naginterfaces.library.lapackeig.dggsvp¶
- naginterfaces.library.lapackeig.dggsvp(jobu, jobv, jobq, a, b, tola, tolb)[source]¶
dggsvp
uses orthogonal transformations to simultaneously reduce the matrix and the matrix to upper triangular form. This factorization is usually used as a preprocessing step for computing the generalized singular value decomposition (GSVD).dggsvp
is marked as deprecated by LAPACK; the replacement routine isdggsvp3()
which makes better use of Level 3 BLAS.Deprecated since version 27.0.0.0:
dggsvp
is deprecated. Please usedggsvp3()
instead. See also the Replacement Calls document.For full information please refer to the NAG Library document for f08ve
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f08/f08vef.html
- Parameters
- jobustr, length 1
If , the orthogonal matrix is computed.
If , is not computed.
- jobvstr, length 1
If , the orthogonal matrix is computed.
If , is not computed.
- jobqstr, length 1
If , the orthogonal matrix is computed.
If , is not computed.
- afloat, array-like, shape
The matrix .
- bfloat, array-like, shape
The matrix .
- tolafloat
and are the thresholds to determine the effective numerical rank of matrix and a subblock of . Generally, they are set to
where is the machine precision.
The size of and may affect the size of backward errors of the decomposition.
- tolbfloat
and are the thresholds to determine the effective numerical rank of matrix and a subblock of . Generally, they are set to
where is the machine precision.
The size of and may affect the size of backward errors of the decomposition.
- Returns
- afloat, ndarray, shape
Contains the triangular (or trapezoidal) matrix described in Notes.
- bfloat, ndarray, shape
Contains the triangular matrix described in Notes.
- kint
and specify the dimension of the subblocks and as described in Notes; is the effective numerical rank of .
- lint
and specify the dimension of the subblocks and as described in Notes; is the effective numerical rank of .
- ufloat, ndarray, shape
If , contains the orthogonal matrix .
If , is not referenced.
- vfloat, ndarray, shape
If , contains the orthogonal matrix .
If , is not referenced.
- qfloat, ndarray, shape
If , contains the orthogonal matrix .
If , is not referenced.
- Raises
- NagValueError
- (errno )
On entry, error in parameter .
Constraint: or .
- (errno )
On entry, error in parameter .
Constraint: or .
- (errno )
On entry, error in parameter .
Constraint: or .
- (errno )
On entry, error in parameter .
Constraint: .
- (errno )
On entry, error in parameter .
Constraint: .
- (errno )
On entry, error in parameter .
Constraint: .
- Notes
dggsvp
computes orthogonal matrices , and such thatwhere the matrix and matrix are nonsingular upper triangular; is upper triangular if and is upper trapezoidal otherwise. is the effective numerical rank of the matrix .
This decomposition is usually used as the preprocessing step for computing the Generalized Singular Value Decomposition (GSVD), see function
dggsvd()
.
- References
Anderson, E, Bai, Z, Bischof, C, Blackford, S, Demmel, J, Dongarra, J J, Du Croz, J J, Greenbaum, A, Hammarling, S, McKenney, A and Sorensen, D, 1999, LAPACK Users’ Guide, (3rd Edition), SIAM, Philadelphia, https://www.netlib.org/lapack/lug
Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore