naginterfaces.library.lapackeig.zungrq¶
- naginterfaces.library.lapackeig.zungrq(a, tau)[source]¶
zungrq
generates all or part of the complex unitary matrix from an factorization computed byzgerqf()
.For full information please refer to the NAG Library document for f08cw
https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/f08/f08cwf.html
- Parameters
- Returns
- acomplex, ndarray, shape
The 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
zungrq
is intended to be used following a call tozgerqf()
, which performs an factorization of a complex matrix and represents the unitary matrix as a product of elementary reflectors of order .This function may be used to generate explicitly as a square matrix, or to form only its trailing rows.
Usually is determined from the factorization of a matrix with . The whole of may be computed by calling
zungrq
with set to and set to or its trailing rows by callingzungrq
with and set to .The rows of returned by the last call form an orthonormal basis for the space spanned by the rows of ; thus
zgerqf()
followed byzungrq
can be used to orthogonalize the rows of .The information returned by
zgerqf()
also yields the factorization of the trailing rows of , where . The unitary matrix arising from this factorization can be computed by callingzungrq
with set to or its leading columns by callingzungrq
with set to .
- 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