835 lines
29 KiB
Python
835 lines
29 KiB
Python
from collections import namedtuple
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import numpy as np
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import scipy.sparse as sps
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from ._numdiff import approx_derivative, group_columns
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from ._hessian_update_strategy import HessianUpdateStrategy
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from scipy.sparse.linalg import LinearOperator
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from scipy._lib._array_api import array_namespace, xp_copy
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from scipy._lib import array_api_extra as xpx
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from scipy._lib._util import _ScalarFunctionWrapper
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FD_METHODS = ('2-point', '3-point', 'cs')
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class _ScalarGradWrapper:
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"""
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Wrapper class for gradient calculation
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"""
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def __init__(
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self,
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grad,
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fun=None,
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args=None,
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finite_diff_options=None,
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):
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self.fun = fun
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self.grad = grad
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self.args = [] if args is None else args
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self.finite_diff_options = finite_diff_options
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self.ngev = 0
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# number of function evaluations consumed by finite difference
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self.nfev = 0
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def __call__(self, x, f0=None, **kwds):
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# Send a copy because the user may overwrite it.
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# The user of this class might want `x` to remain unchanged.
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if callable(self.grad):
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g = np.atleast_1d(self.grad(np.copy(x), *self.args))
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elif self.grad in FD_METHODS:
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g, dct = approx_derivative(
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self.fun,
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x,
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f0=f0,
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**self.finite_diff_options,
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)
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self.nfev += dct['nfev']
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self.ngev += 1
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return g
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class _ScalarHessWrapper:
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"""
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Wrapper class for hess calculation via finite differences
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"""
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def __init__(
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self,
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hess,
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x0=None,
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grad=None,
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args=None,
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finite_diff_options=None,
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):
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self.hess = hess
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self.grad = grad
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self.args = [] if args is None else args
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self.finite_diff_options = finite_diff_options
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# keep track of any finite difference function evaluations for grad
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self.ngev = 0
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self.nhev = 0
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self.H = None
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self._hess_func = None
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if callable(hess):
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self.H = hess(np.copy(x0), *args)
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self.nhev += 1
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if sps.issparse(self.H):
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self._hess_func = self._sparse_callable
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self.H = sps.csr_array(self.H)
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elif isinstance(self.H, LinearOperator):
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self._hess_func = self._linearoperator_callable
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else:
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# dense
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self._hess_func = self._dense_callable
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self.H = np.atleast_2d(np.asarray(self.H))
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elif hess in FD_METHODS:
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self._hess_func = self._fd_hess
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def __call__(self, x, f0=None, **kwds):
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return self._hess_func(np.copy(x), f0=f0)
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def _fd_hess(self, x, f0=None, **kwds):
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self.H, dct = approx_derivative(
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self.grad, x, f0=f0, **self.finite_diff_options
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)
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self.ngev += dct["nfev"]
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return self.H
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def _sparse_callable(self, x, **kwds):
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self.nhev += 1
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self.H = sps.csr_array(self.hess(x, *self.args))
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return self.H
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def _dense_callable(self, x, **kwds):
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self.nhev += 1
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self.H = np.atleast_2d(
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np.asarray(self.hess(x, *self.args))
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)
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return self.H
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def _linearoperator_callable(self, x, **kwds):
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self.nhev += 1
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self.H = self.hess(x, *self.args)
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return self.H
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class ScalarFunction:
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"""Scalar function and its derivatives.
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This class defines a scalar function F: R^n->R and methods for
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computing or approximating its first and second derivatives.
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Parameters
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----------
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fun : callable
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evaluates the scalar function. Must be of the form ``fun(x, *args)``,
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where ``x`` is the argument in the form of a 1-D array and ``args`` is
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a tuple of any additional fixed parameters needed to completely specify
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the function. Should return a scalar.
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x0 : array-like
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Provides an initial set of variables for evaluating fun. Array of real
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elements of size (n,), where 'n' is the number of independent
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variables.
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args : tuple, optional
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Any additional fixed parameters needed to completely specify the scalar
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function.
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grad : {callable, '2-point', '3-point', 'cs'}
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Method for computing the gradient vector.
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If it is a callable, it should be a function that returns the gradient
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vector:
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``grad(x, *args) -> array_like, shape (n,)``
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where ``x`` is an array with shape (n,) and ``args`` is a tuple with
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the fixed parameters.
