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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.
- Callable plot of fitting to Chebyshev polynomial.
- Monitor Chi-Squared for Chebyshev polynomial.
- Impact of mutation and crossover coefficients
Demonstrates:
- standard models
- expanded solver interface
- built-in random initial guess
- solver interactivity
- customized monitors and termination conditions
- customized DE mutation strategies
- use of monitor 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
from mystic.tools import getch, random_seed
from mystic.math import poly1d
import matplotlib.pyplot as plt
plt.ion()
# 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("Differential Evolution")
print("======================")
# set range for random initial guess
ndim = 9
x0 = [(-100,100)]*ndim
random_seed(123)
# 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()
# configure monitor
stepmon = VerboseMonitor(50)
# 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.SetGenerationMonitor(stepmon)
solver.enable_signal_handler()
solver.Solve(chebyshev8cost, termination=VTR(0.01), strategy=Best1Exp, \
CrossProbability=0.8, ScalingFactor=0.5, \
sigint_callback=plot_solution)
solution = solver.Solution()
# use monitor to retrieve results information
iterations = len(stepmon)
cost = stepmon.y[-1]
print("Generation %d has best Chi-Squared: %s" % (iterations, cost))
# use pretty print for polynomials
print(poly1d(solution))
# compare solution with actual 8th-order Chebyshev coefficients
print("\nActual Coefficients:\n %s\n" % poly1d(chebyshev8coeffs))
# plot solution versus exact coefficients
plot_solution(solution)
getch()
# end of file
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