(S|D)SYTRD¶

Single and double SYTRD.

Description¶

Reduces a symmetric matrix to symmetric tridiagonal form using an orthogonal similarity transform.

$T = \trans{Q} \mult A \mult Q$

The matrix T is symmetric tridiagonal and the matrix Q is orthogonal.

The matrix Q is not stored explicitly. Instead, the elements above or below the diagonal of A together with TAU store Q as the product of scaled elementary reflectors.

When UPLO is U:

$Q = H_{N-1} \mult \dots \mult H_2 \mult H_1$

$H_i = I - \tau_i \mult v \mult \trans{v}$

The vector v has components i+1 through n of zero, component i is 1, and components 1 through i-1 are stored in the columns of A above the superdiagonal.

When UPLO is L:

$Q = H_1 \mult H_2 \mult \dots \mult H_{N-1}$

$H_i = I - \tau_i \mult v \mult \trans{v}$

The vector v has components 1 through i of zero, component i+1 is 1, and components i+2 through N are stored in the columns of A below the subdiagonal.

LAPACK Interface¶

void ssytrd(const char *UPLO, const qml_long *N, float *A, const qml_long *LDA,
    float *D, float *E, float *TAU, float *WORK, const qml_long *LWORK,
    qml_long *INFO);

void dsytrd(const char *UPLO, const qml_long *N, double *A, const qml_long *LDA,
    double *D, double *E, double *TAU, double *WORK, const qml_long *LWORK,
    qml_long *INFO);

Arguments¶

UPLO	Store upper ‘U’ or lower ‘L’ triangular part of A
N	Number of rows and columns of A
A	Symmetric matrix, overwritten by T and reflector vectors on exit
LDA	Leading dimension of A
D	On exit contains diagonal elements of T
E	On exit contains the off diagonal elements of T
TAU	On exit contains vector of scale factors for reflectors
WORK	Work space of size at least LWORK
LWORK	Size of work space (-1 to query)
INFO	0 on success