# Copyright 2021 Huawei Technologies Co., Ltd
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
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# ============================================================================
"""minimize"""
from typing import Optional
from typing import NamedTuple
from ...common import Tensor
from ._bfgs import minimize_bfgs
from ._lbfgs import minimize_lbfgs
class OptimizeResults(NamedTuple):
"""Object holding optimization results.
Args:
x (Tensor): final solution.
success (bool): ``True`` if optimization succeeded.
status (int): solver specific return code. 0 means converged (nominal),
1=max BFGS iters reached, 3=zoom failed, 4=saddle point reached,
5=max line search iters reached, -1=undefined
fun (float): final function value.
jac (Tensor): final jacobian array.
hess_inv (Tensor, optional): final inverse Hessian estimate.
nfev (int): number of function calls used.
njev (int): number of gradient evaluations.
nit (int): number of iterations of the optimization algorithm.
"""
x: Tensor
success: bool
status: int
fun: float
jac: Tensor
hess_inv: Optional[Tensor]
nfev: int
njev: int
nit: int
[文档]def minimize(func, x0, args=(), method=None, jac=None, hess=None, hessp=None, bounds=None, constraints=(),
tol=None, callback=None, options=None):
r"""
Minimization of scalar function of one or more variables.
This API for this function matches SciPy with some minor deviations:
- Gradients of ``func`` are calculated automatically using MindSpore's autodiff
support when the value of jac is None.
- The ``method`` argument is required. A exception will be thrown if you don't specify a solver.
- Various optional arguments `"hess"` `"hessp"` `"bounds"` `"constraints"` `"tol"` `"callback"`
in the SciPy interface have not yet been implemented.
- Optimization results may differ from SciPy due to differences in the line
search implementation.
Note:
- `minimize` does not yet support differentiation or arguments in the form of
multi-dimensional Tensor, but support for both is planned.
- `minimize` is not supported on Windows platform yet.
Args:
func (Callable): the objective function to be minimized, :math:`fun(x, *args) -> float`,
where `x` is a 1-D array with shape :math:`(n,)` and `args` is a tuple
of the fixed parameters needed to completely specify the function.
`fun` must support differentiation if jac is None.
x0 (Tensor): initial guess. Array of real elements of size :math:`(n,)`, where `n` is
the number of independent variables.
args (Tuple): extra arguments passed to the objective function. Default: ().
method (str): solver type. Should be one of `"BFGS"` and `"LBFGS"`.
jac (Callable, optional): method for computing the gradient vector. Only for `"BFGS"` and `"LBFGS"`.
if it is None, the gradient will be estimated with gradient of ``func``.
if it is a callable, it should be a function that returns the gradient vector:
:math:`jac(x, *args) -> array\_like, shape (n,)`
where x is an array with shape (n,) and args is a tuple with the fixed parameters.
tol (float, optional): tolerance for termination. For detailed control, use solver-specific
options. Default: None.
options (Mapping[str, Any], optional): a dictionary of solver options. All methods accept the following
generic options, Default: None.
- history_size (int): size of buffer used to help to update inv hessian, only used with method="LBFGS".
Default: 20.
- maxiter (int): Maximum number of iterations to perform. Depending on the
method each iteration may use several function evaluations.
Returns:
OptimizeResults, object holding optimization results.
Supported Platforms:
``CPU`` ``GPU``
Examples:
>>> import numpy as onp
>>> from mindspore.scipy.optimize import minimize
>>> from mindspore.common import Tensor
>>> x0 = Tensor(onp.zeros(2).astype(onp.float32))
>>> def func(p):
>>> x, y = p
>>> return (x ** 2 + y - 11.) ** 2 + (x + y ** 2 - 7.) ** 2
>>> res = minimize(func, x0, method='BFGS', options=dict(maxiter=None, gtol=1e-6))
>>> print(res.x)
>>> l_res = minimize(func, x0, method='LBFGS', options=dict(maxiter=None, gtol=1e-6))
>>> print(res.x)
[3. 2.]
[3. 2.]
"""
if method is None:
raise ValueError("You must specify a solver.")
if options is None:
options = {}
if not isinstance(args, tuple):
msg = "args argument to mindspore.scipy.optimize.minimize must be a tuple, got {}"
raise TypeError(msg.format(args))
def fun_with_args(args):
def inner_func(x):
return func(x, *args)
return inner_func
if method.lower() == 'bfgs':
results = minimize_bfgs(fun_with_args(args), x0, jac, **options)
success = results.converged and not results.failed
return OptimizeResults(x=results.x_k,
success=success,
status=results.status,
fun=results.f_k,
jac=results.g_k,
hess_inv=results.H_k,
nfev=results.nfev,
njev=results.ngev,
nit=results.k)
if method.lower() == 'lbfgs':
results = minimize_lbfgs(fun_with_args(args), x0, jac, **options)
success = results.converged and not results.failed
return OptimizeResults(x=results.x_k,
success=success,
status=results.status,
fun=results.f_k,
jac=results.g_k,
hess_inv=None,
nfev=results.nfev,
njev=results.ngev,
nit=results.k)
raise ValueError("Method {} not recognized".format(method))