zhseqr(3P) Sun Performance Library zhseqr(3P)NAMEzhseqr - 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, doublecom‐
plex* h, int ldh, doublecomplex* w, doublecomplex* z, int
ldz, int* info);
void zhseqr_64 (char job, char compz, long n, long ilo, long ihi, dou‐
blecomplex* h, long ldh, doublecomplex* w, doublecomplex* z,
long ldz, long* info);
PURPOSEzhseqr 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 ZGEBAL, and then passed to ZGEHRD when the
matrix output by ZGEBAL is reduced to Hessenberg form. Other‐
wise 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) 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 ZUNGHR after
the call to ZGEHRD 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, ZHSEQR failed to compute all the eigenval‐
ues 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 suc‐
cessfully computed.
6 Mar 2009 zhseqr(3P)
