from __future__ import division, print_function, absolute_import import warnings import threading import numpy as np from numpy import array, finfo, arange, eye, all, unique, ones, dot, matrix import numpy.random as random from numpy.testing import (TestCase, run_module_suite, assert_array_almost_equal, assert_raises, assert_almost_equal, assert_equal, assert_array_equal, assert_, assert_allclose) import scipy.linalg from scipy.linalg import norm, inv from scipy.sparse import (spdiags, SparseEfficiencyWarning, csc_matrix, csr_matrix, isspmatrix, dok_matrix, lil_matrix, bsr_matrix) from scipy.sparse.linalg.dsolve import (spsolve, use_solver, splu, spilu, MatrixRankWarning, _superlu) warnings.simplefilter('ignore',SparseEfficiencyWarning) # TODO add more comprehensive tests use_solver(useUmfpack=False) def toarray(a): if isspmatrix(a): return a.toarray() else: return a class TestLinsolve(TestCase): def test_singular(self): with warnings.catch_warnings(): warnings.simplefilter("ignore", category=MatrixRankWarning) A = csc_matrix((5,5), dtype='d') b = array([1, 2, 3, 4, 5],dtype='d') x = spsolve(A, b, use_umfpack=False) assert_(not np.isfinite(x).any()) def test_singular_gh_3312(self): # "Bad" test case that leads SuperLU to call LAPACK with invalid # arguments. Check that it fails moderately gracefully. ij = np.array([(17, 0), (17, 6), (17, 12), (10, 13)], dtype=np.int32) v = np.array([0.284213, 0.94933781, 0.15767017, 0.38797296]) A = csc_matrix((v, ij.T), shape=(20, 20)) b = np.arange(20) with warnings.catch_warnings(): try: # should either raise a runtimeerror or return value # appropriate for singular input x = spsolve(A, b, use_umfpack=False) assert_(not np.isfinite(x).any()) except RuntimeError: pass def test_twodiags(self): A = spdiags([[1, 2, 3, 4, 5], [6, 5, 8, 9, 10]], [0, 1], 5, 5) b = array([1, 2, 3, 4, 5]) # condition number of A cond_A = norm(A.todense(),2) * norm(inv(A.todense()),2) for t in ['f','d','F','D']: eps = finfo(t).eps # floating point epsilon b = b.astype(t) for format in ['csc','csr']: Asp = A.astype(t).asformat(format) x = spsolve(Asp,b) assert_(norm(b - Asp*x) < 10 * cond_A * eps) def test_bvector_smoketest(self): Adense = matrix([[0., 1., 1.], [1., 0., 1.], [0., 0., 1.]]) As = csc_matrix(Adense) random.seed(1234) x = random.randn(3) b = As*x x2 = spsolve(As, b) assert_array_almost_equal(x, x2) def test_bmatrix_smoketest(self): Adense = matrix([[0., 1., 1.], [1., 0., 1.], [0., 0., 1.]]) As = csc_matrix(Adense) random.seed(1234) x = random.randn(3, 4) Bdense = As.dot(x) Bs = csc_matrix(Bdense) x2 = spsolve(As, Bs) assert_array_almost_equal(x, x2.todense()) def test_non_square(self): with warnings.catch_warnings(): warnings.simplefilter("ignore", category=SparseEfficiencyWarning) # A is not square. A = ones((3, 4)) b = ones((4, 1)) assert_raises(ValueError, spsolve, A, b) # A2 and b2 have incompatible shapes. A2 = csc_matrix(eye(3)) b2 = array([1.0, 2.0]) assert_raises(ValueError, spsolve, A2, b2) def test_example_comparison(self): with warnings.catch_warnings(): warnings.simplefilter("ignore", category=SparseEfficiencyWarning) row = array([0,0,1,2,2,2]) col = array([0,2,2,0,1,2]) data = array([1,2,3,-4,5,6]) sM = csr_matrix((data,(row,col)), shape=(3,3), dtype=float) M = sM.todense() row = array([0,0,1,1,0,0]) col = array([0,2,1,1,0,0]) data = array([1,1,1,1,1,1]) sN = csr_matrix((data, (row,col)), shape=(3,3), dtype=float) N = sN.todense() sX = spsolve(sM, sN) X = scipy.linalg.solve(M, N) assert_array_almost_equal(X, sX.todense()) def test_shape_compatibility(self): A = csc_matrix([[1., 0], [0, 2]]) bs = [ [1, 6], array([1, 6]), [[1], [6]], array([[1], [6]]), csc_matrix([[1], [6]]), csr_matrix([[1], [6]]), dok_matrix([[1], [6]]), bsr_matrix([[1], [6]]), array([[1., 2., 3.], [6., 8., 10.]]), csc_matrix([[1., 2., 3.], [6., 8., 10.]]), csr_matrix([[1., 2., 3.], [6., 8., 10.]]), dok_matrix([[1., 