chebyt_types[11] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_chebyt_types[12] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_chebyt_types[13] = <char>NPY_CDOUBLE
|
|
ufunc_eval_sh_chebyt_types[14] = <char>NPY_CDOUBLE
|
|
ufunc_eval_sh_chebyt_ptr[2*0] = <void*>_func_eval_sh_chebyt_l
|
|
ufunc_eval_sh_chebyt_ptr[2*0+1] = <void*>(<char*>"eval_sh_chebyt")
|
|
ufunc_eval_sh_chebyt_ptr[2*1] = <void*>_func_eval_sh_chebyt[double]
|
|
ufunc_eval_sh_chebyt_ptr[2*1+1] = <void*>(<char*>"eval_sh_chebyt")
|
|
ufunc_eval_sh_chebyt_ptr[2*2] = <void*>_func_eval_sh_chebyt[double_complex]
|
|
ufunc_eval_sh_chebyt_ptr[2*2+1] = <void*>(<char*>"eval_sh_chebyt")
|
|
ufunc_eval_sh_chebyt_ptr[2*3] = <void*>_func_eval_sh_chebyt[double]
|
|
ufunc_eval_sh_chebyt_ptr[2*3+1] = <void*>(<char*>"eval_sh_chebyt")
|
|
ufunc_eval_sh_chebyt_ptr[2*4] = <void*>_func_eval_sh_chebyt[double_complex]
|
|
ufunc_eval_sh_chebyt_ptr[2*4+1] = <void*>(<char*>"eval_sh_chebyt")
|
|
ufunc_eval_sh_chebyt_data[0] = &ufunc_eval_sh_chebyt_ptr[2*0]
|
|
ufunc_eval_sh_chebyt_data[1] = &ufunc_eval_sh_chebyt_ptr[2*1]
|
|
ufunc_eval_sh_chebyt_data[2] = &ufunc_eval_sh_chebyt_ptr[2*2]
|
|
ufunc_eval_sh_chebyt_data[3] = &ufunc_eval_sh_chebyt_ptr[2*3]
|
|
ufunc_eval_sh_chebyt_data[4] = &ufunc_eval_sh_chebyt_ptr[2*4]
|
|
eval_sh_chebyt = np.PyUFunc_FromFuncAndData(ufunc_eval_sh_chebyt_loops, ufunc_eval_sh_chebyt_data, ufunc_eval_sh_chebyt_types, 5, 2, 1, 0, 'eval_sh_chebyt', ufunc_eval_sh_chebyt_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_eval_sh_chebyu_loops[5]
|
|
cdef void *ufunc_eval_sh_chebyu_ptr[10]
|
|
cdef void *ufunc_eval_sh_chebyu_data[5]
|
|
cdef char ufunc_eval_sh_chebyu_types[15]
|
|
cdef char *ufunc_eval_sh_chebyu_doc = (
|
|
"eval_sh_chebyu(n, x, out=None)\n"
|
|
"\n"
|
|
"Evaluate shifted Chebyshev polynomial of the second kind at a\n"
|
|
"point.\n"
|
|
"\n"
|
|
"These polynomials are defined as\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" U_n^*(x) = U_n(2x - 1)\n"
|
|
"\n"
|
|
"where :math:`U_n` is a Chebyshev polynomial of the first kind. See\n"
|
|
"22.5.15 in [AS]_ for details.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"n : array_like\n"
|
|
" Degree of the polynomial. If not an integer, the result is\n"
|
|
" determined via the relation to `eval_chebyu`.\n"
|
|
"x : array_like\n"
|
|
" Points at which to evaluate the shifted Chebyshev polynomial\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"U : scalar or ndarray\n"
|
|
" Values of the shifted Chebyshev polynomial\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"roots_sh_chebyu : roots and quadrature weights of shifted\n"
|
|
" Chebychev polynomials of the second kind\n"
|
|
"sh_chebyu : shifted Chebyshev polynomial object\n"
|
|
"eval_chebyu : evaluate Chebyshev polynomials of the second kind\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
|
|
" Handbook of Mathematical Functions with Formulas,\n"
|
|
" Graphs, and Mathematical Tables. New York: Dover, 1972.")
|
|
ufunc_eval_sh_chebyu_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
|
|
ufunc_eval_sh_chebyu_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_eval_sh_chebyu_loops[2] = <np.PyUFuncGenericFunction>loop_D_dD__As_fF_F
|
|
ufunc_eval_sh_chebyu_loops[3] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_eval_sh_chebyu_loops[4] = <np.PyUFuncGenericFunction>loop_D_dD__As_dD_D
|
|
ufunc_eval_sh_chebyu_types[0] = <char>NPY_INTP
|
|
ufunc_eval_sh_chebyu_types[1] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_chebyu_types[2] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_chebyu_types[3] = <char>NPY_FLOAT
|
|
ufunc_eval_sh_chebyu_types[4] = <char>NPY_FLOAT
|
|
ufunc_eval_sh_chebyu_types[5] = <char>NPY_FLOAT
|
|
ufunc_eval_sh_chebyu_types[6] = <char>NPY_FLOAT
|
|
ufunc_eval_sh_chebyu_types[7] = <char>NPY_CFLOAT
|
|
ufunc_eval_sh_chebyu_types[8] = <char>NPY_CFLOAT
|
|
ufunc_eval_sh_chebyu_types[9] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_chebyu_types[10] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_chebyu_types[11] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_chebyu_types[12] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_chebyu_types[13] = <char>NPY_CDOUBLE
|
|
ufunc_eval_sh_chebyu_types[14] = <char>NPY_CDOUBLE
|
|
ufunc_eval_sh_chebyu_ptr[2*0] = <void*>_func_eval_sh_chebyu_l
|
|
ufunc_eval_sh_chebyu_ptr[2*0+1] = <void*>(<char*>"eval_sh_chebyu")
|
|
ufunc_eval_sh_chebyu_ptr[2*1] = <void*>_func_eval_sh_chebyu[double]
|
|
ufunc_eval_sh_chebyu_ptr[2*1+1] = <void*>(<char*>"eval_sh_chebyu")
|
|
ufunc_eval_sh_chebyu_ptr[2*2] = <void*>_func_eval_sh_chebyu[double_complex]
|
|
ufunc_eval_sh_chebyu_ptr[2*2+1] = <void*>(<char*>"eval_sh_chebyu")
|
|
ufunc_eval_sh_chebyu_ptr[2*3] = <void*>_func_eval_sh_chebyu[double]
|
|
ufunc_eval_sh_chebyu_ptr[2*3+1] = <void*>(<char*>"eval_sh_chebyu")
|
|
ufunc_eval_sh_chebyu_ptr[2*4] = <void*>_func_eval_sh_chebyu[double_complex]
|
|
ufunc_eval_sh_chebyu_ptr[2*4+1] = <void*>(<char*>"eval_sh_chebyu")
|
|
ufunc_eval_sh_chebyu_data[0] = &ufunc_eval_sh_chebyu_ptr[2*0]
|
|
ufunc_eval_sh_chebyu_data[1] = &ufunc_eval_sh_chebyu_ptr[2*1]
|
|
ufunc_eval_sh_chebyu_data[2] = &ufunc_eval_sh_chebyu_ptr[2*2]
|
|
ufunc_eval_sh_chebyu_data[3] = &ufunc_eval_sh_chebyu_ptr[2*3]
|
|
ufunc_eval_sh_chebyu_data[4] = &ufunc_eval_sh_chebyu_ptr[2*4]
|
|
eval_sh_chebyu = np.PyUFunc_FromFuncAndData(ufunc_eval_sh_chebyu_loops, ufunc_eval_sh_chebyu_data, ufunc_eval_sh_chebyu_types, 5, 2, 1, 0, 'eval_sh_chebyu', ufunc_eval_sh_chebyu_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_eval_sh_jacobi_loops[5]
|
|
cdef void *ufunc_eval_sh_jacobi_ptr[10]
|
|
cdef void *ufunc_eval_sh_jacobi_data[5]
|
|
cdef char ufunc_eval_sh_jacobi_types[25]
|
|
cdef char *ufunc_eval_sh_jacobi_doc = (
|
|
"eval_sh_jacobi(n, p, q, x, out=None)\n"
|
|
"\n"
|
|
"Evaluate shifted Jacobi polynomial at a point.\n"
|
|
"\n"
|
|
"Defined by\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" G_n^{(p, q)}(x)\n"
|
|
" = \\binom{2n + p - 1}{n}^{-1} P_n^{(p - q, q - 1)}(2x - 1),\n"
|
|
"\n"
|
|
"where :math:`P_n^{(\\cdot, \\cdot)}` is the n-th Jacobi\n"
|
|
"polynomial. See 22.5.2 in [AS]_ for details.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"n : int\n"
|
|
" Degree of the polynomial. If not an integer, the result is\n"
|
|
" determined via the relation to `binom` and `eval_jacobi`.\n"
|
|
"p : float\n"
|
|
" Parameter\n"
|
|
"q : float\n"
|
|
" Parameter\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"G : scalar or ndarray\n"
|
|
" Values of the shifted Jacobi polynomial.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"roots_sh_jacobi : roots and quadrature weights of shifted Jacobi\n"
|
|
" polynomials\n"
|
|
"sh_jacobi : shifted Jacobi polynomial object\n"
|
|
"eval_jacobi : evaluate Jacobi polynomials\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
|
|
" Handbook of Mathematical Functions with Formulas,\n"
|
|
" Graphs, and Mathematical Tables. New York: Dover, 1972.")
|
|
ufunc_eval_sh_jacobi_loops[0] = <np.PyUFuncGenericFunction>loop_d_pddd__As_pddd_d
|
|
ufunc_eval_sh_jacobi_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_ffff_f
|
|
ufunc_eval_sh_jacobi_loops[2] = <np.PyUFuncGenericFunction>loop_D_dddD__As_fffF_F
|
|
ufunc_eval_sh_jacobi_loops[3] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
|
|
ufunc_eval_sh_jacobi_loops[4] = <np.PyUFuncGenericFunction>loop_D_dddD__As_dddD_D
|
|
ufunc_eval_sh_jacobi_types[0] = <char>NPY_INTP
|
|
ufunc_eval_sh_jacobi_types[1] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_jacobi_types[2] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_jacobi_types[3] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_jacobi_types[4] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_jacobi_types[5] = <char>NPY_FLOAT
|
|
ufunc_eval_sh_jacobi_types[6] = <char>NPY_FLOAT
|
|
ufunc_eval_sh_jacobi_types[7] = <char>NPY_FLOAT
|
|
ufunc_eval_sh_jacobi_types[8] = <char>NPY_FLOAT
|
|
ufunc_eval_sh_jacobi_types[9] = <char>NPY_FLOAT
|
|
ufunc_eval_sh_jacobi_types[10] = <char>NPY_FLOAT
|
|
ufunc_eval_sh_jacobi_types[11] = <char>NPY_FLOAT
|
|
ufunc_eval_sh_jacobi_types[12] = <char>NPY_FLOAT
|
|
ufunc_eval_sh_jacobi_types[13] = <char>NPY_CFLOAT
|
|
ufunc_eval_sh_jacobi_types[14] = <char>NPY_CFLOAT
|
|
ufunc_eval_sh_jacobi_types[15] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_jacobi_types[16] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_jacobi_types[17] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_jacobi_types[18] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_jacobi_types[19] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_jacobi_types[20] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_jacobi_types[21] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_jacobi_types[22] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_jacobi_types[23] = <char>NPY_CDOUBLE
|
|
ufunc_eval_sh_jacobi_types[24] = <char>NPY_CDOUBLE
|
|
ufunc_eval_sh_jacobi_ptr[2*0] = <void*>_func_eval_sh_jacobi_l
|
|
ufunc_eval_sh_jacobi_ptr[2*0+1] = <void*>(<char*>"eval_sh_jacobi")
|
|
ufunc_eval_sh_jacobi_ptr[2*1] = <void*>_func_eval_sh_jacobi[double]
|
|
ufunc_eval_sh_jacobi_ptr[2*1+1] = <void*>(<char*>"eval_sh_jacobi")
|
|
ufunc_eval_sh_jacobi_ptr[2*2] = <void*>_func_eval_sh_jacobi[double_complex]
|
|
ufunc_eval_sh_jacobi_ptr[2*2+1] = <void*>(<char*>"eval_sh_jacobi")
|
|
ufunc_eval_sh_jacobi_ptr[2*3] = <void*>_func_eval_sh_jacobi[double]
|
|
ufunc_eval_sh_jacobi_ptr[2*3+1] = <void*>(<char*>"eval_sh_jacobi")
|
|
ufunc_eval_sh_jacobi_ptr[2*4] = <void*>_func_eval_sh_jacobi[double_complex]
|
|
ufunc_eval_sh_jacobi_ptr[2*4+1] = <void*>(<char*>"eval_sh_jacobi")
|
|
ufunc_eval_sh_jacobi_data[0] = &ufunc_eval_sh_jacobi_ptr[2*0]
|
|
ufunc_eval_sh_jacobi_data[1] = &ufunc_eval_sh_jacobi_ptr[2*1]
|
|
ufunc_eval_sh_jacobi_data[2] = &ufunc_eval_sh_jacobi_ptr[2*2]
|
|
ufunc_eval_sh_jacobi_data[3] = &ufunc_eval_sh_jacobi_ptr[2*3]
|
|
ufunc_eval_sh_jacobi_data[4] = &ufunc_eval_sh_jacobi_ptr[2*4]
|
|
eval_sh_jacobi = np.PyUFunc_FromFuncAndData(ufunc_eval_sh_jacobi_loops, ufunc_eval_sh_jacobi_data, ufunc_eval_sh_jacobi_types, 5, 4, 1, 0, 'eval_sh_jacobi', ufunc_eval_sh_jacobi_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_eval_sh_legendre_loops[5]
|
|
cdef void *ufunc_eval_sh_legendre_ptr[10]
|
|
cdef void *ufunc_eval_sh_legendre_data[5]
|
|
cdef char ufunc_eval_sh_legendre_types[15]
|
|
cdef char *ufunc_eval_sh_legendre_doc = (
|
|
"eval_sh_legendre(n, x, out=None)\n"
|
|
"\n"
|
|
"Evaluate shifted Legendre polynomial at a point.\n"
|
|
"\n"
|
|
"These polynomials are defined as\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" P_n^*(x) = P_n(2x - 1)\n"
|
|
"\n"
|
|
"where :math:`P_n` is a Legendre polynomial. See 2.2.11 in [AS]_\n"
|
|
"for details.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"n : array_like\n"
|
|
" Degree of the polynomial. If not an integer, the value is\n"
|
|
" determined via the relation to `eval_legendre`.\n"
|
|
"x : array_like\n"
|
|
" Points at which to evaluate the shifted Legendre polynomial\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"P : scalar or ndarray\n"
|
|
" Values of the shifted Legendre polynomial\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"roots_sh_legendre : roots and quadrature weights of shifted\n"
|
|
" Legendre polynomials\n"
|
|
"sh_legendre : shifted Legendre polynomial object\n"
|
|
"eval_legendre : evaluate Legendre polynomials\n"
|
|
"numpy.polynomial.legendre.Legendre : Legendre series\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
|
|
" Handbook of Mathematical Functions with Formulas,\n"
|
|
" Graphs, and Mathematical Tables. New York: Dover, 1972.")
|
|
ufunc_eval_sh_legendre_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
|
|
ufunc_eval_sh_legendre_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_eval_sh_legendre_loops[2] = <np.PyUFuncGenericFunction>loop_D_dD__As_fF_F
|
|
ufunc_eval_sh_legendre_loops[3] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_eval_sh_legendre_loops[4] = <np.PyUFuncGenericFunction>loop_D_dD__As_dD_D
|
|
ufunc_eval_sh_legendre_types[0] = <char>NPY_INTP
|
|
ufunc_eval_sh_legendre_types[1] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_legendre_types[2] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_legendre_types[3] = <char>NPY_FLOAT
|
|
ufunc_eval_sh_legendre_types[4] = <char>NPY_FLOAT
|
|
ufunc_eval_sh_legendre_types[5] = <char>NPY_FLOAT
|
|
ufunc_eval_sh_legendre_types[6] = <char>NPY_FLOAT
|
|
ufunc_eval_sh_legendre_types[7] = <char>NPY_CFLOAT
|
|
ufunc_eval_sh_legendre_types[8] = <char>NPY_CFLOAT
|
|
ufunc_eval_sh_legendre_types[9] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_legendre_types[10] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_legendre_types[11] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_legendre_types[12] = <char>NPY_DOUBLE
|
|
ufunc_eval_sh_legendre_types[13] = <char>NPY_CDOUBLE
|
|
ufunc_eval_sh_legendre_types[14] = <char>NPY_CDOUBLE
|
|
ufunc_eval_sh_legendre_ptr[2*0] = <void*>_func_eval_sh_legendre_l
|
|
ufunc_eval_sh_legendre_ptr[2*0+1] = <void*>(<char*>"eval_sh_legendre")
|
|
ufunc_eval_sh_legendre_ptr[2*1] = <void*>_func_eval_sh_legendre[double]
|
|
ufunc_eval_sh_legendre_ptr[2*1+1] = <void*>(<char*>"eval_sh_legendre")
|
|
ufunc_eval_sh_legendre_ptr[2*2] = <void*>_func_eval_sh_legendre[double_complex]
|
|
ufunc_eval_sh_legendre_ptr[2*2+1] = <void*>(<char*>"eval_sh_legendre")
|
|
ufunc_eval_sh_legendre_ptr[2*3] = <void*>_func_eval_sh_legendre[double]
|
|
ufunc_eval_sh_legendre_ptr[2*3+1] = <void*>(<char*>"eval_sh_legendre")
|
|
ufunc_eval_sh_legendre_ptr[2*4] = <void*>_func_eval_sh_legendre[double_complex]
|
|
ufunc_eval_sh_legendre_ptr[2*4+1] = <void*>(<char*>"eval_sh_legendre")
|
|
ufunc_eval_sh_legendre_data[0] = &ufunc_eval_sh_legendre_ptr[2*0]
|
|
ufunc_eval_sh_legendre_data[1] = &ufunc_eval_sh_legendre_ptr[2*1]
|
|
ufunc_eval_sh_legendre_data[2] = &ufunc_eval_sh_legendre_ptr[2*2]
|
|
ufunc_eval_sh_legendre_data[3] = &ufunc_eval_sh_legendre_ptr[2*3]
|
|
ufunc_eval_sh_legendre_data[4] = &ufunc_eval_sh_legendre_ptr[2*4]
|
|
eval_sh_legendre = np.PyUFunc_FromFuncAndData(ufunc_eval_sh_legendre_loops, ufunc_eval_sh_legendre_data, ufunc_eval_sh_legendre_types, 5, 2, 1, 0, 'eval_sh_legendre', ufunc_eval_sh_legendre_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_expn_loops[3]
|
|
cdef void *ufunc_expn_ptr[6]
|
|
cdef void *ufunc_expn_data[3]
|
|
cdef char ufunc_expn_types[9]
|
|
cdef char *ufunc_expn_doc = (
|
|
"expn(n, x, out=None)\n"
|
|
"\n"
|
|
"Generalized exponential integral En.\n"
|
|
"\n"
|
|
"For integer :math:`n \\geq 0` and real :math:`x \\geq 0` the\n"
|
|
"generalized exponential integral is defined as [dlmf]_\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" E_n(x) = x^{n - 1} \\int_x^\\infty \\frac{e^{-t}}{t^n} dt.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"n : array_like\n"
|
|
" Non-negative integers\n"
|
|
"x : array_like\n"
|
|
" Real argument\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" Values of the generalized exponential integral\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"exp1 : special case of :math:`E_n` for :math:`n = 1`\n"
|
|
"expi : related to :math:`E_n` when :math:`n = 1`\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [dlmf] Digital Library of Mathematical Functions, 8.19.2\n"
|
|
" https://dlmf.nist.gov/8.19#E2\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> import scipy.special as sc\n"
|
|
"\n"
|
|
"Its domain is nonnegative n and x.\n"
|
|
"\n"
|
|
">>> sc.expn(-1, 1.0), sc.expn(1, -1.0)\n"
|
|
"(nan, nan)\n"
|
|
"\n"
|
|
"It has a pole at ``x = 0`` for ``n = 1, 2``; for larger ``n`` it\n"
|
|
"is equal to ``1 / (n - 1)``.\n"
|
|
"\n"
|
|
">>> sc.expn([0, 1, 2, 3, 4], 0)\n"
|
|
"array([ inf, inf, 1. , 0.5 , 0.33333333])\n"
|
|
"\n"
|
|
"For n equal to 0 it reduces to ``exp(-x) / x``.\n"
|
|
"\n"
|
|
">>> x = np.array([1, 2, 3, 4])\n"
|
|
">>> sc.expn(0, x)\n"
|
|
"array([0.36787944, 0.06766764, 0.01659569, 0.00457891])\n"
|
|
">>> np.exp(-x) / x\n"
|
|
"array([0.36787944, 0.06766764, 0.01659569, 0.00457891])\n"
|
|
"\n"
|
|
"For n equal to 1 it reduces to `exp1`.\n"
|
|
"\n"
|
|
">>> sc.expn(1, x)\n"
|
|
"array([0.21938393, 0.04890051, 0.01304838, 0.00377935])\n"
|
|
">>> sc.exp1(x)\n"
|
|
"array([0.21938393, 0.04890051, 0.01304838, 0.00377935])")
|
|
ufunc_expn_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
|
|
ufunc_expn_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_expn_loops[2] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_expn_types[0] = <char>NPY_INTP
|
|
ufunc_expn_types[1] = <char>NPY_DOUBLE
|
|
ufunc_expn_types[2] = <char>NPY_DOUBLE
|
|
ufunc_expn_types[3] = <char>NPY_FLOAT
|
|
ufunc_expn_types[4] = <char>NPY_FLOAT
|
|
ufunc_expn_types[5] = <char>NPY_FLOAT
|
|
ufunc_expn_types[6] = <char>NPY_DOUBLE
|
|
ufunc_expn_types[7] = <char>NPY_DOUBLE
|
|
ufunc_expn_types[8] = <char>NPY_DOUBLE
|
|
ufunc_expn_ptr[2*0] = <void*>_func_cephes_expn_wrap
|
|
ufunc_expn_ptr[2*0+1] = <void*>(<char*>"expn")
|
|
ufunc_expn_ptr[2*1] = <void*>_func_expn_unsafe
|
|
ufunc_expn_ptr[2*1+1] = <void*>(<char*>"expn")
|
|
ufunc_expn_ptr[2*2] = <void*>_func_expn_unsafe
|
|
ufunc_expn_ptr[2*2+1] = <void*>(<char*>"expn")
|
|
ufunc_expn_data[0] = &ufunc_expn_ptr[2*0]
|
|
ufunc_expn_data[1] = &ufunc_expn_ptr[2*1]
|
|
ufunc_expn_data[2] = &ufunc_expn_ptr[2*2]
|
|
expn = np.PyUFunc_FromFuncAndData(ufunc_expn_loops, ufunc_expn_data, ufunc_expn_types, 3, 2, 1, 0, 'expn', ufunc_expn_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_fdtr_loops[2]
|
|
cdef void *ufunc_fdtr_ptr[4]
|
|
cdef void *ufunc_fdtr_data[2]
|
|
cdef char ufunc_fdtr_types[8]
|
|
cdef char *ufunc_fdtr_doc = (
|
|
"fdtr(dfn, dfd, x, out=None)\n"
|
|
"\n"
|
|
"F cumulative distribution function.\n"
|
|
"\n"
|
|
"Returns the value of the cumulative distribution function of the\n"
|
|
"F-distribution, also known as Snedecor's F-distribution or the\n"
|
|
"Fisher-Snedecor distribution.\n"
|
|
"\n"
|
|
"The F-distribution with parameters :math:`d_n` and :math:`d_d` is the\n"
|
|
"distribution of the random variable,\n"
|
|
"\n"
|
|
".. math::\n"
|
|
" X = \\frac{U_n/d_n}{U_d/d_d},\n"
|
|
"\n"
|
|
"where :math:`U_n` and :math:`U_d` are random variables distributed\n"
|
|
":math:`\\chi^2`, with :math:`d_n` and :math:`d_d` degrees of freedom,\n"
|
|
"respectively.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"dfn : array_like\n"
|
|
" First parameter (positive float).\n"
|
|
"dfd : array_like\n"
|
|
" Second parameter (positive float).\n"
|
|
"x : array_like\n"
|
|
" Argument (nonnegative float).\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"y : scalar or ndarray\n"
|
|
" The CDF of the F-distribution with parameters `dfn` and `dfd` at `x`.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"fdtrc : F distribution survival function\n"
|
|
"fdtri : F distribution inverse cumulative distribution\n"
|
|
"scipy.stats.f : F distribution\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"The regularized incomplete beta function is used, according to the\n"
|
|
"formula,\n"
|
|
"\n"
|
|
".. math::\n"
|
|
" F(d_n, d_d; x) = I_{xd_n/(d_d + xd_n)}(d_n/2, d_d/2).\n"
|
|
"\n"
|
|
"Wrapper for the Cephes [1]_ routine `fdtr`. The F distribution is also\n"
|
|
"available as `scipy.stats.f`. Calling `fdtr` directly can improve\n"
|
|
"performance compared to the ``cdf`` method of `scipy.stats.f` (see last\n"
|
|
"example below).\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Cephes Mathematical Functions Library,\n"
|
|
" http://www.netlib.org/cephes/\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"Calculate the function for ``dfn=1`` and ``dfd=2`` at ``x=1``.\n"
|
|
"\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import fdtr\n"
|
|
">>> fdtr(1, 2, 1)\n"
|
|
"0.5773502691896258\n"
|
|
"\n"
|
|
"Calculate the function at several points by providing a NumPy array for\n"
|
|
"`x`.\n"
|
|
"\n"
|
|
">>> x = np.array([0.5, 2., 3.])\n"
|
|
">>> fdtr(1, 2, x)\n"
|
|
"array([0.4472136 , 0.70710678, 0.77459667])\n"
|
|
"\n"
|
|
"Plot the function for several parameter sets.\n"
|
|
"\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
">>> dfn_parameters = [1, 5, 10, 50]\n"
|
|
">>> dfd_parameters = [1, 1, 2, 3]\n"
|
|
">>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']\n"
|
|
">>> parameters_list = list(zip(dfn_parameters, dfd_parameters,\n"
|
|
"... linestyles))\n"
|
|
">>> x = np.linspace(0, 30, 1000)\n"
|
|
">>> fig, ax = plt.subplots()\n"
|
|
">>> for parameter_set in parameters_list:\n"
|
|
"... dfn, dfd, style = parameter_set\n"
|
|
"... fdtr_vals = fdtr(dfn, dfd, x)\n"
|
|
"... ax.plot(x, fdtr_vals, label=rf\"$d_n={dfn},\\, d_d={dfd}$\",\n"
|
|
"... ls=style)\n"
|
|
">>> ax.legend()\n"
|
|
">>> ax.set_xlabel(\"$x$\")\n"
|
|
">>> ax.set_title(\"F distribution cumulative distribution function\")\n"
|
|
">>> plt.show()\n"
|
|
"\n"
|
|
"The F distribution is also available as `scipy.stats.f`. Using `fdtr`\n"
|
|
"directly can be much faster than calling the ``cdf`` method of\n"
|
|
"`scipy.stats.f`, especially for small arrays or individual values.\n"
|
|
"To get the same results one must use the following parametrization:\n"
|
|
"``stats.f(dfn, dfd).cdf(x)=fdtr(dfn, dfd, x)``.\n"
|
|
"\n"
|
|
">>> from scipy.stats import f\n"
|
|
">>> dfn, dfd = 1, 2\n"
|
|
">>> x = 1\n"
|
|
">>> fdtr_res = fdtr(dfn, dfd, x) # this will often be faster than below\n"
|
|
">>> f_dist_res = f(dfn, dfd).cdf(x)\n"
|
|
">>> fdtr_res == f_dist_res # test that results are equal\n"
|
|
"True")
|
|
ufunc_fdtr_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_fdtr_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_fdtr_types[0] = <char>NPY_FLOAT
|
|
ufunc_fdtr_types[1] = <char>NPY_FLOAT
|
|
ufunc_fdtr_types[2] = <char>NPY_FLOAT
|
|
ufunc_fdtr_types[3] = <char>NPY_FLOAT
|
|
ufunc_fdtr_types[4] = <char>NPY_DOUBLE
|
|
ufunc_fdtr_types[5] = <char>NPY_DOUBLE
|
|
ufunc_fdtr_types[6] = <char>NPY_DOUBLE
|
|
ufunc_fdtr_types[7] = <char>NPY_DOUBLE
|
|
ufunc_fdtr_ptr[2*0] = <void*>_func_xsf_fdtr
|
|
ufunc_fdtr_ptr[2*0+1] = <void*>(<char*>"fdtr")
|
|
ufunc_fdtr_ptr[2*1] = <void*>_func_xsf_fdtr
|
|
ufunc_fdtr_ptr[2*1+1] = <void*>(<char*>"fdtr")
|
|
ufunc_fdtr_data[0] = &ufunc_fdtr_ptr[2*0]
|
|
ufunc_fdtr_data[1] = &ufunc_fdtr_ptr[2*1]
|
|
fdtr = np.PyUFunc_FromFuncAndData(ufunc_fdtr_loops, ufunc_fdtr_data, ufunc_fdtr_types, 2, 3, 1, 0, 'fdtr', ufunc_fdtr_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_fdtrc_loops[2]
|
|
cdef void *ufunc_fdtrc_ptr[4]
|
|
cdef void *ufunc_fdtrc_data[2]
|
|
cdef char ufunc_fdtrc_types[8]
|
|
cdef char *ufunc_fdtrc_doc = (
|
|
"fdtrc(dfn, dfd, x, out=None)\n"
|
|
"\n"
|
|
"F survival function.\n"
|
|
"\n"
|
|
"Returns the complemented F-distribution function (the integral of the\n"
|
|
"density from `x` to infinity).\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"dfn : array_like\n"
|
|
" First parameter (positive float).\n"
|
|
"dfd : array_like\n"
|
|
" Second parameter (positive float).\n"
|
|
"x : array_like\n"
|
|
" Argument (nonnegative float).\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"y : scalar or ndarray\n"
|
|
" The complemented F-distribution function with parameters `dfn` and\n"
|
|
" `dfd` at `x`.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"fdtr : F distribution cumulative distribution function\n"
|
|
"fdtri : F distribution inverse cumulative distribution function\n"
|
|
"scipy.stats.f : F distribution\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"The regularized incomplete beta function is used, according to the\n"
|
|
"formula,\n"
|
|
"\n"
|
|
".. math::\n"
|
|
" F(d_n, d_d; x) = I_{d_d/(d_d + xd_n)}(d_d/2, d_n/2).\n"
|
|
"\n"
|
|
"Wrapper for the Cephes [1]_ routine `fdtrc`. The F distribution is also\n"
|
|
"available as `scipy.stats.f`. Calling `fdtrc` directly can improve\n"
|
|
"performance compared to the ``sf`` method of `scipy.stats.f` (see last\n"
|
|
"example below).\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Cephes Mathematical Functions Library,\n"
|
|
" http://www.netlib.org/cephes/\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"Calculate the function for ``dfn=1`` and ``dfd=2`` at ``x=1``.\n"
|
|
"\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import fdtrc\n"
|
|
">>> fdtrc(1, 2, 1)\n"
|
|
"0.42264973081037427\n"
|
|
"\n"
|
|
"Calculate the function at several points by providing a NumPy array for\n"
|
|
"`x`.\n"
|
|
"\n"
|
|
">>> x = np.array([0.5, 2., 3.])\n"
|
|
">>> fdtrc(1, 2, x)\n"
|
|
"array([0.5527864 , 0.29289322, 0.22540333])\n"
|
|
"\n"
|
|
"Plot the function for several parameter sets.\n"
|
|
"\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
">>> dfn_parameters = [1, 5, 10, 50]\n"
|
|
">>> dfd_parameters = [1, 1, 2, 3]\n"
|
|
">>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']\n"
|
|
">>> parameters_list = list(zip(dfn_parameters, dfd_parameters,\n"
|
|
"... linestyles))\n"
|
|
">>> x = np.linspace(0, 30, 1000)\n"
|
|
">>> fig, ax = plt.subplots()\n"
|
|
">>> for parameter_set in parameters_list:\n"
|
|
"... dfn, dfd, style = parameter_set\n"
|
|
"... fdtrc_vals = fdtrc(dfn, dfd, x)\n"
|
|
"... ax.plot(x, fdtrc_vals, label=rf\"$d_n={dfn},\\, d_d={dfd}$\",\n"
|
|
"... ls=style)\n"
|
|
">>> ax.legend()\n"
|
|
">>> ax.set_xlabel(\"$x$\")\n"
|
|
">>> ax.set_title(\"F distribution survival function\")\n"
|
|
">>> plt.show()\n"
|
|
"\n"
|
|
"The F distribution is also available as `scipy.stats.f`. Using `fdtrc`\n"
|
|
"directly can be much faster than calling the ``sf`` method of\n"
|
|
"`scipy.stats.f`, especially for small arrays or individual values.\n"
|
|
"To get the same results one must use the following parametrization:\n"
|
|
"``stats.f(dfn, dfd).sf(x)=fdtrc(dfn, dfd, x)``.\n"
|
|
"\n"
|
|
">>> from scipy.stats import f\n"
|
|
">>> dfn, dfd = 1, 2\n"
|
|
">>> x = 1\n"
|
|
">>> fdtrc_res = fdtrc(dfn, dfd, x) # this will often be faster than below\n"
|
|
">>> f_dist_res = f(dfn, dfd).sf(x)\n"
|
|
">>> f_dist_res == fdtrc_res # test that results are equal\n"
|
|
"True")
|
|
ufunc_fdtrc_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_fdtrc_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_fdtrc_types[0] = <char>NPY_FLOAT
|
|
ufunc_fdtrc_types[1] = <char>NPY_FLOAT
|
|
ufunc_fdtrc_types[2] = <char>NPY_FLOAT
|
|
ufunc_fdtrc_types[3] = <char>NPY_FLOAT
|
|
ufunc_fdtrc_types[4] = <char>NPY_DOUBLE
|
|
ufunc_fdtrc_types[5] = <char>NPY_DOUBLE
|
|
ufunc_fdtrc_types[6] = <char>NPY_DOUBLE
|
|
ufunc_fdtrc_types[7] = <char>NPY_DOUBLE
|
|
ufunc_fdtrc_ptr[2*0] = <void*>_func_xsf_fdtrc
|
|
ufunc_fdtrc_ptr[2*0+1] = <void*>(<char*>"fdtrc")
|
|
ufunc_fdtrc_ptr[2*1] = <void*>_func_xsf_fdtrc
|
|
ufunc_fdtrc_ptr[2*1+1] = <void*>(<char*>"fdtrc")
|
|
ufunc_fdtrc_data[0] = &ufunc_fdtrc_ptr[2*0]
|
|
ufunc_fdtrc_data[1] = &ufunc_fdtrc_ptr[2*1]
|
|
fdtrc = np.PyUFunc_FromFuncAndData(ufunc_fdtrc_loops, ufunc_fdtrc_data, ufunc_fdtrc_types, 2, 3, 1, 0, 'fdtrc', ufunc_fdtrc_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_fdtri_loops[2]
|
|
cdef void *ufunc_fdtri_ptr[4]
|
|
cdef void *ufunc_fdtri_data[2]
|
|
cdef char ufunc_fdtri_types[8]
|
|
cdef char *ufunc_fdtri_doc = (
|
|
"fdtri(dfn, dfd, p, out=None)\n"
|
|
"\n"
|
|
"The `p`-th quantile of the F-distribution.\n"
|
|
"\n"
|
|
"This function is the inverse of the F-distribution CDF, `fdtr`, returning\n"
|
|
"the `x` such that `fdtr(dfn, dfd, x) = p`.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"dfn : array_like\n"
|
|
" First parameter (positive float).\n"
|
|
"dfd : array_like\n"
|
|
" Second parameter (positive float).\n"
|
|
"p : array_like\n"
|
|
" Cumulative probability, in [0, 1].\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"x : scalar or ndarray\n"
|
|
" The quantile corresponding to `p`.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"fdtr : F distribution cumulative distribution function\n"
|
|
"fdtrc : F distribution survival function\n"
|
|
"scipy.stats.f : F distribution\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"The computation is carried out using the relation to the inverse\n"
|
|
"regularized beta function, :math:`I^{-1}_x(a, b)`. Let\n"
|
|
":math:`z = I^{-1}_p(d_d/2, d_n/2).` Then,\n"
|
|
"\n"
|
|
".. math::\n"
|
|
" x = \\frac{d_d (1 - z)}{d_n z}.\n"
|
|
"\n"
|
|
"If `p` is such that :math:`x < 0.5`, the following relation is used\n"
|
|
"instead for improved stability: let\n"
|
|
":math:`z' = I^{-1}_{1 - p}(d_n/2, d_d/2).` Then,\n"
|
|
"\n"
|
|
".. math::\n"
|
|
" x = \\frac{d_d z'}{d_n (1 - z')}.\n"
|
|
"\n"
|
|
"Wrapper for the Cephes [1]_ routine `fdtri`.\n"
|
|
"\n"
|
|
"The F distribution is also available as `scipy.stats.f`. Calling\n"
|
|
"`fdtri` directly can improve performance compared to the ``ppf``\n"
|
|
"method of `scipy.stats.f` (see last example below).\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Cephes Mathematical Functions Library,\n"
|
|
" http://www.netlib.org/cephes/\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"`fdtri` represents the inverse of the F distribution CDF which is\n"
|
|
"available as `fdtr`. Here, we calculate the CDF for ``df1=1``, ``df2=2``\n"
|
|
"at ``x=3``. `fdtri` then returns ``3`` given the same values for `df1`,\n"
|
|
"`df2` and the computed CDF value.\n"
|
|
"\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import fdtri, fdtr\n"
|
|
">>> df1, df2 = 1, 2\n"
|
|
">>> x = 3\n"
|
|
">>> cdf_value = fdtr(df1, df2, x)\n"
|
|
">>> fdtri(df1, df2, cdf_value)\n"
|
|
"3.000000000000006\n"
|
|
"\n"
|
|
"Calculate the function at several points by providing a NumPy array for\n"
|
|
"`x`.\n"
|
|
"\n"
|
|
">>> x = np.array([0.1, 0.4, 0.7])\n"
|
|
">>> fdtri(1, 2, x)\n"
|
|
"array([0.02020202, 0.38095238, 1.92156863])\n"
|
|
"\n"
|
|
"Plot the function for several parameter sets.\n"
|
|
"\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
">>> dfn_parameters = [50, 10, 1, 50]\n"
|
|
">>> dfd_parameters = [0.5, 1, 1, 5]\n"
|
|
">>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']\n"
|
|
">>> parameters_list = list(zip(dfn_parameters, dfd_parameters,\n"
|
|
"... linestyles))\n"
|
|
">>> x = np.linspace(0, 1, 1000)\n"
|
|
">>> fig, ax = plt.subplots()\n"
|
|
">>> for parameter_set in parameters_list:\n"
|
|
"... dfn, dfd, style = parameter_set\n"
|
|
"... fdtri_vals = fdtri(dfn, dfd, x)\n"
|
|
"... ax.plot(x, fdtri_vals, label=rf\"$d_n={dfn},\\, d_d={dfd}$\",\n"
|
|
"... ls=style)\n"
|
|
">>> ax.legend()\n"
|
|
">>> ax.set_xlabel(\"$x$\")\n"
|
|
">>> title = \"F distribution inverse cumulative distribution function\"\n"
|
|
">>> ax.set_title(title)\n"
|
|
">>> ax.set_ylim(0, 30)\n"
|
|
">>> plt.show()\n"
|
|
"\n"
|
|
"The F distribution is also available as `scipy.stats.f`. Using `fdtri`\n"
|
|
"directly can be much faster than calling the ``ppf`` method of\n"
|
|
"`scipy.stats.f`, especially for small arrays or individual values.\n"
|
|
"To get the same results one must use the following parametrization:\n"
|
|
"``stats.f(dfn, dfd).ppf(x)=fdtri(dfn, dfd, x)``.\n"
|
|
"\n"
|
|
">>> from scipy.stats import f\n"
|
|
">>> dfn, dfd = 1, 2\n"
|
|
">>> x = 0.7\n"
|
|
">>> fdtri_res = fdtri(dfn, dfd, x) # this will often be faster than below\n"
|
|
">>> f_dist_res = f(dfn, dfd).ppf(x)\n"
|
|
">>> f_dist_res == fdtri_res # test that results are equal\n"
|
|
"True")
|
|
ufunc_fdtri_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_fdtri_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_fdtri_types[0] = <char>NPY_FLOAT
|
|
ufunc_fdtri_types[1] = <char>NPY_FLOAT
|
|
ufunc_fdtri_types[2] = <char>NPY_FLOAT
|
|
ufunc_fdtri_types[3] = <char>NPY_FLOAT
|
|
ufunc_fdtri_types[4] = <char>NPY_DOUBLE
|
|
ufunc_fdtri_types[5] = <char>NPY_DOUBLE
|
|
ufunc_fdtri_types[6] = <char>NPY_DOUBLE
|
|
ufunc_fdtri_types[7] = <char>NPY_DOUBLE
|
|
ufunc_fdtri_ptr[2*0] = <void*>_func_xsf_fdtri
|
|
ufunc_fdtri_ptr[2*0+1] = <void*>(<char*>"fdtri")
|
|
ufunc_fdtri_ptr[2*1] = <void*>_func_xsf_fdtri
|
|
ufunc_fdtri_ptr[2*1+1] = <void*>(<char*>"fdtri")
|
|
ufunc_fdtri_data[0] = &ufunc_fdtri_ptr[2*0]
|
|
ufunc_fdtri_data[1] = &ufunc_fdtri_ptr[2*1]
|
|
fdtri = np.PyUFunc_FromFuncAndData(ufunc_fdtri_loops, ufunc_fdtri_data, ufunc_fdtri_types, 2, 3, 1, 0, 'fdtri', ufunc_fdtri_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_fdtridfd_loops[2]
|
|
cdef void *ufunc_fdtridfd_ptr[4]
|
|
cdef void *ufunc_fdtridfd_data[2]
|
|
cdef char ufunc_fdtridfd_types[8]
|
|
cdef char *ufunc_fdtridfd_doc = (
|
|
"fdtridfd(dfn, p, x, out=None)\n"
|
|
"\n"
|
|
"Inverse to `fdtr` vs dfd\n"
|
|
"\n"
|
|
"Finds the F density argument dfd such that ``fdtr(dfn, dfd, x) == p``.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"dfn : array_like\n"
|
|
" First parameter (positive float).\n"
|
|
"p : array_like\n"
|
|
" Cumulative probability, in [0, 1].\n"
|
|
"x : array_like\n"
|
|
" Argument (nonnegative float).\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"dfd : scalar or ndarray\n"
|
|
" `dfd` such that ``fdtr(dfn, dfd, x) == p``.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"fdtr : F distribution cumulative distribution function\n"
|
|
"fdtrc : F distribution survival function\n"
|
|
"fdtri : F distribution quantile function\n"
|
|
"scipy.stats.f : F distribution\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"Compute the F distribution cumulative distribution function for one\n"
|
|
"parameter set.\n"
|
|
"\n"
|
|
">>> from scipy.special import fdtridfd, fdtr\n"
|
|
">>> dfn, dfd, x = 10, 5, 2\n"
|
|
">>> cdf_value = fdtr(dfn, dfd, x)\n"
|
|
">>> cdf_value\n"
|
|
"0.7700248806501017\n"
|
|
"\n"
|
|
"Verify that `fdtridfd` recovers the original value for `dfd`:\n"
|
|
"\n"
|
|
">>> fdtridfd(dfn, cdf_value, x)\n"
|
|
"5.0")
|
|
ufunc_fdtridfd_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_fdtridfd_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_fdtridfd_types[0] = <char>NPY_FLOAT
|
|
ufunc_fdtridfd_types[1] = <char>NPY_FLOAT
|
|
ufunc_fdtridfd_types[2] = <char>NPY_FLOAT
|
|
ufunc_fdtridfd_types[3] = <char>NPY_FLOAT
|
|
ufunc_fdtridfd_types[4] = <char>NPY_DOUBLE
|
|
ufunc_fdtridfd_types[5] = <char>NPY_DOUBLE
|
|
ufunc_fdtridfd_types[6] = <char>NPY_DOUBLE
|
|
ufunc_fdtridfd_types[7] = <char>NPY_DOUBLE
|
|
ufunc_fdtridfd_ptr[2*0] = <void*>_func_fdtridfd
|
|
ufunc_fdtridfd_ptr[2*0+1] = <void*>(<char*>"fdtridfd")
|
|
ufunc_fdtridfd_ptr[2*1] = <void*>_func_fdtridfd
|
|
ufunc_fdtridfd_ptr[2*1+1] = <void*>(<char*>"fdtridfd")
|
|
ufunc_fdtridfd_data[0] = &ufunc_fdtridfd_ptr[2*0]
|
|
ufunc_fdtridfd_data[1] = &ufunc_fdtridfd_ptr[2*1]
|
|
fdtridfd = np.PyUFunc_FromFuncAndData(ufunc_fdtridfd_loops, ufunc_fdtridfd_data, ufunc_fdtridfd_types, 2, 3, 1, 0, 'fdtridfd', ufunc_fdtridfd_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_gdtr_loops[2]
|
|
cdef void *ufunc_gdtr_ptr[4]
|
|
cdef void *ufunc_gdtr_data[2]
|
|
cdef char ufunc_gdtr_types[8]
|
|
cdef char *ufunc_gdtr_doc = (
|
|
"gdtr(a, b, x, out=None)\n"
|
|
"\n"
|
|
"Gamma distribution cumulative distribution function.\n"
|
|
"\n"
|
|
"Returns the integral from zero to `x` of the gamma probability density\n"
|
|
"function,\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" F = \\int_0^x \\frac{a^b}{\\Gamma(b)} t^{b-1} e^{-at}\\,dt,\n"
|
|
"\n"
|
|
"where :math:`\\Gamma` is the gamma function.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"a : array_like\n"
|
|
" The rate parameter of the gamma distribution, sometimes denoted\n"
|
|
" :math:`\\beta` (float). It is also the reciprocal of the scale\n"
|
|
" parameter :math:`\\theta`.\n"
|
|
"b : array_like\n"
|
|
" The shape parameter of the gamma distribution, sometimes denoted\n"
|
|
" :math:`\\alpha` (float).\n"
|
|
"x : array_like\n"
|
|
" The quantile (upper limit of integration; float).\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"F : scalar or ndarray\n"
|
|
" The CDF of the gamma distribution with parameters `a` and `b`\n"
|
|
" evaluated at `x`.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"gdtrc : 1 - CDF of the gamma distribution.\n"
|
|
"scipy.stats.gamma: Gamma distribution\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"The evaluation is carried out using the relation to the incomplete gamma\n"
|
|
"integral (regularized gamma function).\n"
|
|
"\n"
|
|
"Wrapper for the Cephes [1]_ routine `gdtr`. Calling `gdtr` directly can\n"
|
|
"improve performance compared to the ``cdf`` method of `scipy.stats.gamma`\n"
|
|
"(see last example below).\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Cephes Mathematical Functions Library,\n"
|
|
" http://www.netlib.org/cephes/\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"Compute the function for ``a=1``, ``b=2`` at ``x=5``.\n"
|
|
"\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import gdtr\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
">>> gdtr(1., 2., 5.)\n"
|
|
"0.9595723180054873\n"
|
|
"\n"
|
|
"Compute the function for ``a=1`` and ``b=2`` at several points by\n"
|
|
"providing a NumPy array for `x`.\n"
|
|
"\n"
|
|
">>> xvalues = np.array([1., 2., 3., 4])\n"
|
|
">>> gdtr(1., 1., xvalues)\n"
|
|
"array([0.63212056, 0.86466472, 0.95021293, 0.98168436])\n"
|
|
"\n"
|
|
"`gdtr` can evaluate different parameter sets by providing arrays with\n"
|
|
"broadcasting compatible shapes for `a`, `b` and `x`. Here we compute the\n"
|
|
"function for three different `a` at four positions `x` and ``b=3``,\n"
|
|
"resulting in a 3x4 array.\n"
|
|
"\n"
|
|
">>> a = np.array([[0.5], [1.5], [2.5]])\n"
|
|
">>> x = np.array([1., 2., 3., 4])\n"
|
|
">>> a.shape, x.shape\n"
|
|
"((3, 1), (4,))\n"
|
|
"\n"
|
|
">>> gdtr(a, 3., x)\n"
|
|
"array([[0.01438768, 0.0803014 , 0.19115317, 0.32332358],\n"
|
|
" [0.19115317, 0.57680992, 0.82642193, 0.9380312 ],\n"
|
|
" [0.45618688, 0.87534798, 0.97974328, 0.9972306 ]])\n"
|
|
"\n"
|
|
"Plot the function for four different parameter sets.\n"
|
|
"\n"
|
|
">>> a_parameters = [0.3, 1, 2, 6]\n"
|
|
">>> b_parameters = [2, 10, 15, 20]\n"
|
|
">>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']\n"
|
|
">>> parameters_list = list(zip(a_parameters, b_parameters, linestyles))\n"
|
|
">>> x = np.linspace(0, 30, 1000)\n"
|
|
">>> fig, ax = plt.subplots()\n"
|
|
">>> for parameter_set in parameters_list:\n"
|
|
"... a, b, style = parameter_set\n"
|
|
"... gdtr_vals = gdtr(a, b, x)\n"
|
|
"... ax.plot(x, gdtr_vals, label=fr\"$a= {a},\\, b={b}$\", ls=style)\n"
|
|
">>> ax.legend()\n"
|
|
">>> ax.set_xlabel(\"$x$\")\n"
|
|
">>> ax.set_title(\"Gamma distribution cumulative distribution function\")\n"
|
|
">>> plt.show()\n"
|
|
"\n"
|
|
"The gamma distribution is also available as `scipy.stats.gamma`. Using\n"
|
|
"`gdtr` directly can be much faster than calling the ``cdf`` method of\n"
|
|
"`scipy.stats.gamma`, especially for small arrays or individual values.\n"
|
|
"To get the same results one must use the following parametrization:\n"
|
|
"``stats.gamma(b, scale=1/a).cdf(x)=gdtr(a, b, x)``.\n"
|
|
"\n"
|
|
">>> from scipy.stats import gamma\n"
|
|
">>> a = 2.\n"
|
|
">>> b = 3\n"
|
|
">>> x = 1.\n"
|
|
">>> gdtr_result = gdtr(a, b, x) # this will often be faster than below\n"
|
|
">>> gamma_dist_result = gamma(b, scale=1/a).cdf(x)\n"
|
|
">>> gdtr_result == gamma_dist_result # test that results are equal\n"
|
|
"True")
|
|
ufunc_gdtr_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_gdtr_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_gdtr_types[0] = <char>NPY_FLOAT
|
|
ufunc_gdtr_types[1] = <char>NPY_FLOAT
|
|
ufunc_gdtr_types[2] = <char>NPY_FLOAT
|
|
ufunc_gdtr_types[3] = <char>NPY_FLOAT
|
|
ufunc_gdtr_types[4] = <char>NPY_DOUBLE
|
|
ufunc_gdtr_types[5] = <char>NPY_DOUBLE
|
|
ufunc_gdtr_types[6] = <char>NPY_DOUBLE
|
|
ufunc_gdtr_types[7] = <char>NPY_DOUBLE
|
|
ufunc_gdtr_ptr[2*0] = <void*>_func_xsf_gdtr
|
|
ufunc_gdtr_ptr[2*0+1] = <void*>(<char*>"gdtr")
|
|
ufunc_gdtr_ptr[2*1] = <void*>_func_xsf_gdtr
|
|
ufunc_gdtr_ptr[2*1+1] = <void*>(<char*>"gdtr")
|
|
ufunc_gdtr_data[0] = &ufunc_gdtr_ptr[2*0]
|
|
ufunc_gdtr_data[1] = &ufunc_gdtr_ptr[2*1]
|
|
gdtr = np.PyUFunc_FromFuncAndData(ufunc_gdtr_loops, ufunc_gdtr_data, ufunc_gdtr_types, 2, 3, 1, 0, 'gdtr', ufunc_gdtr_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_gdtrc_loops[2]
|
|
cdef void *ufunc_gdtrc_ptr[4]
|
|
cdef void *ufunc_gdtrc_data[2]
|
|
cdef char ufunc_gdtrc_types[8]
|
|
cdef char *ufunc_gdtrc_doc = (
|
|
"gdtrc(a, b, x, out=None)\n"
|
|
"\n"
|
|
"Gamma distribution survival function.\n"
|
|
"\n"
|
|
"Integral from `x` to infinity of the gamma probability density function,\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" F = \\int_x^\\infty \\frac{a^b}{\\Gamma(b)} t^{b-1} e^{-at}\\,dt,\n"
|
|
"\n"
|
|
"where :math:`\\Gamma` is the gamma function.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"a : array_like\n"
|
|
" The rate parameter of the gamma distribution, sometimes denoted\n"
|
|
" :math:`\\beta` (float). It is also the reciprocal of the scale\n"
|
|
" parameter :math:`\\theta`.\n"
|
|
"b : array_like\n"
|
|
" The shape parameter of the gamma distribution, sometimes denoted\n"
|
|
" :math:`\\alpha` (float).\n"
|
|
"x : array_like\n"
|
|
" The quantile (lower limit of integration; float).\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"F : scalar or ndarray\n"
|
|
" The survival function of the gamma distribution with parameters `a`\n"
|
|
" and `b` evaluated at `x`.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"gdtr: Gamma distribution cumulative distribution function\n"
|
|
"scipy.stats.gamma: Gamma distribution\n"
|
|
"gdtrix\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"The evaluation is carried out using the relation to the incomplete gamma\n"
|
|
"integral (regularized gamma function).\n"
|
|
"\n"
|
|
"Wrapper for the Cephes [1]_ routine `gdtrc`. Calling `gdtrc` directly can\n"
|
|
"improve performance compared to the ``sf`` method of `scipy.stats.gamma`\n"
|
|
"(see last example below).\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Cephes Mathematical Functions Library,\n"
|
|
" http://www.netlib.org/cephes/\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"Compute the function for ``a=1`` and ``b=2`` at ``x=5``.\n"
|
|
"\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import gdtrc\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
">>> gdtrc(1., 2., 5.)\n"
|
|
"0.04042768199451279\n"
|
|
"\n"
|
|
"Compute the function for ``a=1``, ``b=2`` at several points by providing\n"
|
|
"a NumPy array for `x`.\n"
|
|
"\n"
|
|
">>> xvalues = np.array([1., 2., 3., 4])\n"
|
|
">>> gdtrc(1., 1., xvalues)\n"
|
|
"array([0.36787944, 0.13533528, 0.04978707, 0.01831564])\n"
|
|
"\n"
|
|
"`gdtrc` can evaluate different parameter sets by providing arrays with\n"
|
|
"broadcasting compatible shapes for `a`, `b` and `x`. Here we compute the\n"
|
|
"function for three different `a` at four positions `x` and ``b=3``,\n"
|
|
"resulting in a 3x4 array.\n"
|
|
"\n"
|
|
">>> a = np.array([[0.5], [1.5], [2.5]])\n"
|
|
">>> x = np.array([1., 2., 3., 4])\n"
|
|
">>> a.shape, x.shape\n"
|
|
"((3, 1), (4,))\n"
|
|
"\n"
|
|
">>> gdtrc(a, 3., x)\n"
|
|
"array([[0.98561232, 0.9196986 , 0.80884683, 0.67667642],\n"
|
|
" [0.80884683, 0.42319008, 0.17357807, 0.0619688 ],\n"
|
|
" [0.54381312, 0.12465202, 0.02025672, 0.0027694 ]])\n"
|
|
"\n"
|
|
"Plot the function for four different parameter sets.\n"
|
|
"\n"
|
|
">>> a_parameters = [0.3, 1, 2, 6]\n"
|
|
">>> b_parameters = [2, 10, 15, 20]\n"
|
|
">>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']\n"
|
|
">>> parameters_list = list(zip(a_parameters, b_parameters, linestyles))\n"
|
|
">>> x = np.linspace(0, 30, 1000)\n"
|
|
">>> fig, ax = plt.subplots()\n"
|
|
">>> for parameter_set in parameters_list:\n"
|
|
"... a, b, style = parameter_set\n"
|
|
"... gdtrc_vals = gdtrc(a, b, x)\n"
|
|
"... ax.plot(x, gdtrc_vals, label=fr\"$a= {a},\\, b={b}$\", ls=style)\n"
|
|
">>> ax.legend()\n"
|
|
">>> ax.set_xlabel(\"$x$\")\n"
|
|
">>> ax.set_title(\"Gamma distribution survival function\")\n"
|
|
">>> plt.show()\n"
|
|
"\n"
|
|
"The gamma distribution is also available as `scipy.stats.gamma`.\n"
|
|
"Using `gdtrc` directly can be much faster than calling the ``sf`` method\n"
|
|
"of `scipy.stats.gamma`, especially for small arrays or individual\n"
|
|
"values. To get the same results one must use the following parametrization:\n"
|
|
"``stats.gamma(b, scale=1/a).sf(x)=gdtrc(a, b, x)``.\n"
|
|
"\n"
|
|
">>> from scipy.stats import gamma\n"
|
|
">>> a = 2\n"
|
|
">>> b = 3\n"
|
|
">>> x = 1.\n"
|
|
">>> gdtrc_result = gdtrc(a, b, x) # this will often be faster than below\n"
|
|
">>> gamma_dist_result = gamma(b, scale=1/a).sf(x)\n"
|
|
">>> gdtrc_result == gamma_dist_result # test that results are equal\n"
|
|
"True")
|
|
ufunc_gdtrc_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_gdtrc_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_gdtrc_types[0] = <char>NPY_FLOAT
|
|
ufunc_gdtrc_types[1] = <char>NPY_FLOAT
|
|
ufunc_gdtrc_types[2] = <char>NPY_FLOAT
|
|
ufunc_gdtrc_types[3] = <char>NPY_FLOAT
|
|
ufunc_gdtrc_types[4] = <char>NPY_DOUBLE
|
|
ufunc_gdtrc_types[5] = <char>NPY_DOUBLE
|
|
ufunc_gdtrc_types[6] = <char>NPY_DOUBLE
|
|
ufunc_gdtrc_types[7] = <char>NPY_DOUBLE
|
|
ufunc_gdtrc_ptr[2*0] = <void*>_func_xsf_gdtrc
|
|
ufunc_gdtrc_ptr[2*0+1] = <void*>(<char*>"gdtrc")
|
|
ufunc_gdtrc_ptr[2*1] = <void*>_func_xsf_gdtrc
|
|
ufunc_gdtrc_ptr[2*1+1] = <void*>(<char*>"gdtrc")
|
|
ufunc_gdtrc_data[0] = &ufunc_gdtrc_ptr[2*0]
|
|
ufunc_gdtrc_data[1] = &ufunc_gdtrc_ptr[2*1]
|
|
gdtrc = np.PyUFunc_FromFuncAndData(ufunc_gdtrc_loops, ufunc_gdtrc_data, ufunc_gdtrc_types, 2, 3, 1, 0, 'gdtrc', ufunc_gdtrc_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_gdtria_loops[2]
|
|
cdef void *ufunc_gdtria_ptr[4]
|
|
cdef void *ufunc_gdtria_data[2]
|
|
cdef char ufunc_gdtria_types[8]
|
|
cdef char *ufunc_gdtria_doc = (
|
|
"gdtria(p, b, x, out=None)\n"
|
|
"\n"
|
|
"Inverse of `gdtr` vs a.\n"
|
|
"\n"
|
|
"Returns the inverse with respect to the parameter `a` of ``p =\n"
|
|
"gdtr(a, b, x)``, the cumulative distribution function of the gamma\n"
|
|
"distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"p : array_like\n"
|
|
" Probability values.\n"
|
|
"b : array_like\n"
|
|
" `b` parameter values of `gdtr(a, b, x)`. `b` is the \"shape\" parameter\n"
|
|
" of the gamma distribution.\n"
|
|
"x : array_like\n"
|
|
" Nonnegative real values, from the domain of the gamma distribution.\n"
|
|
"out : ndarray, optional\n"
|
|
" If a fourth argument is given, it must be a numpy.ndarray whose size\n"
|
|
" matches the broadcast result of `a`, `b` and `x`. `out` is then the\n"
|
|
" array returned by the function.\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"a : scalar or ndarray\n"
|
|
" Values of the `a` parameter such that ``p = gdtr(a, b, x)`. ``1/a``\n"
|
|
" is the \"scale\" parameter of the gamma distribution.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"gdtr : CDF of the gamma distribution.\n"
|
|
"gdtrib : Inverse with respect to `b` of `gdtr(a, b, x)`.\n"
|
|
"gdtrix : Inverse with respect to `x` of `gdtr(a, b, x)`.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"Wrapper for the CDFLIB [1]_ Fortran routine `cdfgam`.\n"
|
|
"\n"
|
|
"The cumulative distribution function `p` is computed using a routine by\n"
|
|
"DiDinato and Morris [2]_. Computation of `a` involves a search for a value\n"
|
|
"that produces the desired value of `p`. The search relies on the\n"
|
|
"monotonicity of `p` with `a`.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Barry Brown, James Lovato, and Kathy Russell,\n"
|
|
" CDFLIB: Library of Fortran Routines for Cumulative Distribution\n"
|
|
" Functions, Inverses, and Other Parameters.\n"
|
|
".. [2] DiDinato, A. R. and Morris, A. H.,\n"
|
|
" Computation of the incomplete gamma function ratios and their\n"
|
|
" inverse. ACM Trans. Math. Softw. 12 (1986), 377-393.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"First evaluate `gdtr`.\n"
|
|
"\n"
|
|
">>> from scipy.special import gdtr, gdtria\n"
|
|
">>> p = gdtr(1.2, 3.4, 5.6)\n"
|
|
">>> print(p)\n"
|
|
"0.94378087442\n"
|
|
"\n"
|
|
"Verify the inverse.\n"
|
|
"\n"
|
|
">>> gdtria(p, 3.4, 5.6)\n"
|
|
"1.2")
|
|
ufunc_gdtria_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_gdtria_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_gdtria_types[0] = <char>NPY_FLOAT
|
|
ufunc_gdtria_types[1] = <char>NPY_FLOAT
|
|
ufunc_gdtria_types[2] = <char>NPY_FLOAT
|
|
ufunc_gdtria_types[3] = <char>NPY_FLOAT
|
|
ufunc_gdtria_types[4] = <char>NPY_DOUBLE
|
|
ufunc_gdtria_types[5] = <char>NPY_DOUBLE
|
|
ufunc_gdtria_types[6] = <char>NPY_DOUBLE
|
|
ufunc_gdtria_types[7] = <char>NPY_DOUBLE
|
|
ufunc_gdtria_ptr[2*0] = <void*>_func_gdtria
|
|
ufunc_gdtria_ptr[2*0+1] = <void*>(<char*>"gdtria")
|
|
ufunc_gdtria_ptr[2*1] = <void*>_func_gdtria
|
|
ufunc_gdtria_ptr[2*1+1] = <void*>(<char*>"gdtria")
|
|
ufunc_gdtria_data[0] = &ufunc_gdtria_ptr[2*0]
|
|
ufunc_gdtria_data[1] = &ufunc_gdtria_ptr[2*1]
|
|
gdtria = np.PyUFunc_FromFuncAndData(ufunc_gdtria_loops, ufunc_gdtria_data, ufunc_gdtria_types, 2, 3, 1, 0, 'gdtria', ufunc_gdtria_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_gdtrib_loops[2]
|
|
cdef void *ufunc_gdtrib_ptr[4]
|
|
cdef void *ufunc_gdtrib_data[2]
|
|
cdef char ufunc_gdtrib_types[8]
|
|
cdef char *ufunc_gdtrib_doc = (
|
|
"gdtrib(a, p, x, out=None)\n"
|
|
"\n"
|
|
"Inverse of `gdtr` vs b.\n"
|
|
"\n"
|
|
"Returns the inverse with respect to the parameter `b` of ``p =\n"
|
|
"gdtr(a, b, x)``, the cumulative distribution function of the gamma\n"
|
|
"distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"a : array_like\n"
|
|
" `a` parameter values of ``gdtr(a, b, x)`. ``1/a`` is the \"scale\"\n"
|
|
" parameter of the gamma distribution.\n"
|
|
"p : array_like\n"
|
|
" Probability values.\n"
|
|
"x : array_like\n"
|
|
" Nonnegative real values, from the domain of the gamma distribution.\n"
|
|
"out : ndarray, optional\n"
|
|
" If a fourth argument is given, it must be a numpy.ndarray whose size\n"
|
|
" matches the broadcast result of `a`, `b` and `x`. `out` is then the\n"
|
|
" array returned by the function.\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"b : scalar or ndarray\n"
|
|
" Values of the `b` parameter such that `p = gdtr(a, b, x)`. `b` is\n"
|
|
" the \"shape\" parameter of the gamma distribution.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"gdtr : CDF of the gamma distribution.\n"
|
|
"gdtria : Inverse with respect to `a` of `gdtr(a, b, x)`.\n"
|
|
"gdtrix : Inverse with respect to `x` of `gdtr(a, b, x)`.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"\n"
|
|
"The cumulative distribution function `p` is computed using the Cephes [1]_\n"
|
|
"routines `igam` and `igamc`. Computation of `b` involves a search for a value\n"
|
|
"that produces the desired value of `p` using Chandrupatla's bracketing\n"
|
|
"root finding algorithm [2]_.\n"
|
|
"\n"
|
|
"Note that there are some edge cases where `gdtrib` is extended by taking\n"
|
|
"limits where they are uniquely defined. In particular\n"
|
|
"``x == 0`` with ``p > 0`` and ``p == 0`` with ``x > 0``.\n"
|
|
"For these edge cases, a numerical result will be returned for\n"
|
|
"``gdtrib(a, p, x)`` even though ``gdtr(a, gdtrib(a, p, x), x)`` is\n"
|
|
"undefined.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Cephes Mathematical Functions Library,\n"
|
|
" http://www.netlib.org/cephes/\n"
|
|
".. [2] Chandrupatla, Tirupathi R.\n"
|
|
" \"A new hybrid quadratic/bisection algorithm for finding the zero of a\n"
|
|
" nonlinear function without using derivatives\".\n"
|
|
" Advances in Engineering Software, 28(3), 145-149.\n"
|
|
" https://doi.org/10.1016/s0965-9978(96)00051-8\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"First evaluate `gdtr`.\n"
|
|
"\n"
|
|
">>> from scipy.special import gdtr, gdtrib\n"
|
|
">>> p = gdtr(1.2, 3.4, 5.6)\n"
|
|
">>> print(p)\n"
|
|
"0.94378087442\n"
|
|
"\n"
|
|
"Verify the inverse.\n"
|
|
"\n"
|
|
">>> gdtrib(1.2, p, 5.6)\n"
|
|
"3.3999999999999995")
|
|
ufunc_gdtrib_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_gdtrib_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_gdtrib_types[0] = <char>NPY_FLOAT
|
|
ufunc_gdtrib_types[1] = <char>NPY_FLOAT
|
|
ufunc_gdtrib_types[2] = <char>NPY_FLOAT
|
|
ufunc_gdtrib_types[3] = <char>NPY_FLOAT
|
|
ufunc_gdtrib_types[4] = <char>NPY_DOUBLE
|
|
ufunc_gdtrib_types[5] = <char>NPY_DOUBLE
|
|
ufunc_gdtrib_types[6] = <char>NPY_DOUBLE
|
|
ufunc_gdtrib_types[7] = <char>NPY_DOUBLE
|
|
ufunc_gdtrib_ptr[2*0] = <void*>_func_xsf_gdtrib
|
|
ufunc_gdtrib_ptr[2*0+1] = <void*>(<char*>"gdtrib")
|
|
ufunc_gdtrib_ptr[2*1] = <void*>_func_xsf_gdtrib
|
|
ufunc_gdtrib_ptr[2*1+1] = <void*>(<char*>"gdtrib")
|
|
ufunc_gdtrib_data[0] = &ufunc_gdtrib_ptr[2*0]
|
|
ufunc_gdtrib_data[1] = &ufunc_gdtrib_ptr[2*1]
|
|
gdtrib = np.PyUFunc_FromFuncAndData(ufunc_gdtrib_loops, ufunc_gdtrib_data, ufunc_gdtrib_types, 2, 3, 1, 0, 'gdtrib', ufunc_gdtrib_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_gdtrix_loops[2]
|
|
cdef void *ufunc_gdtrix_ptr[4]
|
|
cdef void *ufunc_gdtrix_data[2]
|
|
cdef char ufunc_gdtrix_types[8]
|
|
cdef char *ufunc_gdtrix_doc = (
|
|
"gdtrix(a, b, p, out=None)\n"
|
|
"\n"
|
|
"Inverse of `gdtr` vs x.\n"
|
|
"\n"
|
|
"Returns the inverse with respect to the parameter `x` of ``p =\n"
|
|
"gdtr(a, b, x)``, the cumulative distribution function of the gamma\n"
|
|
"distribution. This is also known as the pth quantile of the\n"
|
|
"distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"a : array_like\n"
|
|
" `a` parameter values of ``gdtr(a, b, x)``. ``1/a`` is the \"scale\"\n"
|
|
" parameter of the gamma distribution.\n"
|
|
"b : array_like\n"
|
|
" `b` parameter values of ``gdtr(a, b, x)``. `b` is the \"shape\" parameter\n"
|
|
" of the gamma distribution.\n"
|
|
"p : array_like\n"
|
|
" Probability values.\n"
|
|
"out : ndarray, optional\n"
|
|
" If a fourth argument is given, it must be a numpy.ndarray whose size\n"
|
|
" matches the broadcast result of `a`, `b` and `x`. `out` is then the\n"
|
|
" array returned by the function.\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"x : scalar or ndarray\n"
|
|
" Values of the `x` parameter such that `p = gdtr(a, b, x)`.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"gdtr : CDF of the gamma distribution.\n"
|
|
"gdtria : Inverse with respect to `a` of ``gdtr(a, b, x)``.\n"
|
|
"gdtrib : Inverse with respect to `b` of ``gdtr(a, b, x)``.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"Wrapper for the CDFLIB [1]_ Fortran routine `cdfgam`.\n"
|
|
"\n"
|
|
"The cumulative distribution function `p` is computed using a routine by\n"
|
|
"DiDinato and Morris [2]_. Computation of `x` involves a search for a value\n"
|
|
"that produces the desired value of `p`. The search relies on the\n"
|
|
"monotonicity of `p` with `x`.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Barry Brown, James Lovato, and Kathy Russell,\n"
|
|
" CDFLIB: Library of Fortran Routines for Cumulative Distribution\n"
|
|
" Functions, Inverses, and Other Parameters.\n"
|
|
".. [2] DiDinato, A. R. and Morris, A. H.,\n"
|
|
" Computation of the incomplete gamma function ratios and their\n"
|
|
" inverse. ACM Trans. Math. Softw. 12 (1986), 377-393.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"First evaluate `gdtr`.\n"
|
|
"\n"
|
|
">>> from scipy.special import gdtr, gdtrix\n"
|
|
">>> p = gdtr(1.2, 3.4, 5.6)\n"
|
|
">>> print(p)\n"
|
|
"0.94378087442\n"
|
|
"\n"
|
|
"Verify the inverse.\n"
|
|
"\n"
|
|
">>> gdtrix(1.2, 3.4, p)\n"
|
|
"5.5999999999999996")
|
|
ufunc_gdtrix_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_gdtrix_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_gdtrix_types[0] = <char>NPY_FLOAT
|
|
ufunc_gdtrix_types[1] = <char>NPY_FLOAT
|
|
ufunc_gdtrix_types[2] = <char>NPY_FLOAT
|
|
ufunc_gdtrix_types[3] = <char>NPY_FLOAT
|
|
ufunc_gdtrix_types[4] = <char>NPY_DOUBLE
|
|
ufunc_gdtrix_types[5] = <char>NPY_DOUBLE
|
|
ufunc_gdtrix_types[6] = <char>NPY_DOUBLE
|
|
ufunc_gdtrix_types[7] = <char>NPY_DOUBLE
|
|
ufunc_gdtrix_ptr[2*0] = <void*>_func_gdtrix
|
|
ufunc_gdtrix_ptr[2*0+1] = <void*>(<char*>"gdtrix")
|
|
ufunc_gdtrix_ptr[2*1] = <void*>_func_gdtrix
|
|
ufunc_gdtrix_ptr[2*1+1] = <void*>(<char*>"gdtrix")
|
|
ufunc_gdtrix_data[0] = &ufunc_gdtrix_ptr[2*0]
|
|
ufunc_gdtrix_data[1] = &ufunc_gdtrix_ptr[2*1]
|
|
gdtrix = np.PyUFunc_FromFuncAndData(ufunc_gdtrix_loops, ufunc_gdtrix_data, ufunc_gdtrix_types, 2, 3, 1, 0, 'gdtrix', ufunc_gdtrix_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_huber_loops[2]
|
|
cdef void *ufunc_huber_ptr[4]
|
|
cdef void *ufunc_huber_data[2]
|
|
cdef char ufunc_huber_types[6]
|
|
cdef char *ufunc_huber_doc = (
|
|
"huber(delta, r, out=None)\n"
|
|
"\n"
|
|
"Huber loss function.\n"
|
|
"\n"
|
|
".. math:: \\text{huber}(\\delta, r) = \\begin{cases} \\infty & \\delta < 0 \\\\\n"
|
|
" \\frac{1}{2}r^2 & 0 \\le \\delta, | r | \\le \\delta \\\\\n"
|
|
" \\delta ( |r| - \\frac{1}{2}\\delta ) & \\text{otherwise} \\end{cases}\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"delta : ndarray\n"
|
|
" Input array, indicating the quadratic vs. linear loss changepoint.\n"
|
|
"r : ndarray\n"
|
|
" Input array, possibly representing residuals.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" The computed Huber loss function values.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"pseudo_huber : smooth approximation of this function\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"`huber` is useful as a loss function in robust statistics or machine\n"
|
|
"learning to reduce the influence of outliers as compared to the common\n"
|
|
"squared error loss, residuals with a magnitude higher than `delta` are\n"
|
|
"not squared [1]_.\n"
|
|
"\n"
|
|
"Typically, `r` represents residuals, the difference\n"
|
|
"between a model prediction and data. Then, for :math:`|r|\\leq\\delta`,\n"
|
|
"`huber` resembles the squared error and for :math:`|r|>\\delta` the\n"
|
|
"absolute error. This way, the Huber loss often achieves\n"
|
|
"a fast convergence in model fitting for small residuals like the squared\n"
|
|
"error loss function and still reduces the influence of outliers\n"
|
|
"(:math:`|r|>\\delta`) like the absolute error loss. As :math:`\\delta` is\n"
|
|
"the cutoff between squared and absolute error regimes, it has\n"
|
|
"to be tuned carefully for each problem. `huber` is also\n"
|
|
"convex, making it suitable for gradient based optimization.\n"
|
|
"\n"
|
|
".. versionadded:: 0.15.0\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Peter Huber. \"Robust Estimation of a Location Parameter\",\n"
|
|
" 1964. Annals of Statistics. 53 (1): 73 - 101.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"Import all necessary modules.\n"
|
|
"\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import huber\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
"\n"
|
|
"Compute the function for ``delta=1`` at ``r=2``\n"
|
|
"\n"
|
|
">>> huber(1., 2.)\n"
|
|
"1.5\n"
|
|
"\n"
|
|
"Compute the function for different `delta` by providing a NumPy array or\n"
|
|
"list for `delta`.\n"
|
|
"\n"
|
|
">>> huber([1., 3., 5.], 4.)\n"
|
|
"array([3.5, 7.5, 8. ])\n"
|
|
"\n"
|
|
"Compute the function at different points by providing a NumPy array or\n"
|
|
"list for `r`.\n"
|
|
"\n"
|
|
">>> huber(2., np.array([1., 1.5, 3.]))\n"
|
|
"array([0.5 , 1.125, 4. ])\n"
|
|
"\n"
|
|
"The function can be calculated for different `delta` and `r` by\n"
|
|
"providing arrays for both with compatible shapes for broadcasting.\n"
|
|
"\n"
|
|
">>> r = np.array([1., 2.5, 8., 10.])\n"
|
|
">>> deltas = np.array([[1.], [5.], [9.]])\n"
|
|
">>> print(r.shape, deltas.shape)\n"
|
|
"(4,) (3, 1)\n"
|
|
"\n"
|
|
">>> huber(deltas, r)\n"
|
|
"array([[ 0.5 , 2. , 7.5 , 9.5 ],\n"
|
|
" [ 0.5 , 3.125, 27.5 , 37.5 ],\n"
|
|
" [ 0.5 , 3.125, 32. , 49.5 ]])\n"
|
|
"\n"
|
|
"Plot the function for different `delta`.\n"
|
|
"\n"
|
|
">>> x = np.linspace(-4, 4, 500)\n"
|
|
">>> deltas = [1, 2, 3]\n"
|
|
">>> linestyles = [\"dashed\", \"dotted\", \"dashdot\"]\n"
|
|
">>> fig, ax = plt.subplots()\n"
|
|
">>> combined_plot_parameters = list(zip(deltas, linestyles))\n"
|
|
">>> for delta, style in combined_plot_parameters:\n"
|
|
"... ax.plot(x, huber(delta, x), label=fr\"$\\delta={delta}$\", ls=style)\n"
|
|
">>> ax.legend(loc=\"upper center\")\n"
|
|
">>> ax.set_xlabel(\"$x$\")\n"
|
|
">>> ax.set_title(r\"Huber loss function $h_{\\delta}(x)$\")\n"
|
|
">>> ax.set_xlim(-4, 4)\n"
|
|
">>> ax.set_ylim(0, 8)\n"
|
|
">>> plt.show()")
|
|
ufunc_huber_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_huber_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_huber_types[0] = <char>NPY_FLOAT
