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