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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 Powell's method.
- Uses LatticeSolver to provide 'pseudo-global' optimization
- Plot of fitting to Chebyshev polynomial.
Demonstrates:
- standard models
- minimal solver interface
"""
# the Lattice solver
from mystic.solvers import LatticeSolver
# Powell's Directonal solver
from mystic.solvers import PowellDirectionalSolver
# Chebyshev polynomial and cost function
from mystic.models.poly import chebyshev8, chebyshev8cost
from mystic.models.poly import chebyshev8coeffs
# if available, use a pathos worker pool
try:
from pathos.pools import ProcessPool as Pool
#from pathos.pools import ParallelPool as Pool
except ImportError:
from mystic.pools import SerialPool as Pool
# tools
from mystic.termination import NormalizedChangeOverGeneration as NCOG
from mystic.math import poly1d
from mystic.monitors import VerboseMonitor
from mystic.tools import getch
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__':
from pathos.helpers import freeze_support, shutdown
freeze_support() # help Windows use multiprocessing
print("Powell's Method")
print("===============")
# dimensional information
from mystic.tools import random_seed
random_seed(123)
ndim = 9
nbins = 8 #[2,1,2,1,2,1,2,1,1]
# draw frame and exact coefficients
plot_exact()
# configure monitor
stepmon = VerboseMonitor(1)
# use lattice-Powell to solve 8th-order Chebyshev coefficients
solver = LatticeSolver(ndim, nbins)
solver.SetNestedSolver(PowellDirectionalSolver)
solver.SetMapper(Pool().map)
solver.SetGenerationMonitor(stepmon)
solver.SetStrictRanges(min=[-300]*ndim, max=[300]*ndim)
solver.Solve(chebyshev8cost, NCOG(1e-4), disp='all', step=False)
solution = solver.Solution()
shutdown() # help multiprocessing shutdown all workers
# 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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