|
|
ufunc_huber_types[1] = <char>NPY_FLOAT
|
|
ufunc_huber_types[2] = <char>NPY_FLOAT
|
|
ufunc_huber_types[3] = <char>NPY_DOUBLE
|
|
ufunc_huber_types[4] = <char>NPY_DOUBLE
|
|
ufunc_huber_types[5] = <char>NPY_DOUBLE
|
|
ufunc_huber_ptr[2*0] = <void*>_func_huber
|
|
ufunc_huber_ptr[2*0+1] = <void*>(<char*>"huber")
|
|
ufunc_huber_ptr[2*1] = <void*>_func_huber
|
|
ufunc_huber_ptr[2*1+1] = <void*>(<char*>"huber")
|
|
ufunc_huber_data[0] = &ufunc_huber_ptr[2*0]
|
|
ufunc_huber_data[1] = &ufunc_huber_ptr[2*1]
|
|
huber = np.PyUFunc_FromFuncAndData(ufunc_huber_loops, ufunc_huber_data, ufunc_huber_types, 2, 2, 1, 0, 'huber', ufunc_huber_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_hyp0f1_loops[4]
|
|
cdef void *ufunc_hyp0f1_ptr[8]
|
|
cdef void *ufunc_hyp0f1_data[4]
|
|
cdef char ufunc_hyp0f1_types[12]
|
|
cdef char *ufunc_hyp0f1_doc = (
|
|
"hyp0f1(v, z, out=None)\n"
|
|
"\n"
|
|
"Confluent hypergeometric limit function 0F1.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"v : array_like\n"
|
|
" Real-valued parameter\n"
|
|
"z : array_like\n"
|
|
" Real- or complex-valued argument\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" The confluent hypergeometric limit function\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"This function is defined as:\n"
|
|
"\n"
|
|
".. math:: _0F_1(v, z) = \\sum_{k=0}^{\\infty}\\frac{z^k}{(v)_k k!}.\n"
|
|
"\n"
|
|
"It's also the limit as :math:`q \\to \\infty` of :math:`_1F_1(q; v; z/q)`,\n"
|
|
"and satisfies the differential equation :math:`f''(z) + vf'(z) =\n"
|
|
"f(z)`. See [1]_ for more information.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Wolfram MathWorld, \"Confluent Hypergeometric Limit Function\",\n"
|
|
" http://mathworld.wolfram.com/ConfluentHypergeometricLimitFunction.html\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> import scipy.special as sc\n"
|
|
"\n"
|
|
"It is one when `z` is zero.\n"
|
|
"\n"
|
|
">>> sc.hyp0f1(1, 0)\n"
|
|
"1.0\n"
|
|
"\n"
|
|
"It is the limit of the confluent hypergeometric function as `q`\n"
|
|
"goes to infinity.\n"
|
|
"\n"
|
|
">>> q = np.array([1, 10, 100, 1000])\n"
|
|
">>> v = 1\n"
|
|
">>> z = 1\n"
|
|
">>> sc.hyp1f1(q, v, z / q)\n"
|
|
"array([2.71828183, 2.31481985, 2.28303778, 2.27992985])\n"
|
|
">>> sc.hyp0f1(v, z)\n"
|
|
"2.2795853023360673\n"
|
|
"\n"
|
|
"It is related to Bessel functions.\n"
|
|
"\n"
|
|
">>> n = 1\n"
|
|
">>> x = np.linspace(0, 1, 5)\n"
|
|
">>> sc.jv(n, x)\n"
|
|
"array([0. , 0.12402598, 0.24226846, 0.3492436 , 0.44005059])\n"
|
|
">>> (0.5 * x)**n / sc.factorial(n) * sc.hyp0f1(n + 1, -0.25 * x**2)\n"
|
|
"array([0. , 0.12402598, 0.24226846, 0.3492436 , 0.44005059])")
|
|
ufunc_hyp0f1_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_hyp0f1_loops[1] = <np.PyUFuncGenericFunction>loop_D_dD__As_fF_F
|
|
ufunc_hyp0f1_loops[2] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_hyp0f1_loops[3] = <np.PyUFuncGenericFunction>loop_D_dD__As_dD_D
|
|
ufunc_hyp0f1_types[0] = <char>NPY_FLOAT
|
|
ufunc_hyp0f1_types[1] = <char>NPY_FLOAT
|
|
ufunc_hyp0f1_types[2] = <char>NPY_FLOAT
|
|
ufunc_hyp0f1_types[3] = <char>NPY_FLOAT
|
|
ufunc_hyp0f1_types[4] = <char>NPY_CFLOAT
|
|
ufunc_hyp0f1_types[5] = <char>NPY_CFLOAT
|
|
ufunc_hyp0f1_types[6] = <char>NPY_DOUBLE
|
|
ufunc_hyp0f1_types[7] = <char>NPY_DOUBLE
|
|
ufunc_hyp0f1_types[8] = <char>NPY_DOUBLE
|
|
ufunc_hyp0f1_types[9] = <char>NPY_DOUBLE
|
|
ufunc_hyp0f1_types[10] = <char>NPY_CDOUBLE
|
|
ufunc_hyp0f1_types[11] = <char>NPY_CDOUBLE
|
|
ufunc_hyp0f1_ptr[2*0] = <void*>_func__hyp0f1_real
|
|
ufunc_hyp0f1_ptr[2*0+1] = <void*>(<char*>"hyp0f1")
|
|
ufunc_hyp0f1_ptr[2*1] = <void*>_func__hyp0f1_cmplx
|
|
ufunc_hyp0f1_ptr[2*1+1] = <void*>(<char*>"hyp0f1")
|
|
ufunc_hyp0f1_ptr[2*2] = <void*>_func__hyp0f1_real
|
|
ufunc_hyp0f1_ptr[2*2+1] = <void*>(<char*>"hyp0f1")
|
|
ufunc_hyp0f1_ptr[2*3] = <void*>_func__hyp0f1_cmplx
|
|
ufunc_hyp0f1_ptr[2*3+1] = <void*>(<char*>"hyp0f1")
|
|
ufunc_hyp0f1_data[0] = &ufunc_hyp0f1_ptr[2*0]
|
|
ufunc_hyp0f1_data[1] = &ufunc_hyp0f1_ptr[2*1]
|
|
ufunc_hyp0f1_data[2] = &ufunc_hyp0f1_ptr[2*2]
|
|
ufunc_hyp0f1_data[3] = &ufunc_hyp0f1_ptr[2*3]
|
|
hyp0f1 = np.PyUFunc_FromFuncAndData(ufunc_hyp0f1_loops, ufunc_hyp0f1_data, ufunc_hyp0f1_types, 4, 2, 1, 0, 'hyp0f1', ufunc_hyp0f1_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_hyp1f1_loops[4]
|
|
cdef void *ufunc_hyp1f1_ptr[8]
|
|
cdef void *ufunc_hyp1f1_data[4]
|
|
cdef char ufunc_hyp1f1_types[16]
|
|
cdef char *ufunc_hyp1f1_doc = (
|
|
"hyp1f1(a, b, x, out=None)\n"
|
|
"\n"
|
|
"Confluent hypergeometric function 1F1.\n"
|
|
"\n"
|
|
"The confluent hypergeometric function is defined by the series\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" {}_1F_1(a; b; x) = \\sum_{k = 0}^\\infty \\frac{(a)_k}{(b)_k k!} x^k.\n"
|
|
"\n"
|
|
"See [dlmf]_ for more details. Here :math:`(\\cdot)_k` is the\n"
|
|
"Pochhammer symbol; see `poch`.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"a, b : array_like\n"
|
|
" Real parameters\n"
|
|
"x : array_like\n"
|
|
" Real or complex argument\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" Values of the confluent hypergeometric function\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"hyperu : another confluent hypergeometric function\n"
|
|
"hyp0f1 : confluent hypergeometric limit function\n"
|
|
"hyp2f1 : Gaussian hypergeometric function\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"For real values, this function uses the ``hyp1f1`` routine from the C++ Boost\n"
|
|
"library [2]_, for complex values a C translation of the specfun\n"
|
|
"Fortran library [3]_.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [dlmf] NIST Digital Library of Mathematical Functions\n"
|
|
" https://dlmf.nist.gov/13.2#E2\n"
|
|
".. [2] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
|
|
".. [3] Zhang, Jin, \"Computation of Special Functions\", John Wiley\n"
|
|
" and Sons, Inc, 1996.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> import scipy.special as sc\n"
|
|
"\n"
|
|
"It is one when `x` is zero:\n"
|
|
"\n"
|
|
">>> sc.hyp1f1(0.5, 0.5, 0)\n"
|
|
"1.0\n"
|
|
"\n"
|
|
"It is singular when `b` is a nonpositive integer.\n"
|
|
"\n"
|
|
">>> sc.hyp1f1(0.5, -1, 0)\n"
|
|
"inf\n"
|
|
"\n"
|
|
"It is a polynomial when `a` is a nonpositive integer.\n"
|
|
"\n"
|
|
">>> a, b, x = -1, 0.5, np.array([1.0, 2.0, 3.0, 4.0])\n"
|
|
">>> sc.hyp1f1(a, b, x)\n"
|
|
"array([-1., -3., -5., -7.])\n"
|
|
">>> 1 + (a / b) * x\n"
|
|
"array([-1., -3., -5., -7.])\n"
|
|
"\n"
|
|
"It reduces to the exponential function when ``a = b``.\n"
|
|
"\n"
|
|
">>> sc.hyp1f1(2, 2, [1, 2, 3, 4])\n"
|
|
"array([ 2.71828183, 7.3890561 , 20.08553692, 54.59815003])\n"
|
|
">>> np.exp([1, 2, 3, 4])\n"
|
|
"array([ 2.71828183, 7.3890561 , 20.08553692, 54.59815003])")
|
|
ufunc_hyp1f1_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_hyp1f1_loops[1] = <np.PyUFuncGenericFunction>loop_D_ddD__As_ffF_F
|
|
ufunc_hyp1f1_loops[2] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_hyp1f1_loops[3] = <np.PyUFuncGenericFunction>loop_D_ddD__As_ddD_D
|
|
ufunc_hyp1f1_types[0] = <char>NPY_FLOAT
|
|
ufunc_hyp1f1_types[1] = <char>NPY_FLOAT
|
|
ufunc_hyp1f1_types[2] = <char>NPY_FLOAT
|
|
ufunc_hyp1f1_types[3] = <char>NPY_FLOAT
|
|
ufunc_hyp1f1_types[4] = <char>NPY_FLOAT
|
|
ufunc_hyp1f1_types[5] = <char>NPY_FLOAT
|
|
ufunc_hyp1f1_types[6] = <char>NPY_CFLOAT
|
|
ufunc_hyp1f1_types[7] = <char>NPY_CFLOAT
|
|
ufunc_hyp1f1_types[8] = <char>NPY_DOUBLE
|
|
ufunc_hyp1f1_types[9] = <char>NPY_DOUBLE
|
|
ufunc_hyp1f1_types[10] = <char>NPY_DOUBLE
|
|
ufunc_hyp1f1_types[11] = <char>NPY_DOUBLE
|
|
ufunc_hyp1f1_types[12] = <char>NPY_DOUBLE
|
|
ufunc_hyp1f1_types[13] = <char>NPY_DOUBLE
|
|
ufunc_hyp1f1_types[14] = <char>NPY_CDOUBLE
|
|
ufunc_hyp1f1_types[15] = <char>NPY_CDOUBLE
|
|
ufunc_hyp1f1_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_hyp1f1_double
|
|
ufunc_hyp1f1_ptr[2*0+1] = <void*>(<char*>"hyp1f1")
|
|
ufunc_hyp1f1_ptr[2*1] = <void*>_func_chyp1f1_wrap
|
|
ufunc_hyp1f1_ptr[2*1+1] = <void*>(<char*>"hyp1f1")
|
|
ufunc_hyp1f1_ptr[2*2] = <void*>scipy.special._ufuncs_cxx._export_hyp1f1_double
|
|
ufunc_hyp1f1_ptr[2*2+1] = <void*>(<char*>"hyp1f1")
|
|
ufunc_hyp1f1_ptr[2*3] = <void*>_func_chyp1f1_wrap
|
|
ufunc_hyp1f1_ptr[2*3+1] = <void*>(<char*>"hyp1f1")
|
|
ufunc_hyp1f1_data[0] = &ufunc_hyp1f1_ptr[2*0]
|
|
ufunc_hyp1f1_data[1] = &ufunc_hyp1f1_ptr[2*1]
|
|
ufunc_hyp1f1_data[2] = &ufunc_hyp1f1_ptr[2*2]
|
|
ufunc_hyp1f1_data[3] = &ufunc_hyp1f1_ptr[2*3]
|
|
hyp1f1 = np.PyUFunc_FromFuncAndData(ufunc_hyp1f1_loops, ufunc_hyp1f1_data, ufunc_hyp1f1_types, 4, 3, 1, 0, 'hyp1f1', ufunc_hyp1f1_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_hyperu_loops[2]
|
|
cdef void *ufunc_hyperu_ptr[4]
|
|
cdef void *ufunc_hyperu_data[2]
|
|
cdef char ufunc_hyperu_types[8]
|
|
cdef char *ufunc_hyperu_doc = (
|
|
"hyperu(a, b, x, out=None)\n"
|
|
"\n"
|
|
"Confluent hypergeometric function U\n"
|
|
"\n"
|
|
"It is defined as the solution to the equation\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" x \\frac{d^2w}{dx^2} + (b - x) \\frac{dw}{dx} - aw = 0\n"
|
|
"\n"
|
|
"which satisfies the property\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" U(a, b, x) \\sim x^{-a}\n"
|
|
"\n"
|
|
"as :math:`x \\to \\infty`. See [dlmf]_ for more details.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"a, b : array_like\n"
|
|
" Real-valued parameters\n"
|
|
"x : array_like\n"
|
|
" Real-valued argument\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" Values of `U`\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [dlmf] NIST Digital Library of Mathematics Functions\n"
|
|
" https://dlmf.nist.gov/13.2#E6\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> import scipy.special as sc\n"
|
|
"\n"
|
|
"It has a branch cut along the negative `x` axis.\n"
|
|
"\n"
|
|
">>> x = np.linspace(-0.1, -10, 5)\n"
|
|
">>> sc.hyperu(1, 1, x)\n"
|
|
"array([nan, nan, nan, nan, nan])\n"
|
|
"\n"
|
|
"It approaches zero as `x` goes to infinity.\n"
|
|
"\n"
|
|
">>> x = np.array([1, 10, 100])\n"
|
|
">>> sc.hyperu(1, 1, x)\n"
|
|
"array([0.59634736, 0.09156333, 0.00990194])\n"
|
|
"\n"
|
|
"It satisfies Kummer's transformation.\n"
|
|
"\n"
|
|
">>> a, b, x = 2, 1, 1\n"
|
|
">>> sc.hyperu(a, b, x)\n"
|
|
"0.1926947246463881\n"
|
|
">>> x**(1 - b) * sc.hyperu(a - b + 1, 2 - b, x)\n"
|
|
"0.1926947246463881")
|
|
ufunc_hyperu_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_hyperu_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_hyperu_types[0] = <char>NPY_FLOAT
|
|
ufunc_hyperu_types[1] = <char>NPY_FLOAT
|
|
ufunc_hyperu_types[2] = <char>NPY_FLOAT
|
|
ufunc_hyperu_types[3] = <char>NPY_FLOAT
|
|
ufunc_hyperu_types[4] = <char>NPY_DOUBLE
|
|
ufunc_hyperu_types[5] = <char>NPY_DOUBLE
|
|
ufunc_hyperu_types[6] = <char>NPY_DOUBLE
|
|
ufunc_hyperu_types[7] = <char>NPY_DOUBLE
|
|
ufunc_hyperu_ptr[2*0] = <void*>_func_hyperu
|
|
ufunc_hyperu_ptr[2*0+1] = <void*>(<char*>"hyperu")
|
|
ufunc_hyperu_ptr[2*1] = <void*>_func_hyperu
|
|
ufunc_hyperu_ptr[2*1+1] = <void*>(<char*>"hyperu")
|
|
ufunc_hyperu_data[0] = &ufunc_hyperu_ptr[2*0]
|
|
ufunc_hyperu_data[1] = &ufunc_hyperu_ptr[2*1]
|
|
hyperu = np.PyUFunc_FromFuncAndData(ufunc_hyperu_loops, ufunc_hyperu_data, ufunc_hyperu_types, 2, 3, 1, 0, 'hyperu', ufunc_hyperu_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_inv_boxcox_loops[2]
|
|
cdef void *ufunc_inv_boxcox_ptr[4]
|
|
cdef void *ufunc_inv_boxcox_data[2]
|
|
cdef char ufunc_inv_boxcox_types[6]
|
|
cdef char *ufunc_inv_boxcox_doc = (
|
|
"inv_boxcox(y, lmbda, out=None)\n"
|
|
"\n"
|
|
"Compute the inverse of the Box-Cox transformation.\n"
|
|
"\n"
|
|
"Find ``x`` such that::\n"
|
|
"\n"
|
|
" y = (x**lmbda - 1) / lmbda if lmbda != 0\n"
|
|
" log(x) if lmbda == 0\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"y : array_like\n"
|
|
" Data to be transformed.\n"
|
|
"lmbda : array_like\n"
|
|
" Power parameter of the Box-Cox transform.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"x : scalar or ndarray\n"
|
|
" Transformed data.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"\n"
|
|
".. versionadded:: 0.16.0\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> from scipy.special import boxcox, inv_boxcox\n"
|
|
">>> y = boxcox([1, 4, 10], 2.5)\n"
|
|
">>> inv_boxcox(y, 2.5)\n"
|
|
"array([1., 4., 10.])")
|
|
ufunc_inv_boxcox_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_inv_boxcox_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_inv_boxcox_types[0] = <char>NPY_FLOAT
|
|
ufunc_inv_boxcox_types[1] = <char>NPY_FLOAT
|
|
ufunc_inv_boxcox_types[2] = <char>NPY_FLOAT
|
|
ufunc_inv_boxcox_types[3] = <char>NPY_DOUBLE
|
|
ufunc_inv_boxcox_types[4] = <char>NPY_DOUBLE
|
|
ufunc_inv_boxcox_types[5] = <char>NPY_DOUBLE
|
|
ufunc_inv_boxcox_ptr[2*0] = <void*>_func_inv_boxcox
|
|
ufunc_inv_boxcox_ptr[2*0+1] = <void*>(<char*>"inv_boxcox")
|
|
ufunc_inv_boxcox_ptr[2*1] = <void*>_func_inv_boxcox
|
|
ufunc_inv_boxcox_ptr[2*1+1] = <void*>(<char*>"inv_boxcox")
|
|
ufunc_inv_boxcox_data[0] = &ufunc_inv_boxcox_ptr[2*0]
|
|
ufunc_inv_boxcox_data[1] = &ufunc_inv_boxcox_ptr[2*1]
|
|
inv_boxcox = np.PyUFunc_FromFuncAndData(ufunc_inv_boxcox_loops, ufunc_inv_boxcox_data, ufunc_inv_boxcox_types, 2, 2, 1, 0, 'inv_boxcox', ufunc_inv_boxcox_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_inv_boxcox1p_loops[2]
|
|
cdef void *ufunc_inv_boxcox1p_ptr[4]
|
|
cdef void *ufunc_inv_boxcox1p_data[2]
|
|
cdef char ufunc_inv_boxcox1p_types[6]
|
|
cdef char *ufunc_inv_boxcox1p_doc = (
|
|
"inv_boxcox1p(y, lmbda, out=None)\n"
|
|
"\n"
|
|
"Compute the inverse of the Box-Cox transformation.\n"
|
|
"\n"
|
|
"Find ``x`` such that::\n"
|
|
"\n"
|
|
" y = ((1+x)**lmbda - 1) / lmbda if lmbda != 0\n"
|
|
" log(1+x) if lmbda == 0\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"y : array_like\n"
|
|
" Data to be transformed.\n"
|
|
"lmbda : array_like\n"
|
|
" Power parameter of the Box-Cox transform.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"x : scalar or ndarray\n"
|
|
" Transformed data.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"\n"
|
|
".. versionadded:: 0.16.0\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> from scipy.special import boxcox1p, inv_boxcox1p\n"
|
|
">>> y = boxcox1p([1, 4, 10], 2.5)\n"
|
|
">>> inv_boxcox1p(y, 2.5)\n"
|
|
"array([1., 4., 10.])")
|
|
ufunc_inv_boxcox1p_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_inv_boxcox1p_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_inv_boxcox1p_types[0] = <char>NPY_FLOAT
|
|
ufunc_inv_boxcox1p_types[1] = <char>NPY_FLOAT
|
|
ufunc_inv_boxcox1p_types[2] = <char>NPY_FLOAT
|
|
ufunc_inv_boxcox1p_types[3] = <char>NPY_DOUBLE
|
|
ufunc_inv_boxcox1p_types[4] = <char>NPY_DOUBLE
|
|
ufunc_inv_boxcox1p_types[5] = <char>NPY_DOUBLE
|
|
ufunc_inv_boxcox1p_ptr[2*0] = <void*>_func_inv_boxcox1p
|
|
ufunc_inv_boxcox1p_ptr[2*0+1] = <void*>(<char*>"inv_boxcox1p")
|
|
ufunc_inv_boxcox1p_ptr[2*1] = <void*>_func_inv_boxcox1p
|
|
ufunc_inv_boxcox1p_ptr[2*1+1] = <void*>(<char*>"inv_boxcox1p")
|
|
ufunc_inv_boxcox1p_data[0] = &ufunc_inv_boxcox1p_ptr[2*0]
|
|
ufunc_inv_boxcox1p_data[1] = &ufunc_inv_boxcox1p_ptr[2*1]
|
|
inv_boxcox1p = np.PyUFunc_FromFuncAndData(ufunc_inv_boxcox1p_loops, ufunc_inv_boxcox1p_data, ufunc_inv_boxcox1p_types, 2, 2, 1, 0, 'inv_boxcox1p', ufunc_inv_boxcox1p_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_kl_div_loops[2]
|
|
cdef void *ufunc_kl_div_ptr[4]
|
|
cdef void *ufunc_kl_div_data[2]
|
|
cdef char ufunc_kl_div_types[6]
|
|
cdef char *ufunc_kl_div_doc = (
|
|
"kl_div(x, y, out=None)\n"
|
|
"\n"
|
|
"Elementwise function for computing Kullback-Leibler divergence.\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" \\mathrm{kl\\_div}(x, y) =\n"
|
|
" \\begin{cases}\n"
|
|
" x \\log(x / y) - x + y & x > 0, y > 0 \\\\\n"
|
|
" y & x = 0, y \\ge 0 \\\\\n"
|
|
" \\infty & \\text{otherwise}\n"
|
|
" \\end{cases}\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x, y : array_like\n"
|
|
" Real arguments\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" Values of the Kullback-Liebler divergence.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"entr, rel_entr, scipy.stats.entropy\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
".. versionadded:: 0.15.0\n"
|
|
"\n"
|
|
"This function is non-negative and is jointly convex in `x` and `y`.\n"
|
|
"\n"
|
|
"The origin of this function is in convex programming; see [1]_ for\n"
|
|
"details. This is why the function contains the extra :math:`-x\n"
|
|
"+ y` terms over what might be expected from the Kullback-Leibler\n"
|
|
"divergence. For a version of the function without the extra terms,\n"
|
|
"see `rel_entr`.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Boyd, Stephen and Lieven Vandenberghe. *Convex optimization*.\n"
|
|
" Cambridge University Press, 2004.\n"
|
|
" :doi:`https://doi.org/10.1017/CBO9780511804441`")
|
|
ufunc_kl_div_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_kl_div_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_kl_div_types[0] = <char>NPY_FLOAT
|
|
ufunc_kl_div_types[1] = <char>NPY_FLOAT
|
|
ufunc_kl_div_types[2] = <char>NPY_FLOAT
|
|
ufunc_kl_div_types[3] = <char>NPY_DOUBLE
|
|
ufunc_kl_div_types[4] = <char>NPY_DOUBLE
|
|
ufunc_kl_div_types[5] = <char>NPY_DOUBLE
|
|
ufunc_kl_div_ptr[2*0] = <void*>_func_kl_div
|
|
ufunc_kl_div_ptr[2*0+1] = <void*>(<char*>"kl_div")
|
|
ufunc_kl_div_ptr[2*1] = <void*>_func_kl_div
|
|
ufunc_kl_div_ptr[2*1+1] = <void*>(<char*>"kl_div")
|
|
ufunc_kl_div_data[0] = &ufunc_kl_div_ptr[2*0]
|
|
ufunc_kl_div_data[1] = &ufunc_kl_div_ptr[2*1]
|
|
kl_div = np.PyUFunc_FromFuncAndData(ufunc_kl_div_loops, ufunc_kl_div_data, ufunc_kl_div_types, 2, 2, 1, 0, 'kl_div', ufunc_kl_div_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_kn_loops[3]
|
|
cdef void *ufunc_kn_ptr[6]
|
|
cdef void *ufunc_kn_data[3]
|
|
cdef char ufunc_kn_types[9]
|
|
cdef char *ufunc_kn_doc = (
|
|
"kn(n, x, out=None)\n"
|
|
"\n"
|
|
"Modified Bessel function of the second kind of integer order `n`\n"
|
|
"\n"
|
|
"Returns the modified Bessel function of the second kind for integer order\n"
|
|
"`n` at real `z`.\n"
|
|
"\n"
|
|
"These are also sometimes called functions of the third kind, Basset\n"
|
|
"functions, or Macdonald functions.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"n : array_like of int\n"
|
|
" Order of Bessel functions (floats will truncate with a warning)\n"
|
|
"x : array_like of float\n"
|
|
" Argument at which to evaluate the Bessel functions\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results.\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" Value of the Modified Bessel function of the second kind,\n"
|
|
" :math:`K_n(x)`.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"kv : Same function, but accepts real order and complex argument\n"
|
|
"kvp : Derivative of this function\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"Wrapper for AMOS [1]_ routine `zbesk`. For a discussion of the\n"
|
|
"algorithm used, see [2]_ and the references therein.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\n"
|
|
" of a Complex Argument and Nonnegative Order\",\n"
|
|
" http://netlib.org/amos/\n"
|
|
".. [2] Donald E. Amos, \"Algorithm 644: A portable package for Bessel\n"
|
|
" functions of a complex argument and nonnegative order\", ACM\n"
|
|
" TOMS Vol. 12 Issue 3, Sept. 1986, p. 265\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"Plot the function of several orders for real input:\n"
|
|
"\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import kn\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
">>> x = np.linspace(0, 5, 1000)\n"
|
|
">>> for N in range(6):\n"
|
|
"... plt.plot(x, kn(N, x), label='$K_{}(x)$'.format(N))\n"
|
|
">>> plt.ylim(0, 10)\n"
|
|
">>> plt.legend()\n"
|
|
">>> plt.title(r'Modified Bessel function of the second kind $K_n(x)$')\n"
|
|
">>> plt.show()\n"
|
|
"\n"
|
|
"Calculate for a single value at multiple orders:\n"
|
|
"\n"
|
|
">>> kn([4, 5, 6], 1)\n"
|
|
"array([ 44.23241585, 360.9605896 , 3653.83831186])")
|
|
ufunc_kn_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
|
|
ufunc_kn_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_kn_loops[2] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_kn_types[0] = <char>NPY_INTP
|
|
ufunc_kn_types[1] = <char>NPY_DOUBLE
|
|
ufunc_kn_types[2] = <char>NPY_DOUBLE
|
|
ufunc_kn_types[3] = <char>NPY_FLOAT
|
|
ufunc_kn_types[4] = <char>NPY_FLOAT
|
|
ufunc_kn_types[5] = <char>NPY_FLOAT
|
|
ufunc_kn_types[6] = <char>NPY_DOUBLE
|
|
ufunc_kn_types[7] = <char>NPY_DOUBLE
|
|
ufunc_kn_types[8] = <char>NPY_DOUBLE
|
|
ufunc_kn_ptr[2*0] = <void*>_func_special_cyl_bessel_k_int
|
|
ufunc_kn_ptr[2*0+1] = <void*>(<char*>"kn")
|
|
ufunc_kn_ptr[2*1] = <void*>_func_kn_unsafe
|
|
ufunc_kn_ptr[2*1+1] = <void*>(<char*>"kn")
|
|
ufunc_kn_ptr[2*2] = <void*>_func_kn_unsafe
|
|
ufunc_kn_ptr[2*2+1] = <void*>(<char*>"kn")
|
|
ufunc_kn_data[0] = &ufunc_kn_ptr[2*0]
|
|
ufunc_kn_data[1] = &ufunc_kn_ptr[2*1]
|
|
ufunc_kn_data[2] = &ufunc_kn_ptr[2*2]
|
|
kn = np.PyUFunc_FromFuncAndData(ufunc_kn_loops, ufunc_kn_data, ufunc_kn_types, 3, 2, 1, 0, 'kn', ufunc_kn_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_kolmogi_loops[2]
|
|
cdef void *ufunc_kolmogi_ptr[4]
|
|
cdef void *ufunc_kolmogi_data[2]
|
|
cdef char ufunc_kolmogi_types[4]
|
|
cdef char *ufunc_kolmogi_doc = (
|
|
"kolmogi(p, out=None)\n"
|
|
"\n"
|
|
"Inverse Survival Function of Kolmogorov distribution\n"
|
|
"\n"
|
|
"It is the inverse function to `kolmogorov`.\n"
|
|
"Returns y such that ``kolmogorov(y) == p``.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"p : float array_like\n"
|
|
" Probability\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" The value(s) of kolmogi(p)\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"kolmogorov : The Survival Function for the distribution\n"
|
|
"scipy.stats.kstwobign : Provides the functionality as a continuous distribution\n"
|
|
"smirnov, smirnovi : Functions for the one-sided distribution\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"`kolmogorov` is used by `stats.kstest` in the application of the\n"
|
|
"Kolmogorov-Smirnov Goodness of Fit test. For historical reasons this\n"
|
|
"function is exposed in `scpy.special`, but the recommended way to achieve\n"
|
|
"the most accurate CDF/SF/PDF/PPF/ISF computations is to use the\n"
|
|
"`stats.kstwobign` distribution.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> from scipy.special import kolmogi\n"
|
|
">>> kolmogi([0, 0.1, 0.25, 0.5, 0.75, 0.9, 1.0])\n"
|
|
"array([ inf, 1.22384787, 1.01918472, 0.82757356, 0.67644769,\n"
|
|
" 0.57117327, 0. ])")
|
|
ufunc_kolmogi_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
|
|
ufunc_kolmogi_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
|
|
ufunc_kolmogi_types[0] = <char>NPY_FLOAT
|
|
ufunc_kolmogi_types[1] = <char>NPY_FLOAT
|
|
ufunc_kolmogi_types[2] = <char>NPY_DOUBLE
|
|
ufunc_kolmogi_types[3] = <char>NPY_DOUBLE
|
|
ufunc_kolmogi_ptr[2*0] = <void*>_func_xsf_kolmogi
|
|
ufunc_kolmogi_ptr[2*0+1] = <void*>(<char*>"kolmogi")
|
|
ufunc_kolmogi_ptr[2*1] = <void*>_func_xsf_kolmogi
|
|
ufunc_kolmogi_ptr[2*1+1] = <void*>(<char*>"kolmogi")
|
|
ufunc_kolmogi_data[0] = &ufunc_kolmogi_ptr[2*0]
|
|
ufunc_kolmogi_data[1] = &ufunc_kolmogi_ptr[2*1]
|
|
kolmogi = np.PyUFunc_FromFuncAndData(ufunc_kolmogi_loops, ufunc_kolmogi_data, ufunc_kolmogi_types, 2, 1, 1, 0, 'kolmogi', ufunc_kolmogi_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_kolmogorov_loops[2]
|
|
cdef void *ufunc_kolmogorov_ptr[4]
|
|
cdef void *ufunc_kolmogorov_data[2]
|
|
cdef char ufunc_kolmogorov_types[4]
|
|
cdef char *ufunc_kolmogorov_doc = (
|
|
"kolmogorov(y, out=None)\n"
|
|
"\n"
|
|
"Complementary cumulative distribution (Survival Function) function of\n"
|
|
"Kolmogorov distribution.\n"
|
|
"\n"
|
|
"Returns the complementary cumulative distribution function of\n"
|
|
"Kolmogorov's limiting distribution (``D_n*\\sqrt(n)`` as n goes to infinity)\n"
|
|
"of a two-sided test for equality between an empirical and a theoretical\n"
|
|
"distribution. It is equal to the (limit as n->infinity of the)\n"
|
|
"probability that ``sqrt(n) * max absolute deviation > y``.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"y : float array_like\n"
|
|
" Absolute deviation between the Empirical CDF (ECDF) and the target CDF,\n"
|
|
" multiplied by sqrt(n).\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" The value(s) of kolmogorov(y)\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"kolmogi : The Inverse Survival Function for the distribution\n"
|
|
"scipy.stats.kstwobign : Provides the functionality as a continuous distribution\n"
|
|
"smirnov, smirnovi : Functions for the one-sided distribution\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"`kolmogorov` is used by `stats.kstest` in the application of the\n"
|
|
"Kolmogorov-Smirnov Goodness of Fit test. For historical reasons this\n"
|
|
"function is exposed in `scpy.special`, but the recommended way to achieve\n"
|
|
"the most accurate CDF/SF/PDF/PPF/ISF computations is to use the\n"
|
|
"`stats.kstwobign` distribution.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"Show the probability of a gap at least as big as 0, 0.5 and 1.0.\n"
|
|
"\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import kolmogorov\n"
|
|
">>> from scipy.stats import kstwobign\n"
|
|
">>> kolmogorov([0, 0.5, 1.0])\n"
|
|
"array([ 1. , 0.96394524, 0.26999967])\n"
|
|
"\n"
|
|
"Compare a sample of size 1000 drawn from a Laplace(0, 1) distribution against\n"
|
|
"the target distribution, a Normal(0, 1) distribution.\n"
|
|
"\n"
|
|
">>> from scipy.stats import norm, laplace\n"
|
|
">>> rng = np.random.default_rng()\n"
|
|
">>> n = 1000\n"
|
|
">>> lap01 = laplace(0, 1)\n"
|
|
">>> x = np.sort(lap01.rvs(n, random_state=rng))\n"
|
|
">>> np.mean(x), np.std(x)\n"
|
|
"(-0.05841730131499543, 1.3968109101997568)\n"
|
|
"\n"
|
|
"Construct the Empirical CDF and the K-S statistic Dn.\n"
|
|
"\n"
|
|
">>> target = norm(0,1) # Normal mean 0, stddev 1\n"
|
|
">>> cdfs = target.cdf(x)\n"
|
|
">>> ecdfs = np.arange(n+1, dtype=float)/n\n"
|
|
">>> gaps = np.column_stack([cdfs - ecdfs[:n], ecdfs[1:] - cdfs])\n"
|
|
">>> Dn = np.max(gaps)\n"
|
|
">>> Kn = np.sqrt(n) * Dn\n"
|
|
">>> print('Dn=%f, sqrt(n)*Dn=%f' % (Dn, Kn))\n"
|
|
"Dn=0.043363, sqrt(n)*Dn=1.371265\n"
|
|
">>> print(chr(10).join(['For a sample of size n drawn from a N(0, 1) distribution:',\n"
|
|
"... ' the approximate Kolmogorov probability that sqrt(n)*Dn>=%f is %f' %\n"
|
|
"... (Kn, kolmogorov(Kn)),\n"
|
|
"... ' the approximate Kolmogorov probability that sqrt(n)*Dn<=%f is %f' %\n"
|
|
"... (Kn, kstwobign.cdf(Kn))]))\n"
|
|
"For a sample of size n drawn from a N(0, 1) distribution:\n"
|
|
" the approximate Kolmogorov probability that sqrt(n)*Dn>=1.371265 is 0.046533\n"
|
|
" the approximate Kolmogorov probability that sqrt(n)*Dn<=1.371265 is 0.953467\n"
|
|
"\n"
|
|
"Plot the Empirical CDF against the target N(0, 1) CDF.\n"
|
|
"\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
">>> plt.step(np.concatenate([[-3], x]), ecdfs, where='post', label='Empirical CDF')\n"
|
|
">>> x3 = np.linspace(-3, 3, 100)\n"
|
|
">>> plt.plot(x3, target.cdf(x3), label='CDF for N(0, 1)')\n"
|
|
">>> plt.ylim([0, 1]); plt.grid(True); plt.legend();\n"
|
|
">>> # Add vertical lines marking Dn+ and Dn-\n"
|
|
">>> iminus, iplus = np.argmax(gaps, axis=0)\n"
|
|
">>> plt.vlines([x[iminus]], ecdfs[iminus], cdfs[iminus],\n"
|
|
"... color='r', linestyle='dashed', lw=4)\n"
|
|
">>> plt.vlines([x[iplus]], cdfs[iplus], ecdfs[iplus+1],\n"
|
|
"... color='r', linestyle='dashed', lw=4)\n"
|
|
">>> plt.show()")
|
|
ufunc_kolmogorov_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
|
|
ufunc_kolmogorov_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
|
|
ufunc_kolmogorov_types[0] = <char>NPY_FLOAT
|
|
ufunc_kolmogorov_types[1] = <char>NPY_FLOAT
|
|
ufunc_kolmogorov_types[2] = <char>NPY_DOUBLE
|
|
ufunc_kolmogorov_types[3] = <char>NPY_DOUBLE
|
|
ufunc_kolmogorov_ptr[2*0] = <void*>_func_xsf_kolmogorov
|
|
ufunc_kolmogorov_ptr[2*0+1] = <void*>(<char*>"kolmogorov")
|
|
ufunc_kolmogorov_ptr[2*1] = <void*>_func_xsf_kolmogorov
|
|
ufunc_kolmogorov_ptr[2*1+1] = <void*>(<char*>"kolmogorov")
|
|
ufunc_kolmogorov_data[0] = &ufunc_kolmogorov_ptr[2*0]
|
|
ufunc_kolmogorov_data[1] = &ufunc_kolmogorov_ptr[2*1]
|
|
kolmogorov = np.PyUFunc_FromFuncAndData(ufunc_kolmogorov_loops, ufunc_kolmogorov_data, ufunc_kolmogorov_types, 2, 1, 1, 0, 'kolmogorov', ufunc_kolmogorov_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_lpmv_loops[2]
|
|
cdef void *ufunc_lpmv_ptr[4]
|
|
cdef void *ufunc_lpmv_data[2]
|
|
cdef char ufunc_lpmv_types[8]
|
|
cdef char *ufunc_lpmv_doc = (
|
|
"lpmv(m, v, x, out=None)\n"
|
|
"\n"
|
|
"Associated Legendre function of integer order and real degree.\n"
|
|
"\n"
|
|
"Defined as\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" P_v^m = (-1)^m (1 - x^2)^{m/2} \\frac{d^m}{dx^m} P_v(x)\n"
|
|
"\n"
|
|
"where\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" P_v = \\sum_{k = 0}^\\infty \\frac{(-v)_k (v + 1)_k}{(k!)^2}\n"
|
|
" \\left(\\frac{1 - x}{2}\\right)^k\n"
|
|
"\n"
|
|
"is the Legendre function of the first kind. Here :math:`(\\cdot)_k`\n"
|
|
"is the Pochhammer symbol; see `poch`.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"m : array_like\n"
|
|
" Order (int or float). If passed a float not equal to an\n"
|
|
" integer the function returns NaN.\n"
|
|
"v : array_like\n"
|
|
" Degree (float).\n"
|
|
"x : array_like\n"
|
|
" Argument (float). Must have ``|x| <= 1``.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"pmv : scalar or ndarray\n"
|
|
" Value of the associated Legendre function.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"lpmn : Compute the associated Legendre function for all orders\n"
|
|
" ``0, ..., m`` and degrees ``0, ..., n``.\n"
|
|
"clpmn : Compute the associated Legendre function at complex\n"
|
|
" arguments.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"Note that this implementation includes the Condon-Shortley phase.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Zhang, Jin, \"Computation of Special Functions\", John Wiley\n"
|
|
" and Sons, Inc, 1996.")
