Compute the qr factorization of a matrix. Factor the matrix `a` as *qr*, where `q` is orthonormal and `r` is upper-triangular. Parameters ---------- a : array_like, shape (..., M, N) An array-like object with the dimensionality of at least 2. mode : {'reduced',
(a, mode='reduced')
| 975 | |
| 976 | @array_function_dispatch(_qr_dispatcher) |
| 977 | def qr(a, mode='reduced'): |
| 978 | """ |
| 979 | Compute the qr factorization of a matrix. |
| 980 | |
| 981 | Factor the matrix `a` as *qr*, where `q` is orthonormal and `r` is |
| 982 | upper-triangular. |
| 983 | |
| 984 | Parameters |
| 985 | ---------- |
| 986 | a : array_like, shape (..., M, N) |
| 987 | An array-like object with the dimensionality of at least 2. |
| 988 | mode : {'reduced', 'complete', 'r', 'raw'}, optional, default: 'reduced' |
| 989 | If K = min(M, N), then |
| 990 | |
| 991 | * 'reduced' : returns Q, R with dimensions (..., M, K), (..., K, N) |
| 992 | * 'complete' : returns Q, R with dimensions (..., M, M), (..., M, N) |
| 993 | * 'r' : returns R only with dimensions (..., K, N) |
| 994 | * 'raw' : returns h, tau with dimensions (..., N, M), (..., K,) |
| 995 | |
| 996 | The options 'reduced', 'complete, and 'raw' are new in numpy 1.8, |
| 997 | see the notes for more information. The default is 'reduced', and to |
| 998 | maintain backward compatibility with earlier versions of numpy both |
| 999 | it and the old default 'full' can be omitted. Note that array h |
| 1000 | returned in 'raw' mode is transposed for calling Fortran. The |
| 1001 | 'economic' mode is deprecated. The modes 'full' and 'economic' may |
| 1002 | be passed using only the first letter for backwards compatibility, |
| 1003 | but all others must be spelled out. See the Notes for more |
| 1004 | explanation. |
| 1005 | |
| 1006 | |
| 1007 | Returns |
| 1008 | ------- |
| 1009 | Q : ndarray of float or complex, optional |
| 1010 | A matrix with orthonormal columns. When mode = 'complete' the |
| 1011 | result is an orthogonal/unitary matrix depending on whether or not |
| 1012 | a is real/complex. The determinant may be either +/- 1 in that |
| 1013 | case. In case the number of dimensions in the input array is |
| 1014 | greater than 2 then a stack of the matrices with above properties |
| 1015 | is returned. |
| 1016 | R : ndarray of float or complex, optional |
| 1017 | The upper-triangular matrix or a stack of upper-triangular |
| 1018 | matrices if the number of dimensions in the input array is greater |
| 1019 | than 2. |
| 1020 | (h, tau) : ndarrays of np.double or np.cdouble, optional |
| 1021 | The array h contains the Householder reflectors that generate q |
| 1022 | along with r. The tau array contains scaling factors for the |
| 1023 | reflectors. In the deprecated 'economic' mode only h is returned. |
| 1024 | |
| 1025 | Raises |
| 1026 | ------ |
| 1027 | LinAlgError |
| 1028 | If factoring fails. |
| 1029 | |
| 1030 | See Also |
| 1031 | -------- |
| 1032 | scipy.linalg.qr : Similar function in SciPy. |
| 1033 | scipy.linalg.rq : Compute RQ decomposition of a matrix. |
| 1034 |
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