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 byzhptrd()
when reducing a complex Hermitian matrix to tridiagonal form.For full information please refer to the NAG Library document for f08gu
https://support.nag.com/numeric/nl/nagdoc_30.2/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 tozhptrd()
, 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