|
|
ufunc_lpmv_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_lpmv_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_lpmv_types[0] = <char>NPY_FLOAT
|
|
ufunc_lpmv_types[1] = <char>NPY_FLOAT
|
|
ufunc_lpmv_types[2] = <char>NPY_FLOAT
|
|
ufunc_lpmv_types[3] = <char>NPY_FLOAT
|
|
ufunc_lpmv_types[4] = <char>NPY_DOUBLE
|
|
ufunc_lpmv_types[5] = <char>NPY_DOUBLE
|
|
ufunc_lpmv_types[6] = <char>NPY_DOUBLE
|
|
ufunc_lpmv_types[7] = <char>NPY_DOUBLE
|
|
ufunc_lpmv_ptr[2*0] = <void*>_func_pmv_wrap
|
|
ufunc_lpmv_ptr[2*0+1] = <void*>(<char*>"lpmv")
|
|
ufunc_lpmv_ptr[2*1] = <void*>_func_pmv_wrap
|
|
ufunc_lpmv_ptr[2*1+1] = <void*>(<char*>"lpmv")
|
|
ufunc_lpmv_data[0] = &ufunc_lpmv_ptr[2*0]
|
|
ufunc_lpmv_data[1] = &ufunc_lpmv_ptr[2*1]
|
|
lpmv = np.PyUFunc_FromFuncAndData(ufunc_lpmv_loops, ufunc_lpmv_data, ufunc_lpmv_types, 2, 3, 1, 0, 'lpmv', ufunc_lpmv_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_nbdtr_loops[3]
|
|
cdef void *ufunc_nbdtr_ptr[6]
|
|
cdef void *ufunc_nbdtr_data[3]
|
|
cdef char ufunc_nbdtr_types[12]
|
|
cdef char *ufunc_nbdtr_doc = (
|
|
"nbdtr(k, n, p, out=None)\n"
|
|
"\n"
|
|
"Negative binomial cumulative distribution function.\n"
|
|
"\n"
|
|
"Returns the sum of the terms 0 through `k` of the negative binomial\n"
|
|
"distribution probability mass function,\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" F = \\sum_{j=0}^k {{n + j - 1}\\choose{j}} p^n (1 - p)^j.\n"
|
|
"\n"
|
|
"In a sequence of Bernoulli trials with individual success probabilities\n"
|
|
"`p`, this is the probability that `k` or fewer failures precede the nth\n"
|
|
"success.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"k : array_like\n"
|
|
" The maximum number of allowed failures (nonnegative int).\n"
|
|
"n : array_like\n"
|
|
" The target number of successes (positive int).\n"
|
|
"p : array_like\n"
|
|
" Probability of success in a single event (float).\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"F : scalar or ndarray\n"
|
|
" The probability of `k` or fewer failures before `n` successes in a\n"
|
|
" sequence of events with individual success probability `p`.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"nbdtrc : Negative binomial survival function\n"
|
|
"nbdtrik : Negative binomial quantile function\n"
|
|
"scipy.stats.nbinom : Negative binomial distribution\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"If floating point values are passed for `k` or `n`, they will be truncated\n"
|
|
"to integers.\n"
|
|
"\n"
|
|
"The terms are not summed directly; instead the regularized incomplete beta\n"
|
|
"function is employed, according to the formula,\n"
|
|
"\n"
|
|
".. math::\n"
|
|
" \\mathrm{nbdtr}(k, n, p) = I_{p}(n, k + 1).\n"
|
|
"\n"
|
|
"Wrapper for the Cephes [1]_ routine `nbdtr`.\n"
|
|
"\n"
|
|
"The negative binomial distribution is also available as\n"
|
|
"`scipy.stats.nbinom`. Using `nbdtr` directly can improve performance\n"
|
|
"compared to the ``cdf`` method of `scipy.stats.nbinom` (see last example).\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Cephes Mathematical Functions Library,\n"
|
|
" http://www.netlib.org/cephes/\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"Compute the function for ``k=10`` and ``n=5`` at ``p=0.5``.\n"
|
|
"\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import nbdtr\n"
|
|
">>> nbdtr(10, 5, 0.5)\n"
|
|
"0.940765380859375\n"
|
|
"\n"
|
|
"Compute the function for ``n=10`` and ``p=0.5`` at several points by\n"
|
|
"providing a NumPy array or list for `k`.\n"
|
|
"\n"
|
|
">>> nbdtr([5, 10, 15], 10, 0.5)\n"
|
|
"array([0.15087891, 0.58809853, 0.88523853])\n"
|
|
"\n"
|
|
"Plot the function for four different parameter sets.\n"
|
|
"\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
">>> k = np.arange(130)\n"
|
|
">>> n_parameters = [20, 20, 20, 80]\n"
|
|
">>> p_parameters = [0.2, 0.5, 0.8, 0.5]\n"
|
|
">>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']\n"
|
|
">>> parameters_list = list(zip(p_parameters, n_parameters,\n"
|
|
"... linestyles))\n"
|
|
">>> fig, ax = plt.subplots(figsize=(8, 8))\n"
|
|
">>> for parameter_set in parameters_list:\n"
|
|
"... p, n, style = parameter_set\n"
|
|
"... nbdtr_vals = nbdtr(k, n, p)\n"
|
|
"... ax.plot(k, nbdtr_vals, label=rf\"$n={n},\\, p={p}$\",\n"
|
|
"... ls=style)\n"
|
|
">>> ax.legend()\n"
|
|
">>> ax.set_xlabel(\"$k$\")\n"
|
|
">>> ax.set_title(\"Negative binomial cumulative distribution function\")\n"
|
|
">>> plt.show()\n"
|
|
"\n"
|
|
"The negative binomial distribution is also available as\n"
|
|
"`scipy.stats.nbinom`. Using `nbdtr` directly can be much faster than\n"
|
|
"calling the ``cdf`` method of `scipy.stats.nbinom`, especially for small\n"
|
|
"arrays or individual values. To get the same results one must use the\n"
|
|
"following parametrization: ``nbinom(n, p).cdf(k)=nbdtr(k, n, p)``.\n"
|
|
"\n"
|
|
">>> from scipy.stats import nbinom\n"
|
|
">>> k, n, p = 5, 3, 0.5\n"
|
|
">>> nbdtr_res = nbdtr(k, n, p) # this will often be faster than below\n"
|
|
">>> stats_res = nbinom(n, p).cdf(k)\n"
|
|
">>> stats_res, nbdtr_res # test that results are equal\n"
|
|
"(0.85546875, 0.85546875)\n"
|
|
"\n"
|
|
"`nbdtr` can evaluate different parameter sets by providing arrays with\n"
|
|
"shapes compatible for broadcasting for `k`, `n` and `p`. Here we compute\n"
|
|
"the function for three different `k` at four locations `p`, resulting in\n"
|
|
"a 3x4 array.\n"
|
|
"\n"
|
|
">>> k = np.array([[5], [10], [15]])\n"
|
|
">>> p = np.array([0.3, 0.5, 0.7, 0.9])\n"
|
|
">>> k.shape, p.shape\n"
|
|
"((3, 1), (4,))\n"
|
|
"\n"
|
|
">>> nbdtr(k, 5, p)\n"
|
|
"array([[0.15026833, 0.62304687, 0.95265101, 0.9998531 ],\n"
|
|
" [0.48450894, 0.94076538, 0.99932777, 0.99999999],\n"
|
|
" [0.76249222, 0.99409103, 0.99999445, 1. ]])")
|
|
ufunc_nbdtr_loops[0] = <np.PyUFuncGenericFunction>loop_d_ppd__As_ppd_d
|
|
ufunc_nbdtr_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_nbdtr_loops[2] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_nbdtr_types[0] = <char>NPY_INTP
|
|
ufunc_nbdtr_types[1] = <char>NPY_INTP
|
|
ufunc_nbdtr_types[2] = <char>NPY_DOUBLE
|
|
ufunc_nbdtr_types[3] = <char>NPY_DOUBLE
|
|
ufunc_nbdtr_types[4] = <char>NPY_FLOAT
|
|
ufunc_nbdtr_types[5] = <char>NPY_FLOAT
|
|
ufunc_nbdtr_types[6] = <char>NPY_FLOAT
|
|
ufunc_nbdtr_types[7] = <char>NPY_FLOAT
|
|
ufunc_nbdtr_types[8] = <char>NPY_DOUBLE
|
|
ufunc_nbdtr_types[9] = <char>NPY_DOUBLE
|
|
ufunc_nbdtr_types[10] = <char>NPY_DOUBLE
|
|
ufunc_nbdtr_types[11] = <char>NPY_DOUBLE
|
|
ufunc_nbdtr_ptr[2*0] = <void*>_func_cephes_nbdtr_wrap
|
|
ufunc_nbdtr_ptr[2*0+1] = <void*>(<char*>"nbdtr")
|
|
ufunc_nbdtr_ptr[2*1] = <void*>_func_nbdtr_unsafe
|
|
ufunc_nbdtr_ptr[2*1+1] = <void*>(<char*>"nbdtr")
|
|
ufunc_nbdtr_ptr[2*2] = <void*>_func_nbdtr_unsafe
|
|
ufunc_nbdtr_ptr[2*2+1] = <void*>(<char*>"nbdtr")
|
|
ufunc_nbdtr_data[0] = &ufunc_nbdtr_ptr[2*0]
|
|
ufunc_nbdtr_data[1] = &ufunc_nbdtr_ptr[2*1]
|
|
ufunc_nbdtr_data[2] = &ufunc_nbdtr_ptr[2*2]
|
|
nbdtr = np.PyUFunc_FromFuncAndData(ufunc_nbdtr_loops, ufunc_nbdtr_data, ufunc_nbdtr_types, 3, 3, 1, 0, 'nbdtr', ufunc_nbdtr_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_nbdtrc_loops[3]
|
|
cdef void *ufunc_nbdtrc_ptr[6]
|
|
cdef void *ufunc_nbdtrc_data[3]
|
|
cdef char ufunc_nbdtrc_types[12]
|
|
cdef char *ufunc_nbdtrc_doc = (
|
|
"nbdtrc(k, n, p, out=None)\n"
|
|
"\n"
|
|
"Negative binomial survival function.\n"
|
|
"\n"
|
|
"Returns the sum of the terms `k + 1` to infinity of the negative binomial\n"
|
|
"distribution probability mass function,\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" F = \\sum_{j=k + 1}^\\infty {{n + j - 1}\\choose{j}} p^n (1 - p)^j.\n"
|
|
"\n"
|
|
"In a sequence of Bernoulli trials with individual success probabilities\n"
|
|
"`p`, this is the probability that more than `k` failures precede the nth\n"
|
|
"success.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"k : array_like\n"
|
|
" The maximum number of allowed failures (nonnegative int).\n"
|
|
"n : array_like\n"
|
|
" The target number of successes (positive int).\n"
|
|
"p : array_like\n"
|
|
" Probability of success in a single event (float).\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"F : scalar or ndarray\n"
|
|
" The probability of `k + 1` or more failures before `n` successes in a\n"
|
|
" sequence of events with individual success probability `p`.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"nbdtr : Negative binomial cumulative distribution function\n"
|
|
"nbdtrik : Negative binomial percentile function\n"
|
|
"scipy.stats.nbinom : Negative binomial distribution\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"If floating point values are passed for `k` or `n`, they will be truncated\n"
|
|
"to integers.\n"
|
|
"\n"
|
|
"The terms are not summed directly; instead the regularized incomplete beta\n"
|
|
"function is employed, according to the formula,\n"
|
|
"\n"
|
|
".. math::\n"
|
|
" \\mathrm{nbdtrc}(k, n, p) = I_{1 - p}(k + 1, n).\n"
|
|
"\n"
|
|
"Wrapper for the Cephes [1]_ routine `nbdtrc`.\n"
|
|
"\n"
|
|
"The negative binomial distribution is also available as\n"
|
|
"`scipy.stats.nbinom`. Using `nbdtrc` directly can improve performance\n"
|
|
"compared to the ``sf`` method of `scipy.stats.nbinom` (see last example).\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Cephes Mathematical Functions Library,\n"
|
|
" http://www.netlib.org/cephes/\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"Compute the function for ``k=10`` and ``n=5`` at ``p=0.5``.\n"
|
|
"\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import nbdtrc\n"
|
|
">>> nbdtrc(10, 5, 0.5)\n"
|
|
"0.059234619140624986\n"
|
|
"\n"
|
|
"Compute the function for ``n=10`` and ``p=0.5`` at several points by\n"
|
|
"providing a NumPy array or list for `k`.\n"
|
|
"\n"
|
|
">>> nbdtrc([5, 10, 15], 10, 0.5)\n"
|
|
"array([0.84912109, 0.41190147, 0.11476147])\n"
|
|
"\n"
|
|
"Plot the function for four different parameter sets.\n"
|
|
"\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
">>> k = np.arange(130)\n"
|
|
">>> n_parameters = [20, 20, 20, 80]\n"
|
|
">>> p_parameters = [0.2, 0.5, 0.8, 0.5]\n"
|
|
">>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']\n"
|
|
">>> parameters_list = list(zip(p_parameters, n_parameters,\n"
|
|
"... linestyles))\n"
|
|
">>> fig, ax = plt.subplots(figsize=(8, 8))\n"
|
|
">>> for parameter_set in parameters_list:\n"
|
|
"... p, n, style = parameter_set\n"
|
|
"... nbdtrc_vals = nbdtrc(k, n, p)\n"
|
|
"... ax.plot(k, nbdtrc_vals, label=rf\"$n={n},\\, p={p}$\",\n"
|
|
"... ls=style)\n"
|
|
">>> ax.legend()\n"
|
|
">>> ax.set_xlabel(\"$k$\")\n"
|
|
">>> ax.set_title(\"Negative binomial distribution survival function\")\n"
|
|
">>> plt.show()\n"
|
|
"\n"
|
|
"The negative binomial distribution is also available as\n"
|
|
"`scipy.stats.nbinom`. Using `nbdtrc` directly can be much faster than\n"
|
|
"calling the ``sf`` method of `scipy.stats.nbinom`, especially for small\n"
|
|
"arrays or individual values. To get the same results one must use the\n"
|
|
"following parametrization: ``nbinom(n, p).sf(k)=nbdtrc(k, n, p)``.\n"
|
|
"\n"
|
|
">>> from scipy.stats import nbinom\n"
|
|
">>> k, n, p = 3, 5, 0.5\n"
|
|
">>> nbdtr_res = nbdtrc(k, n, p) # this will often be faster than below\n"
|
|
">>> stats_res = nbinom(n, p).sf(k)\n"
|
|
">>> stats_res, nbdtr_res # test that results are equal\n"
|
|
"(0.6367187499999999, 0.6367187499999999)\n"
|
|
"\n"
|
|
"`nbdtrc` can evaluate different parameter sets by providing arrays with\n"
|
|
"shapes compatible for broadcasting for `k`, `n` and `p`. Here we compute\n"
|
|
"the function for three different `k` at four locations `p`, resulting in\n"
|
|
"a 3x4 array.\n"
|
|
"\n"
|
|
">>> k = np.array([[5], [10], [15]])\n"
|
|
">>> p = np.array([0.3, 0.5, 0.7, 0.9])\n"
|
|
">>> k.shape, p.shape\n"
|
|
"((3, 1), (4,))\n"
|
|
"\n"
|
|
">>> nbdtrc(k, 5, p)\n"
|
|
"array([[8.49731667e-01, 3.76953125e-01, 4.73489874e-02, 1.46902600e-04],\n"
|
|
" [5.15491059e-01, 5.92346191e-02, 6.72234070e-04, 9.29610100e-09],\n"
|
|
" [2.37507779e-01, 5.90896606e-03, 5.55025308e-06, 3.26346760e-13]])")
|
|
ufunc_nbdtrc_loops[0] = <np.PyUFuncGenericFunction>loop_d_ppd__As_ppd_d
|
|
ufunc_nbdtrc_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_nbdtrc_loops[2] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_nbdtrc_types[0] = <char>NPY_INTP
|
|
ufunc_nbdtrc_types[1] = <char>NPY_INTP
|
|
ufunc_nbdtrc_types[2] = <char>NPY_DOUBLE
|
|
ufunc_nbdtrc_types[3] = <char>NPY_DOUBLE
|
|
ufunc_nbdtrc_types[4] = <char>NPY_FLOAT
|
|
ufunc_nbdtrc_types[5] = <char>NPY_FLOAT
|
|
ufunc_nbdtrc_types[6] = <char>NPY_FLOAT
|
|
ufunc_nbdtrc_types[7] = <char>NPY_FLOAT
|
|
ufunc_nbdtrc_types[8] = <char>NPY_DOUBLE
|
|
ufunc_nbdtrc_types[9] = <char>NPY_DOUBLE
|
|
ufunc_nbdtrc_types[10] = <char>NPY_DOUBLE
|
|
ufunc_nbdtrc_types[11] = <char>NPY_DOUBLE
|
|
ufunc_nbdtrc_ptr[2*0] = <void*>_func_cephes_nbdtrc_wrap
|
|
ufunc_nbdtrc_ptr[2*0+1] = <void*>(<char*>"nbdtrc")
|
|
ufunc_nbdtrc_ptr[2*1] = <void*>_func_nbdtrc_unsafe
|
|
ufunc_nbdtrc_ptr[2*1+1] = <void*>(<char*>"nbdtrc")
|
|
ufunc_nbdtrc_ptr[2*2] = <void*>_func_nbdtrc_unsafe
|
|
ufunc_nbdtrc_ptr[2*2+1] = <void*>(<char*>"nbdtrc")
|
|
ufunc_nbdtrc_data[0] = &ufunc_nbdtrc_ptr[2*0]
|
|
ufunc_nbdtrc_data[1] = &ufunc_nbdtrc_ptr[2*1]
|
|
ufunc_nbdtrc_data[2] = &ufunc_nbdtrc_ptr[2*2]
|
|
nbdtrc = np.PyUFunc_FromFuncAndData(ufunc_nbdtrc_loops, ufunc_nbdtrc_data, ufunc_nbdtrc_types, 3, 3, 1, 0, 'nbdtrc', ufunc_nbdtrc_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_nbdtri_loops[3]
|
|
cdef void *ufunc_nbdtri_ptr[6]
|
|
cdef void *ufunc_nbdtri_data[3]
|
|
cdef char ufunc_nbdtri_types[12]
|
|
cdef char *ufunc_nbdtri_doc = (
|
|
"nbdtri(k, n, y, out=None)\n"
|
|
"\n"
|
|
"Returns the inverse with respect to the parameter `p` of\n"
|
|
"``y = nbdtr(k, n, p)``, the negative binomial cumulative distribution\n"
|
|
"function.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"k : array_like\n"
|
|
" The maximum number of allowed failures (nonnegative int).\n"
|
|
"n : array_like\n"
|
|
" The target number of successes (positive int).\n"
|
|
"y : array_like\n"
|
|
" The probability of `k` or fewer failures before `n` successes (float).\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"p : scalar or ndarray\n"
|
|
" Probability of success in a single event (float) such that\n"
|
|
" `nbdtr(k, n, p) = y`.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"nbdtr : Cumulative distribution function of the negative binomial.\n"
|
|
"nbdtrc : Negative binomial survival function.\n"
|
|
"scipy.stats.nbinom : negative binomial distribution.\n"
|
|
"nbdtrik : Inverse with respect to `k` of `nbdtr(k, n, p)`.\n"
|
|
"nbdtrin : Inverse with respect to `n` of `nbdtr(k, n, p)`.\n"
|
|
"scipy.stats.nbinom : Negative binomial distribution\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"Wrapper for the Cephes [1]_ routine `nbdtri`.\n"
|
|
"\n"
|
|
"The negative binomial distribution is also available as\n"
|
|
"`scipy.stats.nbinom`. Using `nbdtri` directly can improve performance\n"
|
|
"compared to the ``ppf`` method of `scipy.stats.nbinom`.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Cephes Mathematical Functions Library,\n"
|
|
" http://www.netlib.org/cephes/\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"`nbdtri` is the inverse of `nbdtr` with respect to `p`.\n"
|
|
"Up to floating point errors the following holds:\n"
|
|
"``nbdtri(k, n, nbdtr(k, n, p))=p``.\n"
|
|
"\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import nbdtri, nbdtr\n"
|
|
">>> k, n, y = 5, 10, 0.2\n"
|
|
">>> cdf_val = nbdtr(k, n, y)\n"
|
|
">>> nbdtri(k, n, cdf_val)\n"
|
|
"0.20000000000000004\n"
|
|
"\n"
|
|
"Compute the function for ``k=10`` and ``n=5`` at several points by\n"
|
|
"providing a NumPy array or list for `y`.\n"
|
|
"\n"
|
|
">>> y = np.array([0.1, 0.4, 0.8])\n"
|
|
">>> nbdtri(3, 5, y)\n"
|
|
"array([0.34462319, 0.51653095, 0.69677416])\n"
|
|
"\n"
|
|
"Plot the function for three different parameter sets.\n"
|
|
"\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
">>> n_parameters = [5, 20, 30, 30]\n"
|
|
">>> k_parameters = [20, 20, 60, 80]\n"
|
|
">>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']\n"
|
|
">>> parameters_list = list(zip(n_parameters, k_parameters, linestyles))\n"
|
|
">>> cdf_vals = np.linspace(0, 1, 1000)\n"
|
|
">>> fig, ax = plt.subplots(figsize=(8, 8))\n"
|
|
">>> for parameter_set in parameters_list:\n"
|
|
"... n, k, style = parameter_set\n"
|
|
"... nbdtri_vals = nbdtri(k, n, cdf_vals)\n"
|
|
"... ax.plot(cdf_vals, nbdtri_vals, label=rf\"$k={k},\\ n={n}$\",\n"
|
|
"... ls=style)\n"
|
|
">>> ax.legend()\n"
|
|
">>> ax.set_ylabel(\"$p$\")\n"
|
|
">>> ax.set_xlabel(\"$CDF$\")\n"
|
|
">>> title = \"nbdtri: inverse of negative binomial CDF with respect to $p$\"\n"
|
|
">>> ax.set_title(title)\n"
|
|
">>> plt.show()\n"
|
|
"\n"
|
|
"`nbdtri` can evaluate different parameter sets by providing arrays with\n"
|
|
"shapes compatible for broadcasting for `k`, `n` and `p`. Here we compute\n"
|
|
"the function for three different `k` at four locations `p`, resulting in\n"
|
|
"a 3x4 array.\n"
|
|
"\n"
|
|
">>> k = np.array([[5], [10], [15]])\n"
|
|
">>> y = np.array([0.3, 0.5, 0.7, 0.9])\n"
|
|
">>> k.shape, y.shape\n"
|
|
"((3, 1), (4,))\n"
|
|
"\n"
|
|
">>> nbdtri(k, 5, y)\n"
|
|
"array([[0.37258157, 0.45169416, 0.53249956, 0.64578407],\n"
|
|
" [0.24588501, 0.30451981, 0.36778453, 0.46397088],\n"
|
|
" [0.18362101, 0.22966758, 0.28054743, 0.36066188]])")
|
|
ufunc_nbdtri_loops[0] = <np.PyUFuncGenericFunction>loop_d_ppd__As_ppd_d
|
|
ufunc_nbdtri_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_nbdtri_loops[2] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_nbdtri_types[0] = <char>NPY_INTP
|
|
ufunc_nbdtri_types[1] = <char>NPY_INTP
|
|
ufunc_nbdtri_types[2] = <char>NPY_DOUBLE
|
|
ufunc_nbdtri_types[3] = <char>NPY_DOUBLE
|
|
ufunc_nbdtri_types[4] = <char>NPY_FLOAT
|
|
ufunc_nbdtri_types[5] = <char>NPY_FLOAT
|
|
ufunc_nbdtri_types[6] = <char>NPY_FLOAT
|
|
ufunc_nbdtri_types[7] = <char>NPY_FLOAT
|
|
ufunc_nbdtri_types[8] = <char>NPY_DOUBLE
|
|
ufunc_nbdtri_types[9] = <char>NPY_DOUBLE
|
|
ufunc_nbdtri_types[10] = <char>NPY_DOUBLE
|
|
ufunc_nbdtri_types[11] = <char>NPY_DOUBLE
|
|
ufunc_nbdtri_ptr[2*0] = <void*>_func_cephes_nbdtri_wrap
|
|
ufunc_nbdtri_ptr[2*0+1] = <void*>(<char*>"nbdtri")
|
|
ufunc_nbdtri_ptr[2*1] = <void*>_func_nbdtri_unsafe
|
|
ufunc_nbdtri_ptr[2*1+1] = <void*>(<char*>"nbdtri")
|
|
ufunc_nbdtri_ptr[2*2] = <void*>_func_nbdtri_unsafe
|
|
ufunc_nbdtri_ptr[2*2+1] = <void*>(<char*>"nbdtri")
|
|
ufunc_nbdtri_data[0] = &ufunc_nbdtri_ptr[2*0]
|
|
ufunc_nbdtri_data[1] = &ufunc_nbdtri_ptr[2*1]
|
|
ufunc_nbdtri_data[2] = &ufunc_nbdtri_ptr[2*2]
|
|
nbdtri = np.PyUFunc_FromFuncAndData(ufunc_nbdtri_loops, ufunc_nbdtri_data, ufunc_nbdtri_types, 3, 3, 1, 0, 'nbdtri', ufunc_nbdtri_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_nbdtrik_loops[2]
|
|
cdef void *ufunc_nbdtrik_ptr[4]
|
|
cdef void *ufunc_nbdtrik_data[2]
|
|
cdef char ufunc_nbdtrik_types[8]
|
|
cdef char *ufunc_nbdtrik_doc = (
|
|
"nbdtrik(y, n, p, out=None)\n"
|
|
"\n"
|
|
"Negative binomial percentile function.\n"
|
|
"\n"
|
|
"Returns the inverse with respect to the parameter `k` of\n"
|
|
"``y = nbdtr(k, n, p)``, the negative binomial cumulative distribution\n"
|
|
"function.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"y : array_like\n"
|
|
" The probability of `k` or fewer failures before `n` successes (float).\n"
|
|
"n : array_like\n"
|
|
" The target number of successes (positive int).\n"
|
|
"p : array_like\n"
|
|
" Probability of success in a single event (float).\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"k : scalar or ndarray\n"
|
|
" The maximum number of allowed failures such that `nbdtr(k, n, p) = y`.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"nbdtr : Cumulative distribution function of the negative binomial.\n"
|
|
"nbdtrc : Survival function of the negative binomial.\n"
|
|
"nbdtri : Inverse with respect to `p` of `nbdtr(k, n, p)`.\n"
|
|
"nbdtrin : Inverse with respect to `n` of `nbdtr(k, n, p)`.\n"
|
|
"scipy.stats.nbinom : Negative binomial distribution\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"Wrapper for the CDFLIB [1]_ Fortran routine `cdfnbn`.\n"
|
|
"\n"
|
|
"Formula 26.5.26 of [2]_,\n"
|
|
"\n"
|
|
".. math::\n"
|
|
" \\sum_{j=k + 1}^\\infty {{n + j - 1}\n"
|
|
" \\choose{j}} p^n (1 - p)^j = I_{1 - p}(k + 1, n),\n"
|
|
"\n"
|
|
"is used to reduce calculation of the cumulative distribution function to\n"
|
|
"that of a regularized incomplete beta :math:`I`.\n"
|
|
"\n"
|
|
"Computation of `k` involves a search for a value that produces the desired\n"
|
|
"value of `y`. The search relies on the monotonicity of `y` with `k`.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Barry Brown, James Lovato, and Kathy Russell,\n"
|
|
" CDFLIB: Library of Fortran Routines for Cumulative Distribution\n"
|
|
" Functions, Inverses, and Other Parameters.\n"
|
|
".. [2] Milton Abramowitz and Irene A. Stegun, eds.\n"
|
|
" Handbook of Mathematical Functions with Formulas,\n"
|
|
" Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"Compute the negative binomial cumulative distribution function for an\n"
|
|
"exemplary parameter set.\n"
|
|
"\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import nbdtr, nbdtrik\n"
|
|
">>> k, n, p = 5, 2, 0.5\n"
|
|
">>> cdf_value = nbdtr(k, n, p)\n"
|
|
">>> cdf_value\n"
|
|
"0.9375\n"
|
|
"\n"
|
|
"Verify that `nbdtrik` recovers the original value for `k`.\n"
|
|
"\n"
|
|
">>> nbdtrik(cdf_value, n, p)\n"
|
|
"5.0\n"
|
|
"\n"
|
|
"Plot the function for different parameter sets.\n"
|
|
"\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
">>> p_parameters = [0.2, 0.5, 0.7, 0.5]\n"
|
|
">>> n_parameters = [30, 30, 30, 80]\n"
|
|
">>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']\n"
|
|
">>> parameters_list = list(zip(p_parameters, n_parameters, linestyles))\n"
|
|
">>> cdf_vals = np.linspace(0, 1, 1000)\n"
|
|
">>> fig, ax = plt.subplots(figsize=(8, 8))\n"
|
|
">>> for parameter_set in parameters_list:\n"
|
|
"... p, n, style = parameter_set\n"
|
|
"... nbdtrik_vals = nbdtrik(cdf_vals, n, p)\n"
|
|
"... ax.plot(cdf_vals, nbdtrik_vals, label=rf\"$n={n},\\ p={p}$\",\n"
|
|
"... ls=style)\n"
|
|
">>> ax.legend()\n"
|
|
">>> ax.set_ylabel(\"$k$\")\n"
|
|
">>> ax.set_xlabel(\"$CDF$\")\n"
|
|
">>> ax.set_title(\"Negative binomial percentile function\")\n"
|
|
">>> plt.show()\n"
|
|
"\n"
|
|
"The negative binomial distribution is also available as\n"
|
|
"`scipy.stats.nbinom`. The percentile function method ``ppf``\n"
|
|
"returns the result of `nbdtrik` rounded up to integers:\n"
|
|
"\n"
|
|
">>> from scipy.stats import nbinom\n"
|
|
">>> q, n, p = 0.6, 5, 0.5\n"
|
|
">>> nbinom.ppf(q, n, p), nbdtrik(q, n, p)\n"
|
|
"(5.0, 4.800428460273882)")
|
|
ufunc_nbdtrik_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_nbdtrik_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_nbdtrik_types[0] = <char>NPY_FLOAT
|
|
ufunc_nbdtrik_types[1] = <char>NPY_FLOAT
|
|
ufunc_nbdtrik_types[2] = <char>NPY_FLOAT
|
|
ufunc_nbdtrik_types[3] = <char>NPY_FLOAT
|
|
ufunc_nbdtrik_types[4] = <char>NPY_DOUBLE
|
|
ufunc_nbdtrik_types[5] = <char>NPY_DOUBLE
|
|
ufunc_nbdtrik_types[6] = <char>NPY_DOUBLE
|
|
ufunc_nbdtrik_types[7] = <char>NPY_DOUBLE
|
|
ufunc_nbdtrik_ptr[2*0] = <void*>_func_nbdtrik
|
|
ufunc_nbdtrik_ptr[2*0+1] = <void*>(<char*>"nbdtrik")
|
|
ufunc_nbdtrik_ptr[2*1] = <void*>_func_nbdtrik
|
|
ufunc_nbdtrik_ptr[2*1+1] = <void*>(<char*>"nbdtrik")
|
|
ufunc_nbdtrik_data[0] = &ufunc_nbdtrik_ptr[2*0]
|
|
ufunc_nbdtrik_data[1] = &ufunc_nbdtrik_ptr[2*1]
|
|
nbdtrik = np.PyUFunc_FromFuncAndData(ufunc_nbdtrik_loops, ufunc_nbdtrik_data, ufunc_nbdtrik_types, 2, 3, 1, 0, 'nbdtrik', ufunc_nbdtrik_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_nbdtrin_loops[2]
|
|
cdef void *ufunc_nbdtrin_ptr[4]
|
|
cdef void *ufunc_nbdtrin_data[2]
|
|
cdef char ufunc_nbdtrin_types[8]
|
|
cdef char *ufunc_nbdtrin_doc = (
|
|
"nbdtrin(k, y, p, out=None)\n"
|
|
"\n"
|
|
"Inverse of `nbdtr` vs `n`.\n"
|
|
"\n"
|
|
"Returns the inverse with respect to the parameter `n` of\n"
|
|
"``y = nbdtr(k, n, p)``, the negative binomial cumulative distribution\n"
|
|
"function.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"k : array_like\n"
|
|
" The maximum number of allowed failures (nonnegative int).\n"
|
|
"y : array_like\n"
|
|
" The probability of `k` or fewer failures before `n` successes (float).\n"
|
|
"p : array_like\n"
|
|
" Probability of success in a single event (float).\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"n : scalar or ndarray\n"
|
|
" The number of successes `n` such that `nbdtr(k, n, p) = y`.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"nbdtr : Cumulative distribution function of the negative binomial.\n"
|
|
"nbdtri : Inverse with respect to `p` of `nbdtr(k, n, p)`.\n"
|
|