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Alternatively, the keywords {'2-point', '3-point', 'cs'} can be used
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to select a finite difference scheme for numerical estimation of the
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gradient with a relative step size. These finite difference schemes
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obey any specified `bounds`.
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hess : {callable, '2-point', '3-point', 'cs', HessianUpdateStrategy}
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Method for computing the Hessian matrix. If it is callable, it should
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return the Hessian matrix:
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``hess(x, *args) -> {LinearOperator, spmatrix, array}, (n, n)``
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where x is a (n,) ndarray and `args` is a tuple with the fixed
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parameters. Alternatively, the keywords {'2-point', '3-point', 'cs'}
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select a finite difference scheme for numerical estimation. Or, objects
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implementing `HessianUpdateStrategy` interface can be used to
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approximate the Hessian.
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Whenever the gradient is estimated via finite-differences, the Hessian
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cannot be estimated with options {'2-point', '3-point', 'cs'} and needs
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to be estimated using one of the quasi-Newton strategies.
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finite_diff_rel_step : None or array_like
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Relative step size to use. The absolute step size is computed as
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``h = finite_diff_rel_step * sign(x0) * max(1, abs(x0))``, possibly
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adjusted to fit into the bounds. For ``method='3-point'`` the sign
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of `h` is ignored. If None then finite_diff_rel_step is selected
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automatically,
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finite_diff_bounds : tuple of array_like
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Lower and upper bounds on independent variables. Defaults to no bounds,
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(-np.inf, np.inf). Each bound must match the size of `x0` or be a
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scalar, in the latter case the bound will be the same for all
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variables. Use it to limit the range of function evaluation.
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epsilon : None or array_like, optional
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Absolute step size to use, possibly adjusted to fit into the bounds.
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For ``method='3-point'`` the sign of `epsilon` is ignored. By default
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relative steps are used, only if ``epsilon is not None`` are absolute
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steps used.
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workers : map-like callable, optional
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A map-like callable, such as `multiprocessing.Pool.map` for evaluating
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any numerical differentiation in parallel.
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This evaluation is carried out as ``workers(fun, iterable)``, or
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``workers(grad, iterable)``, depending on what is being numerically
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differentiated.
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Alternatively, if `workers` is an int the task is subdivided into `workers`
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sections and the function evaluated in parallel
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(uses `multiprocessing.Pool <multiprocessing>`).
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Supply -1 to use all available CPU cores.
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It is recommended that a map-like be used instead of int, as repeated
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calls to `approx_derivative` will incur large overhead from setting up
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new processes.
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.. versionadded:: 1.16.0
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Notes
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-----
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This class implements a memoization logic. There are methods `fun`,
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`grad`, hess` and corresponding attributes `f`, `g` and `H`. The following
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things should be considered:
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1. Use only public methods `fun`, `grad` and `hess`.
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2. After one of the methods is called, the corresponding attribute
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will be set. However, a subsequent call with a different argument
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of *any* of the methods may overwrite the attribute.
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"""
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def __init__(self, fun, x0, args, grad, hess, finite_diff_rel_step=None,
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finite_diff_bounds=(-np.inf, np.inf), epsilon=None, workers=None):
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if not callable(grad) and grad not in FD_METHODS:
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raise ValueError(
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f"`grad` must be either callable or one of {FD_METHODS}."
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)
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if not (callable(hess) or hess in FD_METHODS
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or isinstance(hess, HessianUpdateStrategy)):
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raise ValueError(
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f"`hess` must be either callable, HessianUpdateStrategy"
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f" or one of {FD_METHODS}."
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)
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if grad in FD_METHODS and hess in FD_METHODS:
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raise ValueError("Whenever the gradient is estimated via "
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"finite-differences, we require the Hessian "
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"to be estimated using one of the "
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"quasi-Newton strategies.")
