naginterfaces.library.lapackeig.dsytrd

naginterfaces.library.lapackeig.dsytrd(uplo, a)

dsytrd reduces a real symmetric matrix to tridiagonal form.

For full information please refer to the NAG Library document for f08fe

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/f08/f08fef.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.

afloat, array-like, shape $(n,n)$

The $n\times n$ symmetric matrix $A$.

Returns

afloat, ndarray, shape $(n,n)$

$a$ is overwritten by the tridiagonal matrix $T$ and details of the orthogonal matrix $Q$ as specified by $uplo$.

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 $T$.

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

Further details of the orthogonal 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 $\text{n}$.

Constraint: $n\ge 0$.

Notes

dsytrd reduces a real symmetric matrix $A$ to symmetric tridiagonal form $T$ by an orthogonal similarity transformation: $A=QT{Q}^T$.

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