from dataclasses import dataclass import numpy as np import pytest import cvxpy as cp from cvxpy.atoms.quad_form import SymbolicQuadForm from cvxpy.lin_ops.canon_backend import TensorRepresentation from cvxpy.utilities.coeff_extractor import CoeffExtractor @dataclass class MockeInverseData: var_offsets: dict x_length: int var_shapes: dict param_shapes: dict param_to_size: dict param_id_map: dict @pytest.fixture def coeff_extractor(): inverset_data = MockeInverseData( var_offsets={1: 0}, x_length=2, var_shapes={1: (2,)}, param_shapes={2: (), 3: ()}, param_to_size={-1: 1, 2: 1, 3: 1}, param_id_map={2: 0, 3: 1, -1: 2}, ) backend = cp.CPP_CANON_BACKEND return CoeffExtractor(inverset_data, backend) def test_issue_2402_scalar_parameter(): """ This is the problem reported in #2402, failing to solve when two parameters are used on quadratic forms with the same variable. """ r = np.array([-0.48, 0.11, 0.09, -0.39, 0.03]) Sigma = np.array([ [2.4e-04, 1.3e-04, 2.0e-04, 1.6e-04, 2.0e-04], [1.3e-04, 2.8e-04, 2.1e-04, 1.7e-04, 1.5e-04], [2.0e-04, 2.1e-04, 5.8e-04, 3.3e-04, 2.3e-04], [1.6e-04, 1.7e-04, 3.3e-04, 6.9e-04, 2.1e-04], [2.0e-04, 1.5e-04, 2.3e-04, 2.1e-04, 3.6e-04]]) w = cp.Variable(5) risk_aversion = cp.Parameter(value=1., nonneg=True) ridge_coef = cp.Parameter(value=0., nonneg=True) obj_func = r @ w - risk_aversion * cp.quad_form(w, Sigma) - ridge_coef * cp.sum_squares(w) objective = cp.Maximize(obj_func) fixed_w = np.array([10, 11, 12, 13, 14]) constraints = [w == fixed_w] prob = cp.Problem(objective, constraints) prob.solve() expected_value = r @ fixed_w - risk_aversion.value * np.dot(fixed_w, np.dot(Sigma, fixed_w)) - \ ridge_coef.value * np.sum(np.square(fixed_w)) assert np.isclose(prob.value, expected_value) assert np.allclose(w.value, fixed_w) def test_issue_2402_scalar_constant(): """ This slight modification uses a constant instead of a parameter, which was a separate issue in the same problem. """ r = np.array([-0.48, 0.11, 0.09, -0.39, 0.03]) Sigma = np.array([ [2.4e-04, 1.3e-04, 2.0e-04, 1.6e-04, 2.0e-04], [1.3e-04, 2.8e-04, 2.1e-04, 1.7e-04, 1.5e-04], [2.0e-04, 2.1e-04, 5.8e-04, 3.3e-04, 2.3e-04], [1.6e-04, 1.7e-04, 3.3e-04, 6.9e-04, 2.1e-04], [2.0e-04, 1.5e-04, 2.3e-04, 2.1e-04, 3.6e-04]]) w = cp.Variable(5) risk_aversion = cp.Parameter(value=1., nonneg=True) ridge_coef = 0 obj_func = r @ w - risk_aversion * cp.quad_form(w, Sigma) - ridge_coef * cp.sum_squares(w) objective = cp.Maximize(obj_func) fixed_w = np.array([10, 11, 12, 13, 14]) constraints = [w == fixed_w] prob = cp.Problem(objective, constraints) prob.solve() expected_value = r @ fixed_w - risk_aversion.value * np.dot(fixed_w, np.dot(Sigma, fixed_w)) - \ ridge_coef * np.sum(np.square(fixed_w)) assert np.isclose(prob.value, expected_value) assert np.allclose(w.value, fixed_w) def test_issue_2402_vector(): """ This slight modification with the ridge_coef as a vector also failed with a different error due to a dimension mismatch. """ r = np.array([-0.48, 0.11, 0.09, -0.39, 0.03]) Sigma = np.array([ [2.4e-04, 1.3e-04, 2.0e-04, 1.6e-04, 2.0e-04], [1.3e-04, 2.8e-04, 2.1e-04, 1.7e-04, 1.5e-04], [2.0e-04, 2.1e-04, 5.8e-04, 3.3e-04, 2.3e-04], [1.6e-04, 1.7e-04, 3.3e-04, 6.9e-04, 2.1e-04], [2.0e-04, 1.5e-04, 2.3e-04, 2.1e-04, 3.6e-04] ]) w = cp.Variable(5) risk_aversion = cp.Parameter(value=2., nonneg=True) ridge_coef = cp.Parameter((5), value=np.arange(5), nonneg=True) obj_func = r @ w - risk_aversion * cp.quad_form(w, Sigma) - \ cp.sum(cp.multiply(cp.multiply(ridge_coef, np.array([5,6,7,8,9])), cp.square(w))) objective = cp.Maximize(obj_func) fixed_w = np.array([10, 11, 12, 13, 14]) constraints = [w == fixed_w] prob = cp.Problem(objective, constraints) prob.solve() expected_value = r @ fixed_w - risk_aversion.value * np.dot(fixed_w, np.dot(Sigma, fixed_w)) - \ np.sum(ridge_coef.value * np.array([5,6,7,8,9]) * np.square(fixed_w)) assert np.isclose(prob.value, expected_value) assert np.allclose(w.value, fixed_w) def test_problem_end_to_end(): """ This is a MWE / regression test for the issue reported in #2402. """ x = cp.Variable(2) p1 = cp.Parameter(value=1.0, nonneg=True) p2 = cp.Parameter(value=0.0, nonneg=True) P = np.eye(2) objective = cp.Minimize(p1 * cp.quad_form(x, P) + p2 * cp.sum_squares(x)) problem = cp.Problem(objective, constraints=[cp.sum(x) == 1]) problem.solve() assert np.isclose(problem.value, 0.5) assert np.allclose(x.value, [0.5, 0.5]) def test_coeff_extractor(coeff_extractor): """ This is a unit test for the same problem. The variable and parameter namings are derived from the problem above. """ x1 = cp.Variable(2, var_id=1) x14 = cp.Variable((1, 1), var_id=14) x16 = cp.Variable(var_id=16) p2 = cp.Parameter(value=1.0, nonneg=True, id=2) p3 = cp.Parameter(value=0.0, nonneg=True, id=3) affine_expr = p2 * x14 + p3 * x16 quad_forms = { x14.id: ( p2 * x14, 1, SymbolicQuadForm(x1, cp.Constant(np.eye(2)), cp.quad_form(x1, np.eye(2))), ), x16.id: ( p3 * x16, 1, SymbolicQuadForm(x1, cp.Constant(np.eye(2)), cp.quad_over_lin(x1, 1.0)), ), } coeffs, constant = coeff_extractor.extract_quadratic_coeffs(affine_expr, quad_forms) assert len(coeffs) == 1 assert np.allclose(coeffs[1]["q"].toarray(), np.zeros((2, 3))) P = coeffs[1]["P"] assert isinstance(P, TensorRepresentation) assert np.allclose(P.data, np.ones((4))) assert np.allclose(P.row, np.array([0, 1, 0, 1])) assert np.allclose(P.col, np.array([0, 1, 0, 1])) assert P.shape == (2, 2) assert np.allclose(P.parameter_offset, np.array([0, 0, 1, 1])) assert np.allclose(constant.toarray(), np.zeros((3))) def test_issue_2437(): """ This is a MWE / regression test for the issue reported in #2437. """ N = 3 t_cost = np.array([0.01, 0.02, 0.03]) alpha = np.array([0.04, 0.05, 0.06]) ivol = np.array([0.07, 0.08, 0.09]) w = cp.Variable(N, name="w") risk = (cp.multiply(w, ivol) ** 2).sum() U = w @ alpha - risk - cp.abs(w) @ t_cost problem = cp.Problem(cp.Maximize(U), []) assert np.isclose( problem.solve(solver=cp.CLARABEL, use_quad_obj=True), problem.solve(solver=cp.CLARABEL, use_quad_obj=False), rtol=0, atol=1e-3, )