# naginterfaces.library.lapackeig.zupmtr¶

naginterfaces.library.lapackeig.zupmtr(side, uplo, trans, ap, tau, c)[source]

zupmtr multiplies an arbitrary complex matrix by the complex unitary matrix which was determined by zhptrd() when reducing a complex Hermitian matrix to tridiagonal form.

For full information please refer to the NAG Library document for f08gu

https://www.nag.com/numeric/nl/nagdoc_28.6/flhtml/f08/f08guf.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.

uplostr, length 1

This must be the same argument as supplied to zhptrd().

transstr, length 1

Indicates whether or is to be applied to .

is applied to .

is applied to .

apcomplex, array-like, shape

Note: the required length for this argument is determined as follows: if : ; if : ; otherwise: .

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

taucomplex, array-like, shape

Note: the required length for this argument is determined as follows: if : ; if : ; otherwise: .

Further details of the elementary reflectors, as returned by zhptrd().

ccomplex, array-like, shape

The matrix .

Returns
apcomplex, ndarray, shape

Is used as internal workspace prior to being restored and hence is unchanged.

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: or .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

Notes

zupmtr is intended to be used after a call to zhptrd(), which reduces a complex Hermitian matrix to real symmetric tridiagonal form by a unitary similarity transformation: . zhptrd() represents the unitary matrix 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 to transform a matrix of eigenvectors of to the matrix of eigenvectors of .

References

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