(S|D|C|Z)GGEV¶

Single, double, single complex, and double complex GGEV.

Description¶

Computes the generalized eigenvalues and (optionally) generalized eigenvectors of a general matrix.

Given two N by N matrices A and B, computes the generalized eigenvalues and generalized left and right eigenvectors.

A generalized eigenvalue is a solution to the equation:

$A v = \lambda B v$

The vector v is a generalized right eigenvector. Generalized left eigenvectors u satisfy:

$\herm{u} A = \lambda \herm{u} B$

Generalized eigenvalues are represented as a ratio ALPHA / BETA with separate storage for ALPHA and BETA for increased numerical flexibility.

LAPACK Interface¶

void sggev(const char *JOBVL, const char *JOBVR, const qml_long *N, float *A,
    const qml_long *LDA, float *B, const qml_long *LDB, float *ALPHAR,
    float *ALPHAI, float *BETA, float *VL, const qml_long *LDVL, float *VR,
    const qml_long *LDVR, float *WORK, const qml_long *LWORK, qml_long *INFO);

void dggev(const char *JOBVL, const char *JOBVR, const qml_long *N, double *A,
    const qml_long *LDA, double *B, const qml_long *LDB, double *ALPHAR,
    double *ALPHAI, double *BETA, double *VL, const qml_long *LDVL, double *VR,
    const qml_long *LDVR, double *WORK, const qml_long *LWORK, qml_long *INFO);

void cggev(const char *JOBVL, const char *JOBVR, const qml_long *N,
    qml_single_complex *A, const qml_long *LDA, qml_single_complex *B,
    const qml_long *LDB, qml_single_complex *ALPHA, qml_single_complex *BETA,
    qml_single_complex *VL, const qml_long *LDVL, qml_single_complex *VR,
    const qml_long *LDVR, qml_single_complex *WORK, const qml_long *LWORK,
    float *RWORK, qml_long *INFO);

void zggev(const char *JOBVL, const char *JOBVR, const qml_long *N,
    qml_double_complex *A, const qml_long *LDA, qml_double_complex *B,
    const qml_long *LDB, qml_double_complex *ALPHA, qml_double_complex *BETA,
    qml_double_complex *VL, const qml_long *LDVL, qml_double_complex *VR,
    const qml_long *LDVR, qml_double_complex *WORK, const qml_long *LWORK,
    double *RWORK, qml_long *INFO);

Arguments¶

JOBVL	Compute VL if ‘V’, otherwise do not compute
JOBVR	Compute VR if ‘V’, otherwise do not compute
N	Number of rows and columns of A, B, VL, and VR
A	Matrix of size N x N, overwritten on output
LDA	Leading dimension of A
B	Matrix of size N x N, overwritten on output
LDB	Leading dimension of B
ALPHA	On exit contains generalized eigenvalues
ALPHAR	Real part of ALPHA for real versions
ALPHAI	Complex part of ALPHA for real versions
VL	On exit contains left eigenvectors if JOBVL is ‘V’
LDVL	Leading dimension of VL
VR	On exit contains right eigenvectors if JOBVR is ‘V’
LDVR	Leading dimension of VR
WORK	Work space of size at least LWORK
LWORK	Size of work space, at least 8N but optimally a larger multiple of N (-1 to query)
INFO	0 on success