"nbdtrik : Inverse with respect to `k` of `nbdtr(k, n, p)`.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"Wrapper for the CDFLIB [1]_ Fortran routine `cdfnbn`.\n"
|
|
"\n"
|
|
"Formula 26.5.26 of [2]_,\n"
|
|
"\n"
|
|
".. math::\n"
|
|
" \\sum_{j=k + 1}^\\infty {{n + j - 1}\n"
|
|
" \\choose{j}} p^n (1 - p)^j = I_{1 - p}(k + 1, n),\n"
|
|
"\n"
|
|
"is used to reduce calculation of the cumulative distribution function to\n"
|
|
"that of a regularized incomplete beta :math:`I`.\n"
|
|
"\n"
|
|
"Computation of `n` involves a search for a value that produces the desired\n"
|
|
"value of `y`. The search relies on the monotonicity of `y` with `n`.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Barry Brown, James Lovato, and Kathy Russell,\n"
|
|
" CDFLIB: Library of Fortran Routines for Cumulative Distribution\n"
|
|
" Functions, Inverses, and Other Parameters.\n"
|
|
".. [2] Milton Abramowitz and Irene A. Stegun, eds.\n"
|
|
" Handbook of Mathematical Functions with Formulas,\n"
|
|
" Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"Compute the negative binomial cumulative distribution function for an\n"
|
|
"exemplary parameter set.\n"
|
|
"\n"
|
|
">>> from scipy.special import nbdtr, nbdtrin\n"
|
|
">>> k, n, p = 5, 2, 0.5\n"
|
|
">>> cdf_value = nbdtr(k, n, p)\n"
|
|
">>> cdf_value\n"
|
|
"0.9375\n"
|
|
"\n"
|
|
"Verify that `nbdtrin` recovers the original value for `n` up to floating\n"
|
|
"point accuracy.\n"
|
|
"\n"
|
|
">>> nbdtrin(k, cdf_value, p)\n"
|
|
"1.999999999998137")
|
|
ufunc_nbdtrin_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_nbdtrin_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_nbdtrin_types[0] = <char>NPY_FLOAT
|
|
ufunc_nbdtrin_types[1] = <char>NPY_FLOAT
|
|
ufunc_nbdtrin_types[2] = <char>NPY_FLOAT
|
|
ufunc_nbdtrin_types[3] = <char>NPY_FLOAT
|
|
ufunc_nbdtrin_types[4] = <char>NPY_DOUBLE
|
|
ufunc_nbdtrin_types[5] = <char>NPY_DOUBLE
|
|
ufunc_nbdtrin_types[6] = <char>NPY_DOUBLE
|
|
ufunc_nbdtrin_types[7] = <char>NPY_DOUBLE
|
|
ufunc_nbdtrin_ptr[2*0] = <void*>_func_nbdtrin
|
|
ufunc_nbdtrin_ptr[2*0+1] = <void*>(<char*>"nbdtrin")
|
|
ufunc_nbdtrin_ptr[2*1] = <void*>_func_nbdtrin
|
|
ufunc_nbdtrin_ptr[2*1+1] = <void*>(<char*>"nbdtrin")
|
|
ufunc_nbdtrin_data[0] = &ufunc_nbdtrin_ptr[2*0]
|
|
ufunc_nbdtrin_data[1] = &ufunc_nbdtrin_ptr[2*1]
|
|
nbdtrin = np.PyUFunc_FromFuncAndData(ufunc_nbdtrin_loops, ufunc_nbdtrin_data, ufunc_nbdtrin_types, 2, 3, 1, 0, 'nbdtrin', ufunc_nbdtrin_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_ncfdtr_loops[2]
|
|
cdef void *ufunc_ncfdtr_ptr[4]
|
|
cdef void *ufunc_ncfdtr_data[2]
|
|
cdef char ufunc_ncfdtr_types[10]
|
|
cdef char *ufunc_ncfdtr_doc = (
|
|
"ncfdtr(dfn, dfd, nc, f, out=None)\n"
|
|
"\n"
|
|
"Cumulative distribution function of the non-central F distribution.\n"
|
|
"\n"
|
|
"The non-central F describes the distribution of,\n"
|
|
"\n"
|
|
".. math::\n"
|
|
" Z = \\frac{X/d_n}{Y/d_d}\n"
|
|
"\n"
|
|
"where :math:`X` and :math:`Y` are independently distributed, with\n"
|
|
":math:`X` distributed non-central :math:`\\chi^2` with noncentrality\n"
|
|
"parameter `nc` and :math:`d_n` degrees of freedom, and :math:`Y`\n"
|
|
"distributed :math:`\\chi^2` with :math:`d_d` degrees of freedom.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"dfn : array_like\n"
|
|
" Degrees of freedom of the numerator sum of squares. Range (0, inf).\n"
|
|
"dfd : array_like\n"
|
|
" Degrees of freedom of the denominator sum of squares. Range (0, inf).\n"
|
|
"nc : array_like\n"
|
|
" Noncentrality parameter. Range [0, inf).\n"
|
|
"f : array_like\n"
|
|
" Quantiles, i.e. the upper limit of integration.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"cdf : scalar or ndarray\n"
|
|
" The calculated CDF. If all inputs are scalar, the return will be a\n"
|
|
" float. Otherwise it will be an array.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"ncfdtri : Quantile function; inverse of `ncfdtr` with respect to `f`.\n"
|
|
"ncfdtridfd : Inverse of `ncfdtr` with respect to `dfd`.\n"
|
|
"ncfdtridfn : Inverse of `ncfdtr` with respect to `dfn`.\n"
|
|
"ncfdtrinc : Inverse of `ncfdtr` with respect to `nc`.\n"
|
|
"scipy.stats.ncf : Non-central F distribution.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"This function calculates the CDF of the non-central f distribution using\n"
|
|
"the Boost Math C++ library [1]_.\n"
|
|
"\n"
|
|
"The cumulative distribution function is computed using Formula 26.6.20 of\n"
|
|
"[2]_:\n"
|
|
"\n"
|
|
".. math::\n"
|
|
" F(d_n, d_d, n_c, f) = \\sum_{j=0}^\\infty e^{-n_c/2}\n"
|
|
" \\frac{(n_c/2)^j}{j!} I_{x}(\\frac{d_n}{2} + j, \\frac{d_d}{2}),\n"
|
|
"\n"
|
|
"where :math:`I` is the regularized incomplete beta function, and\n"
|
|
":math:`x = f d_n/(f d_n + d_d)`.\n"
|
|
"\n"
|
|
"Note that argument order of `ncfdtr` is different from that of the\n"
|
|
"similar ``cdf`` method of `scipy.stats.ncf`: `f` is the last\n"
|
|
"parameter of `ncfdtr` but the first parameter of ``scipy.stats.ncf.cdf``.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
|
|
".. [2] Milton Abramowitz and Irene A. Stegun, eds.\n"
|
|
" Handbook of Mathematical Functions with Formulas,\n"
|
|
" Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy import special\n"
|
|
">>> from scipy import stats\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
"\n"
|
|
"Plot the CDF of the non-central F distribution, for nc=0. Compare with the\n"
|
|
"F-distribution from scipy.stats:\n"
|
|
"\n"
|
|
">>> x = np.linspace(-1, 8, num=500)\n"
|
|
">>> dfn = 3\n"
|
|
">>> dfd = 2\n"
|
|
">>> ncf_stats = stats.f.cdf(x, dfn, dfd)\n"
|
|
">>> ncf_special = special.ncfdtr(dfn, dfd, 0, x)\n"
|
|
"\n"
|
|
">>> fig = plt.figure()\n"
|
|
">>> ax = fig.add_subplot(111)\n"
|
|
">>> ax.plot(x, ncf_stats, 'b-', lw=3)\n"
|
|
">>> ax.plot(x, ncf_special, 'r-')\n"
|
|
">>> plt.show()")
|
|
ufunc_ncfdtr_loops[0] = <np.PyUFuncGenericFunction>loop_f_ffff__As_ffff_f
|
|
ufunc_ncfdtr_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
|
|
ufunc_ncfdtr_types[0] = <char>NPY_FLOAT
|
|
ufunc_ncfdtr_types[1] = <char>NPY_FLOAT
|
|
ufunc_ncfdtr_types[2] = <char>NPY_FLOAT
|
|
ufunc_ncfdtr_types[3] = <char>NPY_FLOAT
|
|
ufunc_ncfdtr_types[4] = <char>NPY_FLOAT
|
|
ufunc_ncfdtr_types[5] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtr_types[6] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtr_types[7] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtr_types[8] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtr_types[9] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtr_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncf_cdf_float
|
|
ufunc_ncfdtr_ptr[2*0+1] = <void*>(<char*>"ncfdtr")
|
|
ufunc_ncfdtr_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncf_cdf_double
|
|
ufunc_ncfdtr_ptr[2*1+1] = <void*>(<char*>"ncfdtr")
|
|
ufunc_ncfdtr_data[0] = &ufunc_ncfdtr_ptr[2*0]
|
|
ufunc_ncfdtr_data[1] = &ufunc_ncfdtr_ptr[2*1]
|
|
ncfdtr = np.PyUFunc_FromFuncAndData(ufunc_ncfdtr_loops, ufunc_ncfdtr_data, ufunc_ncfdtr_types, 2, 4, 1, 0, 'ncfdtr', ufunc_ncfdtr_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_ncfdtri_loops[2]
|
|
cdef void *ufunc_ncfdtri_ptr[4]
|
|
cdef void *ufunc_ncfdtri_data[2]
|
|
cdef char ufunc_ncfdtri_types[10]
|
|
cdef char *ufunc_ncfdtri_doc = (
|
|
"ncfdtri(dfn, dfd, nc, p, out=None)\n"
|
|
"\n"
|
|
"Inverse with respect to `f` of the CDF of the non-central F distribution.\n"
|
|
"\n"
|
|
"See `ncfdtr` for more details.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"dfn : array_like\n"
|
|
" Degrees of freedom of the numerator sum of squares. Range (0, inf).\n"
|
|
"dfd : array_like\n"
|
|
" Degrees of freedom of the denominator sum of squares. Range (0, inf).\n"
|
|
"nc : array_like\n"
|
|
" Noncentrality parameter. Range [0, inf).\n"
|
|
"p : array_like\n"
|
|
" Value of the cumulative distribution function. Must be in the\n"
|
|
" range [0, 1].\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"f : scalar or ndarray\n"
|
|
" Quantiles, i.e., the upper limit of integration.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"ncfdtr : CDF of the non-central F distribution.\n"
|
|
"ncfdtridfd : Inverse of `ncfdtr` with respect to `dfd`.\n"
|
|
"ncfdtridfn : Inverse of `ncfdtr` with respect to `dfn`.\n"
|
|
"ncfdtrinc : Inverse of `ncfdtr` with respect to `nc`.\n"
|
|
"scipy.stats.ncf : Non-central F distribution.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"This function calculates the Quantile of the non-central f distribution\n"
|
|
"using the Boost Math C++ library [1]_.\n"
|
|
"\n"
|
|
"Note that argument order of `ncfdtri` is different from that of the\n"
|
|
"similar ``ppf`` method of `scipy.stats.ncf`. `p` is the last parameter\n"
|
|
"of `ncfdtri` but the first parameter of ``scipy.stats.ncf.ppf``.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> from scipy.special import ncfdtr, ncfdtri\n"
|
|
"\n"
|
|
"Compute the CDF for several values of `f`:\n"
|
|
"\n"
|
|
">>> f = [0.5, 1, 1.5]\n"
|
|
">>> p = ncfdtr(2, 3, 1.5, f)\n"
|
|
">>> p\n"
|
|
"array([ 0.20782291, 0.36107392, 0.47345752])\n"
|
|
"\n"
|
|
"Compute the inverse. We recover the values of `f`, as expected:\n"
|
|
"\n"
|
|
">>> ncfdtri(2, 3, 1.5, p)\n"
|
|
"array([ 0.5, 1. , 1.5])")
|
|
ufunc_ncfdtri_loops[0] = <np.PyUFuncGenericFunction>loop_f_ffff__As_ffff_f
|
|
ufunc_ncfdtri_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
|
|
ufunc_ncfdtri_types[0] = <char>NPY_FLOAT
|
|
ufunc_ncfdtri_types[1] = <char>NPY_FLOAT
|
|
ufunc_ncfdtri_types[2] = <char>NPY_FLOAT
|
|
ufunc_ncfdtri_types[3] = <char>NPY_FLOAT
|
|
ufunc_ncfdtri_types[4] = <char>NPY_FLOAT
|
|
ufunc_ncfdtri_types[5] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtri_types[6] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtri_types[7] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtri_types[8] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtri_types[9] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtri_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncf_ppf_float
|
|
ufunc_ncfdtri_ptr[2*0+1] = <void*>(<char*>"ncfdtri")
|
|
ufunc_ncfdtri_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncf_ppf_double
|
|
ufunc_ncfdtri_ptr[2*1+1] = <void*>(<char*>"ncfdtri")
|
|
ufunc_ncfdtri_data[0] = &ufunc_ncfdtri_ptr[2*0]
|
|
ufunc_ncfdtri_data[1] = &ufunc_ncfdtri_ptr[2*1]
|
|
ncfdtri = np.PyUFunc_FromFuncAndData(ufunc_ncfdtri_loops, ufunc_ncfdtri_data, ufunc_ncfdtri_types, 2, 4, 1, 0, 'ncfdtri', ufunc_ncfdtri_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_ncfdtridfd_loops[2]
|
|
cdef void *ufunc_ncfdtridfd_ptr[4]
|
|
cdef void *ufunc_ncfdtridfd_data[2]
|
|
cdef char ufunc_ncfdtridfd_types[10]
|
|
cdef char *ufunc_ncfdtridfd_doc = (
|
|
"ncfdtridfd(dfn, p, nc, f, out=None)\n"
|
|
"\n"
|
|
"Calculate degrees of freedom (denominator) for the noncentral F-distribution.\n"
|
|
"\n"
|
|
"This is the inverse with respect to `dfd` of `ncfdtr`.\n"
|
|
"See `ncfdtr` for more details.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"dfn : array_like\n"
|
|
" Degrees of freedom of the numerator sum of squares. Range (0, inf).\n"
|
|
"p : array_like\n"
|
|
" Value of the cumulative distribution function. Must be in the\n"
|
|
" range [0, 1].\n"
|
|
"nc : array_like\n"
|
|
" Noncentrality parameter. Should be in range (0, 1e4).\n"
|
|
"f : array_like\n"
|
|
" Quantiles, i.e., the upper limit of integration.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"dfd : scalar or ndarray\n"
|
|
" Degrees of freedom of the denominator sum of squares.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"ncfdtr : CDF of the non-central F distribution.\n"
|
|
"ncfdtri : Quantile function; inverse of `ncfdtr` with respect to `f`.\n"
|
|
"ncfdtridfn : Inverse of `ncfdtr` with respect to `dfn`.\n"
|
|
"ncfdtrinc : Inverse of `ncfdtr` with respect to `nc`.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"The value of the cumulative noncentral F distribution is not necessarily\n"
|
|
"monotone in either degrees of freedom. There thus may be two values that\n"
|
|
"provide a given CDF value. This routine assumes monotonicity and will\n"
|
|
"find an arbitrary one of the two values.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> from scipy.special import ncfdtr, ncfdtridfd\n"
|
|
"\n"
|
|
"Compute the CDF for several values of `dfd`:\n"
|
|
"\n"
|
|
">>> dfd = [1, 2, 3]\n"
|
|
">>> p = ncfdtr(2, dfd, 0.25, 15)\n"
|
|
">>> p\n"
|
|
"array([ 0.8097138 , 0.93020416, 0.96787852])\n"
|
|
"\n"
|
|
"Compute the inverse. We recover the values of `dfd`, as expected:\n"
|
|
"\n"
|
|
">>> ncfdtridfd(2, p, 0.25, 15)\n"
|
|
"array([ 1., 2., 3.])")
|
|
ufunc_ncfdtridfd_loops[0] = <np.PyUFuncGenericFunction>loop_d_dddd__As_ffff_f
|
|
ufunc_ncfdtridfd_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
|
|
ufunc_ncfdtridfd_types[0] = <char>NPY_FLOAT
|
|
ufunc_ncfdtridfd_types[1] = <char>NPY_FLOAT
|
|
ufunc_ncfdtridfd_types[2] = <char>NPY_FLOAT
|
|
ufunc_ncfdtridfd_types[3] = <char>NPY_FLOAT
|
|
ufunc_ncfdtridfd_types[4] = <char>NPY_FLOAT
|
|
ufunc_ncfdtridfd_types[5] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtridfd_types[6] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtridfd_types[7] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtridfd_types[8] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtridfd_types[9] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtridfd_ptr[2*0] = <void*>_func_ncfdtridfd
|
|
ufunc_ncfdtridfd_ptr[2*0+1] = <void*>(<char*>"ncfdtridfd")
|
|
ufunc_ncfdtridfd_ptr[2*1] = <void*>_func_ncfdtridfd
|
|
ufunc_ncfdtridfd_ptr[2*1+1] = <void*>(<char*>"ncfdtridfd")
|
|
ufunc_ncfdtridfd_data[0] = &ufunc_ncfdtridfd_ptr[2*0]
|
|
ufunc_ncfdtridfd_data[1] = &ufunc_ncfdtridfd_ptr[2*1]
|
|
ncfdtridfd = np.PyUFunc_FromFuncAndData(ufunc_ncfdtridfd_loops, ufunc_ncfdtridfd_data, ufunc_ncfdtridfd_types, 2, 4, 1, 0, 'ncfdtridfd', ufunc_ncfdtridfd_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_ncfdtridfn_loops[2]
|
|
cdef void *ufunc_ncfdtridfn_ptr[4]
|
|
cdef void *ufunc_ncfdtridfn_data[2]
|
|
cdef char ufunc_ncfdtridfn_types[10]
|
|
cdef char *ufunc_ncfdtridfn_doc = (
|
|
"ncfdtridfn(p, dfd, nc, f, out=None)\n"
|
|
"\n"
|
|
"Calculate degrees of freedom (numerator) for the noncentral F-distribution.\n"
|
|
"\n"
|
|
"This is the inverse with respect to `dfn` of `ncfdtr`.\n"
|
|
"See `ncfdtr` for more details.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"p : array_like\n"
|
|
" Value of the cumulative distribution function. Must be in the\n"
|
|
" range [0, 1].\n"
|
|
"dfd : array_like\n"
|
|
" Degrees of freedom of the denominator sum of squares. Range (0, inf).\n"
|
|
"nc : array_like\n"
|
|
" Noncentrality parameter. Should be in range (0, 1e4).\n"
|
|
"f : float\n"
|
|
" Quantiles, i.e., the upper limit of integration.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"dfn : scalar or ndarray\n"
|
|
" Degrees of freedom of the numerator sum of squares.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"ncfdtr : CDF of the non-central F distribution.\n"
|
|
"ncfdtri : Quantile function; inverse of `ncfdtr` with respect to `f`.\n"
|
|
"ncfdtridfd : Inverse of `ncfdtr` with respect to `dfd`.\n"
|
|
"ncfdtrinc : Inverse of `ncfdtr` with respect to `nc`.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"The value of the cumulative noncentral F distribution is not necessarily\n"
|
|
"monotone in either degrees of freedom. There thus may be two values that\n"
|
|
"provide a given CDF value. This routine assumes monotonicity and will\n"
|
|
"find an arbitrary one of the two values.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> from scipy.special import ncfdtr, ncfdtridfn\n"
|
|
"\n"
|
|
"Compute the CDF for several values of `dfn`:\n"
|
|
"\n"
|
|
">>> dfn = [1, 2, 3]\n"
|
|
">>> p = ncfdtr(dfn, 2, 0.25, 15)\n"
|
|
">>> p\n"
|
|
"array([ 0.92562363, 0.93020416, 0.93188394])\n"
|
|
"\n"
|
|
"Compute the inverse. We recover the values of `dfn`, as expected:\n"
|
|
"\n"
|
|
">>> ncfdtridfn(p, 2, 0.25, 15)\n"
|
|
"array([ 1., 2., 3.])")
|
|
ufunc_ncfdtridfn_loops[0] = <np.PyUFuncGenericFunction>loop_d_dddd__As_ffff_f
|
|
ufunc_ncfdtridfn_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
|
|
ufunc_ncfdtridfn_types[0] = <char>NPY_FLOAT
|
|
ufunc_ncfdtridfn_types[1] = <char>NPY_FLOAT
|
|
ufunc_ncfdtridfn_types[2] = <char>NPY_FLOAT
|
|
ufunc_ncfdtridfn_types[3] = <char>NPY_FLOAT
|
|
ufunc_ncfdtridfn_types[4] = <char>NPY_FLOAT
|
|
ufunc_ncfdtridfn_types[5] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtridfn_types[6] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtridfn_types[7] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtridfn_types[8] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtridfn_types[9] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtridfn_ptr[2*0] = <void*>_func_ncfdtridfn
|
|
ufunc_ncfdtridfn_ptr[2*0+1] = <void*>(<char*>"ncfdtridfn")
|
|
ufunc_ncfdtridfn_ptr[2*1] = <void*>_func_ncfdtridfn
|
|
ufunc_ncfdtridfn_ptr[2*1+1] = <void*>(<char*>"ncfdtridfn")
|
|
ufunc_ncfdtridfn_data[0] = &ufunc_ncfdtridfn_ptr[2*0]
|
|
ufunc_ncfdtridfn_data[1] = &ufunc_ncfdtridfn_ptr[2*1]
|
|
ncfdtridfn = np.PyUFunc_FromFuncAndData(ufunc_ncfdtridfn_loops, ufunc_ncfdtridfn_data, ufunc_ncfdtridfn_types, 2, 4, 1, 0, 'ncfdtridfn', ufunc_ncfdtridfn_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_ncfdtrinc_loops[2]
|
|
cdef void *ufunc_ncfdtrinc_ptr[4]
|
|
cdef void *ufunc_ncfdtrinc_data[2]
|
|
cdef char ufunc_ncfdtrinc_types[10]
|
|
cdef char *ufunc_ncfdtrinc_doc = (
|
|
"ncfdtrinc(dfn, dfd, p, f, out=None)\n"
|
|
"\n"
|
|
"Calculate non-centrality parameter for non-central F distribution.\n"
|
|
"\n"
|
|
"This is the inverse with respect to `nc` of `ncfdtr`.\n"
|
|
"See `ncfdtr` for more details.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"dfn : array_like\n"
|
|
" Degrees of freedom of the numerator sum of squares. Range (0, inf).\n"
|
|
"dfd : array_like\n"
|
|
" Degrees of freedom of the denominator sum of squares. Range (0, inf).\n"
|
|
"p : array_like\n"
|
|
" Value of the cumulative distribution function. Must be in the\n"
|
|
" range [0, 1].\n"
|
|
"f : array_like\n"
|
|
" Quantiles, i.e., the upper limit of integration.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"nc : scalar or ndarray\n"
|
|
" Noncentrality parameter.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"ncfdtr : CDF of the non-central F distribution.\n"
|
|
"ncfdtri : Quantile function; inverse of `ncfdtr` with respect to `f`.\n"
|
|
"ncfdtridfd : Inverse of `ncfdtr` with respect to `dfd`.\n"
|
|
"ncfdtridfn : Inverse of `ncfdtr` with respect to `dfn`.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> from scipy.special import ncfdtr, ncfdtrinc\n"
|
|
"\n"
|
|
"Compute the CDF for several values of `nc`:\n"
|
|
"\n"
|
|
">>> nc = [0.5, 1.5, 2.0]\n"
|
|
">>> p = ncfdtr(2, 3, nc, 15)\n"
|
|
">>> p\n"
|
|
"array([ 0.96309246, 0.94327955, 0.93304098])\n"
|
|
"\n"
|
|
"Compute the inverse. We recover the values of `nc`, as expected:\n"
|
|
"\n"
|
|
">>> ncfdtrinc(2, 3, p, 15)\n"
|
|
"array([ 0.5, 1.5, 2. ])")
|
|
ufunc_ncfdtrinc_loops[0] = <np.PyUFuncGenericFunction>loop_d_dddd__As_ffff_f
|
|
ufunc_ncfdtrinc_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
|
|
ufunc_ncfdtrinc_types[0] = <char>NPY_FLOAT
|
|
ufunc_ncfdtrinc_types[1] = <char>NPY_FLOAT
|
|
ufunc_ncfdtrinc_types[2] = <char>NPY_FLOAT
|
|
ufunc_ncfdtrinc_types[3] = <char>NPY_FLOAT
|
|
ufunc_ncfdtrinc_types[4] = <char>NPY_FLOAT
|
|
ufunc_ncfdtrinc_types[5] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtrinc_types[6] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtrinc_types[7] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtrinc_types[8] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtrinc_types[9] = <char>NPY_DOUBLE
|
|
ufunc_ncfdtrinc_ptr[2*0] = <void*>_func_ncfdtrinc
|
|
ufunc_ncfdtrinc_ptr[2*0+1] = <void*>(<char*>"ncfdtrinc")
|
|
ufunc_ncfdtrinc_ptr[2*1] = <void*>_func_ncfdtrinc
|
|
ufunc_ncfdtrinc_ptr[2*1+1] = <void*>(<char*>"ncfdtrinc")
|
|
ufunc_ncfdtrinc_data[0] = &ufunc_ncfdtrinc_ptr[2*0]
|
|
ufunc_ncfdtrinc_data[1] = &ufunc_ncfdtrinc_ptr[2*1]
|
|
ncfdtrinc = np.PyUFunc_FromFuncAndData(ufunc_ncfdtrinc_loops, ufunc_ncfdtrinc_data, ufunc_ncfdtrinc_types, 2, 4, 1, 0, 'ncfdtrinc', ufunc_ncfdtrinc_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_nctdtr_loops[2]
|
|
cdef void *ufunc_nctdtr_ptr[4]
|
|
cdef void *ufunc_nctdtr_data[2]
|
|
cdef char ufunc_nctdtr_types[8]
|
|
cdef char *ufunc_nctdtr_doc = (
|
|
"nctdtr(df, nc, t, out=None)\n"
|
|
"\n"
|
|
"Cumulative distribution function of the non-central `t` distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"df : array_like\n"
|
|
" Degrees of freedom of the distribution. Should be in range (0, inf).\n"
|
|
"nc : array_like\n"
|
|
" Noncentrality parameter.\n"
|
|
"t : array_like\n"
|
|
" Quantiles, i.e., the upper limit of integration.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"cdf : scalar or ndarray\n"
|
|
" The calculated CDF. If all inputs are scalar, the return will be a\n"
|
|
" float. Otherwise, it will be an array.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"nctdtrit : Inverse CDF (iCDF) of the non-central t distribution.\n"
|
|
"nctdtridf : Calculate degrees of freedom, given CDF and iCDF values.\n"
|
|
"nctdtrinc : Calculate non-centrality parameter, given CDF iCDF values.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"This function calculates the CDF of the non-central t distribution using\n"
|
|
"the Boost Math C++ library [1]_.\n"
|
|
"\n"
|
|
"Note that the argument order of `nctdtr` is different from that of the\n"
|
|
"similar ``cdf`` method of `scipy.stats.nct`: `t` is the last\n"
|
|
"parameter of `nctdtr` but the first parameter of ``scipy.stats.nct.cdf``.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy import special\n"
|
|
">>> from scipy import stats\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
"\n"
|
|
"Plot the CDF of the non-central t distribution, for nc=0. Compare with the\n"
|
|
"t-distribution from scipy.stats:\n"
|
|
"\n"
|
|
">>> x = np.linspace(-5, 5, num=500)\n"
|
|
">>> df = 3\n"
|
|
">>> nct_stats = stats.t.cdf(x, df)\n"
|
|
">>> nct_special = special.nctdtr(df, 0, x)\n"
|
|
"\n"
|
|
">>> fig = plt.figure()\n"
|
|
">>> ax = fig.add_subplot(111)\n"
|
|
">>> ax.plot(x, nct_stats, 'b-', lw=3)\n"
|
|
">>> ax.plot(x, nct_special, 'r-')\n"
|
|
">>> plt.show()")
|
|
ufunc_nctdtr_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc_nctdtr_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_nctdtr_types[0] = <char>NPY_FLOAT
|
|
ufunc_nctdtr_types[1] = <char>NPY_FLOAT
|
|
ufunc_nctdtr_types[2] = <char>NPY_FLOAT
|
|
ufunc_nctdtr_types[3] = <char>NPY_FLOAT
|
|
ufunc_nctdtr_types[4] = <char>NPY_DOUBLE
|
|
ufunc_nctdtr_types[5] = <char>NPY_DOUBLE
|
|
ufunc_nctdtr_types[6] = <char>NPY_DOUBLE
|
|
ufunc_nctdtr_types[7] = <char>NPY_DOUBLE
|
|
ufunc_nctdtr_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nct_cdf_float
|
|
ufunc_nctdtr_ptr[2*0+1] = <void*>(<char*>"nctdtr")
|
|
ufunc_nctdtr_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nct_cdf_double
|
|
ufunc_nctdtr_ptr[2*1+1] = <void*>(<char*>"nctdtr")
|
|
ufunc_nctdtr_data[0] = &ufunc_nctdtr_ptr[2*0]
|
|
ufunc_nctdtr_data[1] = &ufunc_nctdtr_ptr[2*1]
|
|
nctdtr = np.PyUFunc_FromFuncAndData(ufunc_nctdtr_loops, ufunc_nctdtr_data, ufunc_nctdtr_types, 2, 3, 1, 0, 'nctdtr', ufunc_nctdtr_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_nctdtridf_loops[2]
|
|
cdef void *ufunc_nctdtridf_ptr[4]
|
|
cdef void *ufunc_nctdtridf_data[2]
|
|
cdef char ufunc_nctdtridf_types[8]
|
|
cdef char *ufunc_nctdtridf_doc = (
|
|
"nctdtridf(p, nc, t, out=None)\n"
|
|
"\n"
|
|
"Calculate degrees of freedom for non-central t distribution.\n"
|
|
"\n"
|
|
"See `nctdtr` for more details.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"p : array_like\n"
|
|
" CDF values, in range (0, 1].\n"
|
|
"nc : array_like\n"
|
|
" Noncentrality parameter. Should be in range (-1e6, 1e6).\n"
|
|
"t : array_like\n"
|
|
" Quantiles, i.e., the upper limit of integration.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"df : scalar or ndarray\n"
|
|
" The degrees of freedom. If all inputs are scalar, the return will be a\n"
|
|
" float. Otherwise, it will be an array.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"nctdtr : CDF of the non-central `t` distribution.\n"
|
|
"nctdtrit : Inverse CDF (iCDF) of the non-central t distribution.\n"
|
|
"nctdtrinc : Calculate non-centrality parameter, given CDF iCDF values.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> from scipy.special import nctdtr, nctdtridf\n"
|
|
"\n"
|
|
"Compute the CDF for several values of `df`:\n"
|
|
"\n"
|
|
">>> df = [1, 2, 3]\n"
|
|
">>> p = nctdtr(df, 0.25, 1)\n"
|
|
">>> p\n"
|
|
"array([0.67491974, 0.716464 , 0.73349456])\n"
|
|
"\n"
|
|
"Compute the inverse. We recover the values of `df`, as expected:\n"
|
|
"\n"
|
|
">>> nctdtridf(p, 0.25, 1)\n"
|
|
"array([1., 2., 3.])")
