tgevc#

stgevc

Functions

void stgevc(
    const char*          side,
    const char*          howmny,
    const INT*  restrict select,
    const INT            n,
    const f32*  restrict S,
    const INT            lds,
    const f32*  restrict P,
    const INT            ldp,
          f32*  restrict VL,
    const INT            ldvl,
          f32*  restrict VR,
    const INT            ldvr,
    const INT            mm,
          INT*           m,
          f32*  restrict work,
          INT*           info
);

void stgevc(const char *side, const char *howmny, const INT *restrict select, const INT n, const f32 *restrict S, const INT lds, const f32 *restrict P, const INT ldp, f32 *restrict VL, const INT ldvl, f32 *restrict VR, const INT ldvr, const INT mm, INT *m, f32 *restrict work, INT *info)#

STGEVC computes some or all of the right and/or left eigenvectors of a pair of real matrices (S,P), where S is a quasi-triangular matrix and P is upper triangular.

Matrix pairs of this type are produced by the generalized Schur factorization of a matrix pair (A,B):

A = Q*S*Z**T, B = Q*P*Z**T

as computed by SGGHRD + SHGEQZ.

The right eigenvector x and the left eigenvector y of (S,P) corresponding to an eigenvalue w are defined by:

S*x = w*P*x, (y**H)*S = w*(y**H)*P,

where y**H denotes the conjugate transpose of y.

Parameters

in

side

= ‘R’: compute right eigenvectors only; = ‘L’: compute left eigenvectors only; = ‘B’: compute both right and left eigenvectors.

in

howmny

= ‘A’: compute all right and/or left eigenvectors; = ‘B’: compute all right and/or left eigenvectors, backtransformed by the matrices in VR and/or VL; = ‘S’: compute selected right and/or left eigenvectors, specified by the logical array select.

in

select

Integer array, dimension (n). If howmny=’S’, select specifies the eigenvectors to be computed. Nonzero means compute the eigenvector.

in

n

The order of the matrices S and P. n >= 0.

in

S

Array of dimension (lds, n). The upper quasi-triangular matrix S from a generalized Schur factorization.

in

lds

The leading dimension of S. lds >= max(1,n).

in

P

Array of dimension (ldp, n). The upper triangular matrix P.

in

ldp

The leading dimension of P. ldp >= max(1,n).

inout

VL

Array of dimension (ldvl, mm). Left eigenvectors.

in

ldvl

The leading dimension of VL. ldvl >= 1, and if side = ‘L’ or ‘B’, ldvl >= n.

inout

VR

Array of dimension (ldvr, mm). Right eigenvectors.

in

ldvr

The leading dimension of VR. ldvr >= 1, and if side = ‘R’ or ‘B’, ldvr >= n.

in

mm

The number of columns in VL and/or VR. mm >= m.

out

m

The number of columns in VL and/or VR actually used.

out

work

Workspace array of dimension (6*n).

out

info

= 0: successful exit.
< 0: if info = -i, the i-th argument had an illegal value.
> 0: the 2-by-2 block (info:info+1) does not have a complex eigenvalue.

dtgevc

Functions

void dtgevc(
    const char*          side,
    const char*          howmny,
    const INT*  restrict select,
    const INT            n,
    const f64*  restrict S,
    const INT            lds,
    const f64*  restrict P,
    const INT            ldp,
          f64*  restrict VL,
    const INT            ldvl,
          f64*  restrict VR,
    const INT            ldvr,
    const INT            mm,
          INT*           m,
          f64*  restrict work,
          INT*           info
);

void dtgevc(const char *side, const char *howmny, const INT *restrict select, const INT n, const f64 *restrict S, const INT lds, const f64 *restrict P, const INT ldp, f64 *restrict VL, const INT ldvl, f64 *restrict VR, const INT ldvr, const INT mm, INT *m, f64 *restrict work, INT *info)#

DTGEVC computes some or all of the right and/or left eigenvectors of a pair of real matrices (S,P), where S is a quasi-triangular matrix and P is upper triangular.

Matrix pairs of this type are produced by the generalized Schur factorization of a matrix pair (A,B):

A = Q*S*Z**T, B = Q*P*Z**T

as computed by DGGHRD + DHGEQZ.

The right eigenvector x and the left eigenvector y of (S,P) corresponding to an eigenvalue w are defined by:

S*x = w*P*x, (y**H)*S = w*(y**H)*P,

where y**H denotes the conjugate transpose of y.

Parameters

in

side

= ‘R’: compute right eigenvectors only; = ‘L’: compute left eigenvectors only; = ‘B’: compute both right and left eigenvectors.

in

howmny

= ‘A’: compute all right and/or left eigenvectors; = ‘B’: compute all right and/or left eigenvectors, backtransformed by the matrices in VR and/or VL; = ‘S’: compute selected right and/or left eigenvectors, specified by the logical array select.

in

select

Integer array, dimension (n). If howmny=’S’, select specifies the eigenvectors to be computed. Nonzero means compute the eigenvector.

in

n

The order of the matrices S and P. n >= 0.

in

S

Array of dimension (lds, n). The upper quasi-triangular matrix S from a generalized Schur factorization.

in

lds

The leading dimension of S. lds >= max(1,n).

in

P

Array of dimension (ldp, n). The upper triangular matrix P.

in

ldp

The leading dimension of P. ldp >= max(1,n).

inout

VL

Array of dimension (ldvl, mm). Left eigenvectors.

in

ldvl

The leading dimension of VL. ldvl >= 1, and if side = ‘L’ or ‘B’, ldvl >= n.

inout

VR

Array of dimension (ldvr, mm). Right eigenvectors.

in

ldvr

The leading dimension of VR. ldvr >= 1, and if side = ‘R’ or ‘B’, ldvr >= n.

in

mm

The number of columns in VL and/or VR. mm >= m.

out

m

The number of columns in VL and/or VR actually used.

out

work

Workspace array of dimension (6*n).

out

info

= 0: successful exit.
< 0: if info = -i, the i-th argument had an illegal value.
> 0: the 2-by-2 block (info:info+1) does not have a complex eigenvalue.

ctgevc

Functions

void ctgevc(
    const char*          side,
    const char*          howmny,
    const INT*  restrict select,
    const INT            n,
    const c64*  restrict S,
    const INT            lds,
    const c64*  restrict P,
    const INT            ldp,
          c64*  restrict VL,
    const INT            ldvl,
          c64*  restrict VR,
    const INT            ldvr,
    const INT            mm,
          INT*           m,
          c64*  restrict work,
          f32*  restrict rwork,
          INT*           info
);

void ctgevc(const char *side, const char *howmny, const INT *restrict select, const INT n, const c64 *restrict S, const INT lds, const c64 *restrict P, const INT ldp, c64 *restrict VL, const INT ldvl, c64 *restrict VR, const INT ldvr, const INT mm, INT *m, c64 *restrict work, f32 *restrict rwork, INT *info)#

CTGEVC computes some or all of the right and/or left eigenvectors of a pair of complex matrices (S,P), where S and P are upper triangular.

Matrix pairs of this type are produced by the generalized Schur factorization of a complex matrix pair (A,B):

A = Q*S*Z**H, B = Q*P*Z**H

as computed by CGGHRD + CHGEQZ.

The right eigenvector x and the left eigenvector y of (S,P) corresponding to an eigenvalue w are defined by:

S*x = w*P*x, (y**H)*S = w*(y**H)*P,

where y**H denotes the conjugate transpose of y. The eigenvalues are not input to this routine, but are computed directly from the diagonal elements of S and P.

This routine returns the matrices X and/or Y of right and left eigenvectors of (S,P), or the products Z*X and/or Q*Y, where Z and Q are input matrices. If Q and Z are the unitary factors from the generalized Schur factorization of a matrix pair (A,B), then Z*X and Q*Y are the matrices of right and left eigenvectors of (A,B).

Parameters

in

side

= ‘R’: compute right eigenvectors only; = ‘L’: compute left eigenvectors only; = ‘B’: compute both right and left eigenvectors.

in

howmny

= ‘A’: compute all right and/or left eigenvectors; = ‘B’: compute all right and/or left eigenvectors, backtransformed by the matrices in VR and/or VL; = ‘S’: compute selected right and/or left eigenvectors, specified by the logical array select.

in

select

Integer array, dimension (n). If howmny=’S’, select specifies the eigenvectors to be computed. Nonzero means compute the eigenvector. Not referenced if howmny = ‘A’ or ‘B’.

in

n

The order of the matrices S and P. n >= 0.

in

S

Complex array, dimension (lds, n). The upper triangular matrix S from a generalized Schur factorization.

in

lds

The leading dimension of S. lds >= max(1,n).

