107 lines
4.3 KiB
Python
107 lines
4.3 KiB
Python
|
"""
|
||
|
|
Unit tests for trust-region optimization routines.
|
||
|
|
|
||
|
|
To run it in its simplest form::
|
||
|
|
nosetests test_optimize.py
|
||
|
|
|
||
|
|
"""
|
||
|
|
from __future__ import division, print_function, absolute_import
|
||
|
|
|
||
|
|
import numpy as np
|
||
|
|
from scipy.optimize import (minimize, rosen, rosen_der, rosen_hess,
|
||
|
|
rosen_hess_prod)
|
||
|
|
from numpy.testing import assert_, assert_equal, assert_allclose
|
||
|
|
|
||
|
|
|
||
|
|
class Accumulator:
|
||
|
|
""" This is for testing callbacks."""
|
||
|
|
def __init__(self):
|
||
|
|
self.count = 0
|
||
|
|
self.accum = None
|
||
|
|
|
||
|
|
def __call__(self, x):
|
||
|
|
self.count += 1
|
||
|
|
if self.accum is None:
|
||
|
|
self.accum = np.array(x)
|
||
|
|
else:
|
||
|
|
self.accum += x
|
||
|
|
|
||
|
|
|
||
|
|
class TestTrustRegionSolvers(object):
|
||
|
|
|
||
|
|
def setup_method(self):
|
||
|
|
self.x_opt = [1.0, 1.0]
|
||
|
|
self.easy_guess = [2.0, 2.0]
|
||
|
|
self.hard_guess = [-1.2, 1.0]
|
||
|
|
|
||
|
|
def test_dogleg_accuracy(self):
|
||
|
|
# test the accuracy and the return_all option
|
||
|
|
x0 = self.hard_guess
|
||
|
|
r = minimize(rosen, x0, jac=rosen_der, hess=rosen_hess, tol=1e-8,
|
||
|
|
method='dogleg', options={'return_all': True},)
|
||
|
|
assert_allclose(x0, r['allvecs'][0])
|
||
|
|
assert_allclose(r['x'], r['allvecs'][-1])
|
||
|
|
assert_allclose(r['x'], self.x_opt)
|
||
|
|
|
||
|
|
def test_dogleg_callback(self):
|
||
|
|
# test the callback mechanism and the maxiter and return_all options
|
||
|
|
accumulator = Accumulator()
|
||
|
|
maxiter = 5
|
||
|
|
r = minimize(rosen, self.hard_guess, jac=rosen_der, hess=rosen_hess,
|
||
|
|
callback=accumulator, method='dogleg',
|
||
|
|
options={'return_all': True, 'maxiter': maxiter},)
|
||
|
|
assert_equal(accumulator.count, maxiter)
|
||
|
|
assert_equal(len(r['allvecs']), maxiter+1)
|
||
|
|
assert_allclose(r['x'], r['allvecs'][-1])
|
||
|
|
assert_allclose(sum(r['allvecs'][1:]), accumulator.accum)
|
||
|
|
|
||
|
|
def test_solver_concordance(self):
|
||
|
|
# Assert that dogleg uses fewer iterations than ncg on the Rosenbrock
|
||
|
|
# test function, although this does not necessarily mean
|
||
|
|
# that dogleg is faster or better than ncg even for this function
|
||
|
|
# and especially not for other test functions.
|
||
|
|
f = rosen
|
||
|
|
g = rosen_der
|
||
|
|
h = rosen_hess
|
||
|
|
for x0 in (self.easy_guess, self.hard_guess):
|
||
|
|
r_dogleg = minimize(f, x0, jac=g, hess=h, tol=1e-8,
|
||
|
|
method='dogleg', options={'return_all': True})
|
||
|
|
r_trust_ncg = minimize(f, x0, jac=g, hess=h, tol=1e-8,
|
||
|
|
method='trust-ncg',
|
||
|
|
options={'return_all': True})
|
||
|
|
r_trust_krylov = minimize(f, x0, jac=g, hess=h, tol=1e-8,
|
||
|
|
method='trust-krylov',
|
||
|
|
options={'return_all': True})
|
||
|
|
r_ncg = minimize(f, x0, jac=g, hess=h, tol=1e-8,
|
||
|
|
method='newton-cg', options={'return_all': True})
|
||
|
|
r_iterative = minimize(f, x0, jac=g, hess=h, tol=1e-8,
|
||
|
|
method='trust-exact',
|
||
|
|
options={'return_all': True})
|
||
|
|
assert_allclose(self.x_opt, r_dogleg['x'])
|
||
|
|
assert_allclose(self.x_opt, r_trust_ncg['x'])
|
||
|
|
assert_allclose(self.x_opt, r_trust_krylov['x'])
|
||
|
|
assert_allclose(self.x_opt, r_ncg['x'])
|
||
|
|
assert_allclose(self.x_opt, r_iterative['x'])
|
||
|
|
assert_(len(r_dogleg['allvecs']) < len(r_ncg['allvecs']))
|
||
|
|
|
||
|
|
def test_trust_ncg_hessp(self):
|
||
|
|
for x0 in (self.easy_guess, self.hard_guess, self.x_opt):
|
||
|
|
r = minimize(rosen, x0, jac=rosen_der, hessp=rosen_hess_prod,
|
||
|
|
tol=1e-8, method='trust-ncg')
|
||
|
|
assert_allclose(self.x_opt, r['x'])
|
||
|
|
|
||
|
|
def test_trust_ncg_start_in_optimum(self):
|
||
|
|
r = minimize(rosen, x0=self.x_opt, jac=rosen_der, hess=rosen_hess,
|
||
|
|
tol=1e-8, method='trust-ncg')
|
||
|
|
assert_allclose(self.x_opt, r['x'])
|
||
|
|
|
||
|
|
def test_trust_krylov_start_in_optimum(self):
|
||
|
|
r = minimize(rosen, x0=self.x_opt, jac=rosen_der, hess=rosen_hess,
|
||
|
|
tol=1e-8, method='trust-krylov')
|
||
|
|
assert_allclose(self.x_opt, r['x'])
|
||
|
|
|
||
|
|
def test_trust_exact_start_in_optimum(self):
|
||
|
|
r = minimize(rosen, x0=self.x_opt, jac=rosen_der, hess=rosen_hess,
|
||
|
|
tol=1e-8, method='trust-exact')
|
||
|
|
assert_allclose(self.x_opt, r['x'])
|