NAME

zhseqr - compute the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors

SYNOPSIS

  SUBROUTINE ZHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, W, Z, LDZ, WORK, 
 *      LWORK, INFO)
  CHARACTER * 1 JOB, COMPZ
  DOUBLE COMPLEX H(LDH,*), W(*), Z(LDZ,*), WORK(*)
  INTEGER N, ILO, IHI, LDH, LDZ, LWORK, INFO

  SUBROUTINE ZHSEQR_64( JOB, COMPZ, N, ILO, IHI, H, LDH, W, Z, LDZ, 
 *      WORK, LWORK, INFO)
  CHARACTER * 1 JOB, COMPZ
  DOUBLE COMPLEX H(LDH,*), W(*), Z(LDZ,*), WORK(*)
  INTEGER*8 N, ILO, IHI, LDH, LDZ, LWORK, INFO

F95 INTERFACE

  SUBROUTINE HSEQR( JOB, COMPZ, N, ILO, IHI, H, [LDH], W, Z, [LDZ], 
 *       [WORK], [LWORK], [INFO])
  CHARACTER(LEN=1) :: JOB, COMPZ
  COMPLEX(8), DIMENSION(:) :: W, WORK
  COMPLEX(8), DIMENSION(:,:) :: H, Z
  INTEGER :: N, ILO, IHI, LDH, LDZ, LWORK, INFO

  SUBROUTINE HSEQR_64( JOB, COMPZ, N, ILO, IHI, H, [LDH], W, Z, [LDZ], 
 *       [WORK], [LWORK], [INFO])
  CHARACTER(LEN=1) :: JOB, COMPZ
  COMPLEX(8), DIMENSION(:) :: W, WORK
  COMPLEX(8), DIMENSION(:,:) :: H, Z
  INTEGER(8) :: N, ILO, IHI, LDH, LDZ, LWORK, INFO

C INTERFACE

#include <sunperf.h>

void zhseqr(char job, char compz, int n, int ilo, int ihi, doublecomplex *h, int ldh, doublecomplex *w, doublecomplex *z, int ldz, int *info);

void zhseqr_64(char job, char compz, long n, long ilo, long ihi, doublecomplex *h, long ldh, doublecomplex *w, doublecomplex *z, long ldz, long *info);

PURPOSE

zhseqr computes the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors.

Optionally Z may be postmultiplied into an input unitary matrix Q, so that this routine can give the Schur factorization of a matrix A which has been reduced to the Hessenberg form H by the unitary matrix Q: A = Q*H*Q**H = (QZ)*T*(QZ)**H.

ARGUMENTS

JOB (input)

 = 'E': compute eigenvalues only;

 = 'S': compute eigenvalues and the Schur form T.

COMPZ (input)

 = 'N': no Schur vectors are computed;

 = 'I': Z is initialized to the unit matrix and the matrix Z
of Schur vectors of H is returned;
 = 'V': Z must contain an unitary matrix Q on entry, and
the product Q*Z is returned.

N (input)
The order of the matrix H. N > = 0.
ILO (input)
It is assumed that H is already upper triangular in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally set by a previous call to CGEBAL, and then passed to CGEHRD when the matrix output by CGEBAL is reduced to Hessenberg form. Otherwise ILO and IHI should be set to 1 and N respectively. 1 < = ILO < = IHI < = N, if N > 0; ILO =1 and IHI =0, if N =0.
IHI (input)
See the description of ILO.
H (input/output)
On entry, the upper Hessenberg matrix H. On exit, if JOB = 'S', H contains the upper triangular matrix T from the Schur decomposition (the Schur form). If JOB = 'E', the contents of H are unspecified on exit.
LDH (input)
The leading dimension of the array H. LDH > = max(1,N).
W (output)
The computed eigenvalues. If JOB = 'S', the eigenvalues are stored in the same order as on the diagonal of the Schur form returned in H, with W(i) = H(i,i).
Z (input/output)
If COMPZ = 'N': Z is not referenced.
If COMPZ = 'I': on entry, Z need not be set, and on exit, Z contains the unitary matrix Z of the Schur vectors of H. If COMPZ = 'V': on entry Z must contain an N-by-N matrix Q, which is assumed to be equal to the unit matrix except for the submatrix Z(ILO:IHI,ILO:IHI); on exit Z contains Q*Z. Normally Q is the unitary matrix generated by CUNGHR after the call to CGEHRD which formed the Hessenberg matrix H.
LDZ (input)
The leading dimension of the array Z. LDZ > = max(1,N) if COMPZ = 'I' or 'V'; LDZ > = 1 otherwise.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input)
The dimension of the array WORK. LWORK > = max(1,N).
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.

INFO (output)

 = 0:  successful exit

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

 > 0:  if INFO  = i, CHSEQR failed to compute all the
eigenvalues in a total of 30*(IHI-ILO+1) iterations;
elements 1:ilo-1 and i+1:n of W contain those
eigenvalues which have been successfully computed.