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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 DE.
- Plot (x2) of convergence to Chebyshev polynomial.
- Monitor (x2) Chi-Squared for Chebyshev polynomial.
Demonstrates:
- standard models
- expanded solver interface
- built-in random initial guess
- customized monitors and termination conditions
- customized DE mutation strategies
- use of solver members to retrieve results information
"""
# Differential Evolution solver
from mystic.solvers import DifferentialEvolutionSolver2
# Chebyshev polynomial and cost function
from mystic.models.poly import chebyshev8, chebyshev8cost
from mystic.models.poly import chebyshev8coeffs
# tools
from mystic.termination import VTR
from mystic.strategy import Best1Exp
from mystic.monitors import VerboseMonitor, Monitor
from mystic.tools import getch, random_seed
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("Differential Evolution %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
if __name__ == '__main__':
print("Differential Evolution")
print("======================")
# set range for random initial guess
ndim = 9
x0 = [(-100,100)]*ndim
random_seed(123)
# configure monitors
stepmon = VerboseMonitor(50)
evalmon = Monitor()
# use DE to solve 8th-order Chebyshev coefficients
npop = 10*ndim
solver = DifferentialEvolutionSolver2(ndim,npop)
solver.SetRandomInitialPoints(min=[-100]*ndim, max=[100]*ndim)
solver.SetEvaluationLimits(generations=999)
solver.SetEvaluationMonitor(evalmon)
solver.SetGenerationMonitor(stepmon)
solver.enable_signal_handler()
solver.Solve(chebyshev8cost, termination=VTR(0.01), strategy=Best1Exp, \
CrossProbability=1.0, ScalingFactor=0.9)
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))
# 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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