(S|D|C|Z)HSEQR¶

Single, double, single complex, and double complex HSEQR.

Description¶

Computes the eigenvalues of a Hessenberg matrix and optionally the Schur decomposition.

The Schur decomposition of the Hessenberg matrix H is:

$H = Z \mult T \mult \herm{Z}$

where T is upper triangular and Z is the unitary matrix of Schur vectors.

LAPACK Interface¶

void shseqr(const char *JOB, const char *COMPZ, const qml_long *N,
    const qml_long *ILO, const qml_long *IHI, float *H,
    const qml_long *LDH, float *WR, float *WI, float *Z,
    const qml_long *LDZ, float *WORK, const qml_long *LWORK,
    qml_long *INFO);

void dhseqr(const char *JOB, const char *COMPZ, const qml_long *N,
    const qml_long *ILO, const qml_long *IHI, double *H,
    const qml_long *LDH, double *WR, double *WI, double *Z,
    const qml_long *LDZ, double *WORK, const qml_long *LWORK,
    qml_long *INFO);

void chseqr(const char *JOB, const char *COMPZ, const qml_long *N,
    const qml_long *ILO, const qml_long *IHI, qml_single_complex *H,
    const qml_long *LDH, qml_single_complex *W, qml_single_complex *Z,
    const qml_long *LDZ, qml_single_complex *WORK, const qml_long *LWORK,
    qml_long *INFO);

void zhseqr(const char *JOB, const char *COMPZ, const qml_long *N,
    const qml_long *ILO, const qml_long *IHI, qml_double_complex *H,
    const qml_long *LDH, qml_double_complex *W, qml_double_complex *Z,
    const qml_long *LDZ, qml_double_complex *WORK, const qml_long *LWORK,
    qml_long *INFO);

Arguments¶

JOB	Compute Schur matrix T (‘S’) or eigenvalues only (‘E’)
COMPZ	Compute Schur matrix Z (‘I’), Q*Z (‘V’), or do not compute (‘N’)
N	Number of rows and columns of H
ILO	Lower bound of already reduced triangular part
IHI	Upper bound of already reduced triangular part
H	Matrix of size N x N, overwritten on exit
LDH	Leading dimension of H
W	Array of size N containing eigenvalues on exit
WR	Real part of W for real versions
WI	Complex part of W for real version
Z	Matrix of size N x N
LDZ	Leading dimension of Z
WORK	Work space of size at least LWORK
LWORK	Size of work space (-1 to query)
RWORK	Work space of size 2N
INFO	0 on success