NAME

chsein - use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H

SYNOPSIS

  SUBROUTINE CHSEIN( SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL, 
 *      LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL, IFAILR, INFO)
  CHARACTER * 1 SIDE, EIGSRC, INITV
  COMPLEX H(LDH,*), W(*), VL(LDVL,*), VR(LDVR,*), WORK(*)
  INTEGER N, LDH, LDVL, LDVR, MM, M, INFO
  INTEGER IFAILL(*), IFAILR(*)
  LOGICAL SELECT(*)
  REAL RWORK(*)

  SUBROUTINE CHSEIN_64( SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL, 
 *      LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL, IFAILR, INFO)
  CHARACTER * 1 SIDE, EIGSRC, INITV
  COMPLEX H(LDH,*), W(*), VL(LDVL,*), VR(LDVR,*), WORK(*)
  INTEGER*8 N, LDH, LDVL, LDVR, MM, M, INFO
  INTEGER*8 IFAILL(*), IFAILR(*)
  LOGICAL*8 SELECT(*)
  REAL RWORK(*)

F95 INTERFACE

  SUBROUTINE HSEIN( SIDE, EIGSRC, INITV, SELECT, [N], H, [LDH], W, VL, 
 *       [LDVL], VR, [LDVR], MM, M, [WORK], [RWORK], IFAILL, IFAILR, [INFO])
  CHARACTER(LEN=1) :: SIDE, EIGSRC, INITV
  COMPLEX, DIMENSION(:) :: W, WORK
  COMPLEX, DIMENSION(:,:) :: H, VL, VR
  INTEGER :: N, LDH, LDVL, LDVR, MM, M, INFO
  INTEGER, DIMENSION(:) :: IFAILL, IFAILR
  LOGICAL, DIMENSION(:) :: SELECT
  REAL, DIMENSION(:) :: RWORK

  SUBROUTINE HSEIN_64( SIDE, EIGSRC, INITV, SELECT, [N], H, [LDH], W, 
 *       VL, [LDVL], VR, [LDVR], MM, M, [WORK], [RWORK], IFAILL, IFAILR, 
 *       [INFO])
  CHARACTER(LEN=1) :: SIDE, EIGSRC, INITV
  COMPLEX, DIMENSION(:) :: W, WORK
  COMPLEX, DIMENSION(:,:) :: H, VL, VR
  INTEGER(8) :: N, LDH, LDVL, LDVR, MM, M, INFO
  INTEGER(8), DIMENSION(:) :: IFAILL, IFAILR
  LOGICAL(8), DIMENSION(:) :: SELECT
  REAL, DIMENSION(:) :: RWORK

void chsein(char side, char eigsrc, char initv, logical *select, int n, complex *h, int ldh, complex *w, complex *vl, int ldvl, complex *vr, int ldvr, int mm, int *m, int *ifaill, int *ifailr, int *info);

void chsein_64(char side, char eigsrc, char initv, logical *select, long n, complex *h, long ldh, complex *w, complex *vl, long ldvl, complex *vr, long ldvr, long mm, long *m, long *ifaill, long *ifailr, long *info);

PURPOSE

chsein uses inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H.

The right eigenvector x and the left eigenvector y of the matrix H corresponding to an eigenvalue w are defined by:

             H * x = w * x,     y**h * H = w * y**h

where y**h denotes the conjugate transpose of the vector y.

ARGUMENTS

SIDE (input)

 = 'R': compute right eigenvectors only;

 = 'L': compute left eigenvectors only;

 = 'B': compute both right and left eigenvectors.

EIGSRC (input)
Specifies the source of eigenvalues supplied in W:

 = 'Q': the eigenvalues were found using CHSEQR; thus, if
H has zero subdiagonal elements, and so is
block-triangular, then the j-th eigenvalue can be
assumed to be an eigenvalue of the block containing
the j-th row/column.  This property allows CHSEIN to
perform inverse iteration on just one diagonal block.
 = 'N': no assumptions are made on the correspondence
between eigenvalues and diagonal blocks.  In this
case, CHSEIN must always perform inverse iteration
using the whole matrix H.

INITV (input)

 = 'N': no initial vectors are supplied;

 = 'U': user-supplied initial vectors are stored in the arrays
VL and/or VR.

SELECT (input)
Specifies the eigenvectors to be computed. To select the eigenvector corresponding to the eigenvalue W(j), SELECT(j) must be set to .TRUE..
N (input)
The order of the matrix H. N > = 0.
H (input)
The upper Hessenberg matrix H.
LDH (input)
The leading dimension of the array H. LDH > = max(1,N).
W (input/output)
On entry, the eigenvalues of H. On exit, the real parts of W may have been altered since close eigenvalues are perturbed slightly in searching for independent eigenvectors.
VL (input/output)
On entry, if INITV = 'U' and SIDE = 'L' or 'B', VL must contain starting vectors for the inverse iteration for the left eigenvectors; the starting vector for each eigenvector must be in the same column in which the eigenvector will be stored. On exit, if SIDE = 'L' or 'B', the left eigenvectors specified by SELECT will be stored consecutively in the columns of VL, in the same order as their eigenvalues. If SIDE = 'R', VL is not referenced.
LDVL (input)
The leading dimension of the array VL. LDVL > = max(1,N) if SIDE = 'L' or 'B'; LDVL > = 1 otherwise.
VR (input/output)
On entry, if INITV = 'U' and SIDE = 'R' or 'B', VR must contain starting vectors for the inverse iteration for the right eigenvectors; the starting vector for each eigenvector must be in the same column in which the eigenvector will be stored. On exit, if SIDE = 'R' or 'B', the right eigenvectors specified by SELECT will be stored consecutively in the columns of VR, in the same order as their eigenvalues. If SIDE = 'L', VR is not referenced.
LDVR (input)
The leading dimension of the array VR. LDVR > = max(1,N) if SIDE = 'R' or 'B'; LDVR > = 1 otherwise.
MM (input)
The number of columns in the arrays VL and/or VR. MM > = M.
M (output)
The number of columns in the arrays VL and/or VR required to store the eigenvectors ( = the number of .TRUE. elements in SELECT).
WORK (workspace)
dimension(N*N)
RWORK (workspace)
dimension(N)
IFAILL (output)
If SIDE = 'L' or 'B', IFAILL(i) = j > 0 if the left eigenvector in the i-th column of VL (corresponding to the eigenvalue w(j)) failed to converge; IFAILL(i) = 0 if the eigenvector converged satisfactorily. If SIDE = 'R', IFAILL is not referenced.
IFAILR (output)
If SIDE = 'R' or 'B', IFAILR(i) = j > 0 if the right eigenvector in the i-th column of VR (corresponding to the eigenvalue w(j)) failed to converge; IFAILR(i) = 0 if the eigenvector converged satisfactorily. If SIDE = 'L', IFAILR is not referenced.

INFO (output)

 = 0:  successful exit

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

 > 0:  if INFO  = i, i is the number of eigenvectors which
failed to converge; see IFAILL and IFAILR for further
details.

FURTHER DETAILS