ggesx#

Functions

void sggesx(
    const char*               jobvsl,
    const char*               jobvsr,
    const char*               sort,
          sselect3_t          selctg,
    const char*               sense,
    const INT                 n,
          f32*       restrict A,
    const INT                 lda,
          f32*       restrict B,
    const INT                 ldb,
          INT*                sdim,
          f32*       restrict alphar,
          f32*       restrict alphai,
          f32*       restrict beta,
          f32*       restrict VSL,
    const INT                 ldvsl,
          f32*       restrict VSR,
    const INT                 ldvsr,
          f32*       restrict rconde,
          f32*       restrict rcondv,
          f32*       restrict work,
    const INT                 lwork,
          INT*       restrict iwork,
    const INT                 liwork,
          INT*       restrict bwork,
          INT*                info
);
void sggesx(const char *jobvsl, const char *jobvsr, const char *sort, sselect3_t selctg, const char *sense, const INT n, f32 *restrict A, const INT lda, f32 *restrict B, const INT ldb, INT *sdim, f32 *restrict alphar, f32 *restrict alphai, f32 *restrict beta, f32 *restrict VSL, const INT ldvsl, f32 *restrict VSR, const INT ldvsr, f32 *restrict rconde, f32 *restrict rcondv, f32 *restrict work, const INT lwork, INT *restrict iwork, const INT liwork, INT *restrict bwork, INT *info)#

SGGESX computes for a pair of N-by-N real nonsymmetric matrices (A,B), the generalized eigenvalues, the real Schur form (S,T), and, optionally, the left and/or right matrices of Schur vectors (VSL and VSR).

This gives the generalized Schur factorization 

 (A,B) = ( (VSL) S (VSR)**T, (VSL) T (VSR)**T )
Optionally, it also orders the eigenvalues so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix S and the upper triangular matrix T; computes a reciprocal condition number for the average of the selected eigenvalues (RCONDE); and computes a reciprocal condition number for the right and left deflating subspaces corresponding to the selected eigenvalues (RCONDV).

Parameters

in
jobvsl

= ‘N’: do not compute the left Schur vectors; = ‘V’: compute the left Schur vectors.

in
jobvsr

= ‘N’: do not compute the right Schur vectors; = ‘V’: compute the right Schur vectors.

in
sort

= ‘N’: Eigenvalues are not ordered; = ‘S’: Eigenvalues are ordered (see selctg).

in
selctg

Selection function for eigenvalue ordering.

in
sense

Determines which reciprocal condition numbers are computed. = ‘N’: None are computed; = ‘E’: Computed for average of selected eigenvalues only; = ‘V’: Computed for selected deflating subspaces only; = ‘B’: Computed for both.

in
n

The order of the matrices A, B, VSL, and VSR. n >= 0.

inout
A

On entry, the first of the pair of matrices. On exit, A has been overwritten by its Schur form S.

in
lda

The leading dimension of A. lda >= max(1,n).

inout
B

On entry, the second of the pair of matrices. On exit, B has been overwritten by its Schur form T.

in
ldb

The leading dimension of B. ldb >= max(1,n).

out
sdim

Number of eigenvalues for which selctg is true.

out
alphar

Real parts of generalized eigenvalues.

out
alphai

Imaginary parts of generalized eigenvalues.

out
beta

Beta values of generalized eigenvalues.

out
VSL

If jobvsl = ‘V’, the left Schur vectors.

in
ldvsl

The leading dimension of VSL.

out
VSR

If jobvsr = ‘V’, the right Schur vectors.

in
ldvsr

The leading dimension of VSR.

out
rconde

Reciprocal condition numbers for eigenvalues (dimension 2).

out
rcondv

Reciprocal condition numbers for subspaces (dimension 2).

out
work

Workspace array.

in
lwork

The dimension of work.

out
iwork

Integer workspace array.

in
liwork

The dimension of iwork.

out
bwork

Integer array, dimension (n).

