naginterfaces.library.lapackeig.zggrqf¶
- naginterfaces.library.lapackeig.zggrqf(a, b)[source]¶
zggrqf
computes a generalized factorization of a complex matrix pair , where is an matrix and is a matrix.For full information please refer to the NAG Library document for f08zt
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f08/f08ztf.html
- Parameters
- acomplex, array-like, shape
The matrix .
- bcomplex, array-like, shape
The matrix .
- Returns
- acomplex, ndarray, shape
If , the upper triangle of the subarray contains the upper triangular matrix .
If , the elements on and above the th subdiagonal contain the upper trapezoidal matrix ; the remaining elements, with the array , represent the unitary matrix as a product of elementary reflectors (see the F08 Introduction).
- tauacomplex, ndarray, shape
The scalar factors of the elementary reflectors which represent the unitary matrix .
- bcomplex, ndarray, shape
The elements on and above the diagonal of the array contain the upper trapezoidal matrix ( is upper triangular if ); the elements below the diagonal, with the array , represent the unitary matrix as a product of elementary reflectors (see the F08 Introduction).
- taubcomplex, ndarray, shape
The scalar factors of the elementary reflectors which represent the unitary matrix .
- Raises
- NagValueError
- (errno )
On entry, error in parameter .
Constraint: .
- (errno )
On entry, error in parameter .
Constraint: .
- (errno )
On entry, error in parameter .
Constraint: .
- Notes
zggrqf
forms the generalized factorization of an matrix and a matrixwhere is an unitary matrix, is a unitary matrix and and are of the form
with or upper triangular,
with upper triangular.
In particular, if is square and nonsingular, the generalized factorization of and implicitly gives the factorization of as
- 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
Anderson, E, Bai, Z and Dongarra, J, 1992, Generalized factorization and its applications, Linear Algebra Appl. (Volume 162–164), 243–271
Hammarling, S, 1987, The numerical solution of the general Gauss-Markov linear model, Mathematics in Signal Processing, (eds T S Durrani, J B Abbiss, J E Hudson, R N Madan, J G McWhirter and T A Moore), 441–456, Oxford University Press
Paige, C C, 1990, Some aspects of generalized factorizations, . In Reliable Numerical Computation, (eds M G Cox and S Hammarling), 73–91, Oxford University Press