int zgges_(char *jobvsl, char *jobvsr, char *sort, L_fp
selctg, int *n, doublecomplex *a, int *lda, doublecomplex *b,
int *ldb, int *sdim, doublecomplex *alpha, doublecomplex *
beta, doublecomplex *vsl, int *ldvsl, doublecomplex *vsr, int
*ldvsr, doublecomplex *work, int *lwork, double *rwork,
int *bwork, int *info)
{
/* System generated locals */
int a_dim1, a_offset, b_dim1, b_offset, vsl_dim1, vsl_offset,
vsr_dim1, vsr_offset, i__1, i__2;
/* Builtin functions */
double sqrt(double);
/* Local variables */
int i__;
double dif[2];
int ihi, ilo;
double eps, anrm, bnrm;
int idum[1], ierr, itau, iwrk;
double pvsl, pvsr;
extern int lsame_(char *, char *);
int ileft, icols;
int cursl, ilvsl, ilvsr;
int irwrk, irows;
extern int dlabad_(double *, double *);
extern double dlamch_(char *);
extern int zggbak_(char *, char *, int *, int *,
int *, double *, double *, int *, doublecomplex *,
int *, int *), zggbal_(char *, int *,
doublecomplex *, int *, doublecomplex *, int *, int *
, int *, double *, double *, double *, int *);
int ilascl, ilbscl;
extern int xerbla_(char *, int *);
extern int ilaenv_(int *, char *, char *, int *, int *,
int *, int *);
extern double zlange_(char *, int *, int *, doublecomplex *,
int *, double *);
double bignum;
int ijobvl, iright;
extern int zgghrd_(char *, char *, int *, int *,
int *, doublecomplex *, int *, doublecomplex *, int *,
doublecomplex *, int *, doublecomplex *, int *, int *
), zlascl_(char *, int *, int *,
double *, double *, int *, int *, doublecomplex *,
int *, int *);
int ijobvr;
extern int zgeqrf_(int *, int *, doublecomplex *,
int *, doublecomplex *, doublecomplex *, int *, int *
);
double anrmto;
int lwkmin;
int lastsl;
double bnrmto;
extern int zlacpy_(char *, int *, int *,
doublecomplex *, int *, doublecomplex *, int *),
zlaset_(char *, int *, int *, doublecomplex *,
doublecomplex *, doublecomplex *, int *), zhgeqz_(
char *, char *, char *, int *, int *, int *,
doublecomplex *, int *, doublecomplex *, int *,
doublecomplex *, doublecomplex *, doublecomplex *, int *,
doublecomplex *, int *, doublecomplex *, int *,
double *, int *), ztgsen_(int
*, int *, int *, int *, int *, doublecomplex *,
int *, doublecomplex *, int *, doublecomplex *,
doublecomplex *, doublecomplex *, int *, doublecomplex *,
int *, int *, double *, double *, double *,
doublecomplex *, int *, int *, int *, int *);
double smlnum;
int wantst, lquery;
int lwkopt;
extern int zungqr_(int *, int *, int *,
doublecomplex *, int *, doublecomplex *, doublecomplex *,
int *, int *), zunmqr_(char *, char *, int *, int
*, int *, doublecomplex *, int *, doublecomplex *,
doublecomplex *, int *, doublecomplex *, int *, int *);
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* .. Function Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGGES computes for a pair of N-by-N complex nonsymmetric matrices */
/* (A,B), the generalized eigenvalues, the generalized complex Schur */
/* form (S, T), and optionally left and/or right Schur vectors (VSL */
/* and VSR). This gives the generalized Schur factorization */
/* (A,B) = ( (VSL)*S*(VSR)**H, (VSL)*T*(VSR)**H ) */
/* where (VSR)**H is the conjugate-transpose of VSR. */
/* Optionally, it also orders the eigenvalues so that a selected cluster */
/* of eigenvalues appears in the leading diagonal blocks of the upper */
/* triangular matrix S and the upper triangular matrix T. The leading */
/* columns of VSL and VSR then form an unitary basis for the */
/* corresponding left and right eigenspaces (deflating subspaces). */
/* (If only the generalized eigenvalues are needed, use the driver */
/* ZGGEV instead, which is faster.) */
/* A generalized eigenvalue for a pair of matrices (A,B) is a scalar w */
/* or a ratio alpha/beta = w, such that A - w*B is singular. It is */
/* usually represented as the pair (alpha,beta), as there is a */
