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