cgeesx(3P) Sun Performance Library cgeesx(3P)NAMEcgeesx - compute for an N-by-N complex nonsymmetric matrix A, the ei‐
genvalues, the Schur form T, and, optionally, the matrix of Schur vec‐
tors Z
SYNOPSIS
SUBROUTINE CGEESX(JOBZ, SORTEV, SELECT, SENSE, N, A, LDA, NOUT, W, Z,
LDZ, RCONE, RCONV, WORK, LDWORK, WORK2, BWORK3, INFO)
CHARACTER * 1 JOBZ, SORTEV, SENSE
COMPLEX A(LDA,*), W(*), Z(LDZ,*), WORK(*)
INTEGER N, LDA, NOUT, LDZ, LDWORK, INFO
LOGICAL SELECT
LOGICAL BWORK3(*)
REAL RCONE, RCONV
REAL WORK2(*)
SUBROUTINE CGEESX_64(JOBZ, SORTEV, SELECT, SENSE, N, A, LDA, NOUT, W,
Z, LDZ, RCONE, RCONV, WORK, LDWORK, WORK2, BWORK3, INFO)
CHARACTER * 1 JOBZ, SORTEV, SENSE
COMPLEX A(LDA,*), W(*), Z(LDZ,*), WORK(*)
INTEGER*8 N, LDA, NOUT, LDZ, LDWORK, INFO
LOGICAL*8 SELECT
LOGICAL*8 BWORK3(*)
REAL RCONE, RCONV
REAL WORK2(*)
F95 INTERFACE
SUBROUTINE GEESX(JOBZ, SORTEV, SELECT, SENSE, [N], A, [LDA], NOUT, W,
Z, [LDZ], RCONE, RCONV, [WORK], [LDWORK], [WORK2], [BWORK3],
[INFO])
CHARACTER(LEN=1) :: JOBZ, SORTEV, SENSE
COMPLEX, DIMENSION(:) :: W, WORK
COMPLEX, DIMENSION(:,:) :: A, Z
INTEGER :: N, LDA, NOUT, LDZ, LDWORK, INFO
LOGICAL :: SELECT
LOGICAL, DIMENSION(:) :: BWORK3
REAL :: RCONE, RCONV
REAL, DIMENSION(:) :: WORK2
SUBROUTINE GEESX_64(JOBZ, SORTEV, SELECT, SENSE, [N], A, [LDA], NOUT,
W, Z, [LDZ], RCONE, RCONV, [WORK], [LDWORK], [WORK2], [BWORK3],
[INFO])
CHARACTER(LEN=1) :: JOBZ, SORTEV, SENSE
COMPLEX, DIMENSION(:) :: W, WORK
COMPLEX, DIMENSION(:,:) :: A, Z
INTEGER(8) :: N, LDA, NOUT, LDZ, LDWORK, INFO
LOGICAL(8) :: SELECT
LOGICAL(8), DIMENSION(:) :: BWORK3
REAL :: RCONE, RCONV
REAL, DIMENSION(:) :: WORK2
C INTERFACE
#include <sunperf.h>
void cgeesx(char jobz, char sortev, int(*select)(complex), char sense,
int n, complex *a, int lda, int *nout, complex *w, complex
*z, int ldz, float *rcone, float *rconv, int *info);
void cgeesx_64(char jobz, char sortev, long(*select)(complex), char
sense, long n, complex *a, long lda, long *nout, complex *w,
complex *z, long ldz, float *rcone, float *rconv, long
*info);
PURPOSEcgeesx computes for an N-by-N complex nonsymmetric matrix A, the eigen‐
values, the Schur form T, and, optionally, the matrix of Schur vectors
Z. This gives the Schur factorization A = Z*T*(Z**H).
Optionally, it also orders the eigenvalues on the diagonal of the Schur
form so that selected eigenvalues are at the top left; computes a
reciprocal condition number for the average of the selected eigenvalues
(RCONDE); and computes a reciprocal condition number for the right
invariant subspace corresponding to the selected eigenvalues (RCONDV).
