#include "blaswrap.h"
#include "f2c.h"
/* Subroutine */ int cgees_(char *jobvs, char *sort, L_fp select, integer *n,
complex *a, integer *lda, integer *sdim, complex *w, complex *vs,
integer *ldvs, complex *work, integer *lwork, real *rwork, logical *
bwork, integer *info)
{
/* -- LAPACK driver routine (version 3.1) --
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
Purpose
=======
CGEES computes for an N-by-N complex nonsymmetric matrix A, the
eigenvalues, 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.
The leading columns of Z then form an orthonormal basis for the
invariant subspace corresponding to the selected eigenvalues.
A complex matrix is in Schur form if it is upper triangular.
Arguments
=========
JOBVS (input) CHARACTER*1
= 'N': Schur vectors are not computed;
= 'V': Schur vectors are computed.
SORT (input) CHARACTER*1
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 (external procedure) LOGICAL FUNCTION of one COMPLEX argument
SELECT must be declared EXTERNAL in the calling subroutine.
If SORT = 'S', SELECT is used to select eigenvalues to order
to the top left of the Schur form.
IF SORT = 'N', SELECT is not referenced.
The eigenvalue W(j) is selected if SELECT(W(j)) is true.
N (input) INTEGER
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 has been overwritten by its Schur form T.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
SDIM (output) INTEGER
If SORT = 'N', SDIM = 0.
If SORT = 'S', SDIM = number of eigenvalues for which
SELECT is true.
W (output) COMPLEX array, dimension (N)
W contains the computed eigenvalues, in the same order that
they appear on the diagonal of the output Schur form T.
VS (output) COMPLEX array, dimension (LDVS,N)
If JOBVS = 'V', VS contains the unitary matrix Z of Schur
vectors.
If JOBVS = 'N', VS is not referenced.
LDVS (input) INTEGER
The leading dimension of the array VS. LDVS >= 1; if
JOBVS = 'V', LDVS >= N.
WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,2*N).
For good performance, LWORK must generally be larger.
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.
RWORK (workspace) REAL array, dimension (N)
BWORK (workspace) LOGICAL array, dimension (N)
Not referenced if SORT = 'N'.
INFO (output) INTEGER
= 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 JOBVS = 'V', VS contains the matrix 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.
=====================================================================
Test the input arguments
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
static integer c__0 = 0;
static integer c_n1 = -1;
/* System generated locals */
integer a_dim1, a_offset, vs_dim1, vs_offset, i__1, i__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static integer i__;
static real s;
static integer ihi, ilo;
static real dum[1], eps, sep;
static integer ibal;
static real anrm;
static integer ierr, itau, iwrk, icond, ieval;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *), cgebak_(char *, char *, integer *, integer
*, integer *, real *, integer *, complex *, integer *, integer *), cgebal_(char *, integer *, complex *, integer *,
integer *, integer *, real *, integer *), slabad_(real *,
real *);
static logical scalea;
extern doublereal clange_(char *, integer *, integer *, complex *,
integer *, real *);
static real cscale;
extern /* Subroutine */ int cgehrd_(integer *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *, integer *),
clascl_(char *, integer *, integer *, real *, real *, integer *,
integer *, complex *, integer *, integer *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
*, integer *, complex *, integer *), xerbla_(char *,
integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static real bignum;
extern /* Subroutine */ int chseqr_(char *, char *, integer *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
complex *, integer *, integer *), cunghr_(integer
*, integer *, integer *, complex *, integer *, complex *, complex
*, integer *, integer *), ctrsen_(char *, char *, logical *,
integer *, complex *, integer *, complex *, integer *, complex *,
integer *, real *, real *, complex *, integer *, integer *);
static integer minwrk, maxwrk;
static real smlnum;
static integer hswork;
static logical wantst, lquery, wantvs;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--w;
vs_dim1 = *ldvs;
vs_offset = 1 + vs_dim1;
vs -= vs_offset;
--work;
--rwork;
--bwork;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
wantvs = lsame_(jobvs, "V");
wantst = lsame_(sort, "S");
if (! wantvs && ! lsame_(jobvs, "N")) {
*info = -1;
} else if (! wantst && ! lsame_(sort, "N")) {
*info = -2;
} else if (*n < 0) {
*info = -4;
} else if (*lda < max(1,*n)) {
*info = -6;
} else if (*ldvs < 1 || wantvs && *ldvs < *n) {
*info = -10;
}
/* Compute workspace
(Note: Comments in the code beginning "Workspace:" describe the
minimal amount of workspace needed at that point in the code,
as well as the preferred amount for good performance.
