team-10/env/Lib/site-packages/scipy/special/tests/test_iv_ratio.py
2025-08-02 07:34:44 +02:00

249 lines
9.9 KiB
Python

# This file contains unit tests for iv_ratio() and related functions.
import pytest
import numpy as np
from numpy.testing import assert_equal, assert_allclose
from scipy.special._ufuncs import ( # type: ignore[attr-defined]
_iv_ratio as iv_ratio,
_iv_ratio_c as iv_ratio_c,
)
class TestIvRatio:
@pytest.mark.parametrize('v,x,r', [
(0.5, 0.16666666666666666, 0.16514041292462933),
(0.5, 0.3333333333333333, 0.32151273753163434),
(0.5, 0.5, 0.46211715726000974),
(0.5, 0.6666666666666666, 0.5827829453479101),
(0.5, 0.8333333333333335, 0.6822617902381698),
(1, 0.3380952380952381, 0.1666773049170313),
(1, 0.7083333333333333, 0.33366443586989925),
(1, 1.1666666666666667, 0.5023355231537423),
(1, 1.8666666666666665, 0.674616572252164),
(1, 3.560606060606061, 0.844207659503163),
(2.34, 0.7975238095238094, 0.16704903081553285),
(2.34, 1.7133333333333334, 0.3360215931268845),
(2.34, 2.953333333333333, 0.50681909317803),
(2.34, 5.0826666666666656, 0.6755252698800679),
(2.34, 10.869696969696973, 0.8379351104498762),
(56.789, 19.46575238095238, 0.1667020505391409),
(56.789, 42.55008333333333, 0.33353809996933026),
(56.789, 75.552, 0.5003932381177826),
(56.789, 135.76026666666667, 0.6670528221946127),
(56.789, 307.8642424242425, 0.8334999441460798),
])
def test_against_reference_values(self, v, x, r):
"""The reference values are computed using mpmath as follows.
from mpmath import mp
mp.dps = 100
def iv_ratio_mp(v, x):
return mp.besseli(v, x) / mp.besseli(v - 1, x)
def _sample(n, *, v):
'''Return n positive real numbers x such that iv_ratio(v, x) are
roughly evenly spaced over (0, 1). The formula is taken from [1].
[1] Banerjee A., Dhillon, I. S., Ghosh, J., Sra, S. (2005).
"Clustering on the Unit Hypersphere using von Mises-Fisher
Distributions." Journal of Machine Learning Research,
6(46):1345-1382.
'''
r = np.arange(1, n+1) / (n+1)
return r * (2*v-r*r) / (1-r*r)
for v in (0.5, 1, 2.34, 56.789):
xs = _sample(5, v=v)
for x in xs:
print(f"({v}, {x}, {float(iv_ratio_mp(v,x))}),")
"""
assert_allclose(iv_ratio(v, x), r, rtol=4e-16, atol=0)
@pytest.mark.parametrize('v,x,r', [
(1, np.inf, 1),
(np.inf, 1, 0),
])
def test_inf(self, v, x, r):
"""If exactly one of v or x is inf and the other is within domain,
should return 0 or 1 accordingly."""
assert_equal(iv_ratio(v, x), r)
@pytest.mark.parametrize('v', [0.49, -np.inf, np.nan, np.inf])
@pytest.mark.parametrize('x', [-np.finfo(float).smallest_normal,
-np.finfo(float).smallest_subnormal,
-np.inf, np.nan, np.inf])
def test_nan(self, v, x):
"""If at least one argument is out of domain, or if v = x = inf,
the function should return nan."""
assert_equal(iv_ratio(v, x), np.nan)
@pytest.mark.parametrize('v', [0.5, 1, np.finfo(float).max, np.inf])
def test_zero_x(self, v):
"""If x is +/-0.0, return x to ensure iv_ratio is an odd function."""
assert_equal(iv_ratio(v, 0.0), 0.0)
assert_equal(iv_ratio(v, -0.0), -0.0)
@pytest.mark.parametrize('v,x', [
(1, np.finfo(float).smallest_normal),
(1, np.finfo(float).smallest_subnormal),
(1, np.finfo(float).smallest_subnormal*2),
(1e20, 123),
(np.finfo(float).max, 1),
(np.finfo(float).max, np.sqrt(np.finfo(float).max)),
])
def test_tiny_x(self, v, x):
"""If x is much less than v, the bounds
x x
--------------------------- <= R <= -----------------------
v-0.5+sqrt(x**2+(v+0.5)**2) v-1+sqrt(x**2+(v+1)**2)
collapses to R ~= x/2v. Test against this asymptotic expression.
"""
assert_equal(iv_ratio(v, x), (0.5*x)/v)
@pytest.mark.parametrize('v,x', [
(1, 1e16),
(1e20, 1e40),
(np.sqrt(np.finfo(float).max), np.finfo(float).max),
])
def test_huge_x(self, v, x):
"""If x is much greater than v, the bounds
x x
--------------------------- <= R <= ---------------------------
v-0.5+sqrt(x**2+(v+0.5)**2) v-0.5+sqrt(x**2+(v-0.5)**2)
collapses to R ~= 1. Test against this asymptotic expression.