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self.xp = xp = array_namespace(x0)
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_x = xpx.atleast_nd(xp.asarray(x0), ndim=1, xp=xp)
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_dtype = xp.float64
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if xp.isdtype(_x.dtype, "real floating"):
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_dtype = _x.dtype
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# original arguments
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self._wrapped_fun = _ScalarFunctionWrapper(fun, args)
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self._orig_fun = fun
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self._orig_grad = grad
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self._orig_hess = hess
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self._args = args
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# promotes to floating
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self.x = xp.astype(_x, _dtype)
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self.x_dtype = _dtype
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self.n = self.x.size
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self.f_updated = False
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self.g_updated = False
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self.H_updated = False
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self._lowest_x = None
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self._lowest_f = np.inf
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# normalize workers
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workers = workers or map
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finite_diff_options = {}
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if grad in FD_METHODS:
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finite_diff_options["method"] = grad
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finite_diff_options["rel_step"] = finite_diff_rel_step
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finite_diff_options["abs_step"] = epsilon
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finite_diff_options["bounds"] = finite_diff_bounds
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finite_diff_options["workers"] = workers
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finite_diff_options["full_output"] = True
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if hess in FD_METHODS:
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finite_diff_options["method"] = hess
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finite_diff_options["rel_step"] = finite_diff_rel_step
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finite_diff_options["abs_step"] = epsilon
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finite_diff_options["as_linear_operator"] = True
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finite_diff_options["workers"] = workers
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finite_diff_options["full_output"] = True
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# Initial function evaluation
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self._nfev = 0
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self._update_fun()
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# Initial gradient evaluation
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self._wrapped_grad = _ScalarGradWrapper(
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grad,
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fun=self._wrapped_fun,
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args=args,
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finite_diff_options=finite_diff_options,
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)
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self._update_grad()
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# Hessian evaluation
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if isinstance(hess, HessianUpdateStrategy):
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self.H = hess
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self.H.initialize(self.n, 'hess')
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self.H_updated = True
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self.x_prev = None
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self.g_prev = None
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_FakeCounter = namedtuple('_FakeCounter', ['ngev', 'nhev'])
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self._wrapped_hess = _FakeCounter(ngev=0, nhev=0)
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else:
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if callable(hess):
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self._wrapped_hess = _ScalarHessWrapper(
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hess,
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x0=x0,
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args=args,
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finite_diff_options=finite_diff_options
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)
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self.H = self._wrapped_hess.H
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self.H_updated = True
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elif hess in FD_METHODS:
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self._wrapped_hess = _ScalarHessWrapper(
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hess,
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x0=x0,
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args=args,
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grad=self._wrapped_grad,
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finite_diff_options=finite_diff_options
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)
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self._update_grad()
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self.H = self._wrapped_hess(self.x, f0=self.g)
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self.H_updated = True
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@property
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def nfev(self):
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return self._nfev + self._wrapped_grad.nfev
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@property
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def ngev(self):
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return self._wrapped_grad.ngev #+ self._wrapped_hess.ngev
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@property
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def nhev(self):
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return self._wrapped_hess.nhev
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def _update_x(self, x):
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if isinstance(self._orig_hess, HessianUpdateStrategy):
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self._update_grad()
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self.x_prev = self.x
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self.g_prev = self.g
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# ensure that self.x is a copy of x. Don't store a reference
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# otherwise the memoization doesn't work properly.
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_x = xpx.atleast_nd(self.xp.asarray(x), ndim=1, xp=self.xp)
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self.x = self.xp.astype(_x, self.x_dtype)
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self.f_updated = False
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self.g_updated = False
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self.H_updated = False
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self._update_hess()
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else:
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# ensure that self.x is a copy of x. Don't store a reference
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# otherwise the memoization doesn't work properly.