CWorkspace refers to complex workspace, and RWorkspace to real
workspace. NB refers to the optimal block size for the
immediately following subroutine, as returned by ILAENV.
HSWORK refers to the workspace preferred by CHSEQR, as
calculated below. HSWORK is computed assuming ILO=1 and IHI=N,
the worst case.) */
if (*info == 0) {
if (*n == 0) {
minwrk = 1;
maxwrk = 1;
} else {
maxwrk = *n + *n * ilaenv_(&c__1, "CGEHRD", " ", n, &c__1, n, &
c__0, (ftnlen)6, (ftnlen)1);
minwrk = *n << 1;
chseqr_("S", jobvs, n, &c__1, n, &a[a_offset], lda, &w[1], &vs[
vs_offset], ldvs, &work[1], &c_n1, &ieval);
hswork = work[1].r;
if (! wantvs) {
maxwrk = max(maxwrk,hswork);
} else {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "CUNGHR",
" ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = max(i__1,i__2);
maxwrk = max(maxwrk,hswork);
}
}
work[1].r = (real) maxwrk, work[1].i = 0.f;
if (*lwork < minwrk && ! lquery) {
*info = -12;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGEES ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
*sdim = 0;
return 0;
}
/* Get machine constants */
eps = slamch_("P");
smlnum = slamch_("S");
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
smlnum = sqrt(smlnum) / eps;
bignum = 1.f / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = clange_("M", n, n, &a[a_offset], lda, dum);
scalea = FALSE_;
if (anrm > 0.f && anrm < smlnum) {
scalea = TRUE_;
cscale = smlnum;
} else if (anrm > bignum) {
scalea = TRUE_;
cscale = bignum;
}
if (scalea) {
clascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
ierr);
}
/* Permute the matrix to make it more nearly triangular
(CWorkspace: none)
(RWorkspace: need N) */
ibal = 1;
cgebal_("P", n, &a[a_offset], lda, &ilo, &ihi, &rwork[ibal], &ierr);
/* Reduce to upper Hessenberg form
(CWorkspace: need 2*N, prefer N+N*NB)
(RWorkspace: none) */
itau = 1;
iwrk = *n + itau;
i__1 = *lwork - iwrk + 1;
cgehrd_(n, &ilo, &ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1,
&ierr);
if (wantvs) {
/* Copy Householder vectors to VS */
clacpy_("L", n, n, &a[a_offset], lda, &vs[vs_offset], ldvs)
;
/* Generate unitary matrix in VS
(CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
(RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
cunghr_(n, &ilo, &ihi, &vs[vs_offset], ldvs, &work[itau], &work[iwrk],
&i__1, &ierr);
}
*sdim = 0;
/* Perform QR iteration, accumulating Schur vectors in VS if desired
(CWorkspace: need 1, prefer HSWORK (see comments) )
(RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
chseqr_("S", jobvs, n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vs[
vs_offset], ldvs, &work[iwrk], &i__1, &ieval);
if (ieval > 0) {
*info = ieval;
}
/* Sort eigenvalues if desired */
if (wantst && *info == 0) {
if (scalea) {
clascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &w[1], n, &
ierr);
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
bwork[i__] = (*select)(&w[i__]);
/* L10: */
}
/* Reorder eigenvalues and transform Schur vectors
(CWorkspace: none)
(RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
ctrsen_("N", jobvs, &bwork[1], n, &a[a_offset], lda, &vs[vs_offset],
ldvs, &w[1], sdim, &s, &sep, &work[iwrk], &i__1, &icond);
}
if (wantvs) {
/* Undo balancing
(CWorkspace: none)
(RWorkspace: need N) */
cgebak_("P", "R", n, &ilo, &ihi, &rwork[ibal], n, &vs[vs_offset],
ldvs, &ierr);
}
if (scalea) {
/* Undo scaling for the Schur form of A */
clascl_("U", &c__0, &c__0, &cscale, &anrm, n, n, &a[a_offset], lda, &
ierr);
i__1 = *lda + 1;
ccopy_(n, &a[a_offset], &i__1, &w[1], &c__1);
}
work[1].r = (real) maxwrk, work[1].i = 0.f;
return 0;
/* End of CGEES */
} /* cgees_ */