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""" Unit tests for optimization routines
Author: Ed Schofield
Nov 2005
"""
from numpy.testing import *
set_package_path()
from scipy import optimize
from numpy import array, zeros, float64, dot, log, exp, inf
from scipy.optimize.tnc import RCSTRINGS, MSG_NONE
restore_path()
from math import sin, cos, pow
class test_optimize(NumpyTestCase):
""" Test case for a simple constrained entropy maximization problem
(the machine translation example of Berger et al in
Computational Linguistics, vol 22, num 1, pp 39--72, 1996.)
"""
def setUp(self):
self.F = array([[1,1,1],[1,1,0],[1,0,1],[1,0,0],[1,0,0]])
self.K = array([1., 0.3, 0.5])
self.startparams = zeros(3, float64)
self.solution = array([0., -0.524869316, 0.487525860])
self.maxiter = 1000
self.funccalls = 0
def func(self, x):
self.funccalls += 1
if self.funccalls > 6000:
raise RuntimeError, "too many iterations in optimization routine"
log_pdot = dot(self.F, x)
logZ = log(sum(exp(log_pdot)))
f = logZ - dot(self.K, x)
return f
def grad(self, x):
log_pdot = dot(self.F, x)
logZ = log(sum(exp(log_pdot)))
p = exp(log_pdot - logZ)
return dot(self.F.transpose(), p) - self.K
def check_cg(self):
""" conjugate gradient optimization routine
"""
retval = optimize.fmin_cg(self.func, self.startparams, self.grad, (), \
maxiter=self.maxiter, \
full_output=True, disp=False, retall=False)
(params, fopt, func_calls, grad_calls, warnflag) = retval
err = abs(self.func(params) - self.func(self.solution))
#print "CG: Difference is: " + str(err)
assert err < 1e-6
def check_bfgs(self):
""" Broyden-Fletcher-Goldfarb-Shanno optimization routine
"""
retval = optimize.fmin_bfgs(self.func, self.startparams, self.grad, \
args=(), maxiter=self.maxiter, \
full_output=True, disp=False, retall=False)
(params, fopt, gopt, Hopt, func_calls, grad_calls, warnflag) = retval
err = abs(self.func(params) - self.func(self.solution))
#print "BFGS: Difference is: " + str(err)
assert err < 1e-6
def check_powell(self):
""" Powell (direction set) optimization routine
"""
retval = optimize.fmin_powell(self.func, self.startparams, \
args=(), maxiter=self.maxiter, \
full_output=True, disp=False, retall=False)
(params, fopt, direc, numiter, func_calls, warnflag) = retval
err = abs(self.func(params) - self.func(self.solution))
#print "Powell: Difference is: " + str(err)
assert err < 1e-6
def check_neldermead(self):
""" Nelder-Mead simplex algorithm
"""
retval = optimize.fmin(self.func, self.startparams, \
args=(), maxiter=self.maxiter, \
full_output=True, disp=False, retall=False)
(params, fopt, numiter, func_calls, warnflag) = retval
err = abs(self.func(params) - self.func(self.solution))
#print "Nelder-Mead: Difference is: " + str(err)
assert err < 1e-6
def check_ncg(self):
""" line-search Newton conjugate gradient optimization routine
"""
retval = optimize.fmin_ncg(self.func, self.startparams, self.grad,
args=(), maxiter=self.maxiter,
full_output=False, disp=False,
retall=False)
params = retval
err = abs(self.func(params) - self.func(self.solution))
#print "NCG: Difference is: " + str(err)
assert err < 1e-6
def check_l_bfgs_b(self):
""" limited-memory bound-constrained BFGS algorithm
"""
retval = optimize.fmin_l_bfgs_b(self.func, self.startparams,
self.grad, args=(),
maxfun=self.maxiter)
(params, fopt, d) = retval
err = abs(self.func(params) - self.func(self.solution))
#print "LBFGSB: Difference is: " + str(err)
assert err < 1e-6
def test_brent(self):
""" brent algorithm
"""
x = optimize.brent(lambda x: (x-1.5)**2-0.8)
err1 = abs(x - 1.5)
x = optimize.brent(lambda x: (x-1.5)**2-0.8, brack = (-3,-2))
err2 = abs(x - 1.5)
x = optimize.brent(lambda x: (x-1.5)**2-0.8, full_output=True)
err3 = abs(x[0] - 1.5)
x = optimize.brent(lambda x: (x-1.5)**2-0.8, brack = (-15,-1,15))
err4 = abs(x - 1.5)
assert max((err1,err2,err3,err4)) < 1e-6
class test_tnc(NumpyTestCase):
"""TNC non-linear optimization.
