EVOLUTION-MANAGER

Edit File: test_tnc.py

""" Unit tests for TNC optimization routine from tnc.py """ from numpy.testing import assert_allclose, assert_equal import numpy as np from math import pow from scipy import optimize from scipy.sparse.sputils import matrix class TestTnc(object): """TNC non-linear optimization. These tests are taken from Prof. K. Schittkowski's test examples for constrained non-linear programming. http://www.uni-bayreuth.de/departments/math/~kschittkowski/home.htm """ def setup_method(self): # options for minimize self.opts = {'disp': False, 'maxiter': 200} # objective functions and jacobian for each test def f1(self, x, a=100.0): return a * pow((x[1] - pow(x[0], 2)), 2) + pow(1.0 - x[0], 2) def g1(self, x, a=100.0): dif = [0, 0] dif[1] = 2 * a * (x[1] - pow(x[0], 2)) dif[0] = -2.0 * (x[0] * (dif[1] - 1.0) + 1.0) return dif def fg1(self, x, a=100.0): return self.f1(x, a), self.g1(x, a) def f3(self, x): return x[1] + pow(x[1] - x[0], 2) * 1.0e-5 def g3(self, x): dif = [0, 0] dif[0] = -2.0 * (x[1] - x[0]) * 1.0e-5 dif[1] = 1.0 - dif[0] return dif def fg3(self, x): return self.f3(x), self.g3(x) def f4(self, x): return pow(x[0] + 1.0, 3) / 3.0 + x[1] def g4(self, x): dif = [0, 0] dif[0] = pow(x[0] + 1.0, 2) dif[1] = 1.0 return dif def fg4(self, x): return self.f4(x), self.g4(x) def f5(self, x): return np.sin(x[0] + x[1]) + pow(x[0] - x[1], 2) - \ 1.5 * x[0] + 2.5 * x[1] + 1.0 def g5(self, x): dif = [0, 0] v1 = np.cos(x[0] + x[1]) v2 = 2.0*(x[0] - x[1]) dif[0] = v1 + v2 - 1.5 dif[1] = v1 - v2 + 2.5 return dif def fg5(self, x): return self.f5(x), self.g5(x) def f38(self, x): return (100.0 * pow(x[1] - pow(x[0], 2), 2) + pow(1.0 - x[0], 2) + 90.0 * pow(x[3] - pow(x[2], 2), 2) + pow(1.0 - x[2], 2) + 10.1 * (pow(x[1] - 1.0, 2) + pow(x[3] - 1.0, 2)) + 19.8 * (x[1] - 1.0) * (x[3] - 1.0)) * 1.0e-5 def g38(self, x): dif = [0, 0, 0, 0] dif[0] = (-400.0 * x[0] * (x[1] - pow(x[0], 2)) - 2.0 * (1.0 - x[0])) * 1.0e-5 dif[1] = (200.0 * (x[1] - pow(x[0], 2)) + 20.2 * (x[1] - 1.0) + 19.8 * (x[3] - 1.0)) * 1.0e-5 dif[2] = (- 360.0 * x[2] * (x[3] - pow(x[2], 2)) - 2.0 * (1.0 - x[2])) * 1.0e-5 dif[3] = (180.0 * (x[3] - pow(x[2], 2)) + 20.2 * (x[3] - 1.0) + 19.8 * (x[1] - 1.0)) * 1.0e-5 return dif def fg38(self, x): return self.f38(x), self.g38(x) def f45(self, x): return 2.0 - x[0] * x[1] * x[2] * x[3] * x[4] / 120.0 def g45(self, x): dif = [0] * 5 dif[0] = - x[1] * x[2] * x[3] * x[4] / 120.0 dif[1] = - x[0] * x[2] * x[3] * x[4] / 120.0 dif[2] = - x[0] * x[1] * x[3] * x[4] / 120.0 dif[3] = - x[0] * x[1] * x[2] * x[4] / 120.0 dif[4] = - x[0] * x[1] * x[2] * x[3] / 120.0 return dif def fg45(self, x): return self.f45(x), self.g45(x) # tests # minimize with method=TNC def test_minimize_tnc1(self): x0, bnds = [-2, 1], ([-np.inf, None], [-1.5, None]) xopt = [1, 1] iterx = [] # to test callback res = optimize.minimize(self.f1, x0, method='TNC', jac=self.g1, bounds=bnds, options=self.opts, callback=iterx.append) assert_allclose(res.fun, self.f1(xopt), atol=1e-8) assert_equal(len(iterx), res.nit) def test_minimize_tnc1b(self): x0, bnds = matrix([-2, 1]), ([-np.inf, None],[-1.5, None]) xopt = [1, 1] x = optimize.minimize(self.f1, x0, method='TNC', bounds=bnds, options=self.opts).x assert_allclose(self.f1(x), self.f1(xopt), atol=1e-4) def test_minimize_tnc1c(self): x0, bnds = [-2, 1], ([-np.inf, None],[-1.5, None]) xopt = [1, 1] x = optimize.minimize(self.fg1, x0, method='TNC', jac=True, bounds=bnds, options=self.opts).x assert_allclose(self.f1(x), self.f1(xopt), atol=1e-8) def test_minimize_tnc2(self): x0, bnds = [-2, 1], ([-np.inf, None], [1.5, None]) xopt = [-1.2210262419616387, 1.5] x = optimize.minimize(self.f1, x0, method='TNC', jac=self.g1, bounds=bnds, options=self.opts).x assert_allclose(self.f1(x), self.f1(xopt), atol=1e-8) def test_minimize_tnc3(self): x0, bnds = [10, 1], ([-np.inf, None], [0.0, None]) xopt = [0, 0] x = optimize.minimize(self.f3, x0, method='TNC', jac=self.g3, bounds=bnds, options=self.opts).x assert_allclose(self.f3(x), self.f3(xopt), atol=1e-8) def test_minimize_tnc4(self): x0,bnds = [1.125, 0.125], [(1, None), (0, None)] xopt = [1, 0] x = optimize.minimize(self.f4, x0, method='TNC', jac=self.g4, bounds=bnds, options=self.opts).x assert_allclose(self.f4(x), self.f4(xopt), atol=1e-8) def test_minimize_tnc5(self): x0, bnds = [0, 0], [(-1.5, 4),(-3, 3)] xopt = [-0.54719755119659763, -1.5471975511965976] x = optimize.minimize(self.f5, x0, method='TNC', jac=self.g5, bounds=bnds, options=self.opts).x assert_allclose(self.f5(x), self.f5(xopt), atol=1e-8) def test_minimize_tnc38(self): x0, bnds = np.array([-3, -1, -3, -1]), [(-10, 10)]*4 xopt = [1]*4 x = optimize.minimize(self.f38, x0, method='TNC', jac=self.g38, bounds=bnds, options=self.opts).x assert_allclose(self.f38(x), self.f38(xopt), atol=1e-8) def test_minimize_tnc45(self): x0, bnds = [2] * 5, [(0, 1), (0, 2), (0, 3), (0, 4), (0, 5)] xopt = [1, 2, 3, 4, 5] x = optimize.minimize(self.f45, x0, method='TNC', jac=self.g45, bounds=bnds, options=self.opts).x assert_allclose(self.f45(x), self.f45(xopt), atol=1e-8) # fmin_tnc def test_tnc1(self): fg, x, bounds = self.fg1, [-2, 1], ([-np.inf, None], [-1.5, None]) xopt = [1, 1] x, nf, rc = optimize.fmin_tnc(fg, x, bounds=bounds, args=(100.0, ), messages=optimize.tnc.MSG_NONE, maxfun=200) assert_allclose(self.f1(x), self.f1(xopt), atol=1e-8, err_msg="TNC