import numpy as np from numpy.linalg import lstsq from numpy.testing import assert_allclose, assert_equal, assert_ from scipy.sparse import rand from scipy.sparse.linalg import aslinearoperator from scipy.optimize import lsq_linear A = np.array([ [0.171, -0.057], [-0.049, -0.248], [-0.166, 0.054], ]) b = np.array([0.074, 1.014, -0.383]) class BaseMixin: def setup_method(self): self.rnd = np.random.RandomState(0) def test_dense_no_bounds(self): for lsq_solver in self.lsq_solvers: res = lsq_linear(A, b, method=self.method, lsq_solver=lsq_solver) assert_allclose(res.x, lstsq(A, b, rcond=-1)[0]) def test_dense_bounds(self): # Solutions for comparison are taken from MATLAB. lb = np.array([-1, -10]) ub = np.array([1, 0]) for lsq_solver in self.lsq_solvers: res = lsq_linear(A, b, (lb, ub), method=self.method, lsq_solver=lsq_solver) assert_allclose(res.x, lstsq(A, b, rcond=-1)[0]) lb = np.array([0.0, -np.inf]) for lsq_solver in self.lsq_solvers: res = lsq_linear(A, b, (lb, np.inf), method=self.method, lsq_solver=lsq_solver) assert_allclose(res.x, np.array([0.0, -4.084174437334673]), atol=1e-6) lb = np.array([-1, 0]) for lsq_solver in self.lsq_solvers: res = lsq_linear(A, b, (lb, np.inf), method=self.method, lsq_solver=lsq_solver) assert_allclose(res.x, np.array([0.448427311733504, 0]), atol=1e-15) ub = np.array([np.inf, -5]) for lsq_solver in self.lsq_solvers: res = lsq_linear(A, b, (-np.inf, ub), method=self.method, lsq_solver=lsq_solver) assert_allclose(res.x, np.array([-0.105560998682388, -5])) ub = np.array([-1, np.inf]) for lsq_solver in self.lsq_solvers: res = lsq_linear(A, b, (-np.inf, ub), method=self.method, lsq_solver=lsq_solver) assert_allclose(res.x, np.array([-1, -4.181102129483254])) lb = np.array([0, -4]) ub = np.array([1, 0]) for lsq_solver in self.lsq_solvers: res = lsq_linear(A, b, (lb, ub), method=self.method, lsq_solver=lsq_solver) assert_allclose(res.x, np.array([0.005236663400791, -4])) def test_np_matrix(self): # gh-10711 with np.testing.suppress_warnings() as sup: sup.filter(PendingDeprecationWarning) A = np.matrix([[20, -4, 0, 2, 3], [10, -2, 1, 0, -1]]) k = np.array([20, 15]) s_t = lsq_linear(A, k) def test_dense_rank_deficient(self): A = np.array([[-0.307, -0.184]]) b = np.array([0.773]) lb = [-0.1, -0.1] ub = [0.1, 0.1] for lsq_solver in self.lsq_solvers: res = lsq_linear(A, b, (lb, ub), method=self.method, lsq_solver=lsq_solver) assert_allclose(res.x, [-0.1, -0.1]) A = np.array([ [0.334, 0.668], [-0.516, -1.032], [0.192, 0.384], ]) b = np.array([-1.436, 0.135, 0.909]) lb = [0, -1] ub = [1, -0.5] for lsq_solver in self.lsq_solvers: res = lsq_linear(A, b, (lb, ub), method=self.method, lsq_solver=lsq_solver) assert_allclose(res.optimality, 0, atol=1e-11) def test_full_result(self): lb = np.array([0, -4]) ub = np.array([1, 0]) res = lsq_linear(A, b, (lb, ub), method=self.method) assert_allclose(res.x, [0.005236663400791, -4]) r = A.dot(res.x) - b assert_allclose(res.cost, 0.5 * np.dot(r, r)) assert_allclose(res.fun, r) assert_allclose(res.optimality, 0.0, atol=1e-12) assert_equal(res.active_mask, [0, -1]) assert_(res.nit < 15) assert_(res.status == 1 or res.status == 3) assert_(isinstance(res.message, str)) assert_(res.success) # This is a test for issue #9982. def test_almost_singular(self): A = np.array( [[0.8854232310355122, 0.0365312146937765, 0.0365312146836789], [0.3742460132129041, 0.0130523214078376, 0.0130523214077873], [0.9680633871281361, 0.0319366128718639, 0.0319366128718388]]) b = np.array( [0.0055029366538097, 0.0026677442422208, 0.0066612514782381]) result = lsq_linear(A, b, method=self.method) assert_(result.cost < 1.1e-8) def test_large_rank_deficient(self): np.random.seed(0) n, m = np.sort(np.random.randint(2, 1000, size=2)) m *= 2 # make m >> n A = 1.0 * np.random.randint(-99, 99, size=[m, n]) b = 1.0 * np.random.randint(-99, 99, size=[m]) bounds = 1.0 * np.sort(np.random.randint(-99, 99, size=(2, n)), axis=0) bounds[1, :] += 1.0 # ensure up > lb # Make the A matrix strongly rank deficient by replicating some columns w = np.random.choice(n, n) # Select random columns with duplicates A = A[:, w] x_bvls = lsq_linear(A, b, bounds=bounds, method='bvls').x x_trf = lsq_linear(A, b, bounds=bounds, method='trf').x cost_bvls = np.sum((A @ x_bvls - b)**2) cost_trf = np.sum((A @ x_trf - b)**2) assert_(abs(cost_bvls - cost_trf) < cost_trf*1e-10) def test_convergence_small_matrix(self): A = np.array([[49.0, 41.0, -32.0], [-19.0, -32.0, -8.0], [-13.0, 10.0, 69.0]]) b = np.array([-41.0, -90.0, 47.0]) bounds = np.array([[31.0, -44.0, 26.0], [54.0, -32.0, 28.0]]) x_bvls = lsq_linear(A, b, bounds=bounds, method='bvls').x x_trf = lsq_linear(A, b, bounds=bounds, method='trf').x cost_bvls = np.sum((A @ x_bvls - b)**2) cost_trf = np.sum((A @ x_trf - b)**2) assert_(abs(cost_bvls - cost_trf) < cost_trf*1e-10) class SparseMixin: def test_sparse_and_LinearOperator(self): m = 5000 n = 1000 A = rand(m, n, random_state=0) b = self.rnd.randn(m) res = lsq_linear(A, b) assert_allclose(res.optimality, 0, atol=1e-6) A = aslinearoperator(A) res = lsq_linear(A, b) assert_allclose(res.optimality, 0, atol=1e-6) def test_sparse_bounds(self): m = 5000 n = 1000 A = rand(m, n, random_state=0) b = self.rnd.randn(m) lb = self.rnd.randn(n) ub = lb + 1 res = lsq_linear(A, b, (lb, ub)) assert_allclose(res.optimality, 0.0, atol=1e-6) res = lsq_linear(A, b, (lb, ub), lsmr_tol=1e-13) assert_allclose(res.optimality, 0.0, atol=1e-6) res = lsq_linear(A, b, (lb, ub), lsmr_tol='auto') assert_allclose(res.optimality, 0.0, atol=1e-6) class TestTRF(BaseMixin, SparseMixin): method = 'trf' lsq_solvers = ['exact', 'lsmr'] class TestBVLS(BaseMixin): method = 'bvls' lsq_solvers = ['exact']