from __future__ import division, absolute_import, print_function from numpy.testing import assert_, assert_allclose, assert_equal from pytest import raises as assert_raises import numpy as np from scipy.sparse.linalg import LinearOperator from scipy.optimize._lsq.common import ( step_size_to_bound, find_active_constraints, make_strictly_feasible, CL_scaling_vector, intersect_trust_region, build_quadratic_1d, minimize_quadratic_1d, evaluate_quadratic, reflective_transformation, left_multiplied_operator, right_multiplied_operator) class TestBounds(object): def test_step_size_to_bounds(self): lb = np.array([-1.0, 2.5, 10.0]) ub = np.array([1.0, 5.0, 100.0]) x = np.array([0.0, 2.5, 12.0]) s = np.array([0.1, 0.0, 0.0]) step, hits = step_size_to_bound(x, s, lb, ub) assert_equal(step, 10) assert_equal(hits, [1, 0, 0]) s = np.array([0.01, 0.05, -1.0]) step, hits = step_size_to_bound(x, s, lb, ub) assert_equal(step, 2) assert_equal(hits, [0, 0, -1]) s = np.array([10.0, -0.0001, 100.0]) step, hits = step_size_to_bound(x, s, lb, ub) assert_equal(step, np.array(-0)) assert_equal(hits, [0, -1, 0]) s = np.array([1.0, 0.5, -2.0]) step, hits = step_size_to_bound(x, s, lb, ub) assert_equal(step, 1.0) assert_equal(hits, [1, 0, -1]) s = np.zeros(3) step, hits = step_size_to_bound(x, s, lb, ub) assert_equal(step, np.inf) assert_equal(hits, [0, 0, 0]) def test_find_active_constraints(self): lb = np.array([0.0, -10.0, 1.0]) ub = np.array([1.0, 0.0, 100.0]) x = np.array([0.5, -5.0, 2.0]) active = find_active_constraints(x, lb, ub) assert_equal(active, [0, 0, 0]) x = np.array([0.0, 0.0, 10.0]) active = find_active_constraints(x, lb, ub) assert_equal(active, [-1, 1, 0]) active = find_active_constraints(x, lb, ub, rtol=0) assert_equal(active, [-1, 1, 0]) x = np.array([1e-9, -1e-8, 100 - 1e-9]) active = find_active_constraints(x, lb, ub) assert_equal(active, [0, 0, 1]) active = find_active_constraints(x, lb, ub, rtol=1.5e-9) assert_equal(active, [-1, 0, 1]) lb = np.array([1.0, -np.inf, -np.inf]) ub = np.array([np.inf, 10.0, np.inf]) x = np.ones(3) active = find_active_constraints(x, lb, ub) assert_equal(active, [-1, 0, 0]) # Handles out-of-bound cases. x = np.array([0.0, 11.0, 0.0]) active = find_active_constraints(x, lb, ub) assert_equal(active, [-1, 1, 0]) active = find_active_constraints(x, lb, ub, rtol=0) assert_equal(active, [-1, 1, 0]) def test_make_strictly_feasible(self): lb = np.array([-0.5, -0.8, 2.0]) ub = np.array([0.8, 1.0, 3.0]) x = np.array([-0.5, 0.0, 2 + 1e-10]) x_new = make_strictly_feasible(x, lb, ub, rstep=0) assert_(x_new[0] > -0.5) assert_equal(x_new[1:], x[1:]) x_new = make_strictly_feasible(x, lb, ub, rstep=1e-4) assert_equal(x_new, [-0.5 + 1e-4, 0.0, 2 * (1 + 1e-4)]) x = np.array([-0.5, -1, 3.1]) x_new = make_strictly_feasible(x, lb, ub) assert_(np.all((x_new >= lb) & (x_new <= ub))) x_new = make_strictly_feasible(x, lb, ub, rstep=0) assert_(np.all((x_new >= lb) & (x_new <= ub))) lb = np.array([-1, 100.0]) ub = np.array([1, 100.0 + 1e-10]) x = np.array([0, 100.0]) x_new = make_strictly_feasible(x, lb, ub, rstep=1e-8) assert_equal(x_new, [0, 100.0 + 0.5e-10]) def test_scaling_vector(self): lb = np.array([-np.inf, -5.0, 1.0, -np.inf]) ub = np.array([1.0, np.inf, 10.0, np.inf]) x = np.array([0.5, 2.0, 5.0, 0.0]) g = np.array([1.0, 0.1, -10.0, 0.0]) v, dv = CL_scaling_vector(x, g, lb, ub) assert_equal(v, [1.0, 7.0, 5.0, 1.0]) assert_equal(dv, [0.0, 1.0, -1.0, 0.0]) class TestQuadraticFunction(object): def setup_method(self): self.J = np.array([ [0.1, 0.2], [-1.0, 1.0], [0.5, 0.2]]) self.g = np.array([0.8, -2.0]) self.diag = np.array([1.0, 2.0]) def test_build_quadratic_1d(self): s = np.zeros(2) a, b = build_quadratic_1d(self.J, self.g, s) assert_equal(a, 0) assert_equal(b, 0) a, b = build_quadratic_1d(self.J, self.g, s, diag=self.diag) assert_equal(a, 0) assert_equal(b, 0) s = np.array([1.0, -1.0]) a, b = build_quadratic_1d(self.J, self.g, s) assert_equal(a, 2.05) assert_equal(b, 2.8) a, b = build_quadratic_1d(self.J, self.g, s, diag=self.diag) assert_equal(a, 3.55) assert_equal(b, 2.8) s0 = np.array([0.5, 0.5]) a, b, c = build_quadratic_1d(self.J, self.g, s, diag=self.diag, s0=s0) assert_equal(a, 3.55) assert_allclose(b, 2.39) assert_allclose(c, -0.1525) def test_minimize_quadratic_1d(self): a = 5 b = -1 t, y = minimize_quadratic_1d(a, b, 1, 2) assert_equal(t, 1) assert_equal(y, a * t**2 + b * t) t, y = minimize_quadratic_1d(a, b, -2, -1) assert_equal(t, -1) assert_equal(y, a * t**2 + b * t) t, y = minimize_quadratic_1d(a, b, -1, 1) assert_equal(t, 0.1) assert_equal(y, a * t**2 + b * t) c = 10 t, y = minimize_quadratic_1d(a, b, -1, 1, c=c) assert_equal(t, 0.1) assert_equal(y, a * t**2 + b * t + c) def test_evaluate_quadratic(self): s = np.array([1.0, -1.0]) value = evaluate_quadratic(self.J, self.g, s) assert_equal(value, 4.85) value = evaluate_quadratic(self.J, self.g, s, diag=self.diag) assert_equal(value, 6.35) s = np.array([[1.0, -1.0], [1.0, 1.0], [0.0, 0.0]]) values = evaluate_quadratic(self.J, self.g, s) assert_allclose(values, [4.85, -0.91, 0.0]) values = evaluate_quadratic(self.J, self.g, s, diag=self.diag) assert_allclose(values, [6.35, 0.59, 0.0]) class TestTrustRegion(object): def test_intersect(self): Delta = 1.0 x = np.zeros(3) s = np.array([1.0, 0.0, 0.0]) t_neg, t_pos = intersect_trust_region(x, s, Delta) assert_equal(t_neg, -1) assert_equal(t_pos, 1) s = np.array([-1.0, 1.0, -1.0]) t_neg, t_pos = intersect_trust_region(x, s, Delta) assert_allclose(t_neg, -3**-0.5) assert_allclose(t_pos, 3**-0.5) x = np.array([0.5, -0.5, 0]) s = np.array([0, 0, 1.0]) t_neg, t_pos = intersect_trust_region(x, s, Delta) assert_allclose(t_neg, -2**-0.5) assert_allclose(t_pos, 2**-0.5) x = np.ones(3) assert_raises(ValueError, intersect_trust_region, x, s, Delta) x = np.zeros(3) s = np.zeros(3) assert_raises(ValueError, intersect_trust_region, x, s, Delta) def test_reflective_transformation(): lb = np.array([-1, -2], dtype=float) ub = np.array([5, 3], dtype=float) y = np.array([0, 0]) x, g = reflective_transformation(y, lb, ub) assert_equal(x, y) assert_equal(g, np.ones(2)) y = np.array([-4, 4], dtype=float) x, g = reflective_transformation(y, lb, np.array([np.inf, np.inf])) assert_equal(x, [2, 4]) assert_equal(g, [-1, 1]) x, g = reflective_transformation(y, np.array([-np.inf, -np.inf]), ub) assert_equal(x, [-4, 2]) assert_equal(g, [1, -1]) x, g = reflective_transformation(y, lb, ub) assert_equal(x, [2, 2]) assert_equal(g, [-1, -1]) lb = np.array([-np.inf, -2]) ub = np.array([5, np.inf]) y = np.array([10, 10], dtype=float) x, g = reflective_transformation(y, lb, ub) assert_equal(x, [0, 10]) assert_equal(g, [-1, 1]) def test_linear_operators(): A = np.arange(6).reshape((3, 2)) d_left = np.array([-1, 2, 5]) DA = np.diag(d_left).dot(A) J_left = left_multiplied_operator(A, d_left) d_right = np.array([5, 10]) AD = A.dot(np.diag(d_right)) J_right = right_multiplied_operator(A, d_right) x = np.array([-2, 3]) X = -2 * np.arange(2, 8).reshape((2, 3)) xt = np.array([0, -2, 15]) assert_allclose(DA.dot(x), J_left.matvec(x)) assert_allclose(DA.dot(X), J_left.matmat(X)) assert_allclose(DA.T.dot(xt), J_left.rmatvec(xt)) assert_allclose(AD.dot(x), J_right.matvec(x)) assert_allclose(AD.dot(X), J_right.matmat(X)) assert_allclose(AD.T.dot(xt), J_right.rmatvec(xt))