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#!/usr/bin/env python
#
# Author: Mike McKerns (mmckerns @caltech and @uqfoundation)
# Copyright (c) 1997-2016 California Institute of Technology.
# Copyright (c) 2016-2024 The Uncertainty Quantification Foundation.
# License: 3-clause BSD. The full license text is available at:
# - https://github.com/uqfoundation/mystic/blob/master/LICENSE
"""
Example:
- Solve 8th-order Chebyshev polynomial coefficients with Nelder-Mead.
- Callable plot of fitting to Chebyshev polynomial.
- Plot (x2) of convergence to Chebyshev polynomial.
- Monitor (x2) Chi-Squared for Chebyshev polynomial.
Demonstrates:
- standard models
- expanded solver interface
- parameter bounds constraints
- solver interactivity
- customized monitors and termination conditions
"""
# Nelder-Mead Simplex solver
from mystic.solvers import NelderMeadSimplexSolver
# Chebyshev polynomial and cost function
from mystic.models.poly import chebyshev8, chebyshev8cost
from mystic.models.poly import chebyshev8coeffs
# tools
from mystic.termination import CandidateRelativeTolerance as CRT
from mystic.monitors import VerboseMonitor, Monitor
from mystic.tools import getch
from mystic.math import poly1d
import matplotlib.pyplot as plt
plt.ion()
# draw the plot
def plot_frame(label=None):
plt.close()
plt.title("8th-order Chebyshev coefficient convergence")
plt.xlabel("Nelder-Mead Simplex Solver %s" % label)
plt.ylabel("Chi-Squared")
plt.draw()
plt.pause(0.001)
return
# plot the polynomial trajectories
def plot_params(monitor):
x = list(range(len(monitor)))
y = monitor.y
plt.plot(x,y,'b-')
plt.axis([1,0.5*x[-1],0,y[1]])#,'k-')
plt.draw()
plt.pause(0.001)
return
# draw the plot
def plot_exact():
plt.title("fitting 8th-order Chebyshev polynomial coefficients")
plt.xlabel("x")
plt.ylabel("f(x)")
import numpy
x = numpy.arange(-1.2, 1.2001, 0.01)
exact = chebyshev8(x)
plt.plot(x,exact,'b-')
plt.legend(["Exact"])
plt.axis([-1.4,1.4,-2,8])#,'k-')
plt.draw()
plt.pause(0.001)
return
# plot the polynomial
def plot_solution(params,style='y-'):
import numpy
x = numpy.arange(-1.2, 1.2001, 0.01)
f = poly1d(params)
y = f(x)
plt.plot(x,y,style)
plt.legend(["Exact","Fitted"])
plt.axis([-1.4,1.4,-2,8])#,'k-')
plt.draw()
plt.pause(0.001)
return
if __name__ == '__main__':
print("Nelder-Mead Simplex")
print("===================")
# initial guess
import random
from mystic.tools import random_seed
random_seed(123)
ndim = 9
x0 = [random.uniform(-5,5) + chebyshev8coeffs[i] for i in range(ndim)]
# suggest that the user interacts with the solver
print("NOTE: while solver is running, press 'Ctrl-C' in console window")
getch()
# draw frame and exact coefficients
plot_exact()
# select parameter bounds constraints
from numpy import inf
min_bounds = [ 0,-1,-300,-1, 0,-1,-100,-inf,-inf]
max_bounds = [200, 1, 0, 1,200, 1, 0, inf, inf]
# configure monitors
stepmon = VerboseMonitor(100)
evalmon = Monitor()
# use Nelder-Mead to solve 8th-order Chebyshev coefficients
solver = NelderMeadSimplexSolver(ndim)
solver.SetInitialPoints(x0)
solver.SetEvaluationLimits(generations=999)
solver.SetEvaluationMonitor(evalmon)
solver.SetGenerationMonitor(stepmon)
solver.SetStrictRanges(min_bounds,max_bounds)
solver.enable_signal_handler()
solver.Solve(chebyshev8cost, termination=CRT(1e-4,1e-4), \
sigint_callback=plot_solution)
solution = solver.bestSolution
# get solved coefficients and Chi-Squared (from solver members)
iterations = solver.generations
cost = solver.bestEnergy
print("Generation %d has best Chi-Squared: %s" % (iterations, cost))
print("Solved Coefficients:\n %s\n" % poly1d(solver.bestSolution))
# compare solution with actual 8th-order Chebyshev coefficients
print("Actual Coefficients:\n %s\n" % poly1d(chebyshev8coeffs))
# plot solution versus exact coefficients
plot_solution(solution)
getch()
# plot convergence of coefficients per iteration
plot_frame('iterations')
plot_params(stepmon)
getch()
# plot convergence of coefficients per function call
plot_frame('function calls')
plot_params(evalmon)
getch()
# end of file
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