diff options
Diffstat (limited to 'numpy/linalg/linalg.py')
| -rw-r--r-- | numpy/linalg/linalg.py | 49 |
1 files changed, 27 insertions, 22 deletions
diff --git a/numpy/linalg/linalg.py b/numpy/linalg/linalg.py index 98af0733b..c3b76ada7 100644 --- a/numpy/linalg/linalg.py +++ b/numpy/linalg/linalg.py @@ -780,7 +780,7 @@ def qr(a, mode='reduced'): dorgqr, and zungqr. For more information on the qr factorization, see for example: - http://en.wikipedia.org/wiki/QR_factorization + https://en.wikipedia.org/wiki/QR_factorization Subclasses of `ndarray` are preserved except for the 'raw' mode. So if `a` is of type `matrix`, all the return values will be matrices too. @@ -858,13 +858,13 @@ def qr(a, mode='reduced'): a, wrap = _makearray(a) _assertRank2(a) - _assertNoEmpty2d(a) m, n = a.shape t, result_t = _commonType(a) a = _fastCopyAndTranspose(t, a) a = _to_native_byte_order(a) mn = min(m, n) tau = zeros((mn,), t) + if isComplexType(t): lapack_routine = lapack_lite.zgeqrf routine_name = 'zgeqrf' @@ -875,14 +875,14 @@ def qr(a, mode='reduced'): # calculate optimal size of work data 'work' lwork = 1 work = zeros((lwork,), t) - results = lapack_routine(m, n, a, m, tau, work, -1, 0) + results = lapack_routine(m, n, a, max(1, m), tau, work, -1, 0) if results['info'] != 0: raise LinAlgError('%s returns %d' % (routine_name, results['info'])) # do qr decomposition - lwork = int(abs(work[0])) + lwork = max(1, n, int(abs(work[0]))) work = zeros((lwork,), t) - results = lapack_routine(m, n, a, m, tau, work, lwork, 0) + results = lapack_routine(m, n, a, max(1, m), tau, work, lwork, 0) if results['info'] != 0: raise LinAlgError('%s returns %d' % (routine_name, results['info'])) @@ -918,14 +918,14 @@ def qr(a, mode='reduced'): # determine optimal lwork lwork = 1 work = zeros((lwork,), t) - results = lapack_routine(m, mc, mn, q, m, tau, work, -1, 0) + results = lapack_routine(m, mc, mn, q, max(1, m), tau, work, -1, 0) if results['info'] != 0: raise LinAlgError('%s returns %d' % (routine_name, results['info'])) # compute q - lwork = int(abs(work[0])) + lwork = max(1, n, int(abs(work[0]))) work = zeros((lwork,), t) - results = lapack_routine(m, mc, mn, q, m, tau, work, lwork, 0) + results = lapack_routine(m, mc, mn, q, max(1, m), tau, work, lwork, 0) if results['info'] != 0: raise LinAlgError('%s returns %d' % (routine_name, results['info'])) @@ -965,8 +965,10 @@ def eigvals(a): See Also -------- eig : eigenvalues and right eigenvectors of general arrays - eigvalsh : eigenvalues of symmetric or Hermitian arrays. - eigh : eigenvalues and eigenvectors of symmetric/Hermitian arrays. + eigvalsh : eigenvalues of real symmetric or complex Hermitian + (conjugate symmetric) arrays. + eigh : eigenvalues and eigenvectors of real symmetric or complex + Hermitian (conjugate symmetric) arrays. Notes ----- @@ -1027,7 +1029,7 @@ def eigvals(a): def eigvalsh(a, UPLO='L'): """ - Compute the eigenvalues of a Hermitian or real symmetric matrix. + Compute the eigenvalues of a complex Hermitian or real symmetric matrix. Main difference from eigh: the eigenvectors are not computed. @@ -1057,7 +1059,8 @@ def eigvalsh(a, UPLO='L'): See Also -------- - eigh : eigenvalues and eigenvectors of symmetric/Hermitian arrays. + eigh : eigenvalues and eigenvectors of real symmetric or complex Hermitian + (conjugate symmetric) arrays. eigvals : eigenvalues of general real or complex arrays. eig : eigenvalues and right eigenvectors of general real or complex arrays. @@ -1159,11 +1162,11 @@ def eig(a): -------- eigvals : eigenvalues of a non-symmetric array. - eigh : eigenvalues and eigenvectors of a symmetric or Hermitian - (conjugate symmetric) array. + eigh : eigenvalues and eigenvectors of a real symmetric or complex + Hermitian (conjugate symmetric) array. - eigvalsh : eigenvalues of a symmetric or Hermitian (conjugate symmetric) - array. + eigvalsh : eigenvalues of a real symmetric or complex Hermitian + (conjugate symmetric) array. Notes ----- @@ -1268,7 +1271,8 @@ def eig(a): def eigh(a, UPLO='L'): """ - Return the eigenvalues and eigenvectors of a Hermitian or symmetric matrix. + Return the eigenvalues and eigenvectors of a complex Hermitian + (conjugate symmetric) or a real symmetric matrix. Returns two objects, a 1-D array containing the eigenvalues of `a`, and a 2-D square array or matrix (depending on the input type) of the @@ -1277,7 +1281,7 @@ def eigh(a, UPLO='L'): Parameters ---------- a : (..., M, M) array - Hermitian/Symmetric matrices whose eigenvalues and + Hermitian or real symmetric matrices whose eigenvalues and eigenvectors are to be computed. UPLO : {'L', 'U'}, optional Specifies whether the calculation is done with the lower triangular @@ -1304,7 +1308,8 @@ def eigh(a, UPLO='L'): See Also -------- - eigvalsh : eigenvalues of symmetric or Hermitian arrays. + eigvalsh : eigenvalues of real symmetric or complex Hermitian + (conjugate symmetric) arrays. eig : eigenvalues and right eigenvectors for non-symmetric arrays. eigvals : eigenvalues of non-symmetric arrays. @@ -1527,7 +1532,6 @@ def svd(a, full_matrices=True, compute_uv=True): """ a, wrap = _makearray(a) - _assertNoEmpty2d(a) _assertRankAtLeast2(a) t, result_t = _commonType(a) @@ -1644,6 +1648,7 @@ def cond(x, p=None): """ x = asarray(x) # in case we have a matrix + _assertNoEmpty2d(x) if p is None or p == 2 or p == -2: s = svd(x, compute_uv=False) with errstate(all='ignore'): @@ -1750,7 +1755,7 @@ def matrix_rank(M, tol=None, hermitian=False): References ---------- .. [1] MATLAB reference documention, "Rank" - http://www.mathworks.com/help/techdoc/ref/rank.html + https://www.mathworks.com/help/techdoc/ref/rank.html .. [2] W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, "Numerical Recipes (3rd edition)", Cambridge University Press, 2007, page 795. @@ -2468,7 +2473,7 @@ def multi_dot(arrays): ---------- .. [1] Cormen, "Introduction to Algorithms", Chapter 15.2, p. 370-378 - .. [2] http://en.wikipedia.org/wiki/Matrix_chain_multiplication + .. [2] https://en.wikipedia.org/wiki/Matrix_chain_multiplication Examples -------- |