(C|Z)HEEVD¶

Single complex and double complex HEEVD.

Description¶

Computes the eigenvalues and (optionally) eigenvectors of a Hermitian matrix using a divide-and-conquer algorithm.

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 cheevd(const char *JOBZ, const char *UPLO, const qml_long *N,
    qml_single_complex *A, const qml_long *LDA, float *W,
    qml_single_complex *WORK, const qml_long *LWORK, float *RWORK,
    const qml_long *LRWORK, qml_long *IWORK, const qml_long *LIWORK,
    qml_long *INFO);

void zheevd(const char *JOBZ, const char *UPLO, const qml_long *N,
    qml_double_complex *A, const qml_long *LDA, double *W,
    qml_double_complex *WORK, const qml_long *LWORK, double *RWORK,
    const qml_long *LRWORK, qml_long *IWORK, const qml_long *LIWORK,
    qml_long *INFO);

Arguments¶

JOBZ	Compute eigenvectors and store in A if ‘V’, otherwise do not compute
UPLO	Specify whether to use ‘U’ upper triangular or ‘L’ lower triangular part of A
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
WORK	Work space of size at least LWORK
LWORK	Size of work space (-1 to query)
RWORK	Work space of size at least LRWORK
LRWORK	Size of secondary work space (-1 to query)
IWORK	Integer work space of size at least LIWORK
LIWORK	Size of integer work space (-1 to query)
INFO	0 on success, <0 for illegal arguments, >0 if convergence failed