346 lines
12 KiB
Python
346 lines
12 KiB
Python
"""
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Unit tests for TNC optimization routine from tnc.py
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"""
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import pytest
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from numpy.testing import assert_allclose, assert_equal
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import numpy as np
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from math import pow
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from scipy import optimize
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class TestTnc:
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"""TNC non-linear optimization.
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These tests are taken from Prof. K. Schittkowski's test examples
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for constrained non-linear programming.
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http://www.uni-bayreuth.de/departments/math/~kschittkowski/home.htm
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"""
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def setup_method(self):
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# options for minimize
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self.opts = {'disp': False, 'maxfun': 200}
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# objective functions and Jacobian for each test
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def f1(self, x, a=100.0):
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return a * pow((x[1] - pow(x[0], 2)), 2) + pow(1.0 - x[0], 2)
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def g1(self, x, a=100.0):
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dif = [0, 0]
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dif[1] = 2 * a * (x[1] - pow(x[0], 2))
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dif[0] = -2.0 * (x[0] * (dif[1] - 1.0) + 1.0)
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return dif
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def fg1(self, x, a=100.0):
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return self.f1(x, a), self.g1(x, a)
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def f3(self, x):
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return x[1] + pow(x[1] - x[0], 2) * 1.0e-5
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def g3(self, x):
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dif = [0, 0]
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dif[0] = -2.0 * (x[1] - x[0]) * 1.0e-5
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dif[1] = 1.0 - dif[0]
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return dif
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def fg3(self, x):
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return self.f3(x), self.g3(x)
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def f4(self, x):
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return pow(x[0] + 1.0, 3) / 3.0 + x[1]
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def g4(self, x):
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dif = [0, 0]
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dif[0] = pow(x[0] + 1.0, 2)
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dif[1] = 1.0
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return dif
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def fg4(self, x):
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return self.f4(x), self.g4(x)
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def f5(self, x):
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return np.sin(x[0] + x[1]) + pow(x[0] - x[1], 2) - \
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1.5 * x[0] + 2.5 * x[1] + 1.0
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def g5(self, x):
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dif = [0, 0]
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v1 = np.cos(x[0] + x[1])
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v2 = 2.0*(x[0] - x[1])
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dif[0] = v1 + v2 - 1.5
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dif[1] = v1 - v2 + 2.5
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return dif
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def fg5(self, x):
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return self.f5(x), self.g5(x)
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def f38(self, x):
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return (100.0 * pow(x[1] - pow(x[0], 2), 2) +
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pow(1.0 - x[0], 2) + 90.0 * pow(x[3] - pow(x[2], 2), 2) +
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pow(1.0 - x[2], 2) + 10.1 * (pow(x[1] - 1.0, 2) +
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pow(x[3] - 1.0, 2)) +
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19.8 * (x[1] - 1.0) * (x[3] - 1.0)) * 1.0e-5
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def g38(self, x):
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dif = [0, 0, 0, 0]
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dif[0] = (-400.0 * x[0] * (x[1] - pow(x[0], 2)) -
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2.0 * (1.0 - x[0])) * 1.0e-5
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dif[1] = (200.0 * (x[1] - pow(x[0], 2)) + 20.2 * (x[1] - 1.0) +
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19.8 * (x[3] - 1.0)) * 1.0e-5
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dif[2] = (- 360.0 * x[2] * (x[3] - pow(x[2], 2)) -
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2.0 * (1.0 - x[2])) * 1.0e-5
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dif[3] = (180.0 * (x[3] - pow(x[2], 2)) + 20.2 * (x[3] - 1.0) +
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19.8 * (x[1] - 1.0)) * 1.0e-5
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return dif
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def fg38(self, x):
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return self.f38(x), self.g38(x)
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def f45(self, x):
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return 2.0 - x[0] * x[1] * x[2] * x[3] * x[4] / 120.0
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def g45(self, x):
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dif = [0] * 5
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dif[0] = - x[1] * x[2] * x[3] * x[4] / 120.0
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dif[1] = - x[0] * x[2] * x[3] * x[4] / 120.0
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dif[2] = - x[0] * x[1] * x[3] * x[4] / 120.0
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dif[3] = - x[0] * x[1] * x[2] * x[4] / 120.0
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dif[4] = - x[0] * x[1] * x[2] * x[3] / 120.0
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return dif
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def fg45(self, x):
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return self.f45(x), self.g45(x)
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# tests
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# minimize with method=TNC
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def test_minimize_tnc1(self):
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x0, bnds = [-2, 1], ([-np.inf, None], [-1.5, None])
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xopt = [1, 1]
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iterx = [] # to test callback
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res = optimize.minimize(self.f1, x0, method='TNC', jac=self.g1,
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bounds=bnds, options=self.opts,
