naginterfaces.library.lapackeig.zunmbr

naginterfaces.library.lapackeig.zunmbr(vect, side, trans, k, a, tau, c)[source]

zunmbr multiplies an arbitrary complex matrix by one of the complex unitary matrices or which were determined by zgebrd() when reducing a complex matrix to bidiagonal form.

For full information please refer to the NAG Library document for f08ku

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/f08/f08kuf.html

Parameters
vectstr, length 1

Indicates whether or or or is to be applied to .

or is applied to .

or is applied to .

sidestr, length 1

Indicates how or or or is to be applied to .

or or or is applied to from the left.

or or or is applied to from the right.

transstr, length 1

Indicates whether or or or is to be applied to .

or is applied to .

or is applied to .

kint

If , the number of columns in the original matrix .

If , the number of rows in the original matrix .

acomplex, array-like, shape

Note: the required extent for this argument in dimension 1 is determined as follows: if : ; if : ; otherwise: .

Note: the required extent for this argument in dimension 2 is determined as follows: if : ; if : ; otherwise: .

Details of the vectors which define the elementary reflectors, as returned by zgebrd().

taucomplex, array-like, shape

Further details of the elementary reflectors, as returned by zgebrd() in its argument if , or in its argument if .

ccomplex, array-like, shape

The matrix .

Returns
ccomplex, ndarray, shape

is overwritten by or or or or 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: or .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

Notes

zunmbr is intended to be used after a call to zgebrd(), which reduces a complex rectangular matrix to real bidiagonal form by a unitary transformation: . zgebrd() represents the matrices and as products 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).

References

Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore