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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:
- Minimize Rosenbrock's Function with Nelder-Mead.
- Plot of Rosenbrock's function minimum.
Demonstrates:
- standard models
- minimal solver interface
"""
# Nelder-Mead solver
from mystic.solvers import fmin
# Rosenbrock function
from mystic.models import rosen
# tools
import matplotlib.pyplot as plt
if __name__ == '__main__':
print("Nelder-Mead Simplex")
print("===================")
# initial guess
x0 = [0.8,1.2,0.7]
# use Nelder-Mead to minimize the Rosenbrock function
solution = fmin(rosen,x0)
print(solution)
# plot the Rosenbrock function (one plot per axis)
x = [0.01*i for i in range(200)]
plt.plot(x,[rosen([i,1.,1.]) for i in x])
plt.plot(x,[rosen([1.,i,1.]) for i in x])
plt.plot(x,[rosen([1.,1.,i]) for i in x])
# plot the solved minimum (for x)
plt.plot([solution[0]],[rosen(solution)],'bo')
# draw the plot
plt.title("minimium of Rosenbrock's function")
plt.xlabel("x, y, z")
plt.ylabel("f(i) = Rosenbrock's function")
plt.legend(["f(x,1,1)","f(1,y,1)","f(1,1,z)"])
plt.show()
# end of file
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