/* reasonable interpretation for beta=0, and even for both being zero. */
/* A pair of matrices (S,T) is in generalized complex Schur form if S */
/* and T are upper triangular and, in addition, the diagonal elements */
/* of T are non-negative float numbers. */
/* Arguments */
/* ========= */
/* JOBVSL (input) CHARACTER*1 */
/* = 'N': do not compute the left Schur vectors; */
/* = 'V': compute the left Schur vectors. */
/* JOBVSR (input) CHARACTER*1 */
/* = 'N': do not compute the right Schur vectors; */
/* = 'V': compute the right Schur vectors. */
/* SORT (input) CHARACTER*1 */
/* Specifies whether or not to order the eigenvalues on the */
/* diagonal of the generalized Schur form. */
/* = 'N': Eigenvalues are not ordered; */
/* = 'S': Eigenvalues are ordered (see SELCTG). */
/* SELCTG (external procedure) LOGICAL FUNCTION of two COMPLEX*16 arguments */
/* SELCTG must be declared EXTERNAL in the calling subroutine. */
/* If SORT = 'N', SELCTG is not referenced. */
/* If SORT = 'S', SELCTG is used to select eigenvalues to sort */
/* to the top left of the Schur form. */
/* An eigenvalue ALPHA(j)/BETA(j) is selected if */
/* SELCTG(ALPHA(j),BETA(j)) is true. */
/* Note that a selected complex eigenvalue may no longer satisfy */
/* SELCTG(ALPHA(j),BETA(j)) = .TRUE. after ordering, since */
/* ordering may change the value of complex eigenvalues */
/* (especially if the eigenvalue is ill-conditioned), in this */
/* case INFO is set to N+2 (See INFO below). */
/* N (input) INTEGER */
/* The order of the matrices A, B, VSL, and VSR. N >= 0. */
/* A (input/output) COMPLEX*16 array, dimension (LDA, N) */
/* On entry, the first of the pair of matrices. */
/* On exit, A has been overwritten by its generalized Schur */
/* form S. */
/* LDA (input) INTEGER */
/* The leading dimension of A. LDA >= MAX(1,N). */
/* B (input/output) COMPLEX*16 array, dimension (LDB, N) */
/* On entry, the second of the pair of matrices. */
/* On exit, B has been overwritten by its generalized Schur */
/* form T. */
/* LDB (input) INTEGER */
/* The leading dimension of B. LDB >= MAX(1,N). */
/* SDIM (output) INTEGER */
/* If SORT = 'N', SDIM = 0. */
/* If SORT = 'S', SDIM = number of eigenvalues (after sorting) */
/* for which SELCTG is true. */
/* ALPHA (output) COMPLEX*16 array, dimension (N) */
/* BETA (output) COMPLEX*16 array, dimension (N) */
/* On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the */
/* generalized eigenvalues. ALPHA(j), j=1,...,N and BETA(j), */
/* j=1,...,N are the diagonals of the complex Schur form (A,B) */
/* output by ZGGES. The BETA(j) will be non-negative float. */
/* Note: the quotients ALPHA(j)/BETA(j) may easily over- or */
/* underflow, and BETA(j) may even be zero. Thus, the user */
/* should avoid naively computing the ratio alpha/beta. */
/* However, ALPHA will be always less than and usually */
/* comparable with norm(A) in magnitude, and BETA always less */
/* than and usually comparable with norm(B). */
/* VSL (output) COMPLEX*16 array, dimension (LDVSL,N) */
/* If JOBVSL = 'V', VSL will contain the left Schur vectors. */
/* Not referenced if JOBVSL = 'N'. */
/* LDVSL (input) INTEGER */
/* The leading dimension of the matrix VSL. LDVSL >= 1, and */
/* if JOBVSL = 'V', LDVSL >= N. */
/* VSR (output) COMPLEX*16 array, dimension (LDVSR,N) */
/* If JOBVSR = 'V', VSR will contain the right Schur vectors. */
/* Not referenced if JOBVSR = 'N'. */
/* LDVSR (input) INTEGER */
/* The leading dimension of the matrix VSR. LDVSR >= 1, and */
/* if JOBVSR = 'V', LDVSR >= N. */
/* WORK (workspace/output) COMPLEX*16 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) DOUBLE PRECISION array, dimension (8*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. */
/* =1,...,N: */
/* The QZ iteration failed. (A,B) are not in Schur */
/* form, but ALPHA(j) and BETA(j) should be correct for */
/* j=INFO+1,...,N. */
