Source code for pygsl.multiminimize

#! /usr/bin/python3 -sP
"""
Wrapper over the functions as described in Chapter 33 of the
reference manual.

Routines for finding the minimum of a function depending on more than one
variable.

"""
from . import _callback
from .gsl_function import gsl_multimin_function_fdf, gsl_multimin_function
from ._generic_solver import _generic_solver

[docs] class _fsolver(_generic_solver): type = None _alloc = _callback.gsl_multimin_fminimizer_alloc _free = _callback.gsl_multimin_fminimizer_free _set = _callback.gsl_multimin_fminimizer_set _name = _callback.gsl_multimin_fminimizer_name _iterate = _callback.gsl_multimin_fminimizer_iterate _minimum = _callback.gsl_multimin_fminimizer_minimum _size = _callback.gsl_multimin_fminimizer_size _getx = _callback.gsl_multimin_fminimizer_x _getf = _callback.gsl_multimin_fminimizer_f def __init__(self, system, size): self._ptr = None assert(self._free != None) assert(self._alloc != None) assert(self._set != None) assert(self._name != None) assert(self._iterate != None) self._ptr = self._alloc(self.type, size) self._isset = 0 self.system = system
[docs] def set(self, x, step_size): """ This function initializes the minimizer to minimize the function starting from the initial point x. The size of the initial trial steps is given in vector STEP_SIZE. The precise meaning of this parameter depends on the method used. """ f = self.system.get_ptr() self._set(self._ptr, f, x, step_size) self._isset = 1
[docs] def minimum(self): """ Get the current minimum """ return self._minimum(self._ptr)
[docs] def size(self): """ Get the characteristic size """ return self._size(self._ptr)
[docs] def getx(self): """ Get the current x value """ return self._getx(self._ptr)
[docs] def getf(self): """ Get the current function value """ return self._getf(self._ptr)
[docs] class _fdfsolver(_fsolver): type = None _alloc = _callback.gsl_multimin_fdfminimizer_alloc _free = _callback.gsl_multimin_fdfminimizer_free _set = _callback.gsl_multimin_fdfminimizer_set _name = _callback.gsl_multimin_fdfminimizer_name _iterate = _callback.gsl_multimin_fdfminimizer_iterate _minimum = _callback.gsl_multimin_fdfminimizer_minimum _gradient= _callback.gsl_multimin_fdfminimizer_gradient _getx = _callback.gsl_multimin_fdfminimizer_x _getf = _callback.gsl_multimin_fdfminimizer_f _restart = _callback.gsl_multimin_fdfminimizer_restart
[docs] def gradient(self): """ Get the last gradient """ return self._gradient(self._ptr)
[docs] def restart(self): """ Restart the iteration at the current point """ return self._restart(self._ptr)
[docs] def set(self, x, step_size, tolerance): """ This function initializes the minimizer S to minimize the function FDF starting from the initial point X. The size of the first trial step is given by STEP_SIZE. The accuracy of the line minimization is specified by TOL. The precise meaning of this parameter depends on the method used. Typically the line minimization is considered successful if the gradient of the function g is orthogonal to the current search direction p to a relative accuracy of TOL, where dot(p,g) < tol |p| |g|. """ f = self.system.get_ptr() self._set(self._ptr, f, x, step_size, tolerance) self._isset = 1
[docs] class steepest_descent(_fdfsolver): """ The steepest descent algorithm follows the downhill gradient of the function at each step. When a downhill step is successful the step-size is increased by factor of two. If the downhill step leads to a higher function value then the algorithm backtracks and the step size is decreased using the parameter TOL. A suitable value of TOL for most applications is 0.1. The steepest descent method is inefficient and is included only for demonstration purposes. """ type = _callback.cvar.gsl_multimin_fdfminimizer_steepest_descent
[docs] class conjugate_pr(_fdfsolver): """ This is the Polak-Ribiere conjugate gradient algorithm. It is similar to the Fletcher-Reeves method, differing only in the choice of the coefficient \beta. Both methods work well when the evaluation point is close enough to the minimum of the objective function that it is well approximated by a quadratic hypersurface. """ type = _callback.cvar.gsl_multimin_fdfminimizer_conjugate_pr