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_x = xpx.atleast_nd(self.xp.asarray(x), ndim=1, xp=self.xp)
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self.x = self.xp.astype(_x, self.x_dtype)
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self.f_updated = False
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self.g_updated = False
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self.H_updated = False
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def _update_fun(self):
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if not self.f_updated:
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fx = self._wrapped_fun(self.x)
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self._nfev += 1
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if fx < self._lowest_f:
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self._lowest_x = self.x
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self._lowest_f = fx
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self.f = fx
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self.f_updated = True
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def _update_grad(self):
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if not self.g_updated:
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if self._orig_grad in FD_METHODS:
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self._update_fun()
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self.g = self._wrapped_grad(self.x, f0=self.f)
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self.g_updated = True
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def _update_hess(self):
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if not self.H_updated:
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if self._orig_hess in FD_METHODS:
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self._update_grad()
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self.H = self._wrapped_hess(self.x, f0=self.g)
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elif isinstance(self._orig_hess, HessianUpdateStrategy):
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self._update_grad()
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self.H.update(self.x - self.x_prev, self.g - self.g_prev)
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else: # should be callable(hess)
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self.H = self._wrapped_hess(self.x)
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self.H_updated = True
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def fun(self, x):
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if not np.array_equal(x, self.x):
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self._update_x(x)
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self._update_fun()
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return self.f
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def grad(self, x):
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if not np.array_equal(x, self.x):
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self._update_x(x)
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self._update_grad()
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return self.g
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def hess(self, x):
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if not np.array_equal(x, self.x):
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self._update_x(x)
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self._update_hess()
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return self.H
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def fun_and_grad(self, x):
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if not np.array_equal(x, self.x):
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self._update_x(x)
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self._update_fun()
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self._update_grad()
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return self.f, self.g
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|
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class _VectorFunWrapper:
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def __init__(self, fun):
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self.fun = fun
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self.nfev = 0
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def __call__(self, x):
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self.nfev += 1
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return np.atleast_1d(self.fun(x))
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|
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class _VectorJacWrapper:
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"""
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Wrapper class for Jacobian calculation
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"""
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def __init__(
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self,
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jac,
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fun=None,
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finite_diff_options=None,
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sparse_jacobian=None
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):
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self.fun = fun
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self.jac = jac
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self.finite_diff_options = finite_diff_options
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self.sparse_jacobian = sparse_jacobian
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self.njev = 0
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# number of function evaluations consumed by finite difference
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self.nfev = 0
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def __call__(self, x, f0=None, **kwds):
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# Send a copy because the user may overwrite it.
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# The user of this class might want `x` to remain unchanged.
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if callable(self.jac):
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J = self.jac(x)
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self.njev += 1
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elif self.jac in FD_METHODS:
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J, dct = approx_derivative(
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self.fun,
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x,
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f0=f0,
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**self.finite_diff_options,
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)
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self.nfev += dct['nfev']
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if self.sparse_jacobian:
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return sps.csr_array(J)
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elif sps.issparse(J):
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return J.toarray()
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elif isinstance(J, LinearOperator):
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return J
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else:
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return np.atleast_2d(J)
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|
|
|
|
class _VectorHessWrapper:
|
|
"""
|
|
Wrapper class for Jacobian calculation
|
|
"""
|
|
def __init__(
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self,
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hess,
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jac=None,
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finite_diff_options=None,
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):
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self.jac = jac
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self.hess = hess
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self.finite_diff_options = finite_diff_options
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self.nhev = 0
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# number of jac evaluations consumed by finite difference
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self.njev = 0
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def __call__(self, x, v, J0=None, **kwds):
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# Send a copy because the user may overwrite it.
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# The user of this class might want `x` to remain unchanged.
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if callable(self.hess):
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self.nhev += 1
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return self._callable_hess(x, v)
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elif self.hess in FD_METHODS:
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return self._fd_hess(x, v, J0=J0)
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def _fd_hess(self, x, v, J0=None):
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if J0 is None:
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J0 = self.jac(x)
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self.njev += 1
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# H will be a LinearOperator
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H = approx_derivative(self.jac_dot_v, x,
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f0=J0.T.dot(v),
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args=(v,),
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**self.finite_diff_options)
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return H
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def jac_dot_v(self, x, v):
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self.njev += 1
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return self.jac(x).T.dot(v)
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|
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def _callable_hess(self, x, v):
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H = self.hess(x, v)
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|
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if sps.issparse(H):
|
|
return sps.csr_array(H)
|
|
elif isinstance(H, LinearOperator):
|
|
return H
|
|
else:
|
|
return np.atleast_2d(np.asarray(H))
|
|
|
|
|
|
class VectorFunction:
|
|
"""Vector function and its derivatives.
|
|
|
|
This class defines a vector function F: R^n->R^m and methods for
|
|
computing or approximating its first and second derivatives.
|
|
|
|
Notes
|
|
-----
|
|
This class implements a memoization logic. There are methods `fun`,
|
|
`jac`, hess` and corresponding attributes `f`, `J` and `H`. The following
|
|
things should be considered:
|
|
|
|
1. Use only public methods `fun`, `jac` and `hess`.
|
|
2. After one of the methods is called, the corresponding attribute
|
|
will be set. However, a subsequent call with a different argument
|
|
of *any* of the methods may overwrite the attribute.
