naginterfaces.library.lapackeig.zgemqrt¶
- naginterfaces.library.lapackeig.zgemqrt(side, trans, v, t, c)[source]¶
zgemqrt
multiplies an arbitrary complex matrix by the complex unitary matrix from a factorization computed byzgeqrt()
.For full information please refer to the NAG Library document for f08aq
https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/f08/f08aqf.html
- Parameters
- sidestr, length 1
Indicates how or is to be applied to .
or is applied to from the left.
or is applied to from the right.
- transstr, length 1
Indicates whether or is to be applied to .
is applied to .
is applied to .
- vcomplex, array-like, shape
Note: the required extent for this argument in dimension 1 is determined as follows: if : ; if : ; otherwise: .
Details of the vectors which define the elementary reflectors, as returned by
zgeqrt()
in the first columns of its array argument .- tcomplex, array-like, shape
Further details of the unitary matrix as returned by
zgeqrt()
. The number of blocks is , where and each block is of order except for the last block, which is of order . For the blocks the upper triangular block reflector factors are stored in the matrix as .- ccomplex, array-like, shape
The matrix .
- Returns
- ccomplex, ndarray, shape
is overwritten by or or or as specified by and .
- 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: .
- (errno )
On entry, error in parameter .
Constraint: .
- (errno )
On entry, error in parameter .
Constraint: .
- (errno )
On entry, error in parameter .
Constraint: .
- (errno )
On entry, error in parameter .
Constraint: .
- (errno )
On entry, error in parameter .
Constraint: .
- Notes
zgemqrt
is intended to be used after a call tozgeqrt()
, which performs a factorization of a complex matrix . The unitary matrix is represented as a product of elementary reflectors.This function may be used to form one of the matrix products
overwriting the result on (which may be any complex rectangular matrix).
A common application of this function is in solving linear least squares problems, as described in the F08 Introduction.
- References
Golub, G H and Van Loan, C F, 2012, Matrix Computations, (4th Edition), Johns Hopkins University Press, Baltimore