[docs] class conjugate_fr(_fdfsolver): """ This is the Fletcher-Reeves conjugate gradient algorithm. The conjugate gradient algorithm proceeds as a succession of line minimizations. The sequence of search directions is used to build up an approximation to the curvature of the function in the neighborhood of the minimum. An initial search direction P is chosen using the gradient and line minimization is carried out in that direction. The accuracy of the line minimization is specified by the parameter TOL. At the minimum along this line the function gradient G and the search direction P are orthogonal. The line minimization terminates when dot(p,g) < tol |p| |g|. The search direction is updated using the Fletcher-Reeves formula p' = g' - \beta g where \beta=-|g'|^2/|g|^2, and the line minimization is then repeated for the new search direction. """ type = _callback.cvar.gsl_multimin_fdfminimizer_conjugate_fr
[docs] class vector_bfgs(_fdfsolver): """ This is the vector Broyden-Fletcher-Goldfarb-Shanno (BFGS) conjugate gradient algorithm. It is a quasi-Newton method which builds up an approximation to the second derivatives of the function f using the difference between successive gradient vectors. By combining the first and second derivatives the algorithm is able to take Newton-type steps towards the function minimum, assuming quadratic behavior in that region. """ type = _callback.cvar.gsl_multimin_fdfminimizer_vector_bfgs
_t_type = _callback.cvar.gsl_multimin_fdfminimizer_vector_bfgs2 if _t_type:
[docs] class vector_bfgs2(_fdfsolver): type = _t_type
_t_type = _callback.cvar.gsl_multimin_fminimizer_nmsimplex if _t_type:
[docs] class nmsimplex(_fsolver): """ This is the Simplex algorithm by Nelder and Mead. It constructs n vectors p_i from the starting vector X as follows: that form the n+1 vertices of a simplex in n dimensions. In each iteration step the algorithm tries to improve the parameter vector p_i corresponding to the highest, i. e. worst, function value by simple geometrical transformations. These are reflection, reflection followed by expansion, contraction and multiple contraction. Using these transformations the simplex moves through the parameter space towards the minimum, where it contracts itself. After each iteration, the best vertex is returned. Note, that due to the nature of the algorithm (getting rid of the worst estimate), every iteration doesn't necessarily improve the current best parameter vector. Usually several iterations are required. The routine calculates the minimizer specific characteristic size as the average distance from the geometrical center of the simplex to all its vertices. This size can be used as a stopping criteria, as the simplex contracts itself near the minimum. The size is returned by the function `gsl_multimin_fminimizer_size'. """ type = _t_type
_t_type = _callback.cvar.gsl_multimin_fminimizer_nmsimplex2 if _t_type: class nmsimplex2(_fsolver): type = _t_type _t_type = _callback.cvar.gsl_multimin_fminimizer_nmsimplex2rand if _t_type: class nmsimplex2rand(_fsolver): type = _t_type
[docs] def test_gradient(g, epsabs): r""" This function tests the norm of the gradient against the absolute tolerance epsabs. The gradient of a multidimensional function goes to zero at a minimum. The test returns `GSL_SUCCESS' if the following condition is achieved, |g| < epsabs and returns `GSL_CONTINUE' otherwise. A suitable choice of EPSABS can be made from the desired accuracy in the function for small variations in x. The relationship between these quantities is given by \delta f = g \delta x. """ return _callback.gsl_multimin_test_gradient(g, epsabs)
[docs] def test_size(gradient, tolerance): """ This function tests the minimizer specific characteristic size (if applicable to the used minimizer) against the absolute tolerance. """ return _callback.gsl_multimin_test_size(gradient, tolerance)