
CHSEQR(l) ) CHSEQR(l)
NAME
CHSEQR  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 trian
gular matrix (the Schur form), and Z is the unitary matrix of Schur vectors
SYNOPSIS
SUBROUTINE CHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, W, Z, LDZ, WORK, LWORK, INFO )
CHARACTER COMPZ, JOB
INTEGER IHI, ILO, INFO, LDH, LDZ, LWORK, N
COMPLEX H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * )
PURPOSE
CHSEQR 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 trian
gular 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) CHARACTER*1
= 'E': compute eigenvalues only;
= 'S': compute eigenvalues and the Schur form T.
COMPZ (input) CHARACTER*1
= '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) INTEGER
The order of the matrix H. N >= 0.
ILO (input) INTEGER
IHI (input) INTEGER It is assumed that H is already upper triangular in rows
and columns 1:ILO1 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.
H (input/output) COMPLEX array, dimension (LDH,N)
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) INTEGER
The leading dimension of the array H. LDH >= max(1,N).
W (output) COMPLEX array, dimension (N)
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) COMPLEX array, dimension (LDZ,N)
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
byN 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) INTEGER
The leading dimension of the array Z. LDZ >= max(1,N) if COMPZ = 'I' or 'V'; LDZ
>= 1 otherwise.
WORK (workspace/output) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
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) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
> 0: if INFO = i, CHSEQR failed to compute all the eigenvalues in a total of
30*(IHIILO+1) iterations; elements 1:ilo1 and i+1:n of W contain those eigenval
ues which have been successfully computed.
LAPACK version 3.0 15 June 2000 CHSEQR(l) 