out
info

  • = 0: successful exit

  • < 0: if info = -i, the i-th argument had an illegal value

  • > 0: errors from QZ iteration or reordering

Functions

void dggesx(
    const char*               jobvsl,
    const char*               jobvsr,
    const char*               sort,
          dselect3_t          selctg,
    const char*               sense,
    const INT                 n,
          f64*       restrict A,
    const INT                 lda,
          f64*       restrict B,
    const INT                 ldb,
          INT*                sdim,
          f64*       restrict alphar,
          f64*       restrict alphai,
          f64*       restrict beta,
          f64*       restrict VSL,
    const INT                 ldvsl,
          f64*       restrict VSR,
    const INT                 ldvsr,
          f64*       restrict rconde,
          f64*       restrict rcondv,
          f64*       restrict work,
    const INT                 lwork,
          INT*       restrict iwork,
    const INT                 liwork,
          INT*       restrict bwork,
          INT*                info
);
void dggesx(const char *jobvsl, const char *jobvsr, const char *sort, dselect3_t selctg, const char *sense, const INT n, f64 *restrict A, const INT lda, f64 *restrict B, const INT ldb, INT *sdim, f64 *restrict alphar, f64 *restrict alphai, f64 *restrict beta, f64 *restrict VSL, const INT ldvsl, f64 *restrict VSR, const INT ldvsr, f64 *restrict rconde, f64 *restrict rcondv, f64 *restrict work, const INT lwork, INT *restrict iwork, const INT liwork, INT *restrict bwork, INT *info)#

DGGESX computes for a pair of N-by-N real nonsymmetric matrices (A,B), the generalized eigenvalues, the real Schur form (S,T), and, optionally, the left and/or right matrices of Schur vectors (VSL and VSR).

This gives the generalized Schur factorization 

 (A,B) = ( (VSL) S (VSR)**T, (VSL) T (VSR)**T )
Optionally, it also orders the eigenvalues so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix S and the upper triangular matrix T; computes a reciprocal condition number for the average of the selected eigenvalues (RCONDE); and computes a reciprocal condition number for the right and left deflating subspaces corresponding to the selected eigenvalues (RCONDV).

Parameters

in
jobvsl

= ‘N’: do not compute the left Schur vectors; = ‘V’: compute the left Schur vectors.

in
jobvsr

= ‘N’: do not compute the right Schur vectors; = ‘V’: compute the right Schur vectors.

in
sort

= ‘N’: Eigenvalues are not ordered; = ‘S’: Eigenvalues are ordered (see selctg).

in
selctg

Selection function for eigenvalue ordering.

in
sense

Determines which reciprocal condition numbers are computed. = ‘N’: None are computed; = ‘E’: Computed for average of selected eigenvalues only; = ‘V’: Computed for selected deflating subspaces only; = ‘B’: Computed for both.

in
n

The order of the matrices A, B, VSL, and VSR. n >= 0.

inout
A

On entry, the first of the pair of matrices. On exit, A has been overwritten by its Schur form S.

in
lda

The leading dimension of A. lda >= max(1,n).

inout
B

On entry, the second of the pair of matrices. On exit, B has been overwritten by its Schur form T.

in
ldb

The leading dimension of B. ldb >= max(1,n).

out
sdim

Number of eigenvalues for which selctg is true.

out
alphar

Real parts of generalized eigenvalues.

out
alphai

Imaginary parts of generalized eigenvalues.

out
beta

Beta values of generalized eigenvalues.

out
VSL

If jobvsl = ‘V’, the left Schur vectors.

in
ldvsl

The leading dimension of VSL.

out
VSR

If jobvsr = ‘V’, the right Schur vectors.

in
ldvsr

The leading dimension of VSR.

out
rconde

Reciprocal condition numbers for eigenvalues (dimension 2).

out
rcondv

Reciprocal condition numbers for subspaces (dimension 2).

out
work

Workspace array.

in
lwork

The dimension of work.

out
iwork

Integer workspace array.

in
liwork

The dimension of iwork.

