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297 lines
9.6 KiB
Python
297 lines
9.6 KiB
Python
import numpy as np
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from numpy.testing import assert_array_equal, assert_equal
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from scipy.optimize._constraints import (NonlinearConstraint, Bounds,
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PreparedConstraint)
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from scipy.optimize._trustregion_constr.canonical_constraint \
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import CanonicalConstraint, initial_constraints_as_canonical
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def create_quadratic_function(n, m, rng):
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a = rng.rand(m)
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A = rng.rand(m, n)
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H = rng.rand(m, n, n)
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HT = np.transpose(H, (1, 2, 0))
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def fun(x):
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return a + A.dot(x) + 0.5 * H.dot(x).dot(x)
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def jac(x):
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return A + H.dot(x)
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def hess(x, v):
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return HT.dot(v)
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return fun, jac, hess
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def test_bounds_cases():
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# Test 1: no constraints.
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user_constraint = Bounds(-np.inf, np.inf)
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x0 = np.array([-1, 2])
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prepared_constraint = PreparedConstraint(user_constraint, x0, False)
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c = CanonicalConstraint.from_PreparedConstraint(prepared_constraint)
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assert_equal(c.n_eq, 0)
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assert_equal(c.n_ineq, 0)
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c_eq, c_ineq = c.fun(x0)
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assert_array_equal(c_eq, [])
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assert_array_equal(c_ineq, [])
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J_eq, J_ineq = c.jac(x0)
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assert_array_equal(J_eq, np.empty((0, 2)))
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assert_array_equal(J_ineq, np.empty((0, 2)))
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assert_array_equal(c.keep_feasible, [])
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# Test 2: infinite lower bound.
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user_constraint = Bounds(-np.inf, [0, np.inf, 1], [False, True, True])
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x0 = np.array([-1, -2, -3], dtype=float)
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prepared_constraint = PreparedConstraint(user_constraint, x0, False)
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c = CanonicalConstraint.from_PreparedConstraint(prepared_constraint)
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assert_equal(c.n_eq, 0)
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assert_equal(c.n_ineq, 2)
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c_eq, c_ineq = c.fun(x0)
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assert_array_equal(c_eq, [])
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assert_array_equal(c_ineq, [-1, -4])
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J_eq, J_ineq = c.jac(x0)
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assert_array_equal(J_eq, np.empty((0, 3)))
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assert_array_equal(J_ineq, np.array([[1, 0, 0], [0, 0, 1]]))
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assert_array_equal(c.keep_feasible, [False, True])
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# Test 3: infinite upper bound.
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user_constraint = Bounds([0, 1, -np.inf], np.inf, [True, False, True])
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x0 = np.array([1, 2, 3], dtype=float)
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prepared_constraint = PreparedConstraint(user_constraint, x0, False)
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c = CanonicalConstraint.from_PreparedConstraint(prepared_constraint)
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assert_equal(c.n_eq, 0)
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assert_equal(c.n_ineq, 2)
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c_eq, c_ineq = c.fun(x0)
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assert_array_equal(c_eq, [])
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assert_array_equal(c_ineq, [-1, -1])
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J_eq, J_ineq = c.jac(x0)
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assert_array_equal(J_eq, np.empty((0, 3)))
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assert_array_equal(J_ineq, np.array([[-1, 0, 0], [0, -1, 0]]))
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assert_array_equal(c.keep_feasible, [True, False])
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# Test 4: interval constraint.
