Add parameter derivative tests for NLP diff engine

Test scalar, vector, dense matrix, and sparse matrix parameter
multiplication with derivative checking and parameter value updates.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

Author: Transurgeon

cvxpy/tests/nlp_tests/stress_tests_diff_engine/test_parameters.py

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+
+import numpy as np
+import pytest
+from scipy import sparse
+
+import cvxpy as cp
+from cvxpy.reductions.solvers.defines import INSTALLED_SOLVERS
+from cvxpy.reductions.solvers.nlp_solvers.nlp_solver import DerivativeChecker
+
+
+@pytest.mark.skipif('IPOPT' not in INSTALLED_SOLVERS, reason='IPOPT is not installed.')
+class TestParametersDiffEngine:
+
+    def test_scalar_param_multiply(self):
+        np.random.seed(0)
+        n = 5
+        a = cp.Parameter(nonneg=True)
+        a.value = 2.0
+        x = cp.Variable(n, bounds=[0.5, 2])
+        prob = cp.Problem(cp.Minimize(cp.sum(cp.exp(a * x))))
+        prob.solve(solver=cp.IPOPT, nlp=True, verbose=False)
+        DerivativeChecker(prob).run_and_assert()
+
+        a.value = 3.5
+        prob.solve(solver=cp.IPOPT, nlp=True, verbose=False)
+        DerivativeChecker(prob).run_and_assert()
+
+    def test_vector_param_multiply(self):
+        np.random.seed(0)
+        n = 5
+        a = cp.Parameter(n, nonneg=True)
+        a.value = np.random.rand(n) + 0.1
+        x = cp.Variable(n, bounds=[0.5, 2])
+        prob = cp.Problem(cp.Minimize(cp.sum(cp.exp(cp.multiply(a, x)))))
+        prob.solve(solver=cp.IPOPT, nlp=True, verbose=False)
+        DerivativeChecker(prob).run_and_assert()
+
+        a.value = np.random.rand(n) + 0.5
+        prob.solve(solver=cp.IPOPT, nlp=True, verbose=False)
+        DerivativeChecker(prob).run_and_assert()
+
+    def test_dense_param_matmul(self):
+        np.random.seed(0)
+        n = 5
+        P = cp.Parameter((n, n))
+        P.value = np.random.rand(n, n)
+        x = cp.Variable(n, bounds=[0.5, 2])
+        prob = cp.Problem(cp.Minimize(cp.sum(cp.exp(P @ x))))
+        prob.solve(solver=cp.IPOPT, nlp=True, verbose=False)
+        DerivativeChecker(prob).run_and_assert()
+
+        P.value = np.random.rand(n, n) * 2
+        prob.solve(solver=cp.IPOPT, nlp=True, verbose=False)
+        DerivativeChecker(prob).run_and_assert()
+
+    def test_sparse_param_matmul(self):
+        np.random.seed(0)
+        n = 6
+        mask = np.random.rand(n, n) > 0.6
+        rows, cols = np.where(mask)
+        P = cp.Parameter((n, n), sparsity=(rows, cols))
+        P.value_sparse = sparse.coo_array(
+            (np.random.rand(len(rows)), (rows, cols)), shape=(n, n))
+        x = cp.Variable(n, bounds=[0.5, 2])
+        prob = cp.Problem(cp.Minimize(cp.sum(cp.exp(P @ x))))
+        prob.solve(solver=cp.IPOPT, nlp=True, verbose=False)
+        DerivativeChecker(prob).run_and_assert()
+
+        P.value_sparse = sparse.coo_array(
+            (np.random.rand(len(rows)) * 2, (rows, cols)), shape=(n, n))
+        prob.solve(solver=cp.IPOPT, nlp=True, verbose=False)
+        DerivativeChecker(prob).run_and_assert()