failed with status: " + optimize.tnc.RCSTRINGS[rc]) def test_tnc1b(self): x, bounds = [-2, 1], ([-np.inf, None], [-1.5, None]) xopt = [1, 1] x, nf, rc = optimize.fmin_tnc(self.f1, x, approx_grad=True, bounds=bounds, messages=optimize.tnc.MSG_NONE, maxfun=200) assert_allclose(self.f1(x), self.f1(xopt), atol=1e-4, err_msg="TNC failed with status: " + optimize.tnc.RCSTRINGS[rc]) def test_tnc1c(self): x, bounds = [-2, 1], ([-np.inf, None], [-1.5, None]) xopt = [1, 1] x, nf, rc = optimize.fmin_tnc(self.f1, x, fprime=self.g1, bounds=bounds, messages=optimize.tnc.MSG_NONE, maxfun=200) assert_allclose(self.f1(x), self.f1(xopt), atol=1e-8, err_msg="TNC failed with status: " + optimize.tnc.RCSTRINGS[rc]) def test_tnc2(self): fg, x, bounds = self.fg1, [-2, 1], ([-np.inf, None], [1.5, None]) xopt = [-1.2210262419616387, 1.5] x, nf, rc = optimize.fmin_tnc(fg, x, bounds=bounds, messages=optimize.tnc.MSG_NONE, maxfun=200) assert_allclose(self.f1(x), self.f1(xopt), atol=1e-8, err_msg="TNC failed with status: " + optimize.tnc.RCSTRINGS[rc]) def test_tnc3(self): fg, x, bounds = self.fg3, [10, 1], ([-np.inf, None], [0.0, None]) xopt = [0, 0] x, nf, rc = optimize.fmin_tnc(fg, x, bounds=bounds, messages=optimize.tnc.MSG_NONE, maxfun=200) assert_allclose(self.f3(x), self.f3(xopt), atol=1e-8, err_msg="TNC failed with status: " + optimize.tnc.RCSTRINGS[rc]) def test_tnc4(self): fg, x, bounds = self.fg4, [1.125, 0.125], [(1, None), (0, None)] xopt = [1, 0] x, nf, rc = optimize.fmin_tnc(fg, x, bounds=bounds, messages=optimize.tnc.MSG_NONE, maxfun=200) assert_allclose(self.f4(x), self.f4(xopt), atol=1e-8, err_msg="TNC failed with status: " + optimize.tnc.RCSTRINGS[rc]) def test_tnc5(self): fg, x, bounds = self.fg5, [0, 0], [(-1.5, 4),(-3, 3)] xopt = [-0.54719755119659763, -1.5471975511965976] x, nf, rc = optimize.fmin_tnc(fg, x, bounds=bounds, messages=optimize.tnc.MSG_NONE, maxfun=200) assert_allclose(self.f5(x), self.f5(xopt), atol=1e-8, err_msg="TNC failed with status: " + optimize.tnc.RCSTRINGS[rc]) def test_tnc38(self): fg, x, bounds = self.fg38, np.array([-3, -1, -3, -1]), [(-10, 10)]*4 xopt = [1]*4 x, nf, rc = optimize.fmin_tnc(fg, x, bounds=bounds, messages=optimize.tnc.MSG_NONE, maxfun=200) assert_allclose(self.f38(x), self.f38(xopt), atol=1e-8, err_msg="TNC failed with status: " + optimize.tnc.RCSTRINGS[rc]) def test_tnc45(self): fg, x, bounds = self.fg45, [2] * 5, [(0, 1), (0, 2), (0, 3), (0, 4), (0, 5)] xopt = [1, 2, 3, 4, 5] x, nf, rc = optimize.fmin_tnc(fg, x, bounds=bounds, messages=optimize.tnc.MSG_NONE, maxfun=200) assert_allclose(self.f45(x), self.f45(xopt), atol=1e-8, err_msg="TNC failed with status: " + optimize.tnc.RCSTRINGS[rc])