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"""
Unit tests for Krylov space trust-region subproblem solver.
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._trlib import (get_trlib_quadratic_subproblem)
from numpy.testing import (assert_, assert_array_equal,
assert_almost_equal,
assert_equal, assert_array_almost_equal,
assert_array_less)
KrylovQP = get_trlib_quadratic_subproblem(tol_rel_i=1e-8, tol_rel_b=1e-6)
KrylovQP_disp = get_trlib_quadratic_subproblem(tol_rel_i=1e-8, tol_rel_b=1e-6, disp=True)
class TestKrylovQuadraticSubproblem(object):
def test_for_the_easy_case(self):
# `H` is chosen such that `g` is not orthogonal to the
# eigenvector associated with the smallest eigenvalue.
H = np.array([[1.0, 0.0, 4.0],
[0.0, 2.0, 0.0],
[4.0, 0.0, 3.0]])
g = np.array([5.0, 0.0, 4.0])
# Trust Radius
trust_radius = 1.0
# Solve Subproblem
subprob = KrylovQP(x=0,
fun=lambda x: 0,
jac=lambda x: g,
hess=lambda x: None,
hessp=lambda x, y: H.dot(y))
p, hits_boundary = subprob.solve(trust_radius)
assert_array_almost_equal(p, np.array([-1.0, 0.0, 0.0]))
assert_equal(hits_boundary, True)
# check kkt satisfaction
assert_almost_equal(
np.linalg.norm(H.dot(p) + subprob.lam * p + g),
0.0)
# check trust region constraint
assert_almost_equal(np.linalg.norm(p), trust_radius)
trust_radius = 0.5
p, hits_boundary = subprob.solve(trust_radius)
assert_array_almost_equal(p,
np.array([-0.46125446, 0., -0.19298788]))
assert_equal(hits_boundary, True)
# check kkt satisfaction
assert_almost_equal(
np.linalg.norm(H.dot(p) + subprob.lam * p + g),
0.0)
# check trust region constraint
assert_almost_equal(np.linalg.norm(p), trust_radius)
def test_for_the_hard_case(self):
# `H` is chosen such that `g` is orthogonal to the
# eigenvector associated with the smallest eigenvalue.
H = np.array([[1.0, 0.0, 4.0],
[0.0, 2.0, 0.0],
[4.0, 0.0, 3.0]])
g = np.array([0.0, 2.0, 0.0])
# Trust Radius
trust_radius = 1.0
# Solve Subproblem
subprob = KrylovQP(x=0,
fun=lambda x: 0,
jac=lambda x: g,
hess=lambda x: None,
hessp=lambda x, y: H.dot(y))
p, hits_boundary = subprob.solve(trust_radius)
assert_array_almost_equal(p, np.array([0.0, -1.0, 0.0]))
# check kkt satisfaction
assert_almost_equal(
np.linalg.norm(H.dot(p) + subprob.lam * p + g),
0.0)
# check trust region constraint
assert_almost_equal(np.linalg.norm(p), trust_radius)
trust_radius = 0.5
p, hits_boundary = subprob.solve(trust_radius)
assert_array_almost_equal(p, np.array([0.0, -0.5, 0.0]))
# check kkt satisfaction
assert_almost_equal(
np.linalg.norm(H.dot(p) + subprob.lam * p + g),
0.0)
# check trust region constraint
assert_almost_equal(np.linalg.norm(p), trust_radius)
def test_for_interior_convergence(self):
H = np.array([[1.812159, 0.82687265, 0.21838879, -0.52487006, 0.25436988],
[0.82687265, 2.66380283, 0.31508988, -0.40144163, 0.08811588],
[0.21838879, 0.31508988, 2.38020726, -0.3166346, 0.27363867],
[-0.52487006, -0.40144163, -0.3166346, 1.61927182, -0.42140166],
[0.25436988, 0.08811588, 0.27363867, -0.42140166, 1.33243101]])
g = np.array([0.75798952, 0.01421945, 0.33847612, 0.83725004, -0.47909534])
trust_radius = 1.1
# Solve Subproblem
subprob = KrylovQP(x=0,
fun=lambda x: 0,
jac=lambda x: g,
hess=lambda x: None,
hessp=lambda x, y: H.dot(y))
p, hits_boundary = subprob.solve(trust_radius)
# check kkt satisfaction
assert_almost_equal(
np.linalg.norm(H.dot(p) + subprob.lam * p + g),
0.0)
assert_array_almost_equal(p, [-0.68585435, 0.1222621, -0.22090999,
-0.67005053, 0.31586769])
assert_array_almost_equal(hits_boundary, False)
def test_for_very_close_to_zero(self):
H = np.array([[0.88547534, 2.90692271, 0.98440885, -0.78911503, -0.28035809],
[2.90692271, -0.04618819, 0.32867263, -0.83737945, 0.17116396],
[0.98440885, 0.32867263, -0.87355957, -0.06521957, -1.43030957],
[-0.78911503, -0.83737945, -0.06521957, -1.645709, -0.33887298],
[-0.28035809, 0.17116396, -1.43030957, -0.33887298, -1.68586978]])
g = np.array([0, 0, 0, 0, 1e-6])
trust_radius = 1.1
# Solve Subproblem
subprob = KrylovQP(x=0,
fun=lambda x: 0,
jac=lambda x: g,
hess=lambda x: None,
hessp=lambda x, y: H.dot(y))
p, hits_boundary = subprob.solve(trust_radius)
# check kkt satisfaction
assert_almost_equal(
np.linalg.norm(H.dot(p) + subprob.lam * p + g),
0.0)
# check trust region constraint
assert_almost_equal(np.linalg.norm(p), trust_radius)
assert_array_almost_equal(p, [0.06910534, -0.01432721,
-0.65311947, -0.23815972,
-0.84954934])
assert_array_almost_equal(hits_boundary, True)
def test_disp(self, capsys):
H = -np.eye(5)
g = np.array([0, 0, 0, 0, 1e-6])
trust_radius = 1.1
subprob = KrylovQP_disp(x=0,
fun=lambda x: 0,
jac=lambda x: g,
hess=lambda x: None,
hessp=lambda x, y: H.dot(y))
p, hits_boundary = subprob.solve(trust_radius)
out, err = capsys.readouterr()
assert_(out.startswith(' TR Solving trust region problem'), repr(out))
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