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import numpy as np from numpy.linalg import norm from numpy.testing import assert_equal, assert_allclose, assert_ from scipy.sparse.linalg._isolve import minres from pytest import raises as assert_raises def get_sample_problem(): # A random 10 x 10 symmetric matrix np.random.seed(1234) matrix = np.random.rand(10, 10) matrix = matrix + matrix.T # A random vector of length 10 vector = np.random.rand(10) return matrix, vector def test_singular(): A, b = get_sample_problem() A[0, ] = 0 b[0] = 0 xp, info = minres(A, b) assert_equal(info, 0) assert norm(A @ xp - b) <= 1e-5 * norm(b) def test_x0_is_used_by(): A, b = get_sample_problem() # Random x0 to feed minres np.random.seed(12345) x0 = np.random.rand(10) trace = [] def trace_iterates(xk): trace.append(xk) minres(A, b, x0=x0, callback=trace_iterates) trace_with_x0 = trace trace = [] minres(A, b, callback=trace_iterates) assert_(not np.array_equal(trace_with_x0[0], trace[0])) def test_shift(): A, b = get_sample_problem() shift = 0.5 shifted_A = A - shift * np.eye(10) x1, info1 = minres(A, b, shift=shift) x2, info2 = minres(shifted_A, b) assert_equal(info1, 0) assert_allclose(x1, x2, rtol=1e-5) def test_asymmetric_fail(): """Asymmetric matrix should raise `ValueError` when check=True""" A, b = get_sample_problem() A[1, 2] = 1 A[2, 1] = 2 with assert_raises(ValueError): xp, info = minres(A, b, check=True) def test_minres_non_default_x0(): np.random.seed(1234) rtol = 1e-6 a = np.random.randn(5, 5) a = np.dot(a, a.T) b = np.random.randn(5) c = np.random.randn(5) x = minres(a, b, x0=c, rtol=rtol)[0] assert norm(a @ x - b) <= rtol * norm(b) def test_minres_precond_non_default_x0(): np.random.seed(12345) rtol = 1e-6 a = np.random.randn(5, 5) a = np.dot(a, a.T) b = np.random.randn(5) c = np.random.randn(5) m = np.random.randn(5, 5) m = np.dot(m, m.T) x = minres(a, b, M=m, x0=c, rtol=rtol)[0] assert norm(a @ x - b) <= rtol * norm(b) def test_minres_precond_exact_x0(): np.random.seed(1234) rtol = 1e-6 a = np.eye(10) b = np.ones(10) c = np.ones(10) m = np.random.randn(10, 10) m = np.dot(m, m.T) x = minres(a, b, M=m, x0=c, rtol=rtol)[0] assert norm(a @ x - b) <= rtol * norm(b)
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