out
bwork

Integer array, dimension (n).

out
info

  • = 0: successful exit

  • < 0: if info = -i, the i-th argument had an illegal value

  • > 0: errors from QZ iteration or reordering

Functions

void cggesx(
    const char*      jobvsl,
    const char*      jobvsr,
    const char*      sort,
          cselect2_t selctg,
    const char*      sense,
    const INT        n,
          c64*       A,
    const INT        lda,
          c64*       B,
    const INT        ldb,
          INT*       sdim,
          c64*       alpha,
          c64*       beta,
          c64*       VSL,
    const INT        ldvsl,
          c64*       VSR,
    const INT        ldvsr,
          f32*       rconde,
          f32*       rcondv,
          c64*       work,
    const INT        lwork,
          f32*       rwork,
          INT*       iwork,
    const INT        liwork,
          INT*       bwork,
          INT*       info
);
void cggesx(const char *jobvsl, const char *jobvsr, const char *sort, cselect2_t selctg, const char *sense, const INT n, c64 *A, const INT lda, c64 *B, const INT ldb, INT *sdim, c64 *alpha, c64 *beta, c64 *VSL, const INT ldvsl, c64 *VSR, const INT ldvsr, f32 *rconde, f32 *rcondv, c64 *work, const INT lwork, f32 *rwork, INT *iwork, const INT liwork, INT *bwork, INT *info)#

CGGESX computes for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, the complex Schur form (S,T), and, optionally, the left and/or right matrices of Schur vectors (VSL and VSR).

This gives the generalized Schur factorization 

 (A,B) = ( (VSL) S (VSR)**H, (VSL) T (VSR)**H )
where (VSR)**H is the conjugate-transpose of VSR.

Optionally, it also orders the eigenvalues so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper triangular matrix S and the upper triangular matrix T; computes a reciprocal condition number for the average of the selected eigenvalues (RCONDE); and computes a reciprocal condition number for the right and left deflating subspaces corresponding to the selected eigenvalues (RCONDV).

Parameters

in
jobvsl

= ‘N’: do not compute the left Schur vectors; = ‘V’: compute the left Schur vectors.

in
jobvsr

= ‘N’: do not compute the right Schur vectors; = ‘V’: compute the right Schur vectors.

in
sort

= ‘N’: Eigenvalues are not ordered; = ‘S’: Eigenvalues are ordered (see selctg).

in
selctg

Selection function for eigenvalue ordering.

in
sense

Determines which reciprocal condition numbers are computed. = ‘N’: None are computed; = ‘E’: Computed for average of selected eigenvalues only; = ‘V’: Computed for selected deflating subspaces only; = ‘B’: Computed for both.

in
n

The order of the matrices A, B, VSL, and VSR. n >= 0.

inout
A

On entry, the first of the pair of matrices. On exit, A has been overwritten by its generalized Schur form S.

in
lda

The leading dimension of A. lda >= max(1,n).

inout
B

On entry, the second of the pair of matrices. On exit, B has been overwritten by its generalized Schur form T.

in
ldb

The leading dimension of B. ldb >= max(1,n).

out
sdim

Number of eigenvalues for which selctg is true.

out
alpha

Complex array, dimension (n).

out
beta

Complex array, dimension (n).

out
VSL

If jobvsl = ‘V’, the left Schur vectors.

in
ldvsl

The leading dimension of VSL.

out
VSR

If jobvsr = ‘V’, the right Schur vectors.

in
ldvsr

The leading dimension of VSR.

out
rconde

Reciprocal condition numbers for eigenvalues (dimension 2).

out
rcondv

Reciprocal condition numbers for subspaces (dimension 2).

out
work

Complex workspace array, dimension (max(1,lwork)).

in
lwork

The dimension of work.

out
rwork

Single precision array, dimension (8*n).

out
iwork

Integer workspace array.

in
liwork

The dimension of iwork.

out
bwork

Integer array, dimension (n).

