ZTGEVC(3F) ZTGEVC(3F)
ZTGEVC - compute some or all of the right and/or left generalized
eigenvectors of a pair of complex upper triangular matrices (A,B)
SUBROUTINE ZTGEVC( SIDE, HOWMNY, SELECT, N, A, LDA, B, LDB, VL, LDVL, VR,
LDVR, MM, M, WORK, RWORK, INFO )
CHARACTER HOWMNY, SIDE
INTEGER INFO, LDA, LDB, LDVL, LDVR, M, MM, N
LOGICAL SELECT( * )
DOUBLE PRECISION RWORK( * )
COMPLEX*16 A( LDA, * ), B( LDB, * ), VL( LDVL, * ), VR( LDVR, *
), WORK( * )
ZTGEVC computes some or all of the right and/or left generalized
eigenvectors of a pair of complex upper triangular matrices (A,B).
The right generalized eigenvector x and the left generalized eigenvector
y of (A,B) corresponding to a generalized eigenvalue w are defined by:
(A - wB) * x = 0 and y**H * (A - wB) = 0
where y**H denotes the conjugate tranpose of y.
If an eigenvalue w is determined by zero diagonal elements of both A and
B, a unit vector is returned as the corresponding eigenvector.
If all eigenvectors are requested, the routine may either return the
matrices X and/or Y of right or left eigenvectors of (A,B), or the
products Z*X and/or Q*Y, where Z and Q are input unitary matrices. If
(A,B) was obtained from the generalized Schur factorization of an
original pair of matrices
(A0,B0) = (Q*A*Z**H,Q*B*Z**H),
then Z*X and Q*Y are the matrices of right or left eigenvectors of A.
SIDE (input) CHARACTER*1
= 'R': compute right eigenvectors only;
= 'L': compute left eigenvectors only;
= 'B': compute both right and left eigenvectors.
HOWMNY (input) CHARACTER*1
= 'A': compute all right and/or left eigenvectors;
= 'B': compute all right and/or left eigenvectors, and
backtransform them using the input matrices supplied in VR and/or
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ZTGEVC(3F) ZTGEVC(3F)
VL; = 'S': compute selected right and/or left eigenvectors,
specified by the logical array SELECT.
SELECT (input) LOGICAL array, dimension (N)
If HOWMNY='S', SELECT specifies the eigenvectors to be computed.
If HOWMNY='A' or 'B', SELECT is not referenced. To select the
eigenvector corresponding to the j-th eigenvalue, SELECT(j) must
be set to .TRUE..
N (input) INTEGER
The order of the matrices A and B. N >= 0.
A (input) COMPLEX*16 array, dimension (LDA,N)
The upper triangular matrix A.
LDA (input) INTEGER
The leading dimension of array A. LDA >= max(1,N).
B (input) COMPLEX*16 array, dimension (LDB,N)
The upper triangular matrix B. B must have real diagonal
elements.
LDB (input) INTEGER
The leading dimension of array B. LDB >= max(1,N).
VL (input/output) COMPLEX*16 array, dimension (LDVL,MM)
On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must contain
an N-by-N matrix Q (usually the unitary matrix Q of left Schur
vectors returned by ZHGEQZ). On exit, if SIDE = 'L' or 'B', VL
contains: if HOWMNY = 'A', the matrix Y of left eigenvectors of
(A,B); if HOWMNY = 'B', the matrix Q*Y; if HOWMNY = 'S', the left
eigenvectors of (A,B) specified by SELECT, stored consecutively
in the columns of VL, in the same order as their eigenvalues. If
SIDE = 'R', VL is not referenced.
LDVL (input) INTEGER
The leading dimension of array VL. LDVL >= max(1,N) if SIDE =
'L' or 'B'; LDVL >= 1 otherwise.
VR (input/output) COMPLEX*16 array, dimension (LDVR,MM)
On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must contain
an N-by-N matrix Q (usually the unitary matrix Z of right Schur
vectors returned by ZHGEQZ). On exit, if SIDE = 'R' or 'B', VR
contains: if HOWMNY = 'A', the matrix X of right eigenvectors of
(A,B); if HOWMNY = 'B', the matrix Z*X; if HOWMNY = 'S', the
right eigenvectors of (A,B) specified by SELECT, stored
consecutively in the columns of VR, in the same order as their
eigenvalues. If SIDE = 'L', VR is not referenced.
LDVR (input) INTEGER
The leading dimension of the array VR. LDVR >= max(1,N) if SIDE
= 'R' or 'B'; LDVR >= 1 otherwise.
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ZTGEVC(3F) ZTGEVC(3F)
MM (input) INTEGER
The leading dimension of the array VR. LDVR >= max(1,N) if SIDE
= 'R' or 'B'; LDVR >= 1 otherwise.
MM (input) INTEGER
The number of columns in the arrays VL and/or VR. MM >= M.
M (output) INTEGER
The number of columns in the arrays VL and/or VR actually used to
store the eigenvectors. If HOWMNY = 'A' or 'B', M is set to N.
Each selected eigenvector occupies one column.