|
|
"""
|
|
def __init__(self, fun, x0, jac, hess,
|
|
finite_diff_rel_step=None, finite_diff_jac_sparsity=None,
|
|
finite_diff_bounds=(-np.inf, np.inf), sparse_jacobian=None,
|
|
workers=None):
|
|
if not callable(jac) and jac not in FD_METHODS:
|
|
raise ValueError(f"`jac` must be either callable or one of {FD_METHODS}.")
|
|
|
|
if not (callable(hess) or hess in FD_METHODS
|
|
or isinstance(hess, HessianUpdateStrategy)):
|
|
raise ValueError("`hess` must be either callable,"
|
|
f"HessianUpdateStrategy or one of {FD_METHODS}.")
|
|
|
|
if jac in FD_METHODS and hess in FD_METHODS:
|
|
raise ValueError("Whenever the Jacobian is estimated via "
|
|
"finite-differences, we require the Hessian to "
|
|
"be estimated using one of the quasi-Newton "
|
|
"strategies.")
|
|
|
|
self.xp = xp = array_namespace(x0)
|
|
_x = xpx.atleast_nd(xp.asarray(x0), ndim=1, xp=xp)
|
|
_dtype = xp.float64
|
|
if xp.isdtype(_x.dtype, "real floating"):
|
|
_dtype = _x.dtype
|
|
|
|
# store original functions
|
|
self._orig_fun = fun
|
|
self._orig_jac = jac
|
|
self._orig_hess = hess
|
|
|
|
# promotes to floating, ensures that it's a copy
|
|
self.x = xp.astype(_x, _dtype)
|
|
self.x_dtype = _dtype
|
|
|
|
self.n = self.x.size
|
|
self._nfev = 0
|
|
self._njev = 0
|
|
self._nhev = 0
|
|
self.f_updated = False
|
|
self.J_updated = False
|
|
self.H_updated = False
|
|
|
|
# normalize workers
|
|
workers = workers or map
|
|
|
|
finite_diff_options = {}
|
|
if jac in FD_METHODS:
|
|
finite_diff_options["method"] = jac
|
|
finite_diff_options["rel_step"] = finite_diff_rel_step
|
|
if finite_diff_jac_sparsity is not None:
|
|
sparsity_groups = group_columns(finite_diff_jac_sparsity)
|
|
finite_diff_options["sparsity"] = (finite_diff_jac_sparsity,
|
|
sparsity_groups)
|
|
finite_diff_options["bounds"] = finite_diff_bounds
|
|
finite_diff_options["workers"] = workers
|
|
finite_diff_options["full_output"] = True
|
|
self.x_diff = np.copy(self.x)
|
|
if hess in FD_METHODS:
|
|
finite_diff_options["method"] = hess
|
|
finite_diff_options["rel_step"] = finite_diff_rel_step
|
|
finite_diff_options["as_linear_operator"] = True
|
|
# workers is not useful for evaluation of the LinearOperator
|
|
# produced by approx_derivative. Only two/three function
|
|
# evaluations are used, and the LinearOperator may persist
|
|
# outside the scope that workers is valid in.
|
|
self.x_diff = np.copy(self.x)
|
|
if jac in FD_METHODS and hess in FD_METHODS:
|
|
raise ValueError("Whenever the Jacobian is estimated via "
|
|
"finite-differences, we require the Hessian to "
|
|
"be estimated using one of the quasi-Newton "
|
|
"strategies.")
|
|
|
|
self.fun_wrapped = _VectorFunWrapper(fun)
|
|
self._update_fun()
|
|
|
|
self.v = np.zeros_like(self.f)
|
|
self.m = self.v.size
|
|
|
|
# Initial Jacobian Evaluation
|
|
if callable(jac):
|
|
self.J = jac(xp_copy(self.x))
|
|
self.J_updated = True
|
|
self._njev += 1
|
|
elif jac in FD_METHODS:
|
|
self.J, dct = approx_derivative(
|
|
self.fun_wrapped, self.x, f0=self.f, **finite_diff_options
|
|
)
|
|
self.J_updated = True
|
|
self._nfev += dct['nfev']
|
|
|
|
self.sparse_jacobian = False
|
|
if (sparse_jacobian or
|
|
sparse_jacobian is None and sps.issparse(self.J)):