The leading columns of Z form an orthonormal basis for this invariant
subspace.
For further explanation of the reciprocal condition numbers RCONDE and
RCONDV, see Section 4.10 of the LAPACK Users' Guide (where these quan‐
tities are called s and sep respectively).
A complex matrix is in Schur form if it is upper triangular.
ARGUMENTS
JOBZ (input)
= 'N': Schur vectors are not computed;
= 'V': Schur vectors are computed.
SORTEV (input)
Specifies whether or not to order the eigenvalues on the
diagonal of the Schur form. = 'N': Eigenvalues are not
ordered;
= 'S': Eigenvalues are ordered (see SELECT).
SELECT (input)
LOGICAL FUNCTION of one COMPLEX argument SELECT must be
declared EXTERNAL in the calling subroutine. If SORTEV =
'S', SELECT is used to select eigenvalues to order to the top
left of the Schur form. If SORTEV = 'N', SELECT is not ref‐
erenced. An eigenvalue W(j) is selected if SELECT(W(j)) is
true.
SENSE (input)
Determines which reciprocal condition numbers are computed.
= 'N': None are computed;
= 'E': Computed for average of selected eigenvalues only;
= 'V': Computed for selected right invariant subspace only;
= 'B': Computed for both. If SENSE = 'E', 'V' or 'B', SORTEV
must equal 'S'.
N (input) The order of the matrix A. N >= 0.
A (input/output)
COMPLEX array, dimension(LDA,N) On entry, the N-by-N matrix
A. On exit, A is overwritten by its Schur form T.
LDA (input)
The leading dimension of the array A. LDA >= max(1,N).
NOUT (output)
If SORTEV = 'N', NOUT = 0. If SORTEV = 'S', NOUT = number of
eigenvalues for which SELECT is true.
W (output)
COMPLEX array, dimension(N) W contains the computed eigenval‐
ues, in the same order that they appear on the diagonal of
the output Schur form T.
Z (output)
COMPLEX array, dimension(LDZ,N) If JOBZ = 'V', Z contains the
unitary matrix Z of Schur vectors. If JOBZ = 'N', Z is not
referenced.
LDZ (input)
The leading dimension of the array Z. LDZ >= 1, and if JOBZ
= 'V', LDZ >= N.
RCONE (output)
If SENSE = 'E' or 'B', RCONE contains the reciprocal condi‐
tion number for the average of the selected eigenvalues. Not
referenced if SENSE = 'N' or 'V'.
RCONV (output)
If SENSE = 'V' or 'B', RCONV contains the reciprocal condi‐
tion number for the selected right invariant subspace. Not
referenced if SENSE = 'N' or 'E'.
WORK (workspace)
COMPLEX array, dimension(LDWORK) On exit, if INFO = 0,
WORK(1) returns the optimal LDWORK.
LDWORK (input)
The dimension of the array WORK. LDWORK >= max(1,2*N).
Also, if SENSE = 'E' or 'V' or 'B', LDWORK >= 2*NOUT*(N-
NOUT), where NOUT is the number of selected eigenvalues com‐
puted by this routine. Note that 2*NOUT*(N-NOUT) <= N*N/2.
For good performance, LDWORK must generally be larger.
WORK2 (workspace)
REAL array, dimension(N)
BWORK3 (workspace)
LOGICAL array, dimension(N) Not referenced if SORTEV = 'N'.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, and i is
<= N: the QR algorithm failed to compute all the
eigenvalues; elements 1:ILO-1 and i+1:N of W contain those
eigenvalues which have converged; if JOBZ = 'V', Z contains
the transformation which reduces A to its partially converged
Schur form. = N+1: the eigenvalues could not be reordered
because some eigenvalues were too close to separate (the
problem is very ill-conditioned); = N+2: after reordering,
roundoff changed values of some complex eigenvalues so that
leading eigenvalues in the Schur form no longer satisfy
SELECT=.TRUE. This could also be caused by underflow due to
scaling.
6 Mar 2009 cgeesx(3P)