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user_constraint = Bounds([-1, -np.inf, 2, 3], [1, np.inf, 10, 3],
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[False, True, True, True])
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x0 = np.array([0, 10, 8, 5])
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prepared_constraint = PreparedConstraint(user_constraint, x0, False)
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c = CanonicalConstraint.from_PreparedConstraint(prepared_constraint)
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assert_equal(c.n_eq, 1)
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assert_equal(c.n_ineq, 4)
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c_eq, c_ineq = c.fun(x0)
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assert_array_equal(c_eq, [2])
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assert_array_equal(c_ineq, [-1, -2, -1, -6])
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J_eq, J_ineq = c.jac(x0)
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assert_array_equal(J_eq, [[0, 0, 0, 1]])
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assert_array_equal(J_ineq, [[1, 0, 0, 0],
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[0, 0, 1, 0],
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[-1, 0, 0, 0],
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[0, 0, -1, 0]])
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assert_array_equal(c.keep_feasible, [False, True, False, True])
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def test_nonlinear_constraint():
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n = 3
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m = 5
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rng = np.random.RandomState(0)
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x0 = rng.rand(n)
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fun, jac, hess = create_quadratic_function(n, m, rng)
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f = fun(x0)
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J = jac(x0)
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lb = [-10, 3, -np.inf, -np.inf, -5]
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ub = [10, 3, np.inf, 3, np.inf]
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user_constraint = NonlinearConstraint(
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fun, lb, ub, jac, hess, [True, False, False, True, False])
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for sparse_jacobian in [False, True]:
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prepared_constraint = PreparedConstraint(user_constraint, x0,
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sparse_jacobian)
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c = CanonicalConstraint.from_PreparedConstraint(prepared_constraint)
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assert_array_equal(c.n_eq, 1)
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assert_array_equal(c.n_ineq, 4)
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c_eq, c_ineq = c.fun(x0)
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assert_array_equal(c_eq, [f[1] - lb[1]])
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assert_array_equal(c_ineq, [f[3] - ub[3], lb[4] - f[4],
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f[0] - ub[0], lb[0] - f[0]])
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J_eq, J_ineq = c.jac(x0)
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if sparse_jacobian:
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J_eq = J_eq.toarray()
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J_ineq = J_ineq.toarray()
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assert_array_equal(J_eq, J[1, None])
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assert_array_equal(J_ineq, np.vstack((J[3], -J[4], J[0], -J[0])))
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v_eq = rng.rand(c.n_eq)
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v_ineq = rng.rand(c.n_ineq)
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v = np.zeros(m)
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v[1] = v_eq[0]
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v[3] = v_ineq[0]
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v[4] = -v_ineq[1]
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v[0] = v_ineq[2] - v_ineq[3]
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assert_array_equal(c.hess(x0, v_eq, v_ineq), hess(x0, v))
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assert_array_equal(c.keep_feasible, [True, False, True, True])
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def test_concatenation():
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rng = np.random.RandomState(0)
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n = 4
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x0 = rng.rand(n)
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f1 = x0
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J1 = np.eye(n)
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lb1 = [-1, -np.inf, -2, 3]
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ub1 = [1, np.inf, np.inf, 3]
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bounds = Bounds(lb1, ub1, [False, False, True, False])
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fun, jac, hess = create_quadratic_function(n, 5, rng)
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f2 = fun(x0)
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J2 = jac(x0)
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lb2 = [-10, 3, -np.inf, -np.inf, -5]
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ub2 = [10, 3, np.inf, 5, np.inf]
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nonlinear = NonlinearConstraint(
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fun, lb2, ub2, jac, hess, [True, False, False, True, False])
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for sparse_jacobian in [False, True]:
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bounds_prepared = PreparedConstraint(bounds, x0, sparse_jacobian)
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nonlinear_prepared = PreparedConstraint(nonlinear, x0, sparse_jacobian)
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c1 = CanonicalConstraint.from_PreparedConstraint(bounds_prepared)
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c2 = CanonicalConstraint.from_PreparedConstraint(nonlinear_prepared)
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c = CanonicalConstraint.concatenate([c1, c2], sparse_jacobian)
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assert_equal(c.n_eq, 2)
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assert_equal(c.n_ineq, 7)
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c_eq, c_ineq = c.fun(x0)
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assert_array_equal(c_eq, [f1[3] - lb1[3], f2[1] - lb2[1]])
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assert_array_equal(c_ineq, [lb1[2] - f1[2], f1[0] - ub1[0],
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lb1[0] - f1[0], f2[3] - ub2[3],
