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