""" Copyright 2019, the cvxpy developers. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. """ import numpy as np import cvxpy as cp from cvxpy.error import SolverError from cvxpy.tests.base_test import BaseTest class TestSupportFunctions(BaseTest): """ Test the implementation of support function atoms. Relevant source code includes: cvxpy.atoms.suppfunc cvxpy.transforms.suppfunc cvxpy.reductions.dcp2cone.canonicalizers.suppfunc_canon """ def test_Rn(self) -> None: np.random.seed(0) n = 5 x = cp.Variable(shape=(n,)) sigma = cp.suppfunc(x, []) a = np.random.randn(n,) y = cp.Variable(shape=(n,)) cons = [sigma(y - a) <= 0] # "<= num" for any num >= 0 is valid. objective = cp.Minimize(a @ y) prob = cp.Problem(objective, cons) prob.solve(solver='CLARABEL') actual = prob.value expected = np.dot(a, a) self.assertLessEqual(abs(actual - expected), 1e-6) actual = y.value expected = a self.assertLessEqual(np.linalg.norm(actual - expected, ord=2), 1e-6) viol = cons[0].violation() self.assertLessEqual(viol, 1e-8) def test_vector1norm(self) -> None: n = 3 np.random.seed(1) a = np.random.randn(n,) x = cp.Variable(shape=(n,)) sigma = cp.suppfunc(x, [cp.norm(x - a, 1) <= 1]) y = np.random.randn(n,) y_var = cp.Variable(shape=(n,)) prob = cp.Problem(cp.Minimize(sigma(y_var)), [y == y_var]) prob.solve(solver='CLARABEL') actual = prob.value expected = a @ y + np.linalg.norm(y, ord=np.inf) self.assertLessEqual(abs(actual - expected), 1e-5) self.assertLessEqual(abs(prob.objective.expr.value - prob.value), 1e-5) def test_vector2norm(self) -> None: n = 3 np.random.seed(1) a = np.random.randn(n,) x = cp.Variable(shape=(n,)) sigma = cp.suppfunc(x, [cp.norm(x - a, 2) <= 1]) y = np.random.randn(n,) y_var = cp.Variable(shape=(n,)) prob = cp.Problem(cp.Minimize(sigma(y_var)), [y == y_var]) prob.solve(solver='CLARABEL') actual = prob.value expected = a @ y + np.linalg.norm(y, ord=2) self.assertLessEqual(abs(actual - expected), 1e-6) self.assertLessEqual(abs(prob.objective.expr.value - prob.value), 1e-6) def test_rectangular_variable(self) -> None: np.random.seed(2) rows, cols = 4, 2 a = np.random.randn(rows, cols) x = cp.Variable(shape=(rows, cols)) sigma = cp.suppfunc(x, [x[:, 0] == 0]) y = cp.Variable(shape=(rows, cols)) cons = [sigma(y - a) <= 0] objective = cp.Minimize(cp.sum_squares(y.flatten(order='F'))) prob = cp.Problem(objective, cons) prob.solve(solver='CLARABEL') expect = np.hstack([np.zeros(shape=(rows, 1)), a[:, [1]]]) actual = y.value self.assertLessEqual(np.linalg.norm(actual - expect, ord=2), 1e-6) viol = cons[0].violation() self.assertLessEqual(viol, 1e-6) def test_psd_dualcone(self) -> None: np.random.seed(5) n = 3 X = cp.Variable(shape=(n, n)) sigma = cp.suppfunc(X, [X >> 0]) A = np.random.randn(n, n) Y = cp.Variable(shape=(n, n)) objective = cp.Minimize(cp.norm(A.ravel(order='F') + Y.flatten(order='F'))) cons = [sigma(Y) <= 0] # Y is negative definite. prob = cp.Problem(objective, cons) prob.solve(solver='SCS', eps=1e-8) viol = cons[0].violation() self.assertLessEqual(viol, 