Source code for mindspore.scipy.optimize.minimize

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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))