/* > N: =N+1: other than QZ iteration failed in ZHGEQZ */
/* =N+2: after reordering, roundoff changed values of */
/* some complex eigenvalues so that leading */
/* eigenvalues in the Generalized Schur form no */
/* longer satisfy SELCTG=.TRUE. This could also */
/* be caused due to scaling. */
/* =N+3: reordering falied in ZTGSEN. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Decode the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--alpha;
--beta;
vsl_dim1 = *ldvsl;
vsl_offset = 1 + vsl_dim1;
vsl -= vsl_offset;
vsr_dim1 = *ldvsr;
vsr_offset = 1 + vsr_dim1;
vsr -= vsr_offset;
--work;
--rwork;
--bwork;
/* Function Body */
if (lsame_(jobvsl, "N")) {
ijobvl = 1;
ilvsl = FALSE;
} else if (lsame_(jobvsl, "V")) {
ijobvl = 2;
ilvsl = TRUE;
} else {
ijobvl = -1;
ilvsl = FALSE;
}
if (lsame_(jobvsr, "N")) {
ijobvr = 1;
ilvsr = FALSE;
} else if (lsame_(jobvsr, "V")) {
ijobvr = 2;
ilvsr = TRUE;
} else {
ijobvr = -1;
ilvsr = FALSE;
}
wantst = lsame_(sort, "S");
/* Test the input arguments */
*info = 0;
lquery = *lwork == -1;
if (ijobvl <= 0) {
*info = -1;
} else if (ijobvr <= 0) {
*info = -2;
} else if (! wantst && ! lsame_(sort, "N")) {
*info = -3;
} else if (*n < 0) {
*info = -5;
} else if (*lda < MAX(1,*n)) {
*info = -7;
} else if (*ldb < MAX(1,*n)) {
*info = -9;
} else if (*ldvsl < 1 || ilvsl && *ldvsl < *n) {
*info = -14;
} else if (*ldvsr < 1 || ilvsr && *ldvsr < *n) {
*info = -16;
}
/* 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. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV.) */
if (*info == 0) {
/* Computing MAX */
i__1 = 1, i__2 = *n << 1;
lwkmin = MAX(i__1,i__2);
/* Computing MAX */
i__1 = 1, i__2 = *n + *n * ilaenv_(&c__1, "ZGEQRF", " ", n, &c__1, n,
&c__0);
lwkopt = MAX(i__1,i__2);
/* Computing MAX */
i__1 = lwkopt, i__2 = *n + *n * ilaenv_(&c__1, "ZUNMQR", " ", n, &
c__1, n, &c_n1);
lwkopt = MAX(i__1,i__2);
if (ilvsl) {
/* Computing MAX */
i__1 = lwkopt, i__2 = *n + *n * ilaenv_(&c__1, "ZUNGQR", " ", n, &
c__1, n, &c_n1);
lwkopt = MAX(i__1,i__2);
}
work[1].r = (double) lwkopt, work[1].i = 0.;
if (*lwork < lwkmin && ! lquery) {
*info = -18;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGGES ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
*sdim = 0;
return 0;
}
/* Get machine constants */
eps = dlamch_("P");
smlnum = dlamch_("S");
bignum = 1. / smlnum;
dlabad_(&smlnum, &bignum);
smlnum = sqrt(smlnum) / eps;
bignum = 1. / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = zlange_("M", n, n, &a[a_offset], lda, &rwork[1]);
ilascl = FALSE;
if (anrm > 0. && anrm < smlnum) {
anrmto = smlnum;
ilascl = TRUE;
} else if (anrm > bignum) {
anrmto = bignum;
ilascl = TRUE;
}
if (ilascl) {
zlascl_("G", &c__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, &
ierr);
}
/* Scale B if max element outside range [SMLNUM,BIGNUM] */
bnrm = zlange_("M", n, n, &b[b_offset], ldb, &rwork[1]);
ilbscl = FALSE;
if (bnrm > 0. && bnrm < smlnum) {
bnrmto = smlnum;
ilbscl = TRUE;
} else if (bnrm > bignum) {
bnrmto = bignum;
ilbscl = TRUE;
}
if (ilbscl) {
zlascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
ierr);
}
/* Permute the matrix to make it more nearly triangular */
/* (Real Workspace: need 6*N) */
ileft = 1;
iright = *n + 1;
irwrk = iright + *n;
zggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &rwork[
ileft], &rwork[iright], &rwork[irwrk], &ierr);
/* Reduce B to triangular form (QR decomposition of B) */
/* (Complex Workspace: need N, prefer N*NB) */
irows = ihi + 1 - ilo;
icols = *n + 1 - ilo;
itau = 1;
iwrk = itau + irows;
i__1 = *lwork + 1 - iwrk;
zgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
iwrk], &i__1, &ierr);
/* Apply the orthogonal transformation to matrix A */
/* (Complex Workspace: need N, prefer N*NB) */
i__1 = *lwork + 1 - iwrk;
zunmqr_("L", "C", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, &
work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwrk], &i__1, &