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lb2[4] - f2[4], f2[0] - ub2[0],
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lb2[0] - f2[0]])
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J_eq, J_ineq = c.jac(x0)
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if sparse_jacobian:
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J_eq = J_eq.toarray()
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J_ineq = J_ineq.toarray()
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assert_array_equal(J_eq, np.vstack((J1[3], J2[1])))
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assert_array_equal(J_ineq, np.vstack((-J1[2], J1[0], -J1[0], J2[3],
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-J2[4], J2[0], -J2[0])))
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v_eq = rng.rand(c.n_eq)
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v_ineq = rng.rand(c.n_ineq)
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v = np.zeros(5)
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v[1] = v_eq[1]
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v[3] = v_ineq[3]
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v[4] = -v_ineq[4]
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v[0] = v_ineq[5] - v_ineq[6]
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H = c.hess(x0, v_eq, v_ineq).dot(np.eye(n))
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assert_array_equal(H, hess(x0, v))
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assert_array_equal(c.keep_feasible,
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[True, False, False, True, False, True, True])
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def test_empty():
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x = np.array([1, 2, 3])
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c = CanonicalConstraint.empty(3)
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assert_equal(c.n_eq, 0)
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assert_equal(c.n_ineq, 0)
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c_eq, c_ineq = c.fun(x)
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assert_array_equal(c_eq, [])
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assert_array_equal(c_ineq, [])
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J_eq, J_ineq = c.jac(x)
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assert_array_equal(J_eq, np.empty((0, 3)))
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assert_array_equal(J_ineq, np.empty((0, 3)))
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H = c.hess(x, None, None).toarray()
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assert_array_equal(H, np.zeros((3, 3)))
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def test_initial_constraints_as_canonical():
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# rng is only used to generate the coefficients of the quadratic
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# function that is used by the nonlinear constraint.
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rng = np.random.RandomState(0)
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x0 = np.array([0.5, 0.4, 0.3, 0.2])
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n = len(x0)
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lb1 = [-1, -np.inf, -2, 3]
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ub1 = [1, np.inf, np.inf, 3]
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bounds = Bounds(lb1, ub1, [False, False, True, False])
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fun, jac, hess = create_quadratic_function(n, 5, rng)
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lb2 = [-10, 3, -np.inf, -np.inf, -5]
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ub2 = [10, 3, np.inf, 5, np.inf]
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nonlinear = NonlinearConstraint(
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fun, lb2, ub2, jac, hess, [True, False, False, True, False])
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for sparse_jacobian in [False, True]:
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bounds_prepared = PreparedConstraint(bounds, x0, sparse_jacobian)
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nonlinear_prepared = PreparedConstraint(nonlinear, x0, sparse_jacobian)
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f1 = bounds_prepared.fun.f
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J1 = bounds_prepared.fun.J
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f2 = nonlinear_prepared.fun.f
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J2 = nonlinear_prepared.fun.J
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c_eq, c_ineq, J_eq, J_ineq = initial_constraints_as_canonical(
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n, [bounds_prepared, nonlinear_prepared], sparse_jacobian)
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assert_array_equal(c_eq, [f1[3] - lb1[3], f2[1] - lb2[1]])
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assert_array_equal(c_ineq, [lb1[2] - f1[2], f1[0] - ub1[0],
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lb1[0] - f1[0], f2[3] - ub2[3],
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lb2[4] - f2[4], f2[0] - ub2[0],
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lb2[0] - f2[0]])
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if sparse_jacobian:
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J1 = J1.toarray()
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J2 = J2.toarray()
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J_eq = J_eq.toarray()
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J_ineq = J_ineq.toarray()
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assert_array_equal(J_eq, np.vstack((J1[3], J2[1])))
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assert_array_equal(J_ineq, np.vstack((-J1[2], J1[0], -J1[0], J2[3],
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-J2[4], J2[0], -J2[0])))
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def test_initial_constraints_as_canonical_empty():
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n = 3
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for sparse_jacobian in [False, True]:
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c_eq, c_ineq, J_eq, J_ineq = initial_constraints_as_canonical(
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n, [], sparse_jacobian)
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assert_array_equal(c_eq, [])
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assert_array_equal(c_ineq, [])
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if sparse_jacobian:
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J_eq = J_eq.toarray()
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J_ineq = J_ineq.toarray()
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assert_array_equal(J_eq, np.empty((0, n)))
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assert_array_equal(J_ineq, np.empty((0, n)))
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