|
|
# something truthy was specified for sparse_jacobian,
|
|
# or it turns out that the Jacobian was sparse.
|
|
self.J = sps.csr_array(self.J)
|
|
self.sparse_jacobian = True
|
|
elif sps.issparse(self.J):
|
|
self.J = self.J.toarray()
|
|
elif isinstance(self.J, LinearOperator):
|
|
pass
|
|
else:
|
|
self.J = np.atleast_2d(self.J)
|
|
|
|
self.jac_wrapped = _VectorJacWrapper(
|
|
jac,
|
|
fun=self.fun_wrapped,
|
|
finite_diff_options=finite_diff_options,
|
|
sparse_jacobian=self.sparse_jacobian
|
|
)
|
|
|
|
self.hess_wrapped = _VectorHessWrapper(
|
|
hess, jac=self.jac_wrapped, finite_diff_options=finite_diff_options
|
|
)
|
|
|
|
# Define Hessian
|
|
if callable(hess) or hess in FD_METHODS:
|
|
self.H = self.hess_wrapped(xp_copy(self.x), self.v, J0=self.J)
|
|
self.H_updated = True
|
|
if callable(hess):
|
|
self._nhev += 1
|
|
elif isinstance(hess, HessianUpdateStrategy):
|
|
self.H = hess
|
|
self.H.initialize(self.n, 'hess')
|
|
self.H_updated = True
|
|
self.x_prev = None
|
|
self.J_prev = None
|
|
|
|
@property
|
|
def nfev(self):
|
|
return self._nfev + self.jac_wrapped.nfev
|
|
|
|
@property
|
|
def njev(self):
|
|
return self._njev + self.hess_wrapped.njev
|
|
|
|
@property
|
|
def nhev(self):
|
|
return self._nhev
|
|
|
|
def _update_v(self, v):
|
|
if not np.array_equal(v, self.v):
|
|
self.v = v
|
|
self.H_updated = False
|
|
|
|
def _update_x(self, x):
|
|
if not np.array_equal(x, self.x):
|
|
if isinstance(self._orig_hess, HessianUpdateStrategy):
|
|
self._update_jac()
|
|
self.x_prev = self.x
|
|
self.J_prev = self.J
|
|
_x = xpx.atleast_nd(self.xp.asarray(x), ndim=1, xp=self.xp)
|
|
self.x = self.xp.astype(_x, self.x_dtype)
|
|
self.f_updated = False
|
|
self.J_updated = False
|
|
self.H_updated = False
|
|
self._update_hess()
|
|
else:
|
|
_x = xpx.atleast_nd(self.xp.asarray(x), ndim=1, xp=self.xp)
|
|
self.x = self.xp.astype(_x, self.x_dtype)
|
|
self.f_updated = False
|
|
self.J_updated = False
|
|
self.H_updated = False
|
|
|
|
def _update_fun(self):
|
|
if not self.f_updated:
|
|
self.f = self.fun_wrapped(xp_copy(self.x))
|
|
self._nfev += 1
|
|
self.f_updated = True
|
|
|
|
def _update_jac(self):
|
|
if not self.J_updated:
|
|
if self._orig_jac in FD_METHODS:
|
|
# need to update fun to get f0
|
|
self._update_fun()
|
|
else:
|
|
self._njev += 1
|
|
|
|
self.J = self.jac_wrapped(xp_copy(self.x), f0=self.f)
|
|
self.J_updated = True
|
|
|
|
def _update_hess(self):
|
|
if not self.H_updated:
|
|
if callable(self._orig_hess):
|
|
self.H = self.hess_wrapped(xp_copy(self.x), self.v)
|
|
self._nhev += 1
|
|
elif self._orig_hess in FD_METHODS:
|
|
self._update_jac()
|
|
self.H = self.hess_wrapped(xp_copy(self.x), self.v, J0=self.J)
|
|
elif isinstance(self._orig_hess, HessianUpdateStrategy):
|
|
self._update_jac()
