scipy tutorial - Baustatik-Info-Server

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Least-squares fit to noisy data
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SciPy Reference Guide, Release 0.8.dev
Fit
Noisy
True
1.5.5 Sequential Least-square fitting with constraints (fmin_slsqp)
This module implements the Sequential Least SQuares Programming optimization algorithm (SLSQP).
min F (x)
subject to Cj(X) = 0, j = 1, ..., MEQ
Cj(x) ≥ 0, j = MEQ + 1, ..., M
XL ≤ x ≤ XU, I = 1, ..., N.
The following script shows examples for how constraints can be specified.
"""
This script tests fmin_slsqp using Example 14.4 from Numerical Methods for
Engineers by Steven Chapra and Raymond Canale. This example maximizes the
function f(x) = 2*x*y + 2*x - x**2 - 2*y**2, which has a maximum at x=2,y=1.
"""
from scipy.optimize import fmin_slsqp
from numpy import array, asfarray, finfo,ones, sqrt, zeros
def testfunc(d,*args):
"""
Arguments:
d - A list of two elements, where d[0] represents x and
d[1] represents y in the following equation.
sign - A multiplier for f. Since we want to optimize it, and the scipy
optimizers can only minimize functions, we need to multiply it by
-1 to achieve the desired solution
Returns:
2*x*y + 2*x - x**2 - 2*y**2
"""
try:
sign = args[0]
1.5. Optimization (optimize) 21