root/trunk/openopt/scikits/openopt/examples/nlsp_1.py

"""
Solving system of equations:
x[0]**3+x[1]**3-9 = 0
x[0]-0.5*x[1] = 0
cos(x[2])+x[0]-1.5 = 0
"""

from scikits.openopt import NLSP
from numpy import asfarray, zeros, cos, sin

f = lambda x: (x[0]**3+x[1]**3-9, x[0]-0.5*x[1], cos(x[2])+x[0]-1.5)
# or:
#f = (lambda x: x[0]**3+x[1]**3-9, lambda x: x[0]-0.5*x[1], lambda x: cos(x[2])+x[0]-1.5)
# Python list, numpy.array are allowed as well:
#f = lambda x: [x[0]**3+x[1]**3-9, x[0]-0.5*x[1], cos(x[2])+x[0]-1.5]
#or f = lambda x: asfarray((x[0]**3+x[1]**3-9, x[0]-0.5*x[1], cos(x[2])+x[0]-1.5))

#optional: gradient
def DF(x):
    df = zeros((3,3))
    df[0,0] = 3*x[0]**2
    df[0,1] = 3*x[1]**2
    df[1,0] = 1
    df[1,1] = -0.5
    df[2,0] = 1
    df[2,2] = -sin(x[2])
    return df

x0 = [8,15, 80]

#w/o gradient:
#p = NLSP(f, x0)
p = NLSP(f, x0, df = DF)

#optional: user-supplied gradient check:
#p.checkdf()

#optional: graphical output, requires matplotlib installed
p.plot = 1

#r = p.solve('scipy_fsolve')
p.maxFunEvals = 1e5
p.iprint = 10

#r = p.solve('scipy_fsolve')
#r = p.solve('nssolve')
#or using converter nlsp2nlp, try to minimize sum(f_i(x)^2):
r = p.solve('nlp:ralg')

print 'solution:', r.xf
print 'max residual:', r.ff
###############################
#should print:
#solution: [  1.           2.          55.50147021]
#max residual: 2.72366951215e-09