ierr);
/* Initialize VSL */
/* (Complex Workspace: need N, prefer N*NB) */
if (ilvsl) {
zlaset_("Full", n, n, &c_b1, &c_b2, &vsl[vsl_offset], ldvsl);
if (irows > 1) {
i__1 = irows - 1;
i__2 = irows - 1;
zlacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vsl[
ilo + 1 + ilo * vsl_dim1], ldvsl);
}
i__1 = *lwork + 1 - iwrk;
zungqr_(&irows, &irows, &irows, &vsl[ilo + ilo * vsl_dim1], ldvsl, &
work[itau], &work[iwrk], &i__1, &ierr);
}
/* Initialize VSR */
if (ilvsr) {
zlaset_("Full", n, n, &c_b1, &c_b2, &vsr[vsr_offset], ldvsr);
}
/* Reduce to generalized Hessenberg form */
/* (Workspace: none needed) */
zgghrd_(jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset],
ldb, &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &ierr);
*sdim = 0;
/* Perform QZ algorithm, computing Schur vectors if desired */
/* (Complex Workspace: need N) */
/* (Real Workspace: need N) */
iwrk = itau;
i__1 = *lwork + 1 - iwrk;
zhgeqz_("S", jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[
b_offset], ldb, &alpha[1], &beta[1], &vsl[vsl_offset], ldvsl, &
vsr[vsr_offset], ldvsr, &work[iwrk], &i__1, &rwork[irwrk], &ierr);
if (ierr != 0) {
if (ierr > 0 && ierr <= *n) {
*info = ierr;
} else if (ierr > *n && ierr <= *n << 1) {
*info = ierr - *n;
} else {
*info = *n + 1;
}
goto L30;
}
/* Sort eigenvalues ALPHA/BETA if desired */
/* (Workspace: none needed) */
if (wantst) {
/* Undo scaling on eigenvalues before selecting */
if (ilascl) {
zlascl_("G", &c__0, &c__0, &anrm, &anrmto, n, &c__1, &alpha[1], n,
&ierr);
}
if (ilbscl) {
zlascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, &c__1, &beta[1], n,
&ierr);
}
/* Select eigenvalues */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
bwork[i__] = (*selctg)(&alpha[i__], &beta[i__]);
/* L10: */
}
i__1 = *lwork - iwrk + 1;
ztgsen_(&c__0, &ilvsl, &ilvsr, &bwork[1], n, &a[a_offset], lda, &b[
b_offset], ldb, &alpha[1], &beta[1], &vsl[vsl_offset], ldvsl,
&vsr[vsr_offset], ldvsr, sdim, &pvsl, &pvsr, dif, &work[iwrk],
&i__1, idum, &c__1, &ierr);
if (ierr == 1) {
*info = *n + 3;
}
}
/* Apply back-permutation to VSL and VSR */
/* (Workspace: none needed) */
if (ilvsl) {
zggbak_("P", "L", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n, &
vsl[vsl_offset], ldvsl, &ierr);
}
if (ilvsr) {
zggbak_("P", "R", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n, &
vsr[vsr_offset], ldvsr, &ierr);
}
/* Undo scaling */
if (ilascl) {
zlascl_("U", &c__0, &c__0, &anrmto, &anrm, n, n, &a[a_offset], lda, &
ierr);
zlascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alpha[1], n, &
ierr);
}
if (ilbscl) {
zlascl_("U", &c__0, &c__0, &bnrmto, &bnrm, n, n, &b[b_offset], ldb, &
ierr);
zlascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
ierr);
}
if (wantst) {
/* Check if reordering is correct */
lastsl = TRUE;
*sdim = 0;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
cursl = (*selctg)(&alpha[i__], &beta[i__]);
if (cursl) {
++(*sdim);
}
if (cursl && ! lastsl) {
*info = *n + 2;
}
lastsl = cursl;
/* L20: */
}
}
L30:
work[1].r = (double) lwkopt, work[1].i = 0.;
return 0;
/* End of ZGGES */
} /* zgges_ */
/* Subroutine */ int zgges_(char *jobvsl, char *jobvsr, char *sort, L_fp
delctg, integer *n, doublecomplex *a, integer *lda, doublecomplex *b,
integer *ldb, integer *sdim, doublecomplex *alpha, doublecomplex *
beta, doublecomplex *vsl, integer *ldvsl, doublecomplex *vsr, integer
*ldvsr, doublecomplex *work, integer *lwork, doublereal *rwork,
logical *bwork, integer *info)
{
/* -- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZGGES computes for a pair of N-by-N complex nonsymmetric matrices
(A,B), the generalized eigenvalues, the generalized complex Schur
form (S, T), and optionally left and/or right Schur vectors (VSL
and VSR). This gives the generalized Schur factorization
(A,B) = ( (VSL)*S*(VSR)**H, (VSL)*T*(VSR)**H )
where (VSR)**H is the conjugate-transpose of VSR.
