naginterfaces.library.lapackeig.zhptrd

naginterfaces.library.lapackeig.zhptrd(uplo, n, ap)

zhptrd reduces a complex Hermitian matrix to tridiagonal form, using packed storage.

For full information please refer to the NAG Library document for f08gs

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f08/f08gsf.html

Parameters

uplostr, length 1

Indicates whether the upper or lower triangular part of $A$ is stored.

$uplo=\text{'U'}$

The upper triangular part of $A$ is stored.

$uplo=\text{'L'}$

The lower triangular part of $A$ is stored.

nint

$n$, the order of the matrix $A$.

apcomplex, array-like, shape $(n\times (n+1)/2)$

The upper or lower triangle of the $n\times n$ Hermitian matrix $A$, packed by columns.

Returns

apcomplex, ndarray, shape $(n\times (n+1)/2)$

$ap$ is overwritten by the tridiagonal matrix $T$ and details of the unitary matrix $Q$.

dfloat, ndarray, shape $\left(n\right)$

The diagonal elements of the tridiagonal matrix $T$.

efloat, ndarray, shape $(max(1,n-1))$

The off-diagonal elements of the tridiagonal matrix $T$.

taucomplex, ndarray, shape $(max(1,n-1))$

Further details of the unitary matrix $Q$.

Raises

NagValueError

(errno $-1$)

On entry, error in parameter $uplo$.

Constraint: $uplo=\text{'U'}$ or $\text{'L'}$.

(errno $-2$)

On entry, error in parameter $n$.

Constraint: $n\ge 0$.

Notes

zhptrd reduces a complex Hermitian matrix $A$, held in packed storage, to real symmetric tridiagonal form $T$ by a unitary similarity transformation: $A=QT{Q}^H$.

The matrix $Q$ is not formed explicitly but is represented as a product of $n-1$ elementary reflectors (see the F08 Introduction for details). Functions are provided to work with $Q$ in this representation (see Further Comments).

References

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