(S|D|C|Z)GEHRD¶

Single, double, single complex, and double complex GEHRD.

Description¶

Reduces a general matrix to upper Hessenberg form using a unitary similarity transform.

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

The matrix H is upper Hessenberg and the matrix Q is unitary.

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

$Q = H_{ILO} \mult H_{ILO+1} \mult \dots \mult H_{IHI-1}$

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

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

LAPACK Interface¶

void sgehrd(const qml_long *N, const qml_long *ILO, const qml_long *IHI, float *A,
    const qml_long *LDA, float *TAU, float *WORK, const qml_long *LWORK,
    qml_long *INFO);

void dgehrd(const qml_long *N, const qml_long *ILO, const qml_long *IHI,
    double *A, const qml_long *LDA, double *TAU, double *WORK,
    const qml_long *LWORK, qml_long *INFO);

void cgehrd(const qml_long *N, const qml_long *ILO, const qml_long *IHI,
    qml_single_complex *A, const qml_long *LDA, qml_single_complex *TAU,
    qml_single_complex *WORK, const qml_long *LWORK, qml_long *INFO);

void zgehrd(const qml_long *N, const qml_long *ILO, const qml_long *IHI,
    qml_double_complex *A, const qml_long *LDA, qml_double_complex *TAU,
    qml_double_complex *WORK, const qml_long *LWORK, qml_long *INFO);

Arguments¶

N	Number of rows and columns of A
ILO	Lower index
IHI	Upper index, 1 <= ILO <= IHI <= N
A	Matrix, overwritten by H and reflector vectors on exit
LDA	Leading dimension of A
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