WORK (workspace) COMPLEX*16 array, dimension (2*N)
RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
ZTGEVC(3F) ZTGEVC(3F)
ZTGEVC - compute some or all of the right and/or left generalized
eigenvectors of a pair of complex upper triangular matrices (A,B)
SUBROUTINE ZTGEVC( SIDE, HOWMNY, SELECT, N, A, LDA, B, LDB, VL, LDVL, VR,
LDVR, MM, M, WORK, RWORK, INFO )
CHARACTER HOWMNY, SIDE
INTEGER INFO, LDA, LDB, LDVL, LDVR, M, MM, N
LOGICAL SELECT( * )
DOUBLE PRECISION RWORK( * )
COMPLEX*16 A( LDA, * ), B( LDB, * ), VL( LDVL, * ), VR( LDVR, *
), WORK( * )
ZTGEVC computes some or all of the right and/or left generalized
eigenvectors of a pair of complex upper triangular matrices (A,B).
The right generalized eigenvector x and the left generalized eigenvector
y of (A,B) corresponding to a generalized eigenvalue w are defined by:
(A - wB) * x = 0 and y**H * (A - wB) = 0
where y**H denotes the conjugate tranpose of y.
If an eigenvalue w is determined by zero diagonal elements of both A and
B, a unit vector is returned as the corresponding eigenvector.
If all eigenvectors are requested, the routine may either return the
matrices X and/or Y of right or left eigenvectors of (A,B), or the
products Z*X and/or Q*Y, where Z and Q are input unitary matrices. If
(A,B) was obtained from the generalized Schur factorization of an
original pair of matrices
(A0,B0) = (Q*A*Z**H,Q*B*Z**H),
then Z*X and Q*Y are the matrices of right or left eigenvectors of A.
SIDE (input) CHARACTER*1
= 'R': compute right eigenvectors only;
= 'L': compute left eigenvectors only;
= 'B': compute both right and left eigenvectors.
HOWMNY (input) CHARACTER*1
= 'A': compute all right and/or left eigenvectors;
= 'B': compute all right and/or left eigenvectors, and
backtransform them using the input matrices supplied in VR and/or
Page 1
ZTGEVC(3F) ZTGEVC(3F)
VL; = 'S': compute selected right and/or left eigenvectors,
specified by the logical array SELECT.
SELECT (input) LOGICAL array, dimension (N)
If HOWMNY='S', SELECT specifies the eigenvectors to be computed.
If HOWMNY='A' or 'B', SELECT is not referenced. To select the
eigenvector corresponding to the j-th eigenvalue, SELECT(j) must
be set to .TRUE..
N (input) INTEGER
The order of the matrices A and B. N >= 0.
A (input) COMPLEX*16 array, dimension (LDA,N)
The upper triangular matrix A.
LDA (input) INTEGER
The leading dimension of array A. LDA >= max(1,N).
B (input) COMPLEX*16 array, dimension (LDB,N)
The upper triangular matrix B. B must have real diagonal
elements.
LDB (input) INTEGER
The leading dimension of array B. LDB >= max(1,N).
VL (input/output) COMPLEX*16 array, dimension (LDVL,MM)
On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must contain
an N-by-N matrix Q (usually the unitary matrix Q of left Schur
vectors returned by ZHGEQZ). On exit, if SIDE = 'L' or 'B', VL
contains: if HOWMNY = 'A', the matrix Y of left eigenvectors of
(A,B); if HOWMNY = 'B', the matrix Q*Y; if HOWMNY = 'S', the left
eigenvectors of (A,B) specified by SELECT, stored consecutively
in the columns of VL, in the same order as their eigenvalues. If
SIDE = 'R', VL is not referenced.
LDVL (input) INTEGER
The leading dimension of array VL. LDVL >= max(1,N) if SIDE =
'L' or 'B'; LDVL >= 1 otherwise.
VR (input/output) COMPLEX*16 array, dimension (LDVR,MM)
On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must contain
an N-by-N matrix Q (usually the unitary matrix Z of right Schur
vectors returned by ZHGEQZ). On exit, if SIDE = 'R' or 'B', VR
contains: if HOWMNY = 'A', the matrix X of right eigenvectors of
(A,B); if HOWMNY = 'B', the matrix Z*X; if HOWMNY = 'S', the
right eigenvectors of (A,B) specified by SELECT, stored
consecutively in the columns of VR, in the same order as their
eigenvalues. If SIDE = 'L', VR is not referenced.
LDVR (input) INTEGER
The leading dimension of the array VR. LDVR >= max(1,N) if SIDE
= 'R' or 'B'; LDVR >= 1 otherwise.
Page 2
ZTGEVC(3F) ZTGEVC(3F)
MM (input) INTEGER
The leading dimension of the array VR. LDVR >= max(1,N) if SIDE
= 'R' or 'B'; LDVR >= 1 otherwise.
MM (input) INTEGER
The number of columns in the arrays VL and/or VR. MM >= M.
M (output) INTEGER
The number of columns in the arrays VL and/or VR actually used to
store the eigenvectors. If HOWMNY = 'A' or 'B', M is set to N.
Each selected eigenvector occupies one column.
WORK (workspace) COMPLEX*16 array, dimension (2*N)
RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
PPPPaaaaggggeeee 3333 [ Back ]
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