# Copyright 2021 Huawei Technologies Co., Ltd
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# 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
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# http://www.apache.org/licenses/LICENSE-2.0
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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
from ._lagrange import minimize_lagrange
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
def lagrange_para_check(func, constraints, options, tol):
"""check the parameter of lagrange method."""
if not callable(func):
raise TypeError("'func' must be of type function, but got {}".format(type(func)))
if 'coincide_func' in options:
if not callable(options['coincide_fun']):
raise TypeError("'coincide_fun' must be of type function, but got {}".format(type(options['coincide_fun'])))
for constraint in constraints:
if not callable(constraint):
raise TypeError("'constraint' must be of type function, but got {}".format(type(constraint)))
if tol is not None:
if len(tol) != len(constraints):
raise ValueError("The len of tol must be same as the len of constraints")
[docs]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.
- `LAGRANGE` method is only supported on "GPU".
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"`, `"LAGRANGE"`.
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 :math:`(n,)` and args is a tuple with the fixed parameters.
hess (Callable, optional): Method for calculating the Hessian Matrix. Not implemented yet.
hessp (Callable, optional): Hessian of objective function times an arbitrary vector `p`. Not implemented yet.
bounds (Sequence, optional): Sequence of `(min, max)` pairs for each element in `x`. Not implemented yet.
constraints (Callable, optional): representing the inequality constrains, each function in constrains indicates
the function < 0 as an inequality constrain.
tol (float, optional): tolerance for termination. For detailed control, use solver-specific
options. Default: ``None`` .
callback (Callable, optional): A callable called after each iteration. Not implemented yet.
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.
The follow options are exclusive to Lagrange method:
- save_tol (list): list of saving tolerance, with the same length with 'constrains'.
- obj_weight (float): weight for objective function, usually between 1.0 - 100000.0.
- lower (Tensor): lower bound constrain for variables, must have same shape with x0.
- upper (Tensor): upper bound constrain for variables, must have same shape with x0.
- learning_rate (float): learning rate for each Adam step.
- coincide_func (Callable): sub-function representing the common parts between objective function
and constrains to avoid redundant computation.
- rounds (int): times to update Lagrange multipliers.
- steps (int): steps to apply Adam per round.
- log_sw (bool): whether to print the loss at each step.
Returns:
OptimizeResults, object holding optimization results.
Supported Platforms:
``GPU`` ``CPU``
Examples:
>>> import numpy as onp
>>> from mindspore.scipy.optimize import minimize
>>> from mindspore 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)
[3. 2.]
>>> l_res = minimize(func, x0, method='LBFGS', options=dict(maxiter=None, gtol=1e-6))
>>> print(l_res.x)
[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)
if method.lower() == 'lagrange':
lagrange_para_check(func, constraints, options, tol)
results = minimize_lagrange(func, x0, constraints, tol, **options)
return results
raise ValueError("Method {} not recognized".format(method))