|
|
ufunc_nctdtridf_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_nctdtridf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_nctdtridf_types[0] = <char>NPY_FLOAT
|
|
ufunc_nctdtridf_types[1] = <char>NPY_FLOAT
|
|
ufunc_nctdtridf_types[2] = <char>NPY_FLOAT
|
|
ufunc_nctdtridf_types[3] = <char>NPY_FLOAT
|
|
ufunc_nctdtridf_types[4] = <char>NPY_DOUBLE
|
|
ufunc_nctdtridf_types[5] = <char>NPY_DOUBLE
|
|
ufunc_nctdtridf_types[6] = <char>NPY_DOUBLE
|
|
ufunc_nctdtridf_types[7] = <char>NPY_DOUBLE
|
|
ufunc_nctdtridf_ptr[2*0] = <void*>_func_nctdtridf
|
|
ufunc_nctdtridf_ptr[2*0+1] = <void*>(<char*>"nctdtridf")
|
|
ufunc_nctdtridf_ptr[2*1] = <void*>_func_nctdtridf
|
|
ufunc_nctdtridf_ptr[2*1+1] = <void*>(<char*>"nctdtridf")
|
|
ufunc_nctdtridf_data[0] = &ufunc_nctdtridf_ptr[2*0]
|
|
ufunc_nctdtridf_data[1] = &ufunc_nctdtridf_ptr[2*1]
|
|
nctdtridf = np.PyUFunc_FromFuncAndData(ufunc_nctdtridf_loops, ufunc_nctdtridf_data, ufunc_nctdtridf_types, 2, 3, 1, 0, 'nctdtridf', ufunc_nctdtridf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_nctdtrinc_loops[2]
|
|
cdef void *ufunc_nctdtrinc_ptr[4]
|
|
cdef void *ufunc_nctdtrinc_data[2]
|
|
cdef char ufunc_nctdtrinc_types[8]
|
|
cdef char *ufunc_nctdtrinc_doc = (
|
|
"nctdtrinc(df, p, t, out=None)\n"
|
|
"\n"
|
|
"Calculate non-centrality parameter for non-central t distribution.\n"
|
|
"\n"
|
|
"See `nctdtr` for more details.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"df : array_like\n"
|
|
" Degrees of freedom of the distribution. Should be in range (0, inf).\n"
|
|
"p : array_like\n"
|
|
" CDF values, in range (0, 1].\n"
|
|
"t : array_like\n"
|
|
" Quantiles, i.e., the upper limit of integration.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"nc : scalar or ndarray\n"
|
|
" Noncentrality parameter\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"nctdtr : CDF of the non-central `t` distribution.\n"
|
|
"nctdtrit : Inverse CDF (iCDF) of the non-central t distribution.\n"
|
|
"nctdtridf : Calculate degrees of freedom, given CDF and iCDF values.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> from scipy.special import nctdtr, nctdtrinc\n"
|
|
"\n"
|
|
"Compute the CDF for several values of `nc`:\n"
|
|
"\n"
|
|
">>> nc = [0.5, 1.5, 2.5]\n"
|
|
">>> p = nctdtr(3, nc, 1.5)\n"
|
|
">>> p\n"
|
|
"array([0.77569497, 0.45524533, 0.1668691 ])\n"
|
|
"\n"
|
|
"Compute the inverse. We recover the values of `nc`, as expected:\n"
|
|
"\n"
|
|
">>> nctdtrinc(3, p, 1.5)\n"
|
|
"array([0.5, 1.5, 2.5])")
|
|
ufunc_nctdtrinc_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_nctdtrinc_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_nctdtrinc_types[0] = <char>NPY_FLOAT
|
|
ufunc_nctdtrinc_types[1] = <char>NPY_FLOAT
|
|
ufunc_nctdtrinc_types[2] = <char>NPY_FLOAT
|
|
ufunc_nctdtrinc_types[3] = <char>NPY_FLOAT
|
|
ufunc_nctdtrinc_types[4] = <char>NPY_DOUBLE
|
|
ufunc_nctdtrinc_types[5] = <char>NPY_DOUBLE
|
|
ufunc_nctdtrinc_types[6] = <char>NPY_DOUBLE
|
|
ufunc_nctdtrinc_types[7] = <char>NPY_DOUBLE
|
|
ufunc_nctdtrinc_ptr[2*0] = <void*>_func_nctdtrinc
|
|
ufunc_nctdtrinc_ptr[2*0+1] = <void*>(<char*>"nctdtrinc")
|
|
ufunc_nctdtrinc_ptr[2*1] = <void*>_func_nctdtrinc
|
|
ufunc_nctdtrinc_ptr[2*1+1] = <void*>(<char*>"nctdtrinc")
|
|
ufunc_nctdtrinc_data[0] = &ufunc_nctdtrinc_ptr[2*0]
|
|
ufunc_nctdtrinc_data[1] = &ufunc_nctdtrinc_ptr[2*1]
|
|
nctdtrinc = np.PyUFunc_FromFuncAndData(ufunc_nctdtrinc_loops, ufunc_nctdtrinc_data, ufunc_nctdtrinc_types, 2, 3, 1, 0, 'nctdtrinc', ufunc_nctdtrinc_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_nctdtrit_loops[2]
|
|
cdef void *ufunc_nctdtrit_ptr[4]
|
|
cdef void *ufunc_nctdtrit_data[2]
|
|
cdef char ufunc_nctdtrit_types[8]
|
|
cdef char *ufunc_nctdtrit_doc = (
|
|
"nctdtrit(df, nc, p, out=None)\n"
|
|
"\n"
|
|
"Inverse cumulative distribution function of the non-central t distribution.\n"
|
|
"\n"
|
|
"See `nctdtr` for more details.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"df : array_like\n"
|
|
" Degrees of freedom of the distribution. Should be in range (0, inf).\n"
|
|
"nc : array_like\n"
|
|
" Noncentrality parameter.\n"
|
|
"p : array_like\n"
|
|
" CDF values, in range (0, 1].\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"t : scalar or ndarray\n"
|
|
" Quantiles\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"nctdtr : CDF of the non-central `t` distribution.\n"
|
|
"nctdtridf : Calculate degrees of freedom, given CDF and iCDF values.\n"
|
|
"nctdtrinc : Calculate non-centrality parameter, given CDF iCDF values.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"This function calculates the quantile of the non-central t distribution using\n"
|
|
"the Boost Math C++ library [1]_.\n"
|
|
"\n"
|
|
"Note that the argument order of `nctdtrit` is different from that of the\n"
|
|
"similar ``ppf`` method of `scipy.stats.nct`: `t` is the last\n"
|
|
"parameter of `nctdtrit` but the first parameter of ``scipy.stats.nct.ppf``.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> from scipy.special import nctdtr, nctdtrit\n"
|
|
"\n"
|
|
"Compute the CDF for several values of `t`:\n"
|
|
"\n"
|
|
">>> t = [0.5, 1, 1.5]\n"
|
|
">>> p = nctdtr(3, 1, t)\n"
|
|
">>> p\n"
|
|
"array([0.29811049, 0.46922687, 0.6257559 ])\n"
|
|
"\n"
|
|
"Compute the inverse. We recover the values of `t`, as expected:\n"
|
|
"\n"
|
|
">>> nctdtrit(3, 1, p)\n"
|
|
"array([0.5, 1. , 1.5])")
|
|
ufunc_nctdtrit_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
|
|
ufunc_nctdtrit_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_nctdtrit_types[0] = <char>NPY_FLOAT
|
|
ufunc_nctdtrit_types[1] = <char>NPY_FLOAT
|
|
ufunc_nctdtrit_types[2] = <char>NPY_FLOAT
|
|
ufunc_nctdtrit_types[3] = <char>NPY_FLOAT
|
|
ufunc_nctdtrit_types[4] = <char>NPY_DOUBLE
|
|
ufunc_nctdtrit_types[5] = <char>NPY_DOUBLE
|
|
ufunc_nctdtrit_types[6] = <char>NPY_DOUBLE
|
|
ufunc_nctdtrit_types[7] = <char>NPY_DOUBLE
|
|
ufunc_nctdtrit_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nct_ppf_float
|
|
ufunc_nctdtrit_ptr[2*0+1] = <void*>(<char*>"nctdtrit")
|
|
ufunc_nctdtrit_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nct_ppf_double
|
|
ufunc_nctdtrit_ptr[2*1+1] = <void*>(<char*>"nctdtrit")
|
|
ufunc_nctdtrit_data[0] = &ufunc_nctdtrit_ptr[2*0]
|
|
ufunc_nctdtrit_data[1] = &ufunc_nctdtrit_ptr[2*1]
|
|
nctdtrit = np.PyUFunc_FromFuncAndData(ufunc_nctdtrit_loops, ufunc_nctdtrit_data, ufunc_nctdtrit_types, 2, 3, 1, 0, 'nctdtrit', ufunc_nctdtrit_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_ndtri_loops[2]
|
|
cdef void *ufunc_ndtri_ptr[4]
|
|
cdef void *ufunc_ndtri_data[2]
|
|
cdef char ufunc_ndtri_types[4]
|
|
cdef char *ufunc_ndtri_doc = (
|
|
"ndtri(y, out=None)\n"
|
|
"\n"
|
|
"Inverse of `ndtr` vs x\n"
|
|
"\n"
|
|
"Returns the argument x for which the area under the standard normal\n"
|
|
"probability density function (integrated from minus infinity to `x`)\n"
|
|
"is equal to y.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"p : array_like\n"
|
|
" Probability\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"x : scalar or ndarray\n"
|
|
" Value of x such that ``ndtr(x) == p``.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"ndtr : Standard normal cumulative probability distribution\n"
|
|
"ndtri_exp : Inverse of log_ndtr\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"`ndtri` is the percentile function of the standard normal distribution.\n"
|
|
"This means it returns the inverse of the cumulative density `ndtr`. First,\n"
|
|
"let us compute a cumulative density value.\n"
|
|
"\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import ndtri, ndtr\n"
|
|
">>> cdf_val = ndtr(2)\n"
|
|
">>> cdf_val\n"
|
|
"0.9772498680518208\n"
|
|
"\n"
|
|
"Verify that `ndtri` yields the original value for `x` up to floating point\n"
|
|
"errors.\n"
|
|
"\n"
|
|
">>> ndtri(cdf_val)\n"
|
|
"2.0000000000000004\n"
|
|
"\n"
|
|
"Plot the function. For that purpose, we provide a NumPy array as argument.\n"
|
|
"\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
">>> x = np.linspace(0.01, 1, 200)\n"
|
|
">>> fig, ax = plt.subplots()\n"
|
|
">>> ax.plot(x, ndtri(x))\n"
|
|
">>> ax.set_title(\"Standard normal percentile function\")\n"
|
|
">>> plt.show()")
|
|
ufunc_ndtri_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
|
|
ufunc_ndtri_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
|
|
ufunc_ndtri_types[0] = <char>NPY_FLOAT
|
|
ufunc_ndtri_types[1] = <char>NPY_FLOAT
|
|
ufunc_ndtri_types[2] = <char>NPY_DOUBLE
|
|
ufunc_ndtri_types[3] = <char>NPY_DOUBLE
|
|
ufunc_ndtri_ptr[2*0] = <void*>_func_xsf_ndtri
|
|
ufunc_ndtri_ptr[2*0+1] = <void*>(<char*>"ndtri")
|
|
ufunc_ndtri_ptr[2*1] = <void*>_func_xsf_ndtri
|
|
ufunc_ndtri_ptr[2*1+1] = <void*>(<char*>"ndtri")
|
|
ufunc_ndtri_data[0] = &ufunc_ndtri_ptr[2*0]
|
|
ufunc_ndtri_data[1] = &ufunc_ndtri_ptr[2*1]
|
|
ndtri = np.PyUFunc_FromFuncAndData(ufunc_ndtri_loops, ufunc_ndtri_data, ufunc_ndtri_types, 2, 1, 1, 0, 'ndtri', ufunc_ndtri_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_ndtri_exp_loops[2]
|
|
cdef void *ufunc_ndtri_exp_ptr[4]
|
|
cdef void *ufunc_ndtri_exp_data[2]
|
|
cdef char ufunc_ndtri_exp_types[4]
|
|
cdef char *ufunc_ndtri_exp_doc = (
|
|
"ndtri_exp(y, out=None)\n"
|
|
"\n"
|
|
"Inverse of `log_ndtr` vs x. Allows for greater precision than\n"
|
|
"`ndtri` composed with `numpy.exp` for very small values of y and for\n"
|
|
"y close to 0.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"y : array_like of float\n"
|
|
" Function argument\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" Inverse of the log CDF of the standard normal distribution, evaluated\n"
|
|
" at y.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"log_ndtr : log of the standard normal cumulative distribution function\n"
|
|
"ndtr : standard normal cumulative distribution function\n"
|
|
"ndtri : standard normal percentile function\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> import scipy.special as sc\n"
|
|
"\n"
|
|
"`ndtri_exp` agrees with the naive implementation when the latter does\n"
|
|
"not suffer from underflow.\n"
|
|
"\n"
|
|
">>> sc.ndtri_exp(-1)\n"
|
|
"-0.33747496376420244\n"
|
|
">>> sc.ndtri(np.exp(-1))\n"
|
|
"-0.33747496376420244\n"
|
|
"\n"
|
|
"For extreme values of y, the naive approach fails\n"
|
|
"\n"
|
|
">>> sc.ndtri(np.exp(-800))\n"
|
|
"-inf\n"
|
|
">>> sc.ndtri(np.exp(-1e-20))\n"
|
|
"inf\n"
|
|
"\n"
|
|
"whereas `ndtri_exp` is still able to compute the result to high precision.\n"
|
|
"\n"
|
|
">>> sc.ndtri_exp(-800)\n"
|
|
"-39.88469483825668\n"
|
|
">>> sc.ndtri_exp(-1e-20)\n"
|
|
"9.262340089798409")
|
|
ufunc_ndtri_exp_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
|
|
ufunc_ndtri_exp_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
|
|
ufunc_ndtri_exp_types[0] = <char>NPY_FLOAT
|
|
ufunc_ndtri_exp_types[1] = <char>NPY_FLOAT
|
|
ufunc_ndtri_exp_types[2] = <char>NPY_DOUBLE
|
|
ufunc_ndtri_exp_types[3] = <char>NPY_DOUBLE
|
|
ufunc_ndtri_exp_ptr[2*0] = <void*>_func_ndtri_exp
|
|
ufunc_ndtri_exp_ptr[2*0+1] = <void*>(<char*>"ndtri_exp")
|
|
ufunc_ndtri_exp_ptr[2*1] = <void*>_func_ndtri_exp
|
|
ufunc_ndtri_exp_ptr[2*1+1] = <void*>(<char*>"ndtri_exp")
|
|
ufunc_ndtri_exp_data[0] = &ufunc_ndtri_exp_ptr[2*0]
|
|
ufunc_ndtri_exp_data[1] = &ufunc_ndtri_exp_ptr[2*1]
|
|
ndtri_exp = np.PyUFunc_FromFuncAndData(ufunc_ndtri_exp_loops, ufunc_ndtri_exp_data, ufunc_ndtri_exp_types, 2, 1, 1, 0, 'ndtri_exp', ufunc_ndtri_exp_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_nrdtrimn_loops[2]
|
|
cdef void *ufunc_nrdtrimn_ptr[4]
|
|
cdef void *ufunc_nrdtrimn_data[2]
|
|
cdef char ufunc_nrdtrimn_types[8]
|
|
cdef char *ufunc_nrdtrimn_doc = (
|
|
"nrdtrimn(p, std, x, out=None)\n"
|
|
"\n"
|
|
"Calculate mean of normal distribution given other params.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"p : array_like\n"
|
|
" CDF values, in range (0, 1].\n"
|
|
"std : array_like\n"
|
|
" Standard deviation.\n"
|
|
"x : array_like\n"
|
|
" Quantiles, i.e. the upper limit of integration.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"mn : scalar or ndarray\n"
|
|
" The mean of the normal distribution.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"scipy.stats.norm : Normal distribution\n"
|
|
"ndtr : Standard normal cumulative probability distribution\n"
|
|
"ndtri : Inverse of standard normal CDF with respect to quantile\n"
|
|
"nrdtrisd : Inverse of normal distribution CDF with respect to\n"
|
|
" standard deviation\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"`nrdtrimn` can be used to recover the mean of a normal distribution\n"
|
|
"if we know the CDF value `p` for a given quantile `x` and the\n"
|
|
"standard deviation `std`. First, we calculate\n"
|
|
"the normal distribution CDF for an exemplary parameter set.\n"
|
|
"\n"
|
|
">>> from scipy.stats import norm\n"
|
|
">>> mean = 3.\n"
|
|
">>> std = 2.\n"
|
|
">>> x = 6.\n"
|
|
">>> p = norm.cdf(x, loc=mean, scale=std)\n"
|
|
">>> p\n"
|
|
"0.9331927987311419\n"
|
|
"\n"
|
|
"Verify that `nrdtrimn` returns the original value for `mean`.\n"
|
|
"\n"
|
|
">>> from scipy.special import nrdtrimn\n"
|
|
">>> nrdtrimn(p, std, x)\n"
|
|
"3.0000000000000004")
|
|
ufunc_nrdtrimn_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_nrdtrimn_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_nrdtrimn_types[0] = <char>NPY_FLOAT
|
|
ufunc_nrdtrimn_types[1] = <char>NPY_FLOAT
|
|
ufunc_nrdtrimn_types[2] = <char>NPY_FLOAT
|
|
ufunc_nrdtrimn_types[3] = <char>NPY_FLOAT
|
|
ufunc_nrdtrimn_types[4] = <char>NPY_DOUBLE
|
|
ufunc_nrdtrimn_types[5] = <char>NPY_DOUBLE
|
|
ufunc_nrdtrimn_types[6] = <char>NPY_DOUBLE
|
|
ufunc_nrdtrimn_types[7] = <char>NPY_DOUBLE
|
|
ufunc_nrdtrimn_ptr[2*0] = <void*>_func_nrdtrimn
|
|
ufunc_nrdtrimn_ptr[2*0+1] = <void*>(<char*>"nrdtrimn")
|
|
ufunc_nrdtrimn_ptr[2*1] = <void*>_func_nrdtrimn
|
|
ufunc_nrdtrimn_ptr[2*1+1] = <void*>(<char*>"nrdtrimn")
|
|
ufunc_nrdtrimn_data[0] = &ufunc_nrdtrimn_ptr[2*0]
|
|
ufunc_nrdtrimn_data[1] = &ufunc_nrdtrimn_ptr[2*1]
|
|
nrdtrimn = np.PyUFunc_FromFuncAndData(ufunc_nrdtrimn_loops, ufunc_nrdtrimn_data, ufunc_nrdtrimn_types, 2, 3, 1, 0, 'nrdtrimn', ufunc_nrdtrimn_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_nrdtrisd_loops[2]
|
|
cdef void *ufunc_nrdtrisd_ptr[4]
|
|
cdef void *ufunc_nrdtrisd_data[2]
|
|
cdef char ufunc_nrdtrisd_types[8]
|
|
cdef char *ufunc_nrdtrisd_doc = (
|
|
"nrdtrisd(mn, p, x, out=None)\n"
|
|
"\n"
|
|
"Calculate standard deviation of normal distribution given other params.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"mn : scalar or ndarray\n"
|
|
" The mean of the normal distribution.\n"
|
|
"p : array_like\n"
|
|
" CDF values, in range (0, 1].\n"
|
|
"x : array_like\n"
|
|
" Quantiles, i.e. the upper limit of integration.\n"
|
|
"\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"std : scalar or ndarray\n"
|
|
" Standard deviation.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"scipy.stats.norm : Normal distribution\n"
|
|
"ndtr : Standard normal cumulative probability distribution\n"
|
|
"ndtri : Inverse of standard normal CDF with respect to quantile\n"
|
|
"nrdtrimn : Inverse of normal distribution CDF with respect to\n"
|
|
" mean\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"`nrdtrisd` can be used to recover the standard deviation of a normal\n"
|
|
"distribution if we know the CDF value `p` for a given quantile `x` and\n"
|
|
"the mean `mn`. First, we calculate the normal distribution CDF for an\n"
|
|
"exemplary parameter set.\n"
|
|
"\n"
|
|
">>> from scipy.stats import norm\n"
|
|
">>> mean = 3.\n"
|
|
">>> std = 2.\n"
|
|
">>> x = 6.\n"
|
|
">>> p = norm.cdf(x, loc=mean, scale=std)\n"
|
|
">>> p\n"
|
|
"0.9331927987311419\n"
|
|
"\n"
|
|
"Verify that `nrdtrisd` returns the original value for `std`.\n"
|
|
"\n"
|
|
">>> from scipy.special import nrdtrisd\n"
|
|
">>> nrdtrisd(mean, p, x)\n"
|
|
"2.0000000000000004")
|
|
ufunc_nrdtrisd_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
|
|
ufunc_nrdtrisd_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
|
|
ufunc_nrdtrisd_types[0] = <char>NPY_FLOAT
|
|
ufunc_nrdtrisd_types[1] = <char>NPY_FLOAT
|
|
ufunc_nrdtrisd_types[2] = <char>NPY_FLOAT
|
|
ufunc_nrdtrisd_types[3] = <char>NPY_FLOAT
|
|
ufunc_nrdtrisd_types[4] = <char>NPY_DOUBLE
|
|
ufunc_nrdtrisd_types[5] = <char>NPY_DOUBLE
|
|
ufunc_nrdtrisd_types[6] = <char>NPY_DOUBLE
|
|
ufunc_nrdtrisd_types[7] = <char>NPY_DOUBLE
|
|
ufunc_nrdtrisd_ptr[2*0] = <void*>_func_nrdtrisd
|
|
ufunc_nrdtrisd_ptr[2*0+1] = <void*>(<char*>"nrdtrisd")
|
|
ufunc_nrdtrisd_ptr[2*1] = <void*>_func_nrdtrisd
|
|
ufunc_nrdtrisd_ptr[2*1+1] = <void*>(<char*>"nrdtrisd")
|
|
ufunc_nrdtrisd_data[0] = &ufunc_nrdtrisd_ptr[2*0]
|
|
ufunc_nrdtrisd_data[1] = &ufunc_nrdtrisd_ptr[2*1]
|
|
nrdtrisd = np.PyUFunc_FromFuncAndData(ufunc_nrdtrisd_loops, ufunc_nrdtrisd_data, ufunc_nrdtrisd_types, 2, 3, 1, 0, 'nrdtrisd', ufunc_nrdtrisd_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_owens_t_loops[2]
|
|
cdef void *ufunc_owens_t_ptr[4]
|
|
cdef void *ufunc_owens_t_data[2]
|
|
cdef char ufunc_owens_t_types[6]
|
|
cdef char *ufunc_owens_t_doc = (
|
|
"owens_t(h, a, out=None)\n"
|
|
"\n"
|
|
"Owen's T Function.\n"
|
|
"\n"
|
|
"The function T(h, a) gives the probability of the event\n"
|
|
"(X > h and 0 < Y < a * X) where X and Y are independent\n"
|
|
"standard normal random variables.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"h: array_like\n"
|
|
" Input value.\n"
|
|
"a: array_like\n"
|
|
" Input value.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"t: scalar or ndarray\n"
|
|
" Probability of the event (X > h and 0 < Y < a * X),\n"
|
|
" where X and Y are independent standard normal random variables.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] M. Patefield and D. Tandy, \"Fast and accurate calculation of\n"
|
|
" Owen's T Function\", Statistical Software vol. 5, pp. 1-25, 2000.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> from scipy import special\n"
|
|
">>> a = 3.5\n"
|
|
">>> h = 0.78\n"
|
|
">>> special.owens_t(h, a)\n"
|
|
"0.10877216734852274")
|
|
ufunc_owens_t_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_owens_t_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_owens_t_types[0] = <char>NPY_FLOAT
|
|
ufunc_owens_t_types[1] = <char>NPY_FLOAT
|
|
ufunc_owens_t_types[2] = <char>NPY_FLOAT
|
|
ufunc_owens_t_types[3] = <char>NPY_DOUBLE
|
|
ufunc_owens_t_types[4] = <char>NPY_DOUBLE
|
|
ufunc_owens_t_types[5] = <char>NPY_DOUBLE
|
|
ufunc_owens_t_ptr[2*0] = <void*>_func_xsf_owens_t
|
|
ufunc_owens_t_ptr[2*0+1] = <void*>(<char*>"owens_t")
|
|
ufunc_owens_t_ptr[2*1] = <void*>_func_xsf_owens_t
|
|
ufunc_owens_t_ptr[2*1+1] = <void*>(<char*>"owens_t")
|
|
ufunc_owens_t_data[0] = &ufunc_owens_t_ptr[2*0]
|
|
ufunc_owens_t_data[1] = &ufunc_owens_t_ptr[2*1]
|
|
owens_t = np.PyUFunc_FromFuncAndData(ufunc_owens_t_loops, ufunc_owens_t_data, ufunc_owens_t_types, 2, 2, 1, 0, 'owens_t', ufunc_owens_t_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_pdtr_loops[2]
|
|
cdef void *ufunc_pdtr_ptr[4]
|
|
cdef void *ufunc_pdtr_data[2]
|
|
cdef char ufunc_pdtr_types[6]
|
|
cdef char *ufunc_pdtr_doc = (
|
|
"pdtr(k, m, out=None)\n"
|
|
"\n"
|
|
"Poisson cumulative distribution function.\n"
|
|
"\n"
|
|
"Defined as the probability that a Poisson-distributed random\n"
|
|
"variable with event rate :math:`m` is less than or equal to\n"
|
|
":math:`k`. More concretely, this works out to be [1]_\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" \\exp(-m) \\sum_{j = 0}^{\\lfloor{k}\\rfloor} \\frac{m^j}{j!}.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"k : array_like\n"
|
|
" Number of occurrences (nonnegative, real)\n"
|
|
"m : array_like\n"
|
|
" Shape parameter (nonnegative, real)\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" Values of the Poisson cumulative distribution function\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"pdtrc : Poisson survival function\n"
|
|
"pdtrik : inverse of `pdtr` with respect to `k`\n"
|
|
"pdtri : inverse of `pdtr` with respect to `m`\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] https://en.wikipedia.org/wiki/Poisson_distribution\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> import scipy.special as sc\n"
|
|
"\n"
|
|
"It is a cumulative distribution function, so it converges to 1\n"
|
|
"monotonically as `k` goes to infinity.\n"
|
|
"\n"
|
|
">>> sc.pdtr([1, 10, 100, np.inf], 1)\n"
|
|
"array([0.73575888, 0.99999999, 1. , 1. ])\n"
|
|
"\n"
|
|
"It is discontinuous at integers and constant between integers.\n"
|
|
"\n"
|
|
">>> sc.pdtr([1, 1.5, 1.9, 2], 1)\n"
|
|
"array([0.73575888, 0.73575888, 0.73575888, 0.9196986 ])")
|
|
ufunc_pdtr_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_pdtr_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_pdtr_types[0] = <char>NPY_FLOAT
|
|
ufunc_pdtr_types[1] = <char>NPY_FLOAT
|
|
ufunc_pdtr_types[2] = <char>NPY_FLOAT
|
|
ufunc_pdtr_types[3] = <char>NPY_DOUBLE
|
|
ufunc_pdtr_types[4] = <char>NPY_DOUBLE
|
|
ufunc_pdtr_types[5] = <char>NPY_DOUBLE
|
|
ufunc_pdtr_ptr[2*0] = <void*>_func_xsf_pdtr
|
|
ufunc_pdtr_ptr[2*0+1] = <void*>(<char*>"pdtr")
|
|
ufunc_pdtr_ptr[2*1] = <void*>_func_xsf_pdtr
|
|
ufunc_pdtr_ptr[2*1+1] = <void*>(<char*>"pdtr")
|
|
ufunc_pdtr_data[0] = &ufunc_pdtr_ptr[2*0]
|
|
ufunc_pdtr_data[1] = &ufunc_pdtr_ptr[2*1]
|
|
pdtr = np.PyUFunc_FromFuncAndData(ufunc_pdtr_loops, ufunc_pdtr_data, ufunc_pdtr_types, 2, 2, 1, 0, 'pdtr', ufunc_pdtr_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_pdtrc_loops[2]
|
|
cdef void *ufunc_pdtrc_ptr[4]
|
|
cdef void *ufunc_pdtrc_data[2]
|
|
cdef char ufunc_pdtrc_types[6]
|
|
cdef char *ufunc_pdtrc_doc = (
|
|
"pdtrc(k, m, out=None)\n"
|
|
"\n"
|
|
"Poisson survival function\n"
|
|
"\n"
|
|
"Returns the sum of the terms from k+1 to infinity of the Poisson\n"
|
|
"distribution: sum(exp(-m) * m**j / j!, j=k+1..inf) = gammainc(\n"
|
|
"k+1, m). Arguments must both be non-negative doubles.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"k : array_like\n"
|
|
" Number of occurrences (nonnegative, real)\n"
|
|
"m : array_like\n"
|
|
" Shape parameter (nonnegative, real)\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" Values of the Poisson survival function\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"pdtr : Poisson cumulative distribution function\n"
|
|
"pdtrik : inverse of `pdtr` with respect to `k`\n"
|
|
"pdtri : inverse of `pdtr` with respect to `m`\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> import scipy.special as sc\n"
|
|
"\n"
|
|
"It is a survival function, so it decreases to 0\n"
|
|
"monotonically as `k` goes to infinity.\n"
|
|
"\n"
|
|
">>> k = np.array([1, 10, 100, np.inf])\n"
|
|
">>> sc.pdtrc(k, 1)\n"
|
|
"array([2.64241118e-001, 1.00477664e-008, 3.94147589e-161, 0.00000000e+000])\n"
|
|
"\n"
|
|
"It can be expressed in terms of the lower incomplete gamma\n"
|
|
"function `gammainc`.\n"
|
|
"\n"
|
|
">>> sc.gammainc(k + 1, 1)\n"
|
|
"array([2.64241118e-001, 1.00477664e-008, 3.94147589e-161, 0.00000000e+000])")
|
|
ufunc_pdtrc_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_pdtrc_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_pdtrc_types[0] = <char>NPY_FLOAT
|
|
ufunc_pdtrc_types[1] = <char>NPY_FLOAT
|
|
ufunc_pdtrc_types[2] = <char>NPY_FLOAT
|
|
ufunc_pdtrc_types[3] = <char>NPY_DOUBLE
|
|
ufunc_pdtrc_types[4] = <char>NPY_DOUBLE
|
|
ufunc_pdtrc_types[5] = <char>NPY_DOUBLE
|
|
ufunc_pdtrc_ptr[2*0] = <void*>_func_xsf_pdtrc
|
|
ufunc_pdtrc_ptr[2*0+1] = <void*>(<char*>"pdtrc")
|
|
ufunc_pdtrc_ptr[2*1] = <void*>_func_xsf_pdtrc
|
|
ufunc_pdtrc_ptr[2*1+1] = <void*>(<char*>"pdtrc")
|
|
ufunc_pdtrc_data[0] = &ufunc_pdtrc_ptr[2*0]
|
|
ufunc_pdtrc_data[1] = &ufunc_pdtrc_ptr[2*1]
|
|
pdtrc = np.PyUFunc_FromFuncAndData(ufunc_pdtrc_loops, ufunc_pdtrc_data, ufunc_pdtrc_types, 2, 2, 1, 0, 'pdtrc', ufunc_pdtrc_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_pdtri_loops[3]
|
|
cdef void *ufunc_pdtri_ptr[6]
|
|
cdef void *ufunc_pdtri_data[3]
|
|
cdef char ufunc_pdtri_types[9]
|
|
cdef char *ufunc_pdtri_doc = (
|
|
"pdtri(k, y, out=None)\n"
|
|
"\n"
|
|
"Inverse to `pdtr` vs m\n"
|
|
"\n"
|
|
"Returns the Poisson variable `m` such that the sum from 0 to `k` of\n"
|
|
"the Poisson density is equal to the given probability `y`:\n"
|
|
"calculated by ``gammaincinv(k + 1, y)``. `k` must be a nonnegative\n"
|
|
"integer and `y` between 0 and 1.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"k : array_like\n"
|
|
" Number of occurrences (nonnegative, real)\n"
|
|
"y : array_like\n"
|
|
" Probability\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" Values of the shape parameter `m` such that ``pdtr(k, m) = p``\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"pdtr : Poisson cumulative distribution function\n"
|
|
"pdtrc : Poisson survival function\n"
|
|
"pdtrik : inverse of `pdtr` with respect to `k`\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import scipy.special as sc\n"
|
|
"\n"
|
|
"Compute the CDF for several values of `m`:\n"
|
|
"\n"
|
|
">>> m = [0.5, 1, 1.5]\n"
|
|
">>> p = sc.pdtr(1, m)\n"
|
|
">>> p\n"
|
|
"array([0.90979599, 0.73575888, 0.5578254 ])\n"
|
|
"\n"
|
|
"Compute the inverse. We recover the values of `m`, as expected:\n"
|
|
"\n"
|
|
">>> sc.pdtri(1, p)\n"
|
|
"array([0.5, 1. , 1.5])")
|
|
ufunc_pdtri_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
|
|
ufunc_pdtri_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_pdtri_loops[2] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_pdtri_types[0] = <char>NPY_INTP
|
|
ufunc_pdtri_types[1] = <char>NPY_DOUBLE
|
|
ufunc_pdtri_types[2] = <char>NPY_DOUBLE
|
|
ufunc_pdtri_types[3] = <char>NPY_FLOAT
|
|
ufunc_pdtri_types[4] = <char>NPY_FLOAT
|
|
ufunc_pdtri_types[5] = <char>NPY_FLOAT
|
|
ufunc_pdtri_types[6] = <char>NPY_DOUBLE
|
|
ufunc_pdtri_types[7] = <char>NPY_DOUBLE
|
|
ufunc_pdtri_types[8] = <char>NPY_DOUBLE
|
|
ufunc_pdtri_ptr[2*0] = <void*>_func_cephes_pdtri_wrap
|
|
ufunc_pdtri_ptr[2*0+1] = <void*>(<char*>"pdtri")
|
|
ufunc_pdtri_ptr[2*1] = <void*>_func_pdtri_unsafe
|
|
ufunc_pdtri_ptr[2*1+1] = <void*>(<char*>"pdtri")
|
|
ufunc_pdtri_ptr[2*2] = <void*>_func_pdtri_unsafe
|
|
ufunc_pdtri_ptr[2*2+1] = <void*>(<char*>"pdtri")
|
|
ufunc_pdtri_data[0] = &ufunc_pdtri_ptr[2*0]
|
|
ufunc_pdtri_data[1] = &ufunc_pdtri_ptr[2*1]
|
|
ufunc_pdtri_data[2] = &ufunc_pdtri_ptr[2*2]
|
|
pdtri = np.PyUFunc_FromFuncAndData(ufunc_pdtri_loops, ufunc_pdtri_data, ufunc_pdtri_types, 3, 2, 1, 0, 'pdtri', ufunc_pdtri_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_pdtrik_loops[2]
|
|
cdef void *ufunc_pdtrik_ptr[4]
|
|
cdef void *ufunc_pdtrik_data[2]
|
|
cdef char ufunc_pdtrik_types[6]
|
|
cdef char *ufunc_pdtrik_doc = (
|
|
"pdtrik(p, m, out=None)\n"
|
|
"\n"
|
|
"Inverse to `pdtr` vs `k`.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"p : array_like\n"
|
|
" Probability\n"
|
|
"m : array_like\n"
|
|
" Shape parameter (nonnegative, real)\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" The number of occurrences `k` such that ``pdtr(k, m) = p``\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"pdtr : Poisson cumulative distribution function\n"
|
|
"pdtrc : Poisson survival function\n"
|
|
"pdtri : inverse of `pdtr` with respect to `m`\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import scipy.special as sc\n"
|
|
"\n"
|
|
"Compute the CDF for several values of `k`:\n"
|
|
"\n"
|
|
">>> k = [1, 2, 3]\n"
|
|
">>> p = sc.pdtr(k, 2)\n"
|
|
">>> p\n"
|
|
"array([0.40600585, 0.67667642, 0.85712346])\n"
|
|
"\n"
|
|
"Compute the inverse. We recover the values of `k`, as expected:\n"
|
|
"\n"
|
|
">>> sc.pdtrik(p, 2)\n"
|
|
"array([1., 2., 3.])")
|
|
ufunc_pdtrik_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_pdtrik_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_pdtrik_types[0] = <char>NPY_FLOAT
|
|
ufunc_pdtrik_types[1] = <char>NPY_FLOAT
|
|
ufunc_pdtrik_types[2] = <char>NPY_FLOAT
|
|
ufunc_pdtrik_types[3] = <char>NPY_DOUBLE
|
|
ufunc_pdtrik_types[4] = <char>NPY_DOUBLE
|
|
ufunc_pdtrik_types[5] = <char>NPY_DOUBLE
|
|
ufunc_pdtrik_ptr[2*0] = <void*>_func_pdtrik
|
|
ufunc_pdtrik_ptr[2*0+1] = <void*>(<char*>"pdtrik")
|
|
ufunc_pdtrik_ptr[2*1] = <void*>_func_pdtrik
|
|
ufunc_pdtrik_ptr[2*1+1] = <void*>(<char*>"pdtrik")
|
|
ufunc_pdtrik_data[0] = &ufunc_pdtrik_ptr[2*0]
|
|
ufunc_pdtrik_data[1] = &ufunc_pdtrik_ptr[2*1]
|
|
pdtrik = np.PyUFunc_FromFuncAndData(ufunc_pdtrik_loops, ufunc_pdtrik_data, ufunc_pdtrik_types, 2, 2, 1, 0, 'pdtrik', ufunc_pdtrik_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_poch_loops[2]
|
|
cdef void *ufunc_poch_ptr[4]
|
|
cdef void *ufunc_poch_data[2]
|
|
cdef char ufunc_poch_types[6]
|
|
cdef char *ufunc_poch_doc = (
|
|
"poch(z, m, out=None)\n"
|
|
"\n"
|
|
"Pochhammer symbol.\n"
|
|
"\n"
|
|
"The Pochhammer symbol (rising factorial) is defined as\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" (z)_m = \\frac{\\Gamma(z + m)}{\\Gamma(z)}\n"
|
|
"\n"
|
|
"For positive integer `m` it reads\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" (z)_m = z (z + 1) ... (z + m - 1)\n"
|
|
"\n"
|
|
"See [dlmf]_ for more details.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"z, m : array_like\n"
|
|
" Real-valued arguments.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" The value of the function.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [dlmf] Nist, Digital Library of Mathematical Functions\n"
|
|
" https://dlmf.nist.gov/5.2#iii\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import scipy.special as sc\n"
|
|
"\n"
|
|
"It is 1 when m is 0.\n"
|
|
"\n"
|
|
">>> sc.poch([1, 2, 3, 4], 0)\n"
|
|
"array([1., 1., 1., 1.])\n"
|
|
"\n"
|
|
"For z equal to 1 it reduces to the factorial function.\n"
|
|
"\n"
|
|
">>> sc.poch(1, 5)\n"
|
|
"120.0\n"
|
|
">>> 1 * 2 * 3 * 4 * 5\n"
|
|
"120\n"
|
|
"\n"
|
|
"It can be expressed in terms of the gamma function.\n"
|
|
"\n"
|
|
">>> z, m = 3.7, 2.1\n"
|
|
">>> sc.poch(z, m)\n"
|
|
"20.529581933776953\n"
|
|
">>> sc.gamma(z + m) / sc.gamma(z)\n"
|
|
"20.52958193377696")
|
|
ufunc_poch_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_poch_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_poch_types[0] = <char>NPY_FLOAT
|
|
ufunc_poch_types[1] = <char>NPY_FLOAT
|
|
ufunc_poch_types[2] = <char>NPY_FLOAT
|
|
ufunc_poch_types[3] = <char>NPY_DOUBLE
|
|
ufunc_poch_types[4] = <char>NPY_DOUBLE
|
|
ufunc_poch_types[5] = <char>NPY_DOUBLE
|
|
ufunc_poch_ptr[2*0] = <void*>_func_cephes_poch
|
|
ufunc_poch_ptr[2*0+1] = <void*>(<char*>"poch")
|
|
ufunc_poch_ptr[2*1] = <void*>_func_cephes_poch
|
|
ufunc_poch_ptr[2*1+1] = <void*>(<char*>"poch")
|
|
ufunc_poch_data[0] = &ufunc_poch_ptr[2*0]
|
|
ufunc_poch_data[1] = &ufunc_poch_ptr[2*1]
|
|
poch = np.PyUFunc_FromFuncAndData(ufunc_poch_loops, ufunc_poch_data, ufunc_poch_types, 2, 2, 1, 0, 'poch', ufunc_poch_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_powm1_loops[2]
|
|
cdef void *ufunc_powm1_ptr[4]
|
|
cdef void *ufunc_powm1_data[2]
|
|
cdef char ufunc_powm1_types[6]
|
|
cdef char *ufunc_powm1_doc = (
|
|
"powm1(x, y, out=None)\n"
|
|
"\n"
|
|
"Computes ``x**y - 1``.\n"
|
|
"\n"
|
|
"This function is useful when `y` is near 0, or when `x` is near 1.\n"
|
|
"\n"
|
|
"The function is implemented for real types only (unlike ``numpy.power``,\n"
|
|
"which accepts complex inputs).\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" The base. Must be a real type (i.e. integer or float, not complex).\n"
|
|
"y : array_like\n"
|
|
" The exponent. Must be a real type (i.e. integer or float, not complex).\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"array_like\n"
|
|
" Result of the calculation\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
".. versionadded:: 1.10.0\n"
|
|
"\n"
|
|
"The underlying code is implemented for single precision and double\n"
|
|
"precision floats only. Unlike `numpy.power`, integer inputs to\n"
|
|
"`powm1` are converted to floating point, and complex inputs are\n"
|
|
"not accepted.\n"
|
|
"\n"
|
|
"Note the following edge cases:\n"
|
|
"\n"
|
|
"* ``powm1(x, 0)`` returns 0 for any ``x``, including 0, ``inf``\n"
|
|
" and ``nan``.\n"
|
|
"* ``powm1(1, y)`` returns 0 for any ``y``, including ``nan``\n"
|
|
" and ``inf``.\n"
|
|
"\n"
|
|
"This function wraps the ``powm1`` routine from the\n"
|
|
"Boost Math C++ library [1]_.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import powm1\n"
|
|
"\n"
|
|
">>> x = np.array([1.2, 10.0, 0.9999999975])\n"
|
|
">>> y = np.array([1e-9, 1e-11, 0.1875])\n"
|
|
">>> powm1(x, y)\n"
|
|
"array([ 1.82321557e-10, 2.30258509e-11, -4.68749998e-10])\n"
|
|
"\n"
|
|
"It can be verified that the relative errors in those results\n"
|
|
"are less than 2.5e-16.\n"
|
|
"\n"
|
|
"Compare that to the result of ``x**y - 1``, where the\n"
|
|
"relative errors are all larger than 8e-8:\n"
|
|
"\n"
|
|
">>> x**y - 1\n"
|
|
"array([ 1.82321491e-10, 2.30258035e-11, -4.68750039e-10])")
|
|
ufunc_powm1_loops[0] = <np.PyUFuncGenericFunction>loop_f_ff__As_ff_f
|
|
ufunc_powm1_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_powm1_types[0] = <char>NPY_FLOAT
|
|
ufunc_powm1_types[1] = <char>NPY_FLOAT
|
|
ufunc_powm1_types[2] = <char>NPY_FLOAT
|
|
ufunc_powm1_types[3] = <char>NPY_DOUBLE
|
|
ufunc_powm1_types[4] = <char>NPY_DOUBLE
|
|
ufunc_powm1_types[5] = <char>NPY_DOUBLE
|
|
ufunc_powm1_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_powm1_float
|
|
ufunc_powm1_ptr[2*0+1] = <void*>(<char*>"powm1")
|
|
ufunc_powm1_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_powm1_double
|
|
ufunc_powm1_ptr[2*1+1] = <void*>(<char*>"powm1")
|
|
ufunc_powm1_data[0] = &ufunc_powm1_ptr[2*0]
|
|
ufunc_powm1_data[1] = &ufunc_powm1_ptr[2*1]
|
|
powm1 = np.PyUFunc_FromFuncAndData(ufunc_powm1_loops, ufunc_powm1_data, ufunc_powm1_types, 2, 2, 1, 0, 'powm1', ufunc_powm1_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_pseudo_huber_loops[2]
|
|
cdef void *ufunc_pseudo_huber_ptr[4]
|
|
cdef void *ufunc_pseudo_huber_data[2]
|
|
cdef char ufunc_pseudo_huber_types[6]
|
|
cdef char *ufunc_pseudo_huber_doc = (
|
|
"pseudo_huber(delta, r, out=None)\n"
|
|
"\n"
|
|
"Pseudo-Huber loss function.\n"
|
|
"\n"
|
|
".. math:: \\mathrm{pseudo\\_huber}(\\delta, r) =\n"
|
|
" \\delta^2 \\left( \\sqrt{ 1 + \\left( \\frac{r}{\\delta} \\right)^2 } - 1 \\right)\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"delta : array_like\n"
|
|
" Input array, indicating the soft quadratic vs. linear loss changepoint.\n"
|
|
"r : array_like\n"
|
|
" Input array, possibly representing residuals.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"res : scalar or ndarray\n"
|
|
" The computed Pseudo-Huber loss function values.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"huber: Similar function which this function approximates\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"Like `huber`, `pseudo_huber` often serves as a robust loss function\n"
|
|
"in statistics or machine learning to reduce the influence of outliers.\n"
|
|
"Unlike `huber`, `pseudo_huber` is smooth.\n"
|
|
"\n"
|
|
"Typically, `r` represents residuals, the difference\n"
|
|
"between a model prediction and data. Then, for :math:`|r|\\leq\\delta`,\n"
|
|
"`pseudo_huber` resembles the squared error and for :math:`|r|>\\delta` the\n"
|
|
"absolute error. This way, the Pseudo-Huber loss often achieves\n"
|
|
"a fast convergence in model fitting for small residuals like the squared\n"
|
|
"error loss function and still reduces the influence of outliers\n"
|
|
"(:math:`|r|>\\delta`) like the absolute error loss. As :math:`\\delta` is\n"
|
|
"the cutoff between squared and absolute error regimes, it has\n"
|
|
"to be tuned carefully for each problem. `pseudo_huber` is also\n"
|
|
"convex, making it suitable for gradient based optimization. [1]_ [2]_\n"
|
|
"\n"
|
|
".. versionadded:: 0.15.0\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Hartley, Zisserman, \"Multiple View Geometry in Computer Vision\".\n"
|
|
" 2003. Cambridge University Press. p. 619\n"
|
|
".. [2] Charbonnier et al. \"Deterministic edge-preserving regularization\n"
|
|
" in computed imaging\". 1997. IEEE Trans. Image Processing.\n"
|
|
" 6 (2): 298 - 311.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"Import all necessary modules.\n"
|
|
"\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import pseudo_huber, huber\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
"\n"
|
|
"Calculate the function for ``delta=1`` at ``r=2``.\n"
|
|
"\n"
|
|
">>> pseudo_huber(1., 2.)\n"
|
|
"1.2360679774997898\n"
|
|
"\n"
|
|
"Calculate the function at ``r=2`` for different `delta` by providing\n"
|
|
"a list or NumPy array for `delta`.\n"
|
|
"\n"
|
|
">>> pseudo_huber([1., 2., 4.], 3.)\n"
|
|
"array([2.16227766, 3.21110255, 4. ])\n"
|
|
"\n"
|
|
"Calculate the function for ``delta=1`` at several points by providing\n"
|
|
"a list or NumPy array for `r`.\n"
|
|
"\n"
|
|
">>> pseudo_huber(2., np.array([1., 1.5, 3., 4.]))\n"
|
|
"array([0.47213595, 1. , 3.21110255, 4.94427191])\n"
|
|
"\n"
|
|
"The function can be calculated for different `delta` and `r` by\n"
|
|
"providing arrays for both with compatible shapes for broadcasting.\n"
|
|
"\n"
|
|
">>> r = np.array([1., 2.5, 8., 10.])\n"
|
|
">>> deltas = np.array([[1.], [5.], [9.]])\n"
|
|
">>> print(r.shape, deltas.shape)\n"
|
|
"(4,) (3, 1)\n"
|
|
"\n"
|
|
">>> pseudo_huber(deltas, r)\n"
|
|
"array([[ 0.41421356, 1.6925824 , 7.06225775, 9.04987562],\n"
|
|
" [ 0.49509757, 2.95084972, 22.16990566, 30.90169944],\n"
|
|
" [ 0.49846624, 3.06693762, 27.37435121, 40.08261642]])\n"
|
|
"\n"
|
|
"Plot the function for different `delta`.\n"
|
|
"\n"
|
|
">>> x = np.linspace(-4, 4, 500)\n"
|
|
">>> deltas = [1, 2, 3]\n"
|
|
">>> linestyles = [\"dashed\", \"dotted\", \"dashdot\"]\n"
|
|
">>> fig, ax = plt.subplots()\n"
|
|
">>> combined_plot_parameters = list(zip(deltas, linestyles))\n"
|
|
">>> for delta, style in combined_plot_parameters:\n"
|
|
"... ax.plot(x, pseudo_huber(delta, x), label=rf\"$\\delta={delta}$\",\n"
|
|
"... ls=style)\n"
|
|
">>> ax.legend(loc=\"upper center\")\n"
|
|
">>> ax.set_xlabel(\"$x$\")\n"
|
|
">>> ax.set_title(r\"Pseudo-Huber loss function $h_{\\delta}(x)$\")\n"
|
|
">>> ax.set_xlim(-4, 4)\n"
|
|
">>> ax.set_ylim(0, 8)\n"
|
|
">>> plt.show()\n"
|
|
"\n"
|
|
"Finally, illustrate the difference between `huber` and `pseudo_huber` by\n"
|
|
"plotting them and their gradients with respect to `r`. The plot shows\n"
|
|
"that `pseudo_huber` is continuously differentiable while `huber` is not\n"
|
|
"at the points :math:`\\pm\\delta`.\n"
|
|
"\n"
|
|
">>> def huber_grad(delta, x):\n"
|
|
"... grad = np.copy(x)\n"
|
|
"... linear_area = np.argwhere(np.abs(x) > delta)\n"
|
|
"... grad[linear_area]=delta*np.sign(x[linear_area])\n"
|
|
"... return grad\n"
|
|
">>> def pseudo_huber_grad(delta, x):\n"
|
|
"... return x* (1+(x/delta)**2)**(-0.5)\n"
|
|
">>> x=np.linspace(-3, 3, 500)\n"
|
|
">>> delta = 1.\n"
|
|
">>> fig, ax = plt.subplots(figsize=(7, 7))\n"
|
|
">>> ax.plot(x, huber(delta, x), label=\"Huber\", ls=\"dashed\")\n"
|
|
">>> ax.plot(x, huber_grad(delta, x), label=\"Huber Gradient\", ls=\"dashdot\")\n"
|
|
">>> ax.plot(x, pseudo_huber(delta, x), label=\"Pseudo-Huber\", ls=\"dotted\")\n"
|
|
">>> ax.plot(x, pseudo_huber_grad(delta, x), label=\"Pseudo-Huber Gradient\",\n"
|
|
"... ls=\"solid\")\n"
|
|
">>> ax.legend(loc=\"upper center\")\n"
|
|
">>> plt.show()")
|
|
ufunc_pseudo_huber_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_pseudo_huber_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_pseudo_huber_types[0] = <char>NPY_FLOAT
|
|
ufunc_pseudo_huber_types[1] = <char>NPY_FLOAT
|
|
ufunc_pseudo_huber_types[2] = <char>NPY_FLOAT
|
|
ufunc_pseudo_huber_types[3] = <char>NPY_DOUBLE
|
|
ufunc_pseudo_huber_types[4] = <char>NPY_DOUBLE
|
|
ufunc_pseudo_huber_types[5] = <char>NPY_DOUBLE
|
|
ufunc_pseudo_huber_ptr[2*0] = <void*>_func_pseudo_huber
|
|
ufunc_pseudo_huber_ptr[2*0+1] = <void*>(<char*>"pseudo_huber")
|
|
ufunc_pseudo_huber_ptr[2*1] = <void*>_func_pseudo_huber
|
|
ufunc_pseudo_huber_ptr[2*1+1] = <void*>(<char*>"pseudo_huber")
|
|
ufunc_pseudo_huber_data[0] = &ufunc_pseudo_huber_ptr[2*0]
|
|
ufunc_pseudo_huber_data[1] = &ufunc_pseudo_huber_ptr[2*1]
|
|
pseudo_huber = np.PyUFunc_FromFuncAndData(ufunc_pseudo_huber_loops, ufunc_pseudo_huber_data, ufunc_pseudo_huber_types, 2, 2, 1, 0, 'pseudo_huber', ufunc_pseudo_huber_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_rel_entr_loops[2]
|
|
cdef void *ufunc_rel_entr_ptr[4]
|
|
cdef void *ufunc_rel_entr_data[2]
|
|
cdef char ufunc_rel_entr_types[6]
|
|
cdef char *ufunc_rel_entr_doc = (
|
|
"rel_entr(x, y, out=None)\n"
|
|
"\n"
|
|
"Elementwise function for computing relative entropy.\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" \\mathrm{rel\\_entr}(x, y) =\n"
|
|
" \\begin{cases}\n"
|
|
" x \\log(x / y) & x > 0, y > 0 \\\\\n"
|
|
" 0 & x = 0, y \\ge 0 \\\\\n"
|
|
" \\infty & \\text{otherwise}\n"
|
|
" \\end{cases}\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x, y : array_like\n"
|
|
" Input arrays\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" Relative entropy of the inputs\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"entr, kl_div, scipy.stats.entropy\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
".. versionadded:: 0.15.0\n"
|
|
"\n"
|
|
"This function is jointly convex in x and y.\n"
|
|
"\n"
|
|
"The origin of this function is in convex programming; see\n"
|
|
"[1]_. Given two discrete probability distributions :math:`p_1,\n"
|
|
"\\ldots, p_n` and :math:`q_1, \\ldots, q_n`, the definition of relative\n"
|
|
"entropy in the context of *information theory* is\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" \\sum_{i = 1}^n \\mathrm{rel\\_entr}(p_i, q_i).\n"
|
|
"\n"
|
|
"To compute the latter quantity, use `scipy.stats.entropy`.\n"
|
|
"\n"
|
|
"See [2]_ for details.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Boyd, Stephen and Lieven Vandenberghe. *Convex optimization*.\n"
|
|
" Cambridge University Press, 2004.\n"
|
|
" :doi:`https://doi.org/10.1017/CBO9780511804441`\n"
|
|
".. [2] Kullback-Leibler divergence,\n"
|
|
" https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence")
|
|
ufunc_rel_entr_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_rel_entr_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_rel_entr_types[0] = <char>NPY_FLOAT
|
|
ufunc_rel_entr_types[1] = <char>NPY_FLOAT
|
|
ufunc_rel_entr_types[2] = <char>NPY_FLOAT
|
|
ufunc_rel_entr_types[3] = <char>NPY_DOUBLE
|
|
ufunc_rel_entr_types[4] = <char>NPY_DOUBLE
|
|
ufunc_rel_entr_types[5] = <char>NPY_DOUBLE
|
|
ufunc_rel_entr_ptr[2*0] = <void*>_func_rel_entr
|
|
ufunc_rel_entr_ptr[2*0+1] = <void*>(<char*>"rel_entr")
|
|
ufunc_rel_entr_ptr[2*1] = <void*>_func_rel_entr
|
|
ufunc_rel_entr_ptr[2*1+1] = <void*>(<char*>"rel_entr")
|
|
ufunc_rel_entr_data[0] = &ufunc_rel_entr_ptr[2*0]
|
|
ufunc_rel_entr_data[1] = &ufunc_rel_entr_ptr[2*1]
|
|
rel_entr = np.PyUFunc_FromFuncAndData(ufunc_rel_entr_loops, ufunc_rel_entr_data, ufunc_rel_entr_types, 2, 2, 1, 0, 'rel_entr', ufunc_rel_entr_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_round_loops[2]
|
|
cdef void *ufunc_round_ptr[4]
|
|
cdef void *ufunc_round_data[2]
|
|
cdef char ufunc_round_types[4]
|
|
cdef char *ufunc_round_doc = (
|
|
"round(x, out=None)\n"
|
|
"\n"
|
|
"Round to the nearest integer.\n"
|
|
"\n"
|
|
"Returns the nearest integer to `x`. If `x` ends in 0.5 exactly,\n"
|
|
"the nearest even integer is chosen.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real valued input.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results.\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" The nearest integers to the elements of `x`. The result is of\n"
|
|
" floating type, not integer type.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import scipy.special as sc\n"
|
|
"\n"
|
|
"It rounds to even.\n"
|
|
"\n"
|
|
">>> sc.round([0.5, 1.5])\n"
|
|
"array([0., 2.])")
