# -*- coding: utf-8 -*-
# mathtoolspy
# -----------
# A fast, efficient Python library for mathematically operations, like
# integration, solver, distributions and other useful functions.
#
# Author: sonntagsgesicht, based on a fork of Deutsche Postbank [pbrisk]
# Version: 0.3, copyright Wednesday, 18 September 2019
# Website: https://github.com/sonntagsgesicht/mathtoolspy
# License: Apache License 2.0 (see LICENSE file)
from mathtoolspy.solver import minimize_algorithm_1dim_brent
[docs]class MinimizeAlgorithmNDimPowell(object):
'''
The minimazation with the Powell algorithm.
Press, et al., 'Numerical Recipes in C', 2nd ed, Powell (p.412).
Minimization of a function func of n variables. Input consists of an initial starting
point p[0..n-1]; an inital matrix xi[0..n-1,0..n-1], whose columns contain the initial
set of directions (usually the n unit vectors); and ftol, the fractional tolerance in
the function value such that failure to decrease by more than this amount on one
iteration signals doneness. On output, p is set to best point found, xi is the
then-current direction set, fret is the returned function value at p. The routine linmin is used.
***
Initial matrix xi[0..n-1,0..n-1], whose columns contain the initial
set of directions (usually the n unit vectors). On output xi is the then-current
direction set.
***
Initial starting point p[0..n-1]. On output p is set to best point found.
'''
TINY = 1.0e-25
TOL = 2.0e-4
def __init__(self):
self.brent = minimize_algorithm_1dim_brent
[docs] def FindMinimun(self, fct, initial_point, tol):
ndim = initial_point.count()
# On output Powell sets the initial point to best point found.
tpoint = initial_point
# Choose the unit vectors as initial set of directions.
directions = self._initialize_directions(ndim)
# Locate the minimum and store the number of iterations.
r = self.powell(directions, tpoint, ndim, tol, fct)
return r
def _initialize_directions(self, ndim):
ret = ((0 if i != j else 1 for i in range(ndim)) for j in range(ndim))
return ret
[docs] def powell(self, initial_xvalues, initial_fvalues, ndim, tol, fct):
p = initial_fvalues
xi = initial_xvalues