1e-6) eigs = np.linalg.eigh(Y.value)[0] self.assertLessEqual(np.max(eigs), 1e-6) def test_largest_singvalue(self) -> None: np.random.seed(3) rows, cols = 3, 4 A = np.random.randn(rows, cols) A_sv = np.linalg.svd(A, compute_uv=False) X = cp.Variable(shape=(rows, cols)) sigma = cp.suppfunc(X, [cp.sigma_max(X) <= 1]) Y = cp.Variable(shape=(rows, cols)) cons = [Y == A] prob = cp.Problem(cp.Minimize(sigma(Y)), cons) prob.solve(solver='SCS', eps=1e-8) actual = prob.value expect = np.sum(A_sv) self.assertLessEqual(abs(actual - expect), 1e-6) def test_expcone_1(self) -> None: x = cp.Variable(shape=(1,)) tempcons = [cp.exp(x[0]) <= np.exp(1), cp.exp(-x[0]) <= np.exp(1)] sigma = cp.suppfunc(x, tempcons) y = cp.Variable(shape=(1,)) obj_expr = y[0] cons = [sigma(y) <= 1] # ^ That just means -1 <= y[0] <= 1 prob = cp.Problem(cp.Minimize(obj_expr), cons) prob.solve(solver='CLARABEL') viol = cons[0].violation() self.assertLessEqual(viol, 1e-6) self.assertLessEqual(abs(y.value - (-1)), 1e-6) def test_expcone_2(self) -> None: x = cp.Variable(shape=(3,)) tempcons = [cp.sum(x) <= 1.0, cp.sum(x) >= 0.1, x >= 0.01, cp.kl_div(x[1], x[0]) + x[1] - x[0] + x[2] <= 0] sigma = cp.suppfunc(x, tempcons) y = cp.Variable(shape=(3,)) a = np.array([-3, -2, -1]) # this is negative of objective in mosek_conif.py example expr = -sigma(y) objective = cp.Maximize(expr) cons = [y == a] prob = cp.Problem(objective, cons) prob.solve(solver='CLARABEL') # Check for expected objective value epi_actual = prob.value direct_actual = expr.value expect = 0.235348211 self.assertLessEqual(abs(epi_actual - expect), 1e-6) self.assertLessEqual(abs(direct_actual - expect), 1e-6) def test_basic_lmi(self) -> None: np.random.seed(4) n = 3 A = np.random.randn(n, n) A = A.T @ A X = cp.Variable(shape=(n, n)) # will fail if you try PSD=True, or symmetric=Trues sigma = cp.suppfunc(X, [0 << X, cp.lambda_max(X) <= 1]) Y = cp.Variable(shape=(n, n)) cons = [Y == A] expr = sigma(Y) prob = cp.Problem(cp.Minimize(expr), cons) # opt value of support func would be at X=I. prob.solve(solver='SCS', eps=1e-8) actual1 = prob.value # computed with epigraph actual2 = expr.value # computed by evaluating support function, as a maximization problem. self.assertLessEqual(abs(actual1 - actual2), 1e-6) expect = np.trace(A) self.assertLessEqual(abs(actual1 - expect), 1e-4) def test_invalid_solver(self) -> None: n = 3 x = cp.Variable(shape=(n,)) sigma = cp.suppfunc(x, [cp.norm(x - np.random.randn(n,), 2) <= 1]) y_var = cp.Variable(shape=(n,)) prob = cp.Problem(cp.Minimize(sigma(y_var)), [np.random.randn(n,) == y_var]) with self.assertRaisesRegex( SolverError, ".*could not be reduced to a QP.*"): prob.solve(solver='OSQP') def test_invalid_variable(self) -> None: x = cp.Variable(shape=(2, 2), symmetric=True) with self.assertRaises(ValueError): cp.suppfunc(x, []) def test_invalid_constraint(self) -> None: x = cp.Variable(shape=(3,)) a = cp.Parameter(shape=(3,)) cons = [a @ x == 1] with self.assertRaises(ValueError): cp.suppfunc(x, cons)