|
|
ufunc_round_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
|
|
ufunc_round_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
|
|
ufunc_round_types[0] = <char>NPY_FLOAT
|
|
ufunc_round_types[1] = <char>NPY_FLOAT
|
|
ufunc_round_types[2] = <char>NPY_DOUBLE
|
|
ufunc_round_types[3] = <char>NPY_DOUBLE
|
|
ufunc_round_ptr[2*0] = <void*>_func_cephes_round
|
|
ufunc_round_ptr[2*0+1] = <void*>(<char*>"round")
|
|
ufunc_round_ptr[2*1] = <void*>_func_cephes_round
|
|
ufunc_round_ptr[2*1+1] = <void*>(<char*>"round")
|
|
ufunc_round_data[0] = &ufunc_round_ptr[2*0]
|
|
ufunc_round_data[1] = &ufunc_round_ptr[2*1]
|
|
round = np.PyUFunc_FromFuncAndData(ufunc_round_loops, ufunc_round_data, ufunc_round_types, 2, 1, 1, 0, 'round', ufunc_round_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_shichi_loops[4]
|
|
cdef void *ufunc_shichi_ptr[8]
|
|
cdef void *ufunc_shichi_data[4]
|
|
cdef char ufunc_shichi_types[12]
|
|
cdef char *ufunc_shichi_doc = (
|
|
"shichi(x, out=None)\n"
|
|
"\n"
|
|
"Hyperbolic sine and cosine integrals.\n"
|
|
"\n"
|
|
"The hyperbolic sine integral is\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" \\int_0^x \\frac{\\sinh{t}}{t}dt\n"
|
|
"\n"
|
|
"and the hyperbolic cosine integral is\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" \\gamma + \\log(x) + \\int_0^x \\frac{\\cosh{t} - 1}{t} dt\n"
|
|
"\n"
|
|
"where :math:`\\gamma` is Euler's constant and :math:`\\log` is the\n"
|
|
"principal branch of the logarithm [1]_.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real or complex points at which to compute the hyperbolic sine\n"
|
|
" and cosine integrals.\n"
|
|
"out : tuple of ndarray, optional\n"
|
|
" Optional output arrays for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"si : scalar or ndarray\n"
|
|
" Hyperbolic sine integral at ``x``\n"
|
|
"ci : scalar or ndarray\n"
|
|
" Hyperbolic cosine integral at ``x``\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"sici : Sine and cosine integrals.\n"
|
|
"exp1 : Exponential integral E1.\n"
|
|
"expi : Exponential integral Ei.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"For real arguments with ``x < 0``, ``chi`` is the real part of the\n"
|
|
"hyperbolic cosine integral. For such points ``chi(x)`` and ``chi(x\n"
|
|
"+ 0j)`` differ by a factor of ``1j*pi``.\n"
|
|
"\n"
|
|
"For real arguments the function is computed by calling Cephes'\n"
|
|
"[2]_ *shichi* routine. For complex arguments the algorithm is based\n"
|
|
"on Mpmath's [3]_ *shi* and *chi* routines.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Milton Abramowitz and Irene A. Stegun, eds.\n"
|
|
" Handbook of Mathematical Functions with Formulas,\n"
|
|
" Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
|
|
" (See Section 5.2.)\n"
|
|
".. [2] Cephes Mathematical Functions Library,\n"
|
|
" http://www.netlib.org/cephes/\n"
|
|
".. [3] Fredrik Johansson and others.\n"
|
|
" \"mpmath: a Python library for arbitrary-precision floating-point\n"
|
|
" arithmetic\" (Version 0.19) http://mpmath.org/\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
">>> from scipy.special import shichi, sici\n"
|
|
"\n"
|
|
"`shichi` accepts real or complex input:\n"
|
|
"\n"
|
|
">>> shichi(0.5)\n"
|
|
"(0.5069967498196671, -0.05277684495649357)\n"
|
|
">>> shichi(0.5 + 2.5j)\n"
|
|
"((0.11772029666668238+1.831091777729851j),\n"
|
|
" (0.29912435887648825+1.7395351121166562j))\n"
|
|
"\n"
|
|
"The hyperbolic sine and cosine integrals Shi(z) and Chi(z) are\n"
|
|
"related to the sine and cosine integrals Si(z) and Ci(z) by\n"
|
|
"\n"
|
|
"* Shi(z) = -i*Si(i*z)\n"
|
|
"* Chi(z) = Ci(-i*z) + i*pi/2\n"
|
|
"\n"
|
|
">>> z = 0.25 + 5j\n"
|
|
">>> shi, chi = shichi(z)\n"
|
|
">>> shi, -1j*sici(1j*z)[0] # Should be the same.\n"
|
|
"((-0.04834719325101729+1.5469354086921228j),\n"
|
|
" (-0.04834719325101729+1.5469354086921228j))\n"
|
|
">>> chi, sici(-1j*z)[1] + 1j*np.pi/2 # Should be the same.\n"
|
|
"((-0.19568708973868087+1.556276312103824j),\n"
|
|
" (-0.19568708973868087+1.556276312103824j))\n"
|
|
"\n"
|
|
"Plot the functions evaluated on the real axis:\n"
|
|
"\n"
|
|
">>> xp = np.geomspace(1e-8, 4.0, 250)\n"
|
|
">>> x = np.concatenate((-xp[::-1], xp))\n"
|
|
">>> shi, chi = shichi(x)\n"
|
|
"\n"
|
|
">>> fig, ax = plt.subplots()\n"
|
|
">>> ax.plot(x, shi, label='Shi(x)')\n"
|
|
">>> ax.plot(x, chi, '--', label='Chi(x)')\n"
|
|
">>> ax.set_xlabel('x')\n"
|
|
">>> ax.set_title('Hyperbolic Sine and Cosine Integrals')\n"
|
|
">>> ax.legend(shadow=True, framealpha=1, loc='lower right')\n"
|
|
">>> ax.grid(True)\n"
|
|
">>> plt.show()")
|
|
ufunc_shichi_loops[0] = <np.PyUFuncGenericFunction>loop_i_d_dd_As_f_ff
|
|
ufunc_shichi_loops[1] = <np.PyUFuncGenericFunction>loop_i_d_dd_As_d_dd
|
|
ufunc_shichi_loops[2] = <np.PyUFuncGenericFunction>loop_i_D_DD_As_F_FF
|
|
ufunc_shichi_loops[3] = <np.PyUFuncGenericFunction>loop_i_D_DD_As_D_DD
|
|
ufunc_shichi_types[0] = <char>NPY_FLOAT
|
|
ufunc_shichi_types[1] = <char>NPY_FLOAT
|
|
ufunc_shichi_types[2] = <char>NPY_FLOAT
|
|
ufunc_shichi_types[3] = <char>NPY_DOUBLE
|
|
ufunc_shichi_types[4] = <char>NPY_DOUBLE
|
|
ufunc_shichi_types[5] = <char>NPY_DOUBLE
|
|
ufunc_shichi_types[6] = <char>NPY_CFLOAT
|
|
ufunc_shichi_types[7] = <char>NPY_CFLOAT
|
|
ufunc_shichi_types[8] = <char>NPY_CFLOAT
|
|
ufunc_shichi_types[9] = <char>NPY_CDOUBLE
|
|
ufunc_shichi_types[10] = <char>NPY_CDOUBLE
|
|
ufunc_shichi_types[11] = <char>NPY_CDOUBLE
|
|
ufunc_shichi_ptr[2*0] = <void*>_func_xsf_shichi
|
|
ufunc_shichi_ptr[2*0+1] = <void*>(<char*>"shichi")
|
|
ufunc_shichi_ptr[2*1] = <void*>_func_xsf_shichi
|
|
ufunc_shichi_ptr[2*1+1] = <void*>(<char*>"shichi")
|
|
ufunc_shichi_ptr[2*2] = <void*>_func_xsf_cshichi
|
|
ufunc_shichi_ptr[2*2+1] = <void*>(<char*>"shichi")
|
|
ufunc_shichi_ptr[2*3] = <void*>_func_xsf_cshichi
|
|
ufunc_shichi_ptr[2*3+1] = <void*>(<char*>"shichi")
|
|
ufunc_shichi_data[0] = &ufunc_shichi_ptr[2*0]
|
|
ufunc_shichi_data[1] = &ufunc_shichi_ptr[2*1]
|
|
ufunc_shichi_data[2] = &ufunc_shichi_ptr[2*2]
|
|
ufunc_shichi_data[3] = &ufunc_shichi_ptr[2*3]
|
|
shichi = np.PyUFunc_FromFuncAndData(ufunc_shichi_loops, ufunc_shichi_data, ufunc_shichi_types, 4, 1, 2, 0, 'shichi', ufunc_shichi_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_sici_loops[4]
|
|
cdef void *ufunc_sici_ptr[8]
|
|
cdef void *ufunc_sici_data[4]
|
|
cdef char ufunc_sici_types[12]
|
|
cdef char *ufunc_sici_doc = (
|
|
"sici(x, out=None)\n"
|
|
"\n"
|
|
"Sine and cosine integrals.\n"
|
|
"\n"
|
|
"The sine integral is\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" \\int_0^x \\frac{\\sin{t}}{t}dt\n"
|
|
"\n"
|
|
"and the cosine integral is\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" \\gamma + \\log(x) + \\int_0^x \\frac{\\cos{t} - 1}{t}dt\n"
|
|
"\n"
|
|
"where :math:`\\gamma` is Euler's constant and :math:`\\log` is the\n"
|
|
"principal branch of the logarithm [1]_.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x : array_like\n"
|
|
" Real or complex points at which to compute the sine and cosine\n"
|
|
" integrals.\n"
|
|
"out : tuple of ndarray, optional\n"
|
|
" Optional output arrays for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"si : scalar or ndarray\n"
|
|
" Sine integral at ``x``\n"
|
|
"ci : scalar or ndarray\n"
|
|
" Cosine integral at ``x``\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"shichi : Hyperbolic sine and cosine integrals.\n"
|
|
"exp1 : Exponential integral E1.\n"
|
|
"expi : Exponential integral Ei.\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"For real arguments with ``x < 0``, ``ci`` is the real part of the\n"
|
|
"cosine integral. For such points ``ci(x)`` and ``ci(x + 0j)``\n"
|
|
"differ by a factor of ``1j*pi``.\n"
|
|
"\n"
|
|
"For real arguments the function is computed by calling Cephes'\n"
|
|
"[2]_ *sici* routine. For complex arguments the algorithm is based\n"
|
|
"on Mpmath's [3]_ *si* and *ci* routines.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Milton Abramowitz and Irene A. Stegun, eds.\n"
|
|
" Handbook of Mathematical Functions with Formulas,\n"
|
|
" Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
|
|
" (See Section 5.2.)\n"
|
|
".. [2] Cephes Mathematical Functions Library,\n"
|
|
" http://www.netlib.org/cephes/\n"
|
|
".. [3] Fredrik Johansson and others.\n"
|
|
" \"mpmath: a Python library for arbitrary-precision floating-point\n"
|
|
" arithmetic\" (Version 0.19) http://mpmath.org/\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
">>> from scipy.special import sici, exp1\n"
|
|
"\n"
|
|
"`sici` accepts real or complex input:\n"
|
|
"\n"
|
|
">>> sici(2.5)\n"
|
|
"(1.7785201734438267, 0.2858711963653835)\n"
|
|
">>> sici(2.5 + 3j)\n"
|
|
"((4.505735874563953+0.06863305018999577j),\n"
|
|
"(0.0793644206906966-2.935510262937543j))\n"
|
|
"\n"
|
|
"For z in the right half plane, the sine and cosine integrals are\n"
|
|
"related to the exponential integral E1 (implemented in SciPy as\n"
|
|
"`scipy.special.exp1`) by\n"
|
|
"\n"
|
|
"* Si(z) = (E1(i*z) - E1(-i*z))/2i + pi/2\n"
|
|
"* Ci(z) = -(E1(i*z) + E1(-i*z))/2\n"
|
|
"\n"
|
|
"See [1]_ (equations 5.2.21 and 5.2.23).\n"
|
|
"\n"
|
|
"We can verify these relations:\n"
|
|
"\n"
|
|
">>> z = 2 - 3j\n"
|
|
">>> sici(z)\n"
|
|
"((4.54751388956229-1.3991965806460565j),\n"
|
|
"(1.408292501520851+2.9836177420296055j))\n"
|
|
"\n"
|
|
">>> (exp1(1j*z) - exp1(-1j*z))/2j + np.pi/2 # Same as sine integral\n"
|
|
"(4.54751388956229-1.3991965806460565j)\n"
|
|
"\n"
|
|
">>> -(exp1(1j*z) + exp1(-1j*z))/2 # Same as cosine integral\n"
|
|
"(1.408292501520851+2.9836177420296055j)\n"
|
|
"\n"
|
|
"Plot the functions evaluated on the real axis; the dotted horizontal\n"
|
|
"lines are at pi/2 and -pi/2:\n"
|
|
"\n"
|
|
">>> x = np.linspace(-16, 16, 150)\n"
|
|
">>> si, ci = sici(x)\n"
|
|
"\n"
|
|
">>> fig, ax = plt.subplots()\n"
|
|
">>> ax.plot(x, si, label='Si(x)')\n"
|
|
">>> ax.plot(x, ci, '--', label='Ci(x)')\n"
|
|
">>> ax.legend(shadow=True, framealpha=1, loc='upper left')\n"
|
|
">>> ax.set_xlabel('x')\n"
|
|
">>> ax.set_title('Sine and Cosine Integrals')\n"
|
|
">>> ax.axhline(np.pi/2, linestyle=':', alpha=0.5, color='k')\n"
|
|
">>> ax.axhline(-np.pi/2, linestyle=':', alpha=0.5, color='k')\n"
|
|
">>> ax.grid(True)\n"
|
|
">>> plt.show()")
|
|
ufunc_sici_loops[0] = <np.PyUFuncGenericFunction>loop_i_d_dd_As_f_ff
|
|
ufunc_sici_loops[1] = <np.PyUFuncGenericFunction>loop_i_d_dd_As_d_dd
|
|
ufunc_sici_loops[2] = <np.PyUFuncGenericFunction>loop_i_D_DD_As_F_FF
|
|
ufunc_sici_loops[3] = <np.PyUFuncGenericFunction>loop_i_D_DD_As_D_DD
|
|
ufunc_sici_types[0] = <char>NPY_FLOAT
|
|
ufunc_sici_types[1] = <char>NPY_FLOAT
|
|
ufunc_sici_types[2] = <char>NPY_FLOAT
|
|
ufunc_sici_types[3] = <char>NPY_DOUBLE
|
|
ufunc_sici_types[4] = <char>NPY_DOUBLE
|
|
ufunc_sici_types[5] = <char>NPY_DOUBLE
|
|
ufunc_sici_types[6] = <char>NPY_CFLOAT
|
|
ufunc_sici_types[7] = <char>NPY_CFLOAT
|
|
ufunc_sici_types[8] = <char>NPY_CFLOAT
|
|
ufunc_sici_types[9] = <char>NPY_CDOUBLE
|
|
ufunc_sici_types[10] = <char>NPY_CDOUBLE
|
|
ufunc_sici_types[11] = <char>NPY_CDOUBLE
|
|
ufunc_sici_ptr[2*0] = <void*>_func_xsf_sici
|
|
ufunc_sici_ptr[2*0+1] = <void*>(<char*>"sici")
|
|
ufunc_sici_ptr[2*1] = <void*>_func_xsf_sici
|
|
ufunc_sici_ptr[2*1+1] = <void*>(<char*>"sici")
|
|
ufunc_sici_ptr[2*2] = <void*>_func_xsf_csici
|
|
ufunc_sici_ptr[2*2+1] = <void*>(<char*>"sici")
|
|
ufunc_sici_ptr[2*3] = <void*>_func_xsf_csici
|
|
ufunc_sici_ptr[2*3+1] = <void*>(<char*>"sici")
|
|
ufunc_sici_data[0] = &ufunc_sici_ptr[2*0]
|
|
ufunc_sici_data[1] = &ufunc_sici_ptr[2*1]
|
|
ufunc_sici_data[2] = &ufunc_sici_ptr[2*2]
|
|
ufunc_sici_data[3] = &ufunc_sici_ptr[2*3]
|
|
sici = np.PyUFunc_FromFuncAndData(ufunc_sici_loops, ufunc_sici_data, ufunc_sici_types, 4, 1, 2, 0, 'sici', ufunc_sici_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_smirnov_loops[3]
|
|
cdef void *ufunc_smirnov_ptr[6]
|
|
cdef void *ufunc_smirnov_data[3]
|
|
cdef char ufunc_smirnov_types[9]
|
|
cdef char *ufunc_smirnov_doc = (
|
|
"smirnov(n, d, out=None)\n"
|
|
"\n"
|
|
"Kolmogorov-Smirnov complementary cumulative distribution function\n"
|
|
"\n"
|
|
"Returns the exact Kolmogorov-Smirnov complementary cumulative\n"
|
|
"distribution function,(aka the Survival Function) of Dn+ (or Dn-)\n"
|
|
"for a one-sided test of equality between an empirical and a\n"
|
|
"theoretical distribution. It is equal to the probability that the\n"
|
|
"maximum difference between a theoretical distribution and an empirical\n"
|
|
"one based on `n` samples is greater than d.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"n : int\n"
|
|
" Number of samples\n"
|
|
"d : float array_like\n"
|
|
" Deviation between the Empirical CDF (ECDF) and the target CDF.\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" The value(s) of smirnov(n, d), Prob(Dn+ >= d) (Also Prob(Dn- >= d))\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"smirnovi : The Inverse Survival Function for the distribution\n"
|
|
"scipy.stats.ksone : Provides the functionality as a continuous distribution\n"
|
|
"kolmogorov, kolmogi : Functions for the two-sided distribution\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"`smirnov` is used by `stats.kstest` in the application of the\n"
|
|
"Kolmogorov-Smirnov Goodness of Fit test. For historical reasons this\n"
|
|
"function is exposed in `scpy.special`, but the recommended way to achieve\n"
|
|
"the most accurate CDF/SF/PDF/PPF/ISF computations is to use the\n"
|
|
"`stats.ksone` distribution.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import smirnov\n"
|
|
">>> from scipy.stats import norm\n"
|
|
"\n"
|
|
"Show the probability of a gap at least as big as 0, 0.5 and 1.0 for a\n"
|
|
"sample of size 5.\n"
|
|
"\n"
|
|
">>> smirnov(5, [0, 0.5, 1.0])\n"
|
|
"array([ 1. , 0.056, 0. ])\n"
|
|
"\n"
|
|
"Compare a sample of size 5 against N(0, 1), the standard normal\n"
|
|
"distribution with mean 0 and standard deviation 1.\n"
|
|
"\n"
|
|
"`x` is the sample.\n"
|
|
"\n"
|
|
">>> x = np.array([-1.392, -0.135, 0.114, 0.190, 1.82])\n"
|
|
"\n"
|
|
">>> target = norm(0, 1)\n"
|
|
">>> cdfs = target.cdf(x)\n"
|
|
">>> cdfs\n"
|
|
"array([0.0819612 , 0.44630594, 0.5453811 , 0.57534543, 0.9656205 ])\n"
|
|
"\n"
|
|
"Construct the empirical CDF and the K-S statistics (Dn+, Dn-, Dn).\n"
|
|
"\n"
|
|
">>> n = len(x)\n"
|
|
">>> ecdfs = np.arange(n+1, dtype=float)/n\n"
|
|
">>> cols = np.column_stack([x, ecdfs[1:], cdfs, cdfs - ecdfs[:n],\n"
|
|
"... ecdfs[1:] - cdfs])\n"
|
|
">>> with np.printoptions(precision=3):\n"
|
|
"... print(cols)\n"
|
|
"[[-1.392 0.2 0.082 0.082 0.118]\n"
|
|
" [-0.135 0.4 0.446 0.246 -0.046]\n"
|
|
" [ 0.114 0.6 0.545 0.145 0.055]\n"
|
|
" [ 0.19 0.8 0.575 -0.025 0.225]\n"
|
|
" [ 1.82 1. 0.966 0.166 0.034]]\n"
|
|
">>> gaps = cols[:, -2:]\n"
|
|
">>> Dnpm = np.max(gaps, axis=0)\n"
|
|
">>> print(f'Dn-={Dnpm[0]:f}, Dn+={Dnpm[1]:f}')\n"
|
|
"Dn-=0.246306, Dn+=0.224655\n"
|
|
">>> probs = smirnov(n, Dnpm)\n"
|
|
">>> print(f'For a sample of size {n} drawn from N(0, 1):',\n"
|
|
"... f' Smirnov n={n}: Prob(Dn- >= {Dnpm[0]:f}) = {probs[0]:.4f}',\n"
|
|
"... f' Smirnov n={n}: Prob(Dn+ >= {Dnpm[1]:f}) = {probs[1]:.4f}',\n"
|
|
"... sep='\\n')\n"
|
|
"For a sample of size 5 drawn from N(0, 1):\n"
|
|
" Smirnov n=5: Prob(Dn- >= 0.246306) = 0.4711\n"
|
|
" Smirnov n=5: Prob(Dn+ >= 0.224655) = 0.5245\n"
|
|
"\n"
|
|
"Plot the empirical CDF and the standard normal CDF.\n"
|
|
"\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
">>> plt.step(np.concatenate(([-2.5], x, [2.5])),\n"
|
|
"... np.concatenate((ecdfs, [1])),\n"
|
|
"... where='post', label='Empirical CDF')\n"
|
|
">>> xx = np.linspace(-2.5, 2.5, 100)\n"
|
|
">>> plt.plot(xx, target.cdf(xx), '--', label='CDF for N(0, 1)')\n"
|
|
"\n"
|
|
"Add vertical lines marking Dn+ and Dn-.\n"
|
|
"\n"
|
|
">>> iminus, iplus = np.argmax(gaps, axis=0)\n"
|
|
">>> plt.vlines([x[iminus]], ecdfs[iminus], cdfs[iminus], color='r',\n"
|
|
"... alpha=0.5, lw=4)\n"
|
|
">>> plt.vlines([x[iplus]], cdfs[iplus], ecdfs[iplus+1], color='m',\n"
|
|
"... alpha=0.5, lw=4)\n"
|
|
"\n"
|
|
">>> plt.grid(True)\n"
|
|
">>> plt.legend(framealpha=1, shadow=True)\n"
|
|
">>> plt.show()")
|
|
ufunc_smirnov_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
|
|
ufunc_smirnov_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_smirnov_loops[2] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_smirnov_types[0] = <char>NPY_INTP
|
|
ufunc_smirnov_types[1] = <char>NPY_DOUBLE
|
|
ufunc_smirnov_types[2] = <char>NPY_DOUBLE
|
|
ufunc_smirnov_types[3] = <char>NPY_FLOAT
|
|
ufunc_smirnov_types[4] = <char>NPY_FLOAT
|
|
ufunc_smirnov_types[5] = <char>NPY_FLOAT
|
|
ufunc_smirnov_types[6] = <char>NPY_DOUBLE
|
|
ufunc_smirnov_types[7] = <char>NPY_DOUBLE
|
|
ufunc_smirnov_types[8] = <char>NPY_DOUBLE
|
|
ufunc_smirnov_ptr[2*0] = <void*>_func_cephes_smirnov_wrap
|
|
ufunc_smirnov_ptr[2*0+1] = <void*>(<char*>"smirnov")
|
|
ufunc_smirnov_ptr[2*1] = <void*>_func_smirnov_unsafe
|
|
ufunc_smirnov_ptr[2*1+1] = <void*>(<char*>"smirnov")
|
|
ufunc_smirnov_ptr[2*2] = <void*>_func_smirnov_unsafe
|
|
ufunc_smirnov_ptr[2*2+1] = <void*>(<char*>"smirnov")
|
|
ufunc_smirnov_data[0] = &ufunc_smirnov_ptr[2*0]
|
|
ufunc_smirnov_data[1] = &ufunc_smirnov_ptr[2*1]
|
|
ufunc_smirnov_data[2] = &ufunc_smirnov_ptr[2*2]
|
|
smirnov = np.PyUFunc_FromFuncAndData(ufunc_smirnov_loops, ufunc_smirnov_data, ufunc_smirnov_types, 3, 2, 1, 0, 'smirnov', ufunc_smirnov_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_smirnovi_loops[3]
|
|
cdef void *ufunc_smirnovi_ptr[6]
|
|
cdef void *ufunc_smirnovi_data[3]
|
|
cdef char ufunc_smirnovi_types[9]
|
|
cdef char *ufunc_smirnovi_doc = (
|
|
"smirnovi(n, p, out=None)\n"
|
|
"\n"
|
|
"Inverse to `smirnov`\n"
|
|
"\n"
|
|
"Returns `d` such that ``smirnov(n, d) == p``, the critical value\n"
|
|
"corresponding to `p`.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"n : int\n"
|
|
" Number of samples\n"
|
|
"p : float array_like\n"
|
|
" Probability\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" The value(s) of smirnovi(n, p), the critical values.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"smirnov : The Survival Function (SF) for the distribution\n"
|
|
"scipy.stats.ksone : Provides the functionality as a continuous distribution\n"
|
|
"kolmogorov, kolmogi : Functions for the two-sided distribution\n"
|
|
"scipy.stats.kstwobign : Two-sided Kolmogorov-Smirnov distribution, large n\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"`smirnov` is used by `stats.kstest` in the application of the\n"
|
|
"Kolmogorov-Smirnov Goodness of Fit test. For historical reasons this\n"
|
|
"function is exposed in `scpy.special`, but the recommended way to achieve\n"
|
|
"the most accurate CDF/SF/PDF/PPF/ISF computations is to use the\n"
|
|
"`stats.ksone` distribution.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> from scipy.special import smirnovi, smirnov\n"
|
|
"\n"
|
|
">>> n = 24\n"
|
|
">>> deviations = [0.1, 0.2, 0.3]\n"
|
|
"\n"
|
|
"Use `smirnov` to compute the complementary CDF of the Smirnov\n"
|
|
"distribution for the given number of samples and deviations.\n"
|
|
"\n"
|
|
">>> p = smirnov(n, deviations)\n"
|
|
">>> p\n"
|
|
"array([0.58105083, 0.12826832, 0.01032231])\n"
|
|
"\n"
|
|
"The inverse function ``smirnovi(n, p)`` returns ``deviations``.\n"
|
|
"\n"
|
|
">>> smirnovi(n, p)\n"
|
|
"array([0.1, 0.2, 0.3])")
|
|
ufunc_smirnovi_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
|
|
ufunc_smirnovi_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_smirnovi_loops[2] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_smirnovi_types[0] = <char>NPY_INTP
|
|
ufunc_smirnovi_types[1] = <char>NPY_DOUBLE
|
|
ufunc_smirnovi_types[2] = <char>NPY_DOUBLE
|
|
ufunc_smirnovi_types[3] = <char>NPY_FLOAT
|
|
ufunc_smirnovi_types[4] = <char>NPY_FLOAT
|
|
ufunc_smirnovi_types[5] = <char>NPY_FLOAT
|
|
ufunc_smirnovi_types[6] = <char>NPY_DOUBLE
|
|
ufunc_smirnovi_types[7] = <char>NPY_DOUBLE
|
|
ufunc_smirnovi_types[8] = <char>NPY_DOUBLE
|
|
ufunc_smirnovi_ptr[2*0] = <void*>_func_cephes_smirnovi_wrap
|
|
ufunc_smirnovi_ptr[2*0+1] = <void*>(<char*>"smirnovi")
|
|
ufunc_smirnovi_ptr[2*1] = <void*>_func_smirnovi_unsafe
|
|
ufunc_smirnovi_ptr[2*1+1] = <void*>(<char*>"smirnovi")
|
|
ufunc_smirnovi_ptr[2*2] = <void*>_func_smirnovi_unsafe
|
|
ufunc_smirnovi_ptr[2*2+1] = <void*>(<char*>"smirnovi")
|
|
ufunc_smirnovi_data[0] = &ufunc_smirnovi_ptr[2*0]
|
|
ufunc_smirnovi_data[1] = &ufunc_smirnovi_ptr[2*1]
|
|
ufunc_smirnovi_data[2] = &ufunc_smirnovi_ptr[2*2]
|
|
smirnovi = np.PyUFunc_FromFuncAndData(ufunc_smirnovi_loops, ufunc_smirnovi_data, ufunc_smirnovi_types, 3, 2, 1, 0, 'smirnovi', ufunc_smirnovi_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_spence_loops[4]
|
|
cdef void *ufunc_spence_ptr[8]
|
|
cdef void *ufunc_spence_data[4]
|
|
cdef char ufunc_spence_types[8]
|
|
cdef char *ufunc_spence_doc = (
|
|
"spence(z, out=None)\n"
|
|
"\n"
|
|
"Spence's function, also known as the dilogarithm.\n"
|
|
"\n"
|
|
"It is defined to be\n"
|
|
"\n"
|
|
".. math::\n"
|
|
" \\int_1^z \\frac{\\log(t)}{1 - t}dt\n"
|
|
"\n"
|
|
"for complex :math:`z`, where the contour of integration is taken\n"
|
|
"to avoid the branch cut of the logarithm. Spence's function is\n"
|
|
"analytic everywhere except the negative real axis where it has a\n"
|
|
"branch cut.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"z : array_like\n"
|
|
" Points at which to evaluate Spence's function\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"s : scalar or ndarray\n"
|
|
" Computed values of Spence's function\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"There is a different convention which defines Spence's function by\n"
|
|
"the integral\n"
|
|
"\n"
|
|
".. math::\n"
|
|
" -\\int_0^z \\frac{\\log(1 - t)}{t}dt;\n"
|
|
"\n"
|
|
"this is our ``spence(1 - z)``.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import spence\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
"\n"
|
|
"The function is defined for complex inputs:\n"
|
|
"\n"
|
|
">>> spence([1-1j, 1.5+2j, 3j, -10-5j])\n"
|
|
"array([-0.20561676+0.91596559j, -0.86766909-1.39560134j,\n"
|
|
" -0.59422064-2.49129918j, -1.14044398+6.80075924j])\n"
|
|
"\n"
|
|
"For complex inputs on the branch cut, which is the negative real axis,\n"
|
|
"the function returns the limit for ``z`` with positive imaginary part.\n"
|
|
"For example, in the following, note the sign change of the imaginary\n"
|
|
"part of the output for ``z = -2`` and ``z = -2 - 1e-8j``:\n"
|
|
"\n"
|
|
">>> spence([-2 + 1e-8j, -2, -2 - 1e-8j])\n"
|
|
"array([2.32018041-3.45139229j, 2.32018042-3.4513923j ,\n"
|
|
" 2.32018041+3.45139229j])\n"
|
|
"\n"
|
|
"The function returns ``nan`` for real inputs on the branch cut:\n"
|
|
"\n"
|
|
">>> spence(-1.5)\n"
|
|
"nan\n"
|
|
"\n"
|
|
"Verify some particular values: ``spence(0) = pi**2/6``,\n"
|
|
"``spence(1) = 0`` and ``spence(2) = -pi**2/12``.\n"
|
|
"\n"
|
|
">>> spence([0, 1, 2])\n"
|
|
"array([ 1.64493407, 0. , -0.82246703])\n"
|
|
">>> np.pi**2/6, -np.pi**2/12\n"
|
|
"(1.6449340668482264, -0.8224670334241132)\n"
|
|
"\n"
|
|
"Verify the identity::\n"
|
|
"\n"
|
|
" spence(z) + spence(1 - z) = pi**2/6 - log(z)*log(1 - z)\n"
|
|
"\n"
|
|
">>> z = 3 + 4j\n"
|
|
">>> spence(z) + spence(1 - z)\n"
|
|
"(-2.6523186143876067+1.8853470951513935j)\n"
|
|
">>> np.pi**2/6 - np.log(z)*np.log(1 - z)\n"
|
|
"(-2.652318614387606+1.885347095151394j)\n"
|
|
"\n"
|
|
"Plot the function for positive real input.\n"
|
|
"\n"
|
|
">>> fig, ax = plt.subplots()\n"
|
|
">>> x = np.linspace(0, 6, 400)\n"
|
|
">>> ax.plot(x, spence(x))\n"
|
|
">>> ax.grid()\n"
|
|
">>> ax.set_xlabel('x')\n"
|
|
">>> ax.set_title('spence(x)')\n"
|
|
">>> plt.show()")
|
|
ufunc_spence_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
|
|
ufunc_spence_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
|
|
ufunc_spence_loops[2] = <np.PyUFuncGenericFunction>loop_D_D__As_F_F
|
|
ufunc_spence_loops[3] = <np.PyUFuncGenericFunction>loop_D_D__As_D_D
|
|
ufunc_spence_types[0] = <char>NPY_FLOAT
|
|
ufunc_spence_types[1] = <char>NPY_FLOAT
|
|
ufunc_spence_types[2] = <char>NPY_DOUBLE
|
|
ufunc_spence_types[3] = <char>NPY_DOUBLE
|
|
ufunc_spence_types[4] = <char>NPY_CFLOAT
|
|
ufunc_spence_types[5] = <char>NPY_CFLOAT
|
|
ufunc_spence_types[6] = <char>NPY_CDOUBLE
|
|
ufunc_spence_types[7] = <char>NPY_CDOUBLE
|
|
ufunc_spence_ptr[2*0] = <void*>_func_cephes_spence
|
|
ufunc_spence_ptr[2*0+1] = <void*>(<char*>"spence")
|
|
ufunc_spence_ptr[2*1] = <void*>_func_cephes_spence
|
|
ufunc_spence_ptr[2*1+1] = <void*>(<char*>"spence")
|
|
ufunc_spence_ptr[2*2] = <void*>_func_cspence
|
|
ufunc_spence_ptr[2*2+1] = <void*>(<char*>"spence")
|
|
ufunc_spence_ptr[2*3] = <void*>_func_cspence
|
|
ufunc_spence_ptr[2*3+1] = <void*>(<char*>"spence")
|
|
ufunc_spence_data[0] = &ufunc_spence_ptr[2*0]
|
|
ufunc_spence_data[1] = &ufunc_spence_ptr[2*1]
|
|
ufunc_spence_data[2] = &ufunc_spence_ptr[2*2]
|
|
ufunc_spence_data[3] = &ufunc_spence_ptr[2*3]
|
|
spence = np.PyUFunc_FromFuncAndData(ufunc_spence_loops, ufunc_spence_data, ufunc_spence_types, 4, 1, 1, 0, 'spence', ufunc_spence_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_stdtr_loops[2]
|
|
cdef void *ufunc_stdtr_ptr[4]
|
|
cdef void *ufunc_stdtr_data[2]
|
|
cdef char ufunc_stdtr_types[6]
|
|
cdef char *ufunc_stdtr_doc = (
|
|
"stdtr(df, t, out=None)\n"
|
|
"\n"
|
|
"Student t distribution cumulative distribution function\n"
|
|
"\n"
|
|
"Returns the integral:\n"
|
|
"\n"
|
|
".. math::\n"
|
|
" \\frac{\\Gamma((df+1)/2)}{\\sqrt{\\pi df} \\Gamma(df/2)}\n"
|
|
" \\int_{-\\infty}^t (1+x^2/df)^{-(df+1)/2}\\, dx\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"df : array_like\n"
|
|
" Degrees of freedom\n"
|
|
"t : array_like\n"
|
|
" Upper bound of the integral\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"scalar or ndarray\n"
|