2., 3.], [6., 8., 10.]]), bsr_matrix([[1., 2., 3.], [6., 8., 10.]]), ] for b in bs: x = np.linalg.solve(A.toarray(), toarray(b)) for spmattype in [csc_matrix, csr_matrix, dok_matrix, lil_matrix]: x1 = spsolve(spmattype(A), b, use_umfpack=True) x2 = spsolve(spmattype(A), b, use_umfpack=False) # check solution if x.ndim == 2 and x.shape[1] == 1: # interprets also these as "vectors" x = x.ravel() assert_array_almost_equal(toarray(x1), x, err_msg=repr((b, spmattype, 1))) assert_array_almost_equal(toarray(x2), x, err_msg=repr((b, spmattype, 2))) # dense vs. sparse output ("vectors" are always dense) if isspmatrix(b) and x.ndim > 1: assert_(isspmatrix(x1), repr((b, spmattype, 1))) assert_(isspmatrix(x2), repr((b, spmattype, 2))) else: assert_(isinstance(x1, np.ndarray), repr((b, spmattype, 1))) assert_(isinstance(x2, np.ndarray), repr((b, spmattype, 2))) # check output shape if x.ndim == 1: # "vector" assert_equal(x1.shape, (A.shape[1],)) assert_equal(x2.shape, (A.shape[1],)) else: # "matrix" assert_equal(x1.shape, x.shape) assert_equal(x2.shape, x.shape) A = csc_matrix((3, 3)) b = csc_matrix((1, 3)) assert_raises(ValueError, spsolve, A, b) def test_ndarray_support(self): A = array([[1., 2.], [2., 0.]]) x = array([[1., 1.], [0.5, -0.5]]) b = array([[2., 0.], [2., 2.]]) assert_array_almost_equal(x, spsolve(A, b)) def test_gssv_badinput(self): N = 10 d = arange(N) + 1.0 A = spdiags((d, 2*d, d[::-1]), (-3, 0, 5), N, N) for spmatrix in (csc_matrix, csr_matrix): A = spmatrix(A) b = np.arange(N) def not_c_contig(x): return x.repeat(2)[::2] def not_1dim(x): return x[:,None] def bad_type(x): return x.astype(bool) def too_short(x): return x[:-1] badops = [not_c_contig, not_1dim, bad_type, too_short] for badop in badops: msg = "%r %r" % (spmatrix, badop) # Not C-contiguous assert_raises((ValueError, TypeError), _superlu.gssv, N, A.nnz, badop(A.data), A.indices, A.indptr, b, int(spmatrix == csc_matrix), err_msg=msg) assert_raises((ValueError, TypeError), _superlu.gssv, N, A.nnz, A.data, badop(A.indices), A.indptr, b, int(spmatrix == csc_matrix), err_msg=msg) assert_raises((ValueError, TypeError), _superlu.gssv, N, A.nnz, A.data, A.indices, badop(A.indptr), b, int(spmatrix == csc_matrix), err_msg=msg) def test_sparsity_preservation(self): ident = csc_matrix([ [1, 0, 0], [0, 1, 0], [0, 0, 1]]) b = csc_matrix([ [0, 1], [1, 0], [0, 0]]) x = spsolve(ident, b) assert_equal(ident.nnz, 3) assert_equal(b.nnz, 2) assert_equal(x.nnz, 2) assert_allclose(x.A, b.A, atol=1e-12, rtol=1e-12) class TestSplu(object): def setUp(self): n = 40 d = arange(n) + 1 self.n = n self.A = spdiags((d, 2*d, d[::-1]), (-3, 0, 5), n, n) random.seed(1234) def _smoketest(self, spxlu, check, dtype): if np.issubdtype(dtype, np.complexfloating): A = self.A + 1j*self.A.T else: A = self.A A = A.astype(dtype) lu = spxlu(A) rng = random.RandomState(1234) # Input shapes for k in [None, 1, 2, self.n, self.n+2]: msg = "k=%r" % (k,) if k is None: b = rng.rand(self.n) else: b = rng.rand(self.n, k) if np.issubdtype(dtype, np.complexfloating): b = b + 1j*rng.rand(*b.shape) b = b.astype(dtype) x = lu.solve(b) check(A, b, x, msg) x = lu.solve(b, 'T') check(A.T, b, x, msg) x = lu.solve(b, 'H') check(A.T.conj(), b, x, msg) def test_splu_smoketest(self): # Check that splu works at all with warnings.catch_warnings(): warnings.simplefilter("ignore", category=SparseEfficiencyWarning) def check(A, b, x, msg=""): eps = np.finfo(A.dtype).eps r = A * x assert_(abs(r - b).max() < 1e3*eps, msg) self._smoketest(splu, check, np.float32) self._smoketest(splu, check, np.float64) self._smoketest(splu, check, np.complex64) self._smoketest(splu, check, np.complex128) def test_spilu_smoketest(self): with warnings.catch_warnings(): warnings.simplefilter("ignore", category=SparseEfficiencyWarning) errors = [] def check(A, b, x, msg=""): r = A * x err = abs(r - b).max() assert_(err < 1e-2, msg) if