in

P

Complex array, dimension (ldp, n). The upper triangular matrix P. P must have real diagonal elements.

in

ldp

The leading dimension of P. ldp >= max(1,n).

inout

VL

Complex array, dimension (ldvl, mm). Left eigenvectors.

in

ldvl

The leading dimension of VL. ldvl >= 1, and if side = ‘L’ or ‘B’, ldvl >= n.

inout

VR

Complex array, dimension (ldvr, mm). Right eigenvectors.

in

ldvr

The leading dimension of VR. ldvr >= 1, and if side = ‘R’ or ‘B’, ldvr >= n.

in

mm

The number of columns in VL and/or VR. mm >= m.

out

m

The number of columns in VL and/or VR actually used.

out

work

Complex workspace array, dimension (2*n).

out

rwork

Single precision workspace array, dimension (2*n).

out

info

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

ztgevc

Functions

void ztgevc(
    const char*          side,
    const char*          howmny,
    const INT*  restrict select,
    const INT            n,
    const c128* restrict S,
    const INT            lds,
    const c128* restrict P,
    const INT            ldp,
          c128* restrict VL,
    const INT            ldvl,
          c128* restrict VR,
    const INT            ldvr,
    const INT            mm,
          INT*           m,
          c128* restrict work,
          f64*  restrict rwork,
          INT*           info
);

void ztgevc(const char *side, const char *howmny, const INT *restrict select, const INT n, const c128 *restrict S, const INT lds, const c128 *restrict P, const INT ldp, c128 *restrict VL, const INT ldvl, c128 *restrict VR, const INT ldvr, const INT mm, INT *m, c128 *restrict work, f64 *restrict rwork, INT *info)#

ZTGEVC computes some or all of the right and/or left eigenvectors of a pair of complex matrices (S,P), where S and P are upper triangular.

Matrix pairs of this type are produced by the generalized Schur factorization of a complex matrix pair (A,B):

A = Q*S*Z**H, B = Q*P*Z**H

as computed by ZGGHRD + ZHGEQZ.

The right eigenvector x and the left eigenvector y of (S,P) corresponding to an eigenvalue w are defined by:

S*x = w*P*x, (y**H)*S = w*(y**H)*P,

where y**H denotes the conjugate transpose of y. The eigenvalues are not input to this routine, but are computed directly from the diagonal elements of S and P.

This routine returns the matrices X and/or Y of right and left eigenvectors of (S,P), or the products Z*X and/or Q*Y, where Z and Q are input matrices. If Q and Z are the unitary factors from the generalized Schur factorization of a matrix pair (A,B), then Z*X and Q*Y are the matrices of right and left eigenvectors of (A,B).

Parameters

in

side

= ‘R’: compute right eigenvectors only; = ‘L’: compute left eigenvectors only; = ‘B’: compute both right and left eigenvectors.

in

howmny

= ‘A’: compute all right and/or left eigenvectors; = ‘B’: compute all right and/or left eigenvectors, backtransformed by the matrices in VR and/or VL; = ‘S’: compute selected right and/or left eigenvectors, specified by the logical array select.

in

select

Integer array, dimension (n). If howmny=’S’, select specifies the eigenvectors to be computed. Nonzero means compute the eigenvector. Not referenced if howmny = ‘A’ or ‘B’.

in

n

The order of the matrices S and P. n >= 0.

in

S

Complex array, dimension (lds, n). The upper triangular matrix S from a generalized Schur factorization.

in

lds

The leading dimension of S. lds >= max(1,n).

in

P

Complex array, dimension (ldp, n). The upper triangular matrix P. P must have real diagonal elements.

in

ldp

The leading dimension of P. ldp >= max(1,n).

inout

VL

Complex array, dimension (ldvl, mm). Left eigenvectors.

in

ldvl

The leading dimension of VL. ldvl >= 1, and if side = ‘L’ or ‘B’, ldvl >= n.

inout

VR

Complex array, dimension (ldvr, mm). Right eigenvectors.

in

ldvr

The leading dimension of VR. ldvr >= 1, and if side = ‘R’ or ‘B’, ldvr >= n.

in

mm

The number of columns in VL and/or VR. mm >= m.

out

m

The number of columns in VL and/or VR actually used.

out

work

Complex workspace array, dimension (2*n).

out

rwork

Double precision workspace array, dimension (2*n).

out

info

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

tgevc#

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