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callback=iterx.append)
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assert_allclose(res.fun, self.f1(xopt), atol=1e-8)
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assert_equal(len(iterx), res.nit)
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def test_minimize_tnc1b(self):
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x0, bnds = np.array([-2, 1]), ([-np.inf, None], [-1.5, None])
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xopt = [1, 1]
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x = optimize.minimize(self.f1, x0, method='TNC',
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bounds=bnds, options=self.opts).x
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assert_allclose(self.f1(x), self.f1(xopt), atol=1e-4)
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def test_minimize_tnc1c(self):
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x0, bnds = [-2, 1], ([-np.inf, None],[-1.5, None])
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xopt = [1, 1]
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x = optimize.minimize(self.fg1, x0, method='TNC',
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jac=True, bounds=bnds,
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options=self.opts).x
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assert_allclose(self.f1(x), self.f1(xopt), atol=1e-8)
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def test_minimize_tnc2(self):
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x0, bnds = [-2, 1], ([-np.inf, None], [1.5, None])
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xopt = [-1.2210262419616387, 1.5]
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x = optimize.minimize(self.f1, x0, method='TNC',
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jac=self.g1, bounds=bnds,
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options=self.opts).x
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assert_allclose(self.f1(x), self.f1(xopt), atol=1e-8)
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def test_minimize_tnc3(self):
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x0, bnds = [10, 1], ([-np.inf, None], [0.0, None])
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xopt = [0, 0]
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x = optimize.minimize(self.f3, x0, method='TNC',
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jac=self.g3, bounds=bnds,
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options=self.opts).x
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assert_allclose(self.f3(x), self.f3(xopt), atol=1e-8)
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def test_minimize_tnc4(self):
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x0,bnds = [1.125, 0.125], [(1, None), (0, None)]
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xopt = [1, 0]
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x = optimize.minimize(self.f4, x0, method='TNC',
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jac=self.g4, bounds=bnds,
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options=self.opts).x
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assert_allclose(self.f4(x), self.f4(xopt), atol=1e-8)
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def test_minimize_tnc5(self):
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x0, bnds = [0, 0], [(-1.5, 4),(-3, 3)]
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xopt = [-0.54719755119659763, -1.5471975511965976]
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x = optimize.minimize(self.f5, x0, method='TNC',
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jac=self.g5, bounds=bnds,
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options=self.opts).x
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assert_allclose(self.f5(x), self.f5(xopt), atol=1e-8)
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def test_minimize_tnc38(self):
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x0, bnds = np.array([-3, -1, -3, -1]), [(-10, 10)]*4
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xopt = [1]*4
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x = optimize.minimize(self.f38, x0, method='TNC',
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jac=self.g38, bounds=bnds,
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options=self.opts).x
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assert_allclose(self.f38(x), self.f38(xopt), atol=1e-8)
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def test_minimize_tnc45(self):
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x0, bnds = [2] * 5, [(0, 1), (0, 2), (0, 3), (0, 4), (0, 5)]
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xopt = [1, 2, 3, 4, 5]
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x = optimize.minimize(self.f45, x0, method='TNC',
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jac=self.g45, bounds=bnds,
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options=self.opts).x
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assert_allclose(self.f45(x), self.f45(xopt), atol=1e-8)
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# fmin_tnc
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def test_tnc1(self):
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fg, x, bounds = self.fg1, [-2, 1], ([-np.inf, None], [-1.5, None])
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xopt = [1, 1]
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x, nf, rc = optimize.fmin_tnc(fg, x, bounds=bounds, args=(100.0, ),
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messages=optimize._tnc.MSG_NONE,
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maxfun=200)
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assert_allclose(self.f1(x), self.f1(xopt), atol=1e-8,
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err_msg="TNC failed with status: " +
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optimize._tnc.RCSTRINGS[rc])
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def test_tnc1b(self):
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x, bounds = [-2, 1], ([-np.inf, None], [-1.5, None])
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xopt = [1, 1]
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x, nf, rc = optimize.fmin_tnc(self.f1, x, approx_grad=True,
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bounds=bounds,
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messages=optimize._tnc.MSG_NONE,
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maxfun=200)
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assert_allclose(self.f1(x), self.f1(xopt), atol=1e-4,
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err_msg="TNC failed with status: " +
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optimize._tnc.RCSTRINGS[rc])
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def test_tnc1c(self):
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x, bounds = [-2, 1], ([-np.inf, None], [-1.5, None])
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xopt = [1, 1]
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x, nf, rc = optimize.fmin_tnc(self.f1, x, fprime=self.g1,
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bounds=bounds,
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messages=optimize._tnc.MSG_NONE,
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maxfun=200)
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assert_allclose(self.f1(x), self.f1(xopt), atol=1e-8,
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err_msg="TNC failed with status: " +
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optimize._tnc.RCSTRINGS[rc])
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def test_tnc2(self):
