(S|D|C|Z)GEES¶

Single, double, single complex, and double complex GEES.

Description¶

Computes the eigenvalues, Schur form, and (optionally) Schur vectors of a general matrix.

Given an N by N matrix A, computes the Schur factorization:

$\fvar{A} = Z \mult T \mult \herm{Z}$

The matrix T is in Schur form, meaning it is upper quasi-triangular with blocks of size 1x1 or 2x2. Blocks of size 2x2 are of the form:

$\begin{bmatrix} a & b \\ c & a \end{bmatrix}$

Each 2x2 block corresponds to a pair of eigenvalues $a\pm \sqrt{bc}$ .

LAPACK Interface¶

void sgees(const char *JOBVS, const char *SORT, void *SELECT, const qml_long *N,
    float *A, const qml_long *LDA, qml_long *SDIM, float *WR, float *WI,
    float *VS, const qml_long *LDVS, float *WORK, const qml_long *LWORK,
    qml_int *BWORK, qml_long *INFO);

void dgees(const char *JOBVS, const char *SORT, void *SELECT, const qml_long *N,
    double *A, const qml_long *LDA, qml_long *SDIM, double *WR, double *WI,
    double *VS, const qml_long *LDVS, double *WORK, const qml_long *LWORK,
    qml_int *BWORK, qml_long *INFO);

void cgees(const char *JOBVS, const char *SORT, void *SELECT, const qml_long *N,
    qml_single_complex *A, const qml_long *LDA, qml_long *SDIM,
    qml_single_complex *W, qml_single_complex *VS, const qml_long *LDVS,
    qml_single_complex *WORK, const qml_long *LWORK, float *RWORK,
    qml_int *BWORK, qml_long *INFO);

void zgees(const char *JOBVS, const char *SORT, void *SELECT, const qml_long *N,
    qml_double_complex *A, const qml_long *LDA, qml_long *SDIM,
    qml_double_complex *W, qml_double_complex *VS, const qml_long *LDVS,
    qml_double_complex *WORK, const qml_long *LWORK, double *RWORK,
    qml_int *BWORK, qml_long *INFO);

Arguments¶

JOBVS	Compute VS if ‘V’, otherwise do not compute
SORT	Sort eigenvalues, only ‘N’ supported
SELECT	Function pointers, not supported (pass NULL)
N	Number of rows and columns of A
A	Matrix of size N x N, overwritten with T on exit
LDA	Leading dimension of A
SDIM	Not used
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
VS	On exit contains Schur vectors matrix Z if JOBVS is ‘V’
LDVS	Leading dimension of VS
WORK	Work space of size at least LWORK
LWORK	Size of work space, at least 3N but optimally a larger multiple of N (-1 to query)
RWORK	Work space of size N
BWORK	Not used
INFO	0 on success