out
info

  • = 0: successful exit

  • < 0: if info = -i, the i-th argument had an illegal value

  • > 0: errors from QZ iteration or reordering

Functions

void zggesx(
    const char*      jobvsl,
    const char*      jobvsr,
    const char*      sort,
          zselect2_t selctg,
    const char*      sense,
    const INT        n,
          c128*      A,
    const INT        lda,
          c128*      B,
    const INT        ldb,
          INT*       sdim,
          c128*      alpha,
          c128*      beta,
          c128*      VSL,
    const INT        ldvsl,
          c128*      VSR,
    const INT        ldvsr,
          f64*       rconde,
          f64*       rcondv,
          c128*      work,
    const INT        lwork,
          f64*       rwork,
          INT*       iwork,
    const INT        liwork,
          INT*       bwork,
          INT*       info
);
void zggesx(const char *jobvsl, const char *jobvsr, const char *sort, zselect2_t selctg, const char *sense, const INT n, c128 *A, const INT lda, c128 *B, const INT ldb, INT *sdim, c128 *alpha, c128 *beta, c128 *VSL, const INT ldvsl, c128 *VSR, const INT ldvsr, f64 *rconde, f64 *rcondv, c128 *work, const INT lwork, f64 *rwork, INT *iwork, const INT liwork, INT *bwork, INT *info)#

ZGGESX computes for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, the complex Schur form (S,T), and, optionally, the left and/or right matrices of Schur vectors (VSL and VSR).

This gives the generalized Schur factorization 

 (A,B) = ( (VSL) S (VSR)**H, (VSL) T (VSR)**H )
where (VSR)**H is the conjugate-transpose of VSR.

Optionally, it also orders the eigenvalues so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper triangular matrix S and the upper triangular matrix T; computes a reciprocal condition number for the average of the selected eigenvalues (RCONDE); and computes a reciprocal condition number for the right and left deflating subspaces corresponding to the selected eigenvalues (RCONDV).

Parameters

in
jobvsl

= ‘N’: do not compute the left Schur vectors; = ‘V’: compute the left Schur vectors.

in
jobvsr

= ‘N’: do not compute the right Schur vectors; = ‘V’: compute the right Schur vectors.

in
sort

= ‘N’: Eigenvalues are not ordered; = ‘S’: Eigenvalues are ordered (see selctg).

in
selctg

Selection function for eigenvalue ordering.

in
sense

Determines which reciprocal condition numbers are computed. = ‘N’: None are computed; = ‘E’: Computed for average of selected eigenvalues only; = ‘V’: Computed for selected deflating subspaces only; = ‘B’: Computed for both.

in
n

The order of the matrices A, B, VSL, and VSR. n >= 0.

inout
A

On entry, the first of the pair of matrices. On exit, A has been overwritten by its generalized Schur form S.

in
lda

The leading dimension of A. lda >= max(1,n).

inout
B

On entry, the second of the pair of matrices. On exit, B has been overwritten by its generalized Schur form T.

in
ldb

The leading dimension of B. ldb >= max(1,n).

out
sdim

Number of eigenvalues for which selctg is true.

out
alpha

Complex array, dimension (n).

out
beta

Complex array, dimension (n).

out
VSL

If jobvsl = ‘V’, the left Schur vectors.

in
ldvsl

The leading dimension of VSL.

out
VSR

If jobvsr = ‘V’, the right Schur vectors.

in
ldvsr

The leading dimension of VSR.

out
rconde

Reciprocal condition numbers for eigenvalues (dimension 2).

out
rcondv

Reciprocal condition numbers for subspaces (dimension 2).

out
work

Complex workspace array, dimension (max(1,lwork)).

in
lwork

The dimension of work.

out
rwork

Double precision array, dimension (8*n).

out
iwork

Integer workspace array.

in
liwork

The dimension of iwork.

out
bwork

Integer array, dimension (n).

out
info

  • = 0: successful exit

  • < 0: if info = -i, the i-th argument had an illegal value

  • > 0: errors from QZ iteration or reordering

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