"""
assert_equal(iv_ratio(v, x), 1.0)
@pytest.mark.parametrize('v,x', [
(np.finfo(float).max, np.finfo(float).max),
(np.finfo(float).max / 3, np.finfo(float).max),
(np.finfo(float).max, np.finfo(float).max / 3),
])
def test_huge_v_x(self, v, x):
"""If both x and v are very large, the bounds
x x
--------------------------- <= R <= -----------------------
v-0.5+sqrt(x**2+(v+0.5)**2) v-1+sqrt(x**2+(v+1)**2)
collapses to R ~= x/(v+sqrt(x**2+v**2). Test against this asymptotic
expression, and in particular that no numerical overflow occurs during
intermediate calculations.
"""
t = x / v
expected = t / (1 + np.hypot(1, t))
assert_allclose(iv_ratio(v, x), expected, rtol=4e-16, atol=0)
class TestIvRatioC:
@pytest.mark.parametrize('v,x,r', [
(0.5, 0.16666666666666666, 0.8348595870753707),
(0.5, 0.3333333333333333, 0.6784872624683657),
(0.5, 0.5, 0.5378828427399902),
(0.5, 0.6666666666666666, 0.4172170546520899),
(0.5, 0.8333333333333335, 0.3177382097618302),
(1, 0.3380952380952381, 0.8333226950829686),
(1, 0.7083333333333333, 0.6663355641301008),
(1, 1.1666666666666667, 0.4976644768462577),
(1, 1.8666666666666665, 0.325383427747836),
(1, 3.560606060606061, 0.155792340496837),
(2.34, 0.7975238095238094, 0.8329509691844672),
(2.34, 1.7133333333333334, 0.6639784068731155),
(2.34, 2.953333333333333, 0.49318090682197),
(2.34, 5.0826666666666656, 0.3244747301199321),
(2.34, 10.869696969696973, 0.16206488955012377),
(56.789, 19.46575238095238, 0.8332979494608591),
(56.789, 42.55008333333333, 0.6664619000306697),
(56.789, 75.552, 0.4996067618822174),
(56.789, 135.76026666666667, 0.3329471778053873),
(56.789, 307.8642424242425, 0.16650005585392025),
])
def test_against_reference_values(self, v, x, r):
"""The reference values are one minus those of TestIvRatio."""
assert_allclose(iv_ratio_c(v, x), r, rtol=1e-15, atol=0)
@pytest.mark.parametrize('v,x,r', [
(1, np.inf, 0),
(np.inf, 1, 1),
])
def test_inf(self, v, x, r):
"""If exactly one of v or x is inf and the other is within domain,
should return 0 or 1 accordingly."""
assert_equal(iv_ratio_c(v, x), r)
@pytest.mark.parametrize('v', [0.49, -np.inf, np.nan, np.inf])
@pytest.mark.parametrize('x', [-np.finfo(float).smallest_normal,
-np.finfo(float).smallest_subnormal,
-np.inf, np.nan, np.inf])
def test_nan(self, v, x):
"""If at least one argument is out of domain, or if v = x = inf,
the function should return nan."""
assert_equal(iv_ratio_c(v, x), np.nan)
@pytest.mark.parametrize('v', [0.5, 1, np.finfo(float).max, np.inf])
def test_zero_x(self, v):
"""If x is +/-0.0, return 1."""
assert_equal(iv_ratio_c(v, 0.0), 1.0)
assert_equal(iv_ratio_c(v, -0.0), 1.0)
@pytest.mark.parametrize('v,x', [
(1, np.finfo(float).smallest_normal),
(1, np.finfo(float).smallest_subnormal),
(1, np.finfo(float).smallest_subnormal*2),
(1e20, 123),
(np.finfo(float).max, 1),
(np.finfo(float).max, np.sqrt(np.finfo(float).max)),
])
def test_tiny_x(self, v, x):
"""If x is much less than v, the bounds
x x
--------------------------- <= R <= -----------------------
v-0.5+sqrt(x**2+(v+0.5)**2) v-1+sqrt(x**2+(v+1)**2)
collapses to 1-R ~= 1-x/2v. Test against this asymptotic expression.
"""
assert_equal(iv_ratio_c(v, x), 1.0-(0.5*x)/v)
@pytest.mark.parametrize('v,x', [
(1, 1e16),
(1e20, 1e40),
(np.sqrt(np.finfo(float).max), np.finfo(float).max),
])
def test_huge_x(self, v, x):
"""If x is much greater than v, the bounds
x x
--------------------------- <= R <= ---------------------------
v-0.5+sqrt(x**2+(v+0.5)**2) v-0.5+sqrt(x**2+(v-0.5)**2)
collapses to 1-R ~= (v-0.5)/x. Test against this asymptotic expression.
"""
assert_allclose(iv_ratio_c(v, x), (v-0.5)/x, rtol=1e-15, atol=0)
@pytest.mark.parametrize('v,x', [
(np.finfo(float).max, np.finfo(float).max),
(np.finfo(float).max / 3, np.finfo(float).max),
(np.finfo(float).max, np.finfo(float).max / 3),
])
def test_huge_v_x(self, v, x):
"""If both x and v are very large, the bounds
x x
--------------------------- <= R <= -----------------------
v-0.5+sqrt(x**2+(v+0.5)**2) v-1+sqrt(x**2+(v+1)**2)
collapses to 1 - R ~= 1 - x/(v+sqrt(x**2+v**2). Test against this
asymptotic expression, and in particular that no numerical overflow
occurs during intermediate calculations.
"""
t = x / v
expected = 1 - t / (1 + np.hypot(1, t))
assert_allclose(iv_ratio_c(v, x), expected, rtol=4e-16, atol=0)