(C|Z)HETRD¶

Single complex and double complex HETRD.

Description¶

Reduces a Hermitian matrix to symmetric tridiagonal form using a unitary similarity transform.

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

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

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:

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

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

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:

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

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

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

void zhetrd(const char *UPLO, const qml_long *N, qml_double_complex *A,
    const qml_long *LDA, double *D, double *E, qml_double_complex *TAU,
    qml_double_complex *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	Hermitian 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