These tests are taken from Prof. K. Schittkowski's test examples
for constrained non-linear programming.
http://www.uni-bayreuth.de/departments/math/~kschittkowski/home.htm
"""
tests = []
def setUp(self):
def test1fg(x):
f = 100.0*pow((x[1]-pow(x[0],2)),2)+pow(1.0-x[0],2)
dif = [0,0]
dif[1] = 200.0*(x[1]-pow(x[0],2))
dif[0] = -2.0*(x[0]*(dif[1]-1.0)+1.0)
return f, dif
self.tests.append((test1fg, [-2,1], ([-inf,None],[-1.5,None]),
[1,1]))
def test2fg(x):
f = 100.0*pow((x[1]-pow(x[0],2)),2)+pow(1.0-x[0],2)
dif = [0,0]
dif[1] = 200.0*(x[1]-pow(x[0],2))
dif[0] = -2.0*(x[0]*(dif[1]-1.0)+1.0)
return f, dif
self.tests.append((test2fg, [-2,1], [(-inf,None),(1.5,None)],
[-1.2210262419616387,1.5]))
def test3fg(x):
f = x[1]+pow(x[1]-x[0],2)*1.0e-5
dif = [0,0]
dif[0] = -2.0*(x[1]-x[0])*1.0e-5
dif[1] = 1.0-dif[0]
return f, dif
self.tests.append((test3fg, [10,1], [(-inf,None),(0.0, None)],
[0,0]))
def test4fg(x):
f = pow(x[0]+1.0,3)/3.0+x[1]
dif = [0,0]
dif[0] = pow(x[0]+1.0,2)
dif[1] = 1.0
return f, dif
self.tests.append((test4fg, [1.125,0.125], [(1, None),(0, None)],
[1,0]))
def test5fg(x):
f = sin(x[0]+x[1])+pow(x[0]-x[1],2)-1.5*x[0]+2.5*x[1]+1.0
dif = [0,0]
v1 = cos(x[0]+x[1]);
v2 = 2.0*(x[0]-x[1]);
dif[0] = v1+v2-1.5;
dif[1] = v1-v2+2.5;
return f, dif
self.tests.append((test5fg, [0,0], [(-1.5, 4),(-3,3)],
[-0.54719755119659763, -1.5471975511965976]))
def test38fg(x):
f = (100.0*pow(x[1]-pow(x[0],2),2) + \
pow(1.0-x[0],2)+90.0*pow(x[3]-pow(x[2],2),2) + \
pow(1.0-x[2],2)+10.1*(pow(x[1]-1.0,2)+pow(x[3]-1.0,2)) + \
19.8*(x[1]-1.0)*(x[3]-1.0))*1.0e-5
dif = [0,0,0,0]
dif[0] = (-400.0*x[0]*(x[1]-pow(x[0],2))-2.0*(1.0-x[0]))*1.0e-5
dif[1] = (200.0*(x[1]-pow(x[0],2))+20.2 \
*(x[1]-1.0)+19.8*(x[3]-1.0))*1.0e-5
dif[2] = (-360.0*x[2]*(x[3]-pow(x[2],2))-2.0\
*(1.0-x[2]))*1.0e-5
dif[3] = (180.0*(x[3]-pow(x[2],2))+20.2\
*(x[3]-1.0)+19.8*(x[1]-1.0))*1.0e-5
return f, dif
self.tests.append((test38fg, array([-3,-1,-3,-1]), [(-10,10)]*4, [1]*4))
def test45fg(x):
f = 2.0-x[0]*x[1]*x[2]*x[3]*x[4]/120.0
dif = [0]*5
dif[0] = -x[1]*x[2]*x[3]*x[4]/120.0
dif[1] = -x[0]*x[2]*x[3]*x[4]/120.0
dif[2] = -x[0]*x[1]*x[3]*x[4]/120.0
dif[3] = -x[0]*x[1]*x[2]*x[4]/120.0
dif[4] = -x[0]*x[1]*x[2]*x[3]/120.0
return f, dif
self.tests.append((test45fg, [2]*5, [(0,1),(0,2),(0,3),(0,4),(0,5)],
[1,2,3,4,5]))
def test_tnc(self):
for fg, x, bounds, xopt in self.tests:
x, nf, rc = optimize.fmin_tnc(fg, x, bounds=bounds,
messages=MSG_NONE, maxfun=200)
err = "Failed optimization of %s.\n" \
"After %d function evaluations, TNC returned: %s.""" % \
(fg.__name__, nf, RCSTRINGS[rc])
ef = abs(fg(xopt)[0] - fg(x)[0])
if ef > 1e-8:
raise err
if __name__ == "__main__":
NumpyTest().run()
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