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fg, x, bounds = self.fg1, [-2, 1], ([-np.inf, None], [1.5, None])
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xopt = [-1.2210262419616387, 1.5]
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x, nf, rc = optimize.fmin_tnc(fg, x, bounds=bounds,
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messages=optimize._tnc.MSG_NONE,
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maxfun=200)
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assert_allclose(self.f1(x), self.f1(xopt), atol=1e-8,
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err_msg="TNC failed with status: " +
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optimize._tnc.RCSTRINGS[rc])
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def test_tnc3(self):
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fg, x, bounds = self.fg3, [10, 1], ([-np.inf, None], [0.0, None])
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xopt = [0, 0]
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x, nf, rc = optimize.fmin_tnc(fg, x, bounds=bounds,
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messages=optimize._tnc.MSG_NONE,
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maxfun=200)
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assert_allclose(self.f3(x), self.f3(xopt), atol=1e-8,
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err_msg="TNC failed with status: " +
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optimize._tnc.RCSTRINGS[rc])
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def test_tnc4(self):
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fg, x, bounds = self.fg4, [1.125, 0.125], [(1, None), (0, None)]
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xopt = [1, 0]
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x, nf, rc = optimize.fmin_tnc(fg, x, bounds=bounds,
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messages=optimize._tnc.MSG_NONE,
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maxfun=200)
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assert_allclose(self.f4(x), self.f4(xopt), atol=1e-8,
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err_msg="TNC failed with status: " +
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optimize._tnc.RCSTRINGS[rc])
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def test_tnc5(self):
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fg, x, bounds = self.fg5, [0, 0], [(-1.5, 4),(-3, 3)]
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xopt = [-0.54719755119659763, -1.5471975511965976]
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x, nf, rc = optimize.fmin_tnc(fg, x, bounds=bounds,
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messages=optimize._tnc.MSG_NONE,
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maxfun=200)
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assert_allclose(self.f5(x), self.f5(xopt), atol=1e-8,
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err_msg="TNC failed with status: " +
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optimize._tnc.RCSTRINGS[rc])
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def test_tnc38(self):
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fg, x, bounds = self.fg38, np.array([-3, -1, -3, -1]), [(-10, 10)]*4
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xopt = [1]*4
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x, nf, rc = optimize.fmin_tnc(fg, x, bounds=bounds,
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messages=optimize._tnc.MSG_NONE,
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maxfun=200)
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assert_allclose(self.f38(x), self.f38(xopt), atol=1e-8,
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err_msg="TNC failed with status: " +
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optimize._tnc.RCSTRINGS[rc])
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def test_tnc45(self):
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fg, x, bounds = self.fg45, [2] * 5, [(0, 1), (0, 2), (0, 3),
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(0, 4), (0, 5)]
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xopt = [1, 2, 3, 4, 5]
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x, nf, rc = optimize.fmin_tnc(fg, x, bounds=bounds,
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messages=optimize._tnc.MSG_NONE,
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maxfun=200)
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assert_allclose(self.f45(x), self.f45(xopt), atol=1e-8,
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err_msg="TNC failed with status: " +
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optimize._tnc.RCSTRINGS[rc])
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def test_raising_exceptions(self):
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# tnc was ported to cython from hand-crafted cpython code
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# check that Exception handling works.
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def myfunc(x):
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raise RuntimeError("myfunc")
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def myfunc1(x):
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return optimize.rosen(x)
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def callback(x):
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raise ValueError("callback")
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with pytest.raises(RuntimeError):
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optimize.minimize(myfunc, [0, 1], method="TNC")
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with pytest.raises(ValueError):
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optimize.minimize(
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myfunc1, [0, 1], method="TNC", callback=callback
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)
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def test_callback_shouldnt_affect_minimization(self):
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# gh14879. The output of a TNC minimization was different depending
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# on whether a callback was used or not. The two should be equivalent.
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# The issue was that TNC was unscaling/scaling x, and this process was
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# altering x in the process. Now the callback uses an unscaled
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# temporary copy of x.
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def callback(x):
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pass
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fun = optimize.rosen
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bounds = [(0, 10)] * 4
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x0 = [1, 2, 3, 4.]
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res = optimize.minimize(
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fun, x0, bounds=bounds, method="TNC", options={"maxfun": 1000}
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)
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res2 = optimize.minimize(
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fun, x0, bounds=bounds, method="TNC", options={"maxfun": 1000},
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callback=callback
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)
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assert_allclose(res2.x, res.x)
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assert_allclose(res2.fun, res.fun)
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assert_equal(res2.nfev, res.nfev)
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