|
" Value of the Student t CDF at t\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"stdtridf : inverse of stdtr with respect to `df`\n"
|
|
"stdtrit : inverse of stdtr with respect to `t`\n"
|
|
"scipy.stats.t : student t distribution\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"The student t distribution is also available as `scipy.stats.t`.\n"
|
|
"Calling `stdtr` directly can improve performance compared to the\n"
|
|
"``cdf`` method of `scipy.stats.t` (see last example below).\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"Calculate the function for ``df=3`` at ``t=1``.\n"
|
|
"\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import stdtr\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
">>> stdtr(3, 1)\n"
|
|
"0.8044988905221148\n"
|
|
"\n"
|
|
"Plot the function for three different degrees of freedom.\n"
|
|
"\n"
|
|
">>> x = np.linspace(-10, 10, 1000)\n"
|
|
">>> fig, ax = plt.subplots()\n"
|
|
">>> parameters = [(1, \"solid\"), (3, \"dashed\"), (10, \"dotted\")]\n"
|
|
">>> for (df, linestyle) in parameters:\n"
|
|
"... ax.plot(x, stdtr(df, x), ls=linestyle, label=f\"$df={df}$\")\n"
|
|
">>> ax.legend()\n"
|
|
">>> ax.set_title(\"Student t distribution cumulative distribution function\")\n"
|
|
">>> plt.show()\n"
|
|
"\n"
|
|
"The function can be computed for several degrees of freedom at the same\n"
|
|
"time by providing a NumPy array or list for `df`:\n"
|
|
"\n"
|
|
">>> stdtr([1, 2, 3], 1)\n"
|
|
"array([0.75 , 0.78867513, 0.80449889])\n"
|
|
"\n"
|
|
"It is possible to calculate the function at several points for several\n"
|
|
"different degrees of freedom simultaneously by providing arrays for `df`\n"
|
|
"and `t` with shapes compatible for broadcasting. Compute `stdtr` at\n"
|
|
"4 points for 3 degrees of freedom resulting in an array of shape 3x4.\n"
|
|
"\n"
|
|
">>> dfs = np.array([[1], [2], [3]])\n"
|
|
">>> t = np.array([2, 4, 6, 8])\n"
|
|
">>> dfs.shape, t.shape\n"
|
|
"((3, 1), (4,))\n"
|
|
"\n"
|
|
">>> stdtr(dfs, t)\n"
|
|
"array([[0.85241638, 0.92202087, 0.94743154, 0.96041658],\n"
|
|
" [0.90824829, 0.97140452, 0.98666426, 0.99236596],\n"
|
|
" [0.93033702, 0.98599577, 0.99536364, 0.99796171]])\n"
|
|
"\n"
|
|
"The t distribution is also available as `scipy.stats.t`. Calling `stdtr`\n"
|
|
"directly can be much faster than calling the ``cdf`` method of\n"
|
|
"`scipy.stats.t`. To get the same results, one must use the following\n"
|
|
"parametrization: ``scipy.stats.t(df).cdf(x) = stdtr(df, x)``.\n"
|
|
"\n"
|
|
">>> from scipy.stats import t\n"
|
|
">>> df, x = 3, 1\n"
|
|
">>> stdtr_result = stdtr(df, x) # this can be faster than below\n"
|
|
">>> stats_result = t(df).cdf(x)\n"
|
|
">>> stats_result == stdtr_result # test that results are equal\n"
|
|
"True")
|
|
ufunc_stdtr_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_stdtr_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_stdtr_types[0] = <char>NPY_FLOAT
|
|
ufunc_stdtr_types[1] = <char>NPY_FLOAT
|
|
ufunc_stdtr_types[2] = <char>NPY_FLOAT
|
|
ufunc_stdtr_types[3] = <char>NPY_DOUBLE
|
|
ufunc_stdtr_types[4] = <char>NPY_DOUBLE
|
|
ufunc_stdtr_types[5] = <char>NPY_DOUBLE
|
|
ufunc_stdtr_ptr[2*0] = <void*>_func_stdtr
|
|
ufunc_stdtr_ptr[2*0+1] = <void*>(<char*>"stdtr")
|
|
ufunc_stdtr_ptr[2*1] = <void*>_func_stdtr
|
|
ufunc_stdtr_ptr[2*1+1] = <void*>(<char*>"stdtr")
|
|
ufunc_stdtr_data[0] = &ufunc_stdtr_ptr[2*0]
|
|
ufunc_stdtr_data[1] = &ufunc_stdtr_ptr[2*1]
|
|
stdtr = np.PyUFunc_FromFuncAndData(ufunc_stdtr_loops, ufunc_stdtr_data, ufunc_stdtr_types, 2, 2, 1, 0, 'stdtr', ufunc_stdtr_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_stdtridf_loops[2]
|
|
cdef void *ufunc_stdtridf_ptr[4]
|
|
cdef void *ufunc_stdtridf_data[2]
|
|
cdef char ufunc_stdtridf_types[6]
|
|
cdef char *ufunc_stdtridf_doc = (
|
|
"stdtridf(p, t, out=None)\n"
|
|
"\n"
|
|
"Inverse of `stdtr` vs df\n"
|
|
"\n"
|
|
"Returns the argument df such that stdtr(df, t) is equal to `p`.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"p : array_like\n"
|
|
" Probability\n"
|
|
"t : array_like\n"
|
|
" Upper bound of the integral\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"df : scalar or ndarray\n"
|
|
" Value of `df` such that ``stdtr(df, t) == p``\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"stdtr : Student t CDF\n"
|
|
"stdtrit : inverse of stdtr with respect to `t`\n"
|
|
"scipy.stats.t : Student t distribution\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"Compute the student t cumulative distribution function for one\n"
|
|
"parameter set.\n"
|
|
"\n"
|
|
">>> from scipy.special import stdtr, stdtridf\n"
|
|
">>> df, x = 5, 2\n"
|
|
">>> cdf_value = stdtr(df, x)\n"
|
|
">>> cdf_value\n"
|
|
"0.9490302605850709\n"
|
|
"\n"
|
|
"Verify that `stdtridf` recovers the original value for `df` given\n"
|
|
"the CDF value and `x`.\n"
|
|
"\n"
|
|
">>> stdtridf(cdf_value, x)\n"
|
|
"5.0")
|
|
ufunc_stdtridf_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_stdtridf_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_stdtridf_types[0] = <char>NPY_FLOAT
|
|
ufunc_stdtridf_types[1] = <char>NPY_FLOAT
|
|
ufunc_stdtridf_types[2] = <char>NPY_FLOAT
|
|
ufunc_stdtridf_types[3] = <char>NPY_DOUBLE
|
|
ufunc_stdtridf_types[4] = <char>NPY_DOUBLE
|
|
ufunc_stdtridf_types[5] = <char>NPY_DOUBLE
|
|
ufunc_stdtridf_ptr[2*0] = <void*>_func_stdtridf
|
|
ufunc_stdtridf_ptr[2*0+1] = <void*>(<char*>"stdtridf")
|
|
ufunc_stdtridf_ptr[2*1] = <void*>_func_stdtridf
|
|
ufunc_stdtridf_ptr[2*1+1] = <void*>(<char*>"stdtridf")
|
|
ufunc_stdtridf_data[0] = &ufunc_stdtridf_ptr[2*0]
|
|
ufunc_stdtridf_data[1] = &ufunc_stdtridf_ptr[2*1]
|
|
stdtridf = np.PyUFunc_FromFuncAndData(ufunc_stdtridf_loops, ufunc_stdtridf_data, ufunc_stdtridf_types, 2, 2, 1, 0, 'stdtridf', ufunc_stdtridf_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_stdtrit_loops[2]
|
|
cdef void *ufunc_stdtrit_ptr[4]
|
|
cdef void *ufunc_stdtrit_data[2]
|
|
cdef char ufunc_stdtrit_types[6]
|
|
cdef char *ufunc_stdtrit_doc = (
|
|
"stdtrit(df, p, out=None)\n"
|
|
"\n"
|
|
"The `p`-th quantile of the student t distribution.\n"
|
|
"\n"
|
|
"This function is the inverse of the student t distribution cumulative\n"
|
|
"distribution function (CDF), returning `t` such that `stdtr(df, t) = p`.\n"
|
|
"\n"
|
|
"Returns the argument `t` such that stdtr(df, t) is equal to `p`.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"df : array_like\n"
|
|
" Degrees of freedom\n"
|
|
"p : array_like\n"
|
|
" Probability\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"t : scalar or ndarray\n"
|
|
" Value of `t` such that ``stdtr(df, t) == p``\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"stdtr : Student t CDF\n"
|
|
"stdtridf : inverse of stdtr with respect to `df`\n"
|
|
"scipy.stats.t : Student t distribution\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"The student t distribution is also available as `scipy.stats.t`. Calling\n"
|
|
"`stdtrit` directly can improve performance compared to the ``ppf``\n"
|
|
"method of `scipy.stats.t` (see last example below).\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"`stdtrit` represents the inverse of the student t distribution CDF which\n"
|
|
"is available as `stdtr`. Here, we calculate the CDF for ``df`` at\n"
|
|
"``x=1``. `stdtrit` then returns ``1`` up to floating point errors\n"
|
|
"given the same value for `df` and the computed CDF value.\n"
|
|
"\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import stdtr, stdtrit\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
">>> df = 3\n"
|
|
">>> x = 1\n"
|
|
">>> cdf_value = stdtr(df, x)\n"
|
|
">>> stdtrit(df, cdf_value)\n"
|
|
"0.9999999994418539\n"
|
|
"\n"
|
|
"Plot the function for three different degrees of freedom.\n"
|
|
"\n"
|
|
">>> x = np.linspace(0, 1, 1000)\n"
|
|
">>> parameters = [(1, \"solid\"), (2, \"dashed\"), (5, \"dotted\")]\n"
|
|
">>> fig, ax = plt.subplots()\n"
|
|
">>> for (df, linestyle) in parameters:\n"
|
|
"... ax.plot(x, stdtrit(df, x), ls=linestyle, label=f\"$df={df}$\")\n"
|
|
">>> ax.legend()\n"
|
|
">>> ax.set_ylim(-10, 10)\n"
|
|
">>> ax.set_title(\"Student t distribution quantile function\")\n"
|
|
">>> plt.show()\n"
|
|
"\n"
|
|
"The function can be computed for several degrees of freedom at the same\n"
|
|
"time by providing a NumPy array or list for `df`:\n"
|
|
"\n"
|
|
">>> stdtrit([1, 2, 3], 0.7)\n"
|
|
"array([0.72654253, 0.6172134 , 0.58438973])\n"
|
|
"\n"
|
|
"It is possible to calculate the function at several points for several\n"
|
|
"different degrees of freedom simultaneously by providing arrays for `df`\n"
|
|
"and `p` with shapes compatible for broadcasting. Compute `stdtrit` at\n"
|
|
"4 points for 3 degrees of freedom resulting in an array of shape 3x4.\n"
|
|
"\n"
|
|
">>> dfs = np.array([[1], [2], [3]])\n"
|
|
">>> p = np.array([0.2, 0.4, 0.7, 0.8])\n"
|
|
">>> dfs.shape, p.shape\n"
|
|
"((3, 1), (4,))\n"
|
|
"\n"
|
|
">>> stdtrit(dfs, p)\n"
|
|
"array([[-1.37638192, -0.3249197 , 0.72654253, 1.37638192],\n"
|
|
" [-1.06066017, -0.28867513, 0.6172134 , 1.06066017],\n"
|
|
" [-0.97847231, -0.27667066, 0.58438973, 0.97847231]])\n"
|
|
"\n"
|
|
"The t distribution is also available as `scipy.stats.t`. Calling `stdtrit`\n"
|
|
"directly can be much faster than calling the ``ppf`` method of\n"
|
|
"`scipy.stats.t`. To get the same results, one must use the following\n"
|
|
"parametrization: ``scipy.stats.t(df).ppf(x) = stdtrit(df, x)``.\n"
|
|
"\n"
|
|
">>> from scipy.stats import t\n"
|
|
">>> df, x = 3, 0.5\n"
|
|
">>> stdtrit_result = stdtrit(df, x) # this can be faster than below\n"
|
|
">>> stats_result = t(df).ppf(x)\n"
|
|
">>> stats_result == stdtrit_result # test that results are equal\n"
|
|
"True")
|
|
ufunc_stdtrit_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_stdtrit_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_stdtrit_types[0] = <char>NPY_FLOAT
|
|
ufunc_stdtrit_types[1] = <char>NPY_FLOAT
|
|
ufunc_stdtrit_types[2] = <char>NPY_FLOAT
|
|
ufunc_stdtrit_types[3] = <char>NPY_DOUBLE
|
|
ufunc_stdtrit_types[4] = <char>NPY_DOUBLE
|
|
ufunc_stdtrit_types[5] = <char>NPY_DOUBLE
|
|
ufunc_stdtrit_ptr[2*0] = <void*>_func_stdtrit
|
|
ufunc_stdtrit_ptr[2*0+1] = <void*>(<char*>"stdtrit")
|
|
ufunc_stdtrit_ptr[2*1] = <void*>_func_stdtrit
|
|
ufunc_stdtrit_ptr[2*1+1] = <void*>(<char*>"stdtrit")
|
|
ufunc_stdtrit_data[0] = &ufunc_stdtrit_ptr[2*0]
|
|
ufunc_stdtrit_data[1] = &ufunc_stdtrit_ptr[2*1]
|
|
stdtrit = np.PyUFunc_FromFuncAndData(ufunc_stdtrit_loops, ufunc_stdtrit_data, ufunc_stdtrit_types, 2, 2, 1, 0, 'stdtrit', ufunc_stdtrit_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_tklmbda_loops[2]
|
|
cdef void *ufunc_tklmbda_ptr[4]
|
|
cdef void *ufunc_tklmbda_data[2]
|
|
cdef char ufunc_tklmbda_types[6]
|
|
cdef char *ufunc_tklmbda_doc = (
|
|
"tklmbda(x, lmbda, out=None)\n"
|
|
"\n"
|
|
"Cumulative distribution function of the Tukey lambda distribution.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"x, lmbda : array_like\n"
|
|
" Parameters\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"cdf : scalar or ndarray\n"
|
|
" Value of the Tukey lambda CDF\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"scipy.stats.tukeylambda : Tukey lambda distribution\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
">>> from scipy.special import tklmbda, expit\n"
|
|
"\n"
|
|
"Compute the cumulative distribution function (CDF) of the Tukey lambda\n"
|
|
"distribution at several ``x`` values for `lmbda` = -1.5.\n"
|
|
"\n"
|
|
">>> x = np.linspace(-2, 2, 9)\n"
|
|
">>> x\n"
|
|
"array([-2. , -1.5, -1. , -0.5, 0. , 0.5, 1. , 1.5, 2. ])\n"
|
|
">>> tklmbda(x, -1.5)\n"
|
|
"array([0.34688734, 0.3786554 , 0.41528805, 0.45629737, 0.5 ,\n"
|
|
" 0.54370263, 0.58471195, 0.6213446 , 0.65311266])\n"
|
|
"\n"
|
|
"When `lmbda` is 0, the function is the logistic sigmoid function,\n"
|
|
"which is implemented in `scipy.special` as `expit`.\n"
|
|
"\n"
|
|
">>> tklmbda(x, 0)\n"
|
|
"array([0.11920292, 0.18242552, 0.26894142, 0.37754067, 0.5 ,\n"
|
|
" 0.62245933, 0.73105858, 0.81757448, 0.88079708])\n"
|
|
">>> expit(x)\n"
|
|
"array([0.11920292, 0.18242552, 0.26894142, 0.37754067, 0.5 ,\n"
|
|
" 0.62245933, 0.73105858, 0.81757448, 0.88079708])\n"
|
|
"\n"
|
|
"When `lmbda` is 1, the Tukey lambda distribution is uniform on the\n"
|
|
"interval [-1, 1], so the CDF increases linearly.\n"
|
|
"\n"
|
|
">>> t = np.linspace(-1, 1, 9)\n"
|
|
">>> tklmbda(t, 1)\n"
|
|
"array([0. , 0.125, 0.25 , 0.375, 0.5 , 0.625, 0.75 , 0.875, 1. ])\n"
|
|
"\n"
|
|
"In the following, we generate plots for several values of `lmbda`.\n"
|
|
"\n"
|
|
"The first figure shows graphs for `lmbda` <= 0.\n"
|
|
"\n"
|
|
">>> styles = ['-', '-.', '--', ':']\n"
|
|
">>> fig, ax = plt.subplots()\n"
|
|
">>> x = np.linspace(-12, 12, 500)\n"
|
|
">>> for k, lmbda in enumerate([-1.0, -0.5, 0.0]):\n"
|
|
"... y = tklmbda(x, lmbda)\n"
|
|
"... ax.plot(x, y, styles[k], label=rf'$\\lambda$ = {lmbda:-4.1f}')\n"
|
|
"\n"
|
|
">>> ax.set_title(r'tklmbda(x, $\\lambda$)')\n"
|
|
">>> ax.set_label('x')\n"
|
|
">>> ax.legend(framealpha=1, shadow=True)\n"
|
|
">>> ax.grid(True)\n"
|
|
"\n"
|
|
"The second figure shows graphs for `lmbda` > 0. The dots in the\n"
|
|
"graphs show the bounds of the support of the distribution.\n"
|
|
"\n"
|
|
">>> fig, ax = plt.subplots()\n"
|
|
">>> x = np.linspace(-4.2, 4.2, 500)\n"
|
|
">>> lmbdas = [0.25, 0.5, 1.0, 1.5]\n"
|
|
">>> for k, lmbda in enumerate(lmbdas):\n"
|
|
"... y = tklmbda(x, lmbda)\n"
|
|
"... ax.plot(x, y, styles[k], label=fr'$\\lambda$ = {lmbda}')\n"
|
|
"\n"
|
|
">>> ax.set_prop_cycle(None)\n"
|
|
">>> for lmbda in lmbdas:\n"
|
|
"... ax.plot([-1/lmbda, 1/lmbda], [0, 1], '.', ms=8)\n"
|
|
"\n"
|
|
">>> ax.set_title(r'tklmbda(x, $\\lambda$)')\n"
|
|
">>> ax.set_xlabel('x')\n"
|
|
">>> ax.legend(framealpha=1, shadow=True)\n"
|
|
">>> ax.grid(True)\n"
|
|
"\n"
|
|
">>> plt.tight_layout()\n"
|
|
">>> plt.show()\n"
|
|
"\n"
|
|
"The CDF of the Tukey lambda distribution is also implemented as the\n"
|
|
"``cdf`` method of `scipy.stats.tukeylambda`. In the following,\n"
|
|
"``tukeylambda.cdf(x, -0.5)`` and ``tklmbda(x, -0.5)`` compute the\n"
|
|
"same values:\n"
|
|
"\n"
|
|
">>> from scipy.stats import tukeylambda\n"
|
|
">>> x = np.linspace(-2, 2, 9)\n"
|
|
"\n"
|
|
">>> tukeylambda.cdf(x, -0.5)\n"
|
|
"array([0.21995157, 0.27093858, 0.33541677, 0.41328161, 0.5 ,\n"
|
|
" 0.58671839, 0.66458323, 0.72906142, 0.78004843])\n"
|
|
"\n"
|
|
">>> tklmbda(x, -0.5)\n"
|
|
"array([0.21995157, 0.27093858, 0.33541677, 0.41328161, 0.5 ,\n"
|
|
" 0.58671839, 0.66458323, 0.72906142, 0.78004843])\n"
|
|
"\n"
|
|
"The implementation in ``tukeylambda`` also provides location and scale\n"
|
|
"parameters, and other methods such as ``pdf()`` (the probability\n"
|
|
"density function) and ``ppf()`` (the inverse of the CDF), so for\n"
|
|
"working with the Tukey lambda distribution, ``tukeylambda`` is more\n"
|
|
"generally useful. The primary advantage of ``tklmbda`` is that it is\n"
|
|
"significantly faster than ``tukeylambda.cdf``.")
|
|
ufunc_tklmbda_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_tklmbda_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_tklmbda_types[0] = <char>NPY_FLOAT
|
|
ufunc_tklmbda_types[1] = <char>NPY_FLOAT
|
|
ufunc_tklmbda_types[2] = <char>NPY_FLOAT
|
|
ufunc_tklmbda_types[3] = <char>NPY_DOUBLE
|
|
ufunc_tklmbda_types[4] = <char>NPY_DOUBLE
|
|
ufunc_tklmbda_types[5] = <char>NPY_DOUBLE
|
|
ufunc_tklmbda_ptr[2*0] = <void*>_func_xsf_tukeylambdacdf
|
|
ufunc_tklmbda_ptr[2*0+1] = <void*>(<char*>"tklmbda")
|
|
ufunc_tklmbda_ptr[2*1] = <void*>_func_xsf_tukeylambdacdf
|
|
ufunc_tklmbda_ptr[2*1+1] = <void*>(<char*>"tklmbda")
|
|
ufunc_tklmbda_data[0] = &ufunc_tklmbda_ptr[2*0]
|
|
ufunc_tklmbda_data[1] = &ufunc_tklmbda_ptr[2*1]
|
|
tklmbda = np.PyUFunc_FromFuncAndData(ufunc_tklmbda_loops, ufunc_tklmbda_data, ufunc_tklmbda_types, 2, 2, 1, 0, 'tklmbda', ufunc_tklmbda_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_wrightomega_loops[4]
|
|
cdef void *ufunc_wrightomega_ptr[8]
|
|
cdef void *ufunc_wrightomega_data[4]
|
|
cdef char ufunc_wrightomega_types[8]
|
|
cdef char *ufunc_wrightomega_doc = (
|
|
"wrightomega(z, out=None)\n"
|
|
"\n"
|
|
"Wright Omega function.\n"
|
|
"\n"
|
|
"Defined as the solution to\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" \\omega + \\log(\\omega) = z\n"
|
|
"\n"
|
|
"where :math:`\\log` is the principal branch of the complex logarithm.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"z : array_like\n"
|
|
" Points at which to evaluate the Wright Omega function\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function values\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"omega : scalar or ndarray\n"
|
|
" Values of the Wright Omega function\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"lambertw : The Lambert W function\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
".. versionadded:: 0.19.0\n"
|
|
"\n"
|
|
"The function can also be defined as\n"
|
|
"\n"
|
|
".. math::\n"
|
|
"\n"
|
|
" \\omega(z) = W_{K(z)}(e^z)\n"
|
|
"\n"
|
|
"where :math:`K(z) = \\lceil (\\Im(z) - \\pi)/(2\\pi) \\rceil` is the\n"
|
|
"unwinding number and :math:`W` is the Lambert W function.\n"
|
|
"\n"
|
|
"The implementation here is taken from [1]_.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Lawrence, Corless, and Jeffrey, \"Algorithm 917: Complex\n"
|
|
" Double-Precision Evaluation of the Wright :math:`\\omega`\n"
|
|
" Function.\" ACM Transactions on Mathematical Software,\n"
|
|
" 2012. :doi:`10.1145/2168773.2168779`.\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
">>> import numpy as np\n"
|
|
">>> from scipy.special import wrightomega, lambertw\n"
|
|
"\n"
|
|
">>> wrightomega([-2, -1, 0, 1, 2])\n"
|
|
"array([0.12002824, 0.27846454, 0.56714329, 1. , 1.5571456 ])\n"
|
|
"\n"
|
|
"Complex input:\n"
|
|
"\n"
|
|
">>> wrightomega(3 + 5j)\n"
|
|
"(1.5804428632097158+3.8213626783287937j)\n"
|
|
"\n"
|
|
"Verify that ``wrightomega(z)`` satisfies ``w + log(w) = z``:\n"
|
|
"\n"
|
|
">>> w = -5 + 4j\n"
|
|
">>> wrightomega(w + np.log(w))\n"
|
|
"(-5+4j)\n"
|
|
"\n"
|
|
"Verify the connection to ``lambertw``:\n"
|
|
"\n"
|
|
">>> z = 0.5 + 3j\n"
|
|
">>> wrightomega(z)\n"
|
|
"(0.0966015889280649+1.4937828458191993j)\n"
|
|
">>> lambertw(np.exp(z))\n"
|
|
"(0.09660158892806493+1.4937828458191993j)\n"
|
|
"\n"
|
|
">>> z = 0.5 + 4j\n"
|
|
">>> wrightomega(z)\n"
|
|
"(-0.3362123489037213+2.282986001579032j)\n"
|
|
">>> lambertw(np.exp(z), k=1)\n"
|
|
"(-0.33621234890372115+2.282986001579032j)")
|
|
ufunc_wrightomega_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
|
|
ufunc_wrightomega_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
|
|
ufunc_wrightomega_loops[2] = <np.PyUFuncGenericFunction>loop_D_D__As_F_F
|
|
ufunc_wrightomega_loops[3] = <np.PyUFuncGenericFunction>loop_D_D__As_D_D
|
|
ufunc_wrightomega_types[0] = <char>NPY_FLOAT
|
|
ufunc_wrightomega_types[1] = <char>NPY_FLOAT
|
|
ufunc_wrightomega_types[2] = <char>NPY_DOUBLE
|
|
ufunc_wrightomega_types[3] = <char>NPY_DOUBLE
|
|
ufunc_wrightomega_types[4] = <char>NPY_CFLOAT
|
|
ufunc_wrightomega_types[5] = <char>NPY_CFLOAT
|
|
ufunc_wrightomega_types[6] = <char>NPY_CDOUBLE
|
|
ufunc_wrightomega_types[7] = <char>NPY_CDOUBLE
|
|
ufunc_wrightomega_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_wrightomega_real
|
|
ufunc_wrightomega_ptr[2*0+1] = <void*>(<char*>"wrightomega")
|
|
ufunc_wrightomega_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_wrightomega_real
|
|
ufunc_wrightomega_ptr[2*1+1] = <void*>(<char*>"wrightomega")
|
|
ufunc_wrightomega_ptr[2*2] = <void*>scipy.special._ufuncs_cxx._export_wrightomega
|
|
ufunc_wrightomega_ptr[2*2+1] = <void*>(<char*>"wrightomega")
|
|
ufunc_wrightomega_ptr[2*3] = <void*>scipy.special._ufuncs_cxx._export_wrightomega
|
|
ufunc_wrightomega_ptr[2*3+1] = <void*>(<char*>"wrightomega")
|
|
ufunc_wrightomega_data[0] = &ufunc_wrightomega_ptr[2*0]
|
|
ufunc_wrightomega_data[1] = &ufunc_wrightomega_ptr[2*1]
|
|
ufunc_wrightomega_data[2] = &ufunc_wrightomega_ptr[2*2]
|
|
ufunc_wrightomega_data[3] = &ufunc_wrightomega_ptr[2*3]
|
|
wrightomega = np.PyUFunc_FromFuncAndData(ufunc_wrightomega_loops, ufunc_wrightomega_data, ufunc_wrightomega_types, 4, 1, 1, 0, 'wrightomega', ufunc_wrightomega_doc, 0)
|
|
|
|
cdef np.PyUFuncGenericFunction ufunc_yn_loops[3]
|
|
cdef void *ufunc_yn_ptr[6]
|
|
cdef void *ufunc_yn_data[3]
|
|
cdef char ufunc_yn_types[9]
|
|
cdef char *ufunc_yn_doc = (
|
|
"yn(n, x, out=None)\n"
|
|
"\n"
|
|
"Bessel function of the second kind of integer order and real argument.\n"
|
|
"\n"
|
|
"Parameters\n"
|
|
"----------\n"
|
|
"n : array_like\n"
|
|
" Order (integer).\n"
|
|
"x : array_like\n"
|
|
" Argument (float).\n"
|
|
"out : ndarray, optional\n"
|
|
" Optional output array for the function results\n"
|
|
"\n"
|
|
"Returns\n"
|
|
"-------\n"
|
|
"Y : scalar or ndarray\n"
|
|
" Value of the Bessel function, :math:`Y_n(x)`.\n"
|
|
"\n"
|
|
"See Also\n"
|
|
"--------\n"
|
|
"yv : For real order and real or complex argument.\n"
|
|
"y0: faster implementation of this function for order 0\n"
|
|
"y1: faster implementation of this function for order 1\n"
|
|
"\n"
|
|
"Notes\n"
|
|
"-----\n"
|
|
"Wrapper for the Cephes [1]_ routine `yn`.\n"
|
|
"\n"
|
|
"The function is evaluated by forward recurrence on `n`, starting with\n"
|
|
"values computed by the Cephes routines `y0` and `y1`. If ``n = 0`` or 1,\n"
|
|
"the routine for `y0` or `y1` is called directly.\n"
|
|
"\n"
|
|
"References\n"
|
|
"----------\n"
|
|
".. [1] Cephes Mathematical Functions Library,\n"
|
|
" http://www.netlib.org/cephes/\n"
|
|
"\n"
|
|
"Examples\n"
|
|
"--------\n"
|
|
"Evaluate the function of order 0 at one point.\n"
|
|
"\n"
|
|
">>> from scipy.special import yn\n"
|
|
">>> yn(0, 1.)\n"
|
|
"0.08825696421567697\n"
|
|
"\n"
|
|
"Evaluate the function at one point for different orders.\n"
|
|
"\n"
|
|
">>> yn(0, 1.), yn(1, 1.), yn(2, 1.)\n"
|
|
"(0.08825696421567697, -0.7812128213002888, -1.6506826068162546)\n"
|
|
"\n"
|
|
"The evaluation for different orders can be carried out in one call by\n"
|
|
"providing a list or NumPy array as argument for the `v` parameter:\n"
|
|
"\n"
|
|
">>> yn([0, 1, 2], 1.)\n"
|
|
"array([ 0.08825696, -0.78121282, -1.65068261])\n"
|
|
"\n"
|
|
"Evaluate the function at several points for order 0 by providing an\n"
|
|
"array for `z`.\n"
|
|
"\n"
|
|
">>> import numpy as np\n"
|
|
">>> points = np.array([0.5, 3., 8.])\n"
|
|
">>> yn(0, points)\n"
|
|
"array([-0.44451873, 0.37685001, 0.22352149])\n"
|
|
"\n"
|
|
"If `z` is an array, the order parameter `v` must be broadcastable to\n"
|
|
"the correct shape if different orders shall be computed in one call.\n"
|
|
"To calculate the orders 0 and 1 for an 1D array:\n"
|
|
"\n"
|
|
">>> orders = np.array([[0], [1]])\n"
|
|
">>> orders.shape\n"
|
|
"(2, 1)\n"
|
|
"\n"
|
|
">>> yn(orders, points)\n"
|
|
"array([[-0.44451873, 0.37685001, 0.22352149],\n"
|
|
" [-1.47147239, 0.32467442, -0.15806046]])\n"
|
|
"\n"
|
|
"Plot the functions of order 0 to 3 from 0 to 10.\n"
|
|
"\n"
|
|
">>> import matplotlib.pyplot as plt\n"
|
|
">>> fig, ax = plt.subplots()\n"
|
|
">>> x = np.linspace(0., 10., 1000)\n"
|
|
">>> for i in range(4):\n"
|
|
"... ax.plot(x, yn(i, x), label=f'$Y_{i!r}$')\n"
|
|
">>> ax.set_ylim(-3, 1)\n"
|
|
">>> ax.legend()\n"
|
|
">>> plt.show()")
|
|
ufunc_yn_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
|
|
ufunc_yn_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
|
|
ufunc_yn_loops[2] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
|
|
ufunc_yn_types[0] = <char>NPY_INTP
|
|
ufunc_yn_types[1] = <char>NPY_DOUBLE
|
|
ufunc_yn_types[2] = <char>NPY_DOUBLE
|
|
ufunc_yn_types[3] = <char>NPY_FLOAT
|
|
ufunc_yn_types[4] = <char>NPY_FLOAT
|
|
ufunc_yn_types[5] = <char>NPY_FLOAT
|
|
ufunc_yn_types[6] = <char>NPY_DOUBLE
|
|
ufunc_yn_types[7] = <char>NPY_DOUBLE
|
|
ufunc_yn_types[8] = <char>NPY_DOUBLE
|
|
ufunc_yn_ptr[2*0] = <void*>_func_cephes_yn_wrap
|
|
ufunc_yn_ptr[2*0+1] = <void*>(<char*>"yn")
|
|
ufunc_yn_ptr[2*1] = <void*>_func_yn_unsafe
|
|
ufunc_yn_ptr[2*1+1] = <void*>(<char*>"yn")
|
|
ufunc_yn_ptr[2*2] = <void*>_func_yn_unsafe
|
|
ufunc_yn_ptr[2*2+1] = <void*>(<char*>"yn")
|
|
ufunc_yn_data[0] = &ufunc_yn_ptr[2*0]
|
|
ufunc_yn_data[1] = &ufunc_yn_ptr[2*1]
|
|
ufunc_yn_data[2] = &ufunc_yn_ptr[2*2]
|
|
yn = np.PyUFunc_FromFuncAndData(ufunc_yn_loops, ufunc_yn_data, ufunc_yn_types, 3, 2, 1, 0, 'yn', ufunc_yn_doc, 0)
|
|
|
|
from ._special_ufuncs import (_cospi, _lambertw, _scaled_exp1, _sinpi, _spherical_jn, _spherical_jn_d, _spherical_yn, _spherical_yn_d, _spherical_in, _spherical_in_d, _spherical_kn, _spherical_kn_d, airy, airye, bei, beip, ber, berp, binom, exp1, expi, expit, exprel, gamma, gammaln, hankel1, hankel1e, hankel2, hankel2e, hyp2f1, it2i0k0, it2j0y0, it2struve0, itairy, iti0k0, itj0y0, itmodstruve0, itstruve0, iv, _iv_ratio, _iv_ratio_c, ive, jv, jve, kei, keip, kelvin, ker, kerp, kv, kve, log_expit, log_wright_bessel, loggamma, logit, mathieu_a, mathieu_b, mathieu_cem, mathieu_modcem1, mathieu_modcem2, mathieu_modsem1, mathieu_modsem2, mathieu_sem, modfresnelm, modfresnelp, obl_ang1, obl_ang1_cv, obl_cv, obl_rad1, obl_rad1_cv, obl_rad2, obl_rad2_cv, pbdv, pbvv, pbwa, pro_ang1, pro_ang1_cv, pro_cv, pro_rad1, pro_rad1_cv, pro_rad2, pro_rad2_cv, psi, rgamma, sph_harm, wright_bessel, yv, yve, zetac, _zeta, sindg, cosdg, tandg, cotdg, i0, i0e, i1, i1e, k0, k0e, k1, k1e, y0, y1, j0, j1, struve, modstruve, beta, betaln, besselpoly, gammaln, gammasgn, cbrt, radian, cosm1, gammainc, gammaincinv, gammaincc, gammainccinv, fresnel, ellipe, ellipeinc, ellipk, ellipkinc, ellipkm1, ellipj, _riemann_zeta, erf, erfc, erfcx, erfi, voigt_profile, wofz, dawsn, ndtr, log_ndtr, exp2, exp10, expm1, log1p, xlogy, xlog1py, _log1pmx, _log1mexp)
|
|
|
|
#
|
|
# Aliases
|
|
#
|
|
jn = jv
|