b.dtype in (np.float64, np.complex128): errors.append(err) self._smoketest(spilu, check, np.float32) self._smoketest(spilu, check, np.float64) self._smoketest(spilu, check, np.complex64) self._smoketest(spilu, check, np.complex128) assert_(max(errors) > 1e-5) def test_splu_nnz0(self): A = csc_matrix((5,5), dtype='d') assert_raises(RuntimeError, splu, A) def test_spilu_nnz0(self): A = csc_matrix((5,5), dtype='d') assert_raises(RuntimeError, spilu, A) def test_splu_basic(self): # Test basic splu functionality. n = 30 rng = random.RandomState(12) a = rng.rand(n, n) a[a < 0.95] = 0 # First test with a singular matrix a[:, 0] = 0 a_ = csc_matrix(a) # Matrix is exactly singular assert_raises(RuntimeError, splu, a_) # Make a diagonal dominant, to make sure it is not singular a += 4*eye(n) a_ = csc_matrix(a) lu = splu(a_) b = ones(n) x = lu.solve(b) assert_almost_equal(dot(a, x), b) def test_splu_perm(self): # Test the permutation vectors exposed by splu. n = 30 a = random.random((n, n)) a[a < 0.95] = 0 # Make a diagonal dominant, to make sure it is not singular a += 4*eye(n) a_ = csc_matrix(a) lu = splu(a_) # Check that the permutation indices do belong to [0, n-1]. for perm in (lu.perm_r, lu.perm_c): assert_(all(perm > -1)) assert_(all(perm < n)) assert_equal(len(unique(perm)), len(perm)) # Now make a symmetric, and test that the two permutation vectors are # the same # Note: a += a.T relies on undefined behavior. a = a + a.T a_ = csc_matrix(a) lu = splu(a_) assert_array_equal(lu.perm_r, lu.perm_c) def test_lu_refcount(self): # Test that we are keeping track of the reference count with splu. n = 30 a = random.random((n, n)) a[a < 0.95] = 0 # Make a diagonal dominant, to make sure it is not singular a += 4*eye(n) a_ = csc_matrix(a) lu = splu(a_) # And now test that we don't have a refcount bug import sys rc = sys.getrefcount(lu) for attr in ('perm_r', 'perm_c'): perm = getattr(lu, attr) assert_equal(sys.getrefcount(lu), rc + 1) del perm assert_equal(sys.getrefcount(lu), rc) def test_bad_inputs(self): A = self.A.tocsc() assert_raises(ValueError, splu, A[:,:4]) assert_raises(ValueError, spilu, A[:,:4]) for lu in [splu(A), spilu(A)]: b = random.rand(42) B = random.rand(42, 3) BB = random.rand(self.n, 3, 9) assert_raises(ValueError, lu.solve, b) assert_raises(ValueError, lu.solve, B) assert_raises(ValueError, lu.solve, BB) assert_raises(TypeError, lu.solve, b.astype(np.complex64)) assert_raises(TypeError, lu.solve, b.astype(np.complex128)) def test_superlu_dlamch_i386_nan(self): # SuperLU 4.3 calls some functions returning floats without # declaring them. On i386@linux call convention, this fails to # clear floating point registers after call. As a result, NaN # can appear in the next floating point operation made. # # Here's a test case that triggered the issue. n = 8 d = np.arange(n) + 1 A = spdiags((d, 2*d, d[::-1]), (-3, 0, 5), n, n) A = A.astype(np.float32) spilu(A) A = A + 1j*A B = A.A assert_(not np.isnan(B).any()) def test_lu_attr(self): def check(dtype, complex_2=False): A = self.A.astype(dtype) if complex_2: A = A + 1j*A.T n = A.shape[0] lu = splu(A) # Check that the decomposition is as advertized Pc = np.zeros((n, n)) Pc[np.arange(n), lu.perm_c] = 1 Pr = np.zeros((n, n)) Pr[lu.perm_r, np.arange(n)] = 1 Ad = A.toarray() lhs = Pr.dot(Ad).dot(Pc) rhs = (lu.L * lu.U).toarray() eps = np.finfo(dtype).eps assert_allclose(lhs, rhs, atol=100*eps) check(np.float32) check(np.float64) check(np.complex64) check(np.complex128) check(np.complex64, True) check(np.complex128, True) def test_threads_parallel(self): oks = [] def worker(): try: self.test_splu_basic() self.test_splu_smoketest() self.test_spilu_smoketest() oks.append(True) except: pass threads = [threading.Thread(target=worker) for k in range(20)] for t in threads: t.start() for t in threads: t.join() assert_equal(len(oks), 20) if __name__ == "__main__": run_module_suite()