Contents
zhseqr - compute the eigenvalues of a complex upper Hessen-
berg 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
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, char, int, int, int, doublecomplex*, int,
doublecomplex*, doublecomplex*, int, int*);
void zhseqr_64 (char, char, long, long, long, doublecom-
plex*, long, doublecomplex*, doublecomplex*, long,
long*);
zhseqr computes the eigenvalues of a complex upper Hessen-
berg 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 factoriza-
tion 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.
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 eigen-
values 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 sub-
matrix 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 other-
wise.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal
LWORK.
LWORK (output)
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 ille-
gal 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 con-
tain those eigenvalues which have been success-
fully computed.