#!/usr/bin/env python3
"``naginterfaces.library.opt.lsq_uncon_mod_func_comp`` Python Example."
# NAG Copyright 2021.
# pylint: disable=invalid-name,too-many-arguments
import numpy as np
from naginterfaces.library import opt
[docs]def main():
"""
Example for :func:`naginterfaces.library.opt.lsq_uncon_mod_func_comp`.
Find an unconstrained minimum of a sum of squares of m nonlinear
functions in n variables (m at least n). No derivatives are required.
>>> main()
naginterfaces.library.opt.lsq_uncon_mod_func_comp Python Example Results.
Find an unconstrained minimum of a sum of squares.
<BLANKLINE>
Best fit model parameters are:
x_0 = 0.082
x_1 = 1.133
x_2 = 2.344
<BLANKLINE>
Residuals for observed data:
-0.0059 -0.0003 0.0003 0.0065 -0.0008
-0.0013 -0.0045 -0.0200 0.0822 -0.0182
-0.0148 -0.0147 -0.0112 -0.0042 0.0068
<BLANKLINE>
Sum of squares of residuals: 0.0082
"""
print(
'naginterfaces.library.opt.lsq_uncon_mod_func_comp '
'Python Example Results.'
)
print('Find an unconstrained minimum of a sum of squares.')
def cb_lsqfun(iflag, m, xc):
"""Evaluate the residuals."""
fvec = (xc[0] + t[:,0]/(xc[1]*t[:,1]+xc[2]*t[:,2]) - y[:])
return iflag, fvec
y = [
0.14, 0.18, 0.22, 0.25, 0.29, 0.32, 0.35, 0.39, 0.37,
0.58, 0.73, 0.96, 1.34, 2.10, 4.39,
]
m = len(y)
t = np.array([
[1.0, 15.0, 1.0],
[2.0, 14.0, 2.0],
[3.0, 13.0, 3.0],
[4.0, 12.0, 4.0],
[5.0, 11.0, 5.0],
[6.0, 10.0, 6.0],
[7.0, 9.0, 7.0],
[8.0, 8.0, 8.0],
[9.0, 7.0, 7.0],
[10.0, 6.0, 6.0],
[11.0, 5.0, 5.0],
[12.0, 4.0, 4.0],
[13.0, 3.0, 3.0],
[14.0, 2.0, 2.0],
[15.0, 1.0, 1.0],
])
# Initial guess
x = [.5, 1., 1.5]
soln = opt.lsq_uncon_mod_func_comp(
m, cb_lsqfun, x,
)
print('\nBest fit model parameters are:')
for i in range(len(x)):
print(' x_{:d} = {:10.3f}'.format(i, soln.x[i]))
print('\nResiduals for observed data:')
print('\n'.join([''.join([' {:8.4f}']*5)]*3).format(*soln.fvec))
print('\nSum of squares of residuals: {:6.4f}'.format(soln.fsumsq))
if __name__ == '__main__':
import doctest
import sys
sys.exit(
doctest.testmod(
None, verbose=True, report=False,
optionflags=doctest.REPORT_NDIFF,
).failed
)