Optionally, it also orders the eigenvalues so that a selected cluster
of eigenvalues appears in the leading diagonal blocks of the upper
triangular matrix S and the upper triangular matrix T. The leading
columns of VSL and VSR then form an unitary basis for the
corresponding left and right eigenspaces (deflating subspaces).
(If only the generalized eigenvalues are needed, use the driver
ZGGEV instead, which is faster.)
A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
or a ratio alpha/beta = w, such that A - w*B is singular. It is
usually represented as the pair (alpha,beta), as there is a
reasonable interpretation for beta=0, and even for both being zero.
A pair of matrices (S,T) is in generalized complex Schur form if S
and T are upper triangular and, in addition, the diagonal elements
of T are non-negative real numbers.
Arguments
=========
JOBVSL (input) CHARACTER*1
= 'N': do not compute the left Schur vectors;
= 'V': compute the left Schur vectors.
JOBVSR (input) CHARACTER*1
= 'N': do not compute the right Schur vectors;
= 'V': compute the right Schur vectors.
SORT (input) CHARACTER*1
Specifies whether or not to order the eigenvalues on the
diagonal of the generalized Schur form.
= 'N': Eigenvalues are not ordered;
= 'S': Eigenvalues are ordered (see DELZTG).
DELZTG (input) LOGICAL FUNCTION of two COMPLEX*16 arguments
DELZTG must be declared EXTERNAL in the calling subroutine.
If SORT = 'N', DELZTG is not referenced.
If SORT = 'S', DELZTG is used to select eigenvalues to sort
to the top left of the Schur form.
An eigenvalue ALPHA(j)/BETA(j) is selected if
DELZTG(ALPHA(j),BETA(j)) is true.
Note that a selected complex eigenvalue may no longer satisfy
DELZTG(ALPHA(j),BETA(j)) = .TRUE. after ordering, since
ordering may change the value of complex eigenvalues
(especially if the eigenvalue is ill-conditioned), in this
case INFO is set to N+2 (See INFO below).
N (input) INTEGER
The order of the matrices A, B, VSL, and VSR. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA, N)
On entry, the first of the pair of matrices.
On exit, A has been overwritten by its generalized Schur
form S.
LDA (input) INTEGER
The leading dimension of A. LDA >= max(1,N).
B (input/output) COMPLEX*16 array, dimension (LDB, N)
On entry, the second of the pair of matrices.
On exit, B has been overwritten by its generalized Schur
form T.
LDB (input) INTEGER
The leading dimension of B. LDB >= max(1,N).
SDIM (output) INTEGER
If SORT = 'N', SDIM = 0.
If SORT = 'S', SDIM = number of eigenvalues (after sorting)
for which DELZTG is true.
ALPHA (output) COMPLEX*16 array, dimension (N)
BETA (output) COMPLEX*16 array, dimension (N)
On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the
generalized eigenvalues. ALPHA(j), j=1,...,N and BETA(j),
j=1,...,N are the diagonals of the complex Schur form (A,B)
output by ZGGES. The BETA(j) will be non-negative real.
Note: the quotients ALPHA(j)/BETA(j) may easily over- or
underflow, and BETA(j) may even be zero. Thus, the user
should avoid naively computing the ratio alpha/beta.
However, ALPHA will be always less than and usually
comparable with norm(A) in magnitude, and BETA always less
than and usually comparable with norm(B).
VSL (output) COMