NAME

SYNOPSIS

  SUBROUTINE STGSNA( 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(*)
  REAL A(LDA,*), B(LDB,*), VL(LDVL,*), VR(LDVR,*), S(*), DIF(*), WORK(*)
 
  SUBROUTINE STGSNA_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(*)
  REAL A(LDA,*), B(LDB,*), VL(LDVL,*), VR(LDVR,*), S(*), DIF(*), WORK(*)
 

F95 INTERFACE

  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, DIMENSION(:) :: S, DIF, WORK
  REAL, 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, DIMENSION(:) :: S, DIF, WORK
  REAL, DIMENSION(:,:) :: A, B, VL, VR
 

C INTERFACE

void stgsna(char job, char howmnt, logical *select, int n, float *a, int lda, float *b, int ldb, float *vl, int ldvl, float *vr, int ldvr, float *s, float *dif, int mm, int *m, int *info);

void stgsna_64(char job, char howmnt, logical *select, long n, float *a, long lda, float *b, long ldb, float *vl, long ldvl, float *vr, long ldvr, float *s, float *dif, long mm, long *m, long *info);

PURPOSE

(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.

ARGUMENTS

* 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)