|
|
# When v is updated before x was updated, then x_prev and
|
|
# J_prev are None and we need this check.
|
|
if self.x_prev is not None and self.J_prev is not None:
|
|
delta_x = self.x - self.x_prev
|
|
delta_g = self.J.T.dot(self.v) - self.J_prev.T.dot(self.v)
|
|
self.H.update(delta_x, delta_g)
|
|
|
|
self.H_updated = True
|
|
|
|
def fun(self, x):
|
|
self._update_x(x)
|
|
self._update_fun()
|
|
# returns a copy so that downstream can't overwrite the
|
|
# internal attribute
|
|
return xp_copy(self.f)
|
|
|
|
def jac(self, x):
|
|
self._update_x(x)
|
|
self._update_jac()
|
|
if hasattr(self.J, "astype"):
|
|
# returns a copy so that downstream can't overwrite the
|
|
# internal attribute. But one can't copy a LinearOperator
|
|
return self.J.astype(self.J.dtype)
|
|
return self.J
|
|
|
|
def hess(self, x, v):
|
|
# v should be updated before x.
|
|
self._update_v(v)
|
|
self._update_x(x)
|
|
self._update_hess()
|
|
if hasattr(self.H, "astype"):
|
|
# returns a copy so that downstream can't overwrite the
|
|
# internal attribute. But one can't copy non-arrays
|
|
return self.H.astype(self.H.dtype)
|
|
return self.H
|
|
|
|
|
|
class LinearVectorFunction:
|
|
"""Linear vector function and its derivatives.
|
|
|
|
Defines a linear function F = A x, where x is N-D vector and
|
|
A is m-by-n matrix. The Jacobian is constant and equals to A. The Hessian
|
|
is identically zero and it is returned as a csr matrix.
|
|
"""
|
|
def __init__(self, A, x0, sparse_jacobian):
|
|
if sparse_jacobian or sparse_jacobian is None and sps.issparse(A):
|
|
self.J = sps.csr_array(A)
|
|
self.sparse_jacobian = True
|
|
elif sps.issparse(A):
|
|
self.J = A.toarray()
|
|
self.sparse_jacobian = False
|
|
else:
|
|
# np.asarray makes sure A is ndarray and not matrix
|
|
self.J = np.atleast_2d(np.asarray(A))
|
|
self.sparse_jacobian = False
|
|
|
|
self.m, self.n = self.J.shape
|
|
|
|
self.xp = xp = array_namespace(x0)
|
|
_x = xpx.atleast_nd(xp.asarray(x0), ndim=1, xp=xp)
|
|
_dtype = xp.float64
|
|
if xp.isdtype(_x.dtype, "real floating"):
|
|
_dtype = _x.dtype
|
|
|
|
# promotes to floating
|
|
self.x = xp.astype(_x, _dtype)
|
|
self.x_dtype = _dtype
|
|
|
|
self.f = self.J.dot(self.x)
|
|
self.f_updated = True
|
|
|
|
self.v = np.zeros(self.m, dtype=float)
|
|
self.H = sps.csr_array((self.n, self.n))
|
|
|
|
def _update_x(self, x):
|
|
if not np.array_equal(x, self.x):
|
|
_x = xpx.atleast_nd(self.xp.asarray(x), ndim=1, xp=self.xp)
|
|
self.x = self.xp.astype(_x, self.x_dtype)
|
|
self.f_updated = False
|
|
|
|
def fun(self, x):
|
|
self._update_x(x)
|
|
if not self.f_updated:
|
|
self.f = self.J.dot(x)
|
|
self.f_updated = True
|
|
return self.f
|
|
|
|
def jac(self, x):
|
|
self._update_x(x)
|
|
return self.J
|
|
|
|
def hess(self, x, v):
|
|
self._update_x(x)
|
|
self.v = v
|
|
return self.H
|
|
|
|
|
|
class IdentityVectorFunction(LinearVectorFunction):
|
|
"""Identity vector function and its derivatives.
|
|
|
|
The Jacobian is the identity matrix, returned as a dense array when
|
|
`sparse_jacobian=False` and as a csr matrix otherwise. The Hessian is
|
|
identically zero and it is returned as a csr matrix.
|
|
"""
|
|
def __init__(self, x0, sparse_jacobian):
|
|
n = len(x0)
|
|
if sparse_jacobian or sparse_jacobian is None:
|
|
A = sps.eye_array(n, format='csr')
|
|
sparse_jacobian = True
|
|
else:
|
|
A = np.eye(n)
|
|
sparse_jacobian = False
|
|
super().__init__(A, x0, sparse_jacobian)
|