ZHSEQR(3F) ZHSEQR(3F)
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
SUBROUTINE ZHSEQR( 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*16 H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * )
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.
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:ILO-1 and IHI+1:N. ILO and IHI
are normally set by a previous call to ZGEBAL, and then passed to
CGEHRD when the matrix output by ZGEBAL 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.
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ZHSEQR(3F) ZHSEQR(3F)
H (input/output) COMPLEX*16 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*16 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*16 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-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) INTEGER
The leading dimension of the array Z. LDZ >= max(1,N) if COMPZ =
'I' or 'V'; LDZ >= 1 otherwise.
WORK (workspace) COMPLEX*16 array, dimension (N)
LWORK (input) INTEGER
This argument is currently redundant.
INFO (output) INTEGER
= 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 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.
ZHSEQR(3F) ZHSEQR(3F)
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
SUBROUTINE ZHSEQR( 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*16 H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * )
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.
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:ILO-1 and IHI+1:N. ILO and IHI
are normally set by a previous call to ZGEBAL, and then passed to
CGEHRD when the matrix output by ZGEBAL 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.
Page 1
ZHSEQR(3F) ZHSEQR(3F)
H (input/output) COMPLEX*16 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*16 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*16 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-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) INTEGER
The leading dimension of the array Z. LDZ >= max(1,N) if COMPZ =
'I' or 'V'; LDZ >= 1 otherwise.
WORK (workspace) COMPLEX*16 array, dimension (N)
LWORK (input) INTEGER
This argument is currently redundant.
INFO (output) INTEGER
= 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 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.
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