(S|D|C|Z)GEEV¶

Single, double, single complex, and double complex GEEV.

Description¶

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

Right eigenvectors satisfy:

$\fvar{A} \mult v_i = \lambda_i v_i$

Left eigenvectors satisfy:

$\herm{u_i} \mult \fvar{A} = \lambda \herm{u_i}$

Computed eigenvectors are normalized to have Euclidean unit length and largest real component.

LAPACK Interface¶

void sgeev(const char *JOBVL, const char *JOBVR, const qml_long *N, float *A,
    const qml_long *LDA, float *WR, float *WI, float *VL,
    const qml_long *LDVL, float *VR, const qml_long *LDVR, float *WORK,
    const qml_long *LWORK, qml_long *INFO);

void dgeev(const char *JOBVL, const char *JOBVR, const qml_long *N, double *A,
    const qml_long *LDA, double *WR, double *WI, double *VL,
    const qml_long *LDVL, double *VR, const qml_long *LDVR, double *WORK,
    const qml_long *LWORK, qml_long *INFO);

void cgeev(const char *JOBVL, const char *JOBVR, const qml_long *N,
    qml_single_complex *A, const qml_long *LDA, qml_single_complex *W,
    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 zgeev(const char *JOBVL, const char *JOBVR, const qml_long *N,
    qml_double_complex *A, const qml_long *LDA, qml_double_complex *W,
    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
A	Matrix of size N x N, overwritten on exit
LDA	Leading dimension of A
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
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 4N but optimally a larger multiple of N (-1 to query)
RWORK	Work space of size 2N
INFO	0 on success