dtgsna
dtgsna - estimate reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a matrix pair (A, B) in generalized real Schur canonical form (or of any matrix pair (Q*A*Z', Q*B*Z') with orthogonal matrices Q and Z, where Z' denotes the transpose of Z
SUBROUTINE DTGSNA( JOB, HOWMNT, SELECT, N, A, LDA, B, LDB, VL, LDVL,
* VR, LDVR, S, DIF, MM, M, WORK, LWORK, IWORK, INFO)
CHARACTER * 1 JOB, HOWMNT
INTEGER N, LDA, LDB, LDVL, LDVR, MM, M, LWORK, INFO
INTEGER IWORK(*)
LOGICAL SELECT(*)
DOUBLE PRECISION A(LDA,*), B(LDB,*), VL(LDVL,*), VR(LDVR,*), S(*), DIF(*), WORK(*)
SUBROUTINE DTGSNA_64( JOB, HOWMNT, SELECT, N, A, LDA, B, LDB, VL,
* LDVL, VR, LDVR, S, DIF, MM, M, WORK, LWORK, IWORK, INFO)
CHARACTER * 1 JOB, HOWMNT
INTEGER*8 N, LDA, LDB, LDVL, LDVR, MM, M, LWORK, INFO
INTEGER*8 IWORK(*)
LOGICAL*8 SELECT(*)
DOUBLE PRECISION A(LDA,*), B(LDB,*), VL(LDVL,*), VR(LDVR,*), S(*), DIF(*), WORK(*)
SUBROUTINE TGSNA( JOB, HOWMNT, SELECT, [N], A, [LDA], B, [LDB], VL,
* [LDVL], VR, [LDVR], S, DIF, MM, M, [WORK], [LWORK], [IWORK],
* [INFO])
CHARACTER(LEN=1) :: JOB, HOWMNT
INTEGER :: N, LDA, LDB, LDVL, LDVR, MM, M, LWORK, INFO
INTEGER, DIMENSION(:) :: IWORK
LOGICAL, DIMENSION(:) :: SELECT
REAL(8), DIMENSION(:) :: S, DIF, WORK
REAL(8), DIMENSION(:,:) :: A, B, VL, VR
SUBROUTINE TGSNA_64( JOB, HOWMNT, SELECT, [N], A, [LDA], B, [LDB],
* VL, [LDVL], VR, [LDVR], S, DIF, MM, M, [WORK], [LWORK], [IWORK],
* [INFO])
CHARACTER(LEN=1) :: JOB, HOWMNT
INTEGER(8) :: N, LDA, LDB, LDVL, LDVR, MM, M, LWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK
LOGICAL(8), DIMENSION(:) :: SELECT
REAL(8), DIMENSION(:) :: S, DIF, WORK
REAL(8), DIMENSION(:,:) :: A, B, VL, VR
#include <sunperf.h>
void dtgsna(char job, char howmnt, logical *select, int n, double *a, int lda, double *b, int ldb, double *vl, int ldvl, double *vr, int ldvr, double *s, double *dif, int mm, int *m, int *info);
void dtgsna_64(char job, char howmnt, logical *select, long n, double *a, long lda, double *b, long ldb, double *vl, long ldvl, double *vr, long ldvr, double *s, double *dif, long mm, long *m, long *info);
dtgsna estimates reciprocal condition numbers for specified
eigenvalues and/or eigenvectors of a matrix pair (A, B) in
generalized real Schur canonical form (or of any matrix pair
(Q*A*Z', Q*B*Z') with orthogonal matrices Q and Z, where
Z' denotes the transpose of Z.
(A, B) must be in generalized real Schur form (as returned by SGGES),
i.e. A is block upper triangular with 1-by-1 and 2-by-2 diagonal
blocks. B is upper triangular.
-
* JOB (input)
-
Specifies whether condition numbers are required for
eigenvalues (S) or eigenvectors (DIF):
-
* HOWMNT (input)
-
-
* SELECT (input)
-
If HOWMNT = 'S', SELECT specifies the eigenpairs for which
condition numbers are required. To select condition numbers
for the eigenpair corresponding to a real eigenvalue w(j),
SELECT(j) must be set to .TRUE.. To select condition numbers
corresponding to a complex conjugate pair of eigenvalues w(j)
and w(j+1), either SELECT(j) or SELECT(j+1) or both, must be
set to .TRUE..
If HOWMNT = 'A', SELECT is not referenced.
-
* N (input)
-
The order of the square matrix pair (A, B). N >= 0.
-
* A (input)
-
The upper quasi-triangular matrix A in the pair (A,B).
-
* LDA (input)
-
The leading dimension of the array A. LDA >= max(1,N).
-
* B (input)
-
The upper triangular matrix B in the pair (A,B).
-
* LDB (input)
-
The leading dimension of the array B. LDB >= max(1,N).
-
* VL (input)
-
If JOB = 'E' or 'B', VL must contain left eigenvectors of
(A, B), corresponding to the eigenpairs specified by HOWMNT
and SELECT. The eigenvectors must be stored in consecutive
columns of VL, as returned by STGEVC.
If JOB = 'V', VL is not referenced.
-
* LDVL (input)
-
The leading dimension of the array VL. LDVL >= 1.
If JOB = 'E' or 'B', LDVL >= N.
-
* VR (input)
-
If JOB = 'E' or 'B', VR must contain right eigenvectors of
(A, B), corresponding to the eigenpairs specified by HOWMNT
and SELECT. The eigenvectors must be stored in consecutive
columns ov VR, as returned by STGEVC.
If JOB = 'V', VR is not referenced.
-
* LDVR (input)
-
The leading dimension of the array VR. LDVR >= 1.
If JOB = 'E' or 'B', LDVR >= N.
-
* S (output)
-
If JOB = 'E' or 'B', the reciprocal condition numbers of the
selected eigenvalues, stored in consecutive elements of the
array. For a complex conjugate pair of eigenvalues two
consecutive elements of S are set to the same value. Thus
S(j), DIF(j), and the j-th columns of VL and VR all
correspond to the same eigenpair (but not in general the
j-th eigenpair, unless all eigenpairs are selected).
If JOB = 'V', S is not referenced.
-
* DIF (output)
-
If JOB = 'V' or 'B', the estimated reciprocal condition
numbers of the selected eigenvectors, stored in consecutive
elements of the array. For a complex eigenvector two
consecutive elements of DIF are set to the same value. If
the eigenvalues cannot be reordered to compute DIF(j), DIF(j)
is set to 0; this can only occur when the true value would be
very small anyway.
If JOB = 'E', DIF is not referenced.
-
* MM (input)
-
The number of elements in the arrays S and DIF. MM >= M.
-
* M (output)
-
The number of elements of the arrays S and DIF used to store
the specified condition numbers; for each selected real
eigenvalue one element is used, and for each selected complex
conjugate pair of eigenvalues, two elements are used.
If HOWMNT = 'A', M is set to N.
-
* WORK (workspace)
-
If JOB = 'E', WORK is not referenced. Otherwise,
on exit, if INFO = 0, WORK(1) returns the optimal LWORK.
-
* LWORK (input)
-
The dimension of the array WORK. LWORK >= N.
If JOB = 'V' or 'B' LWORK >= 2*N*(N+2)+16.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
-
* IWORK (workspace)
-
If JOB = 'E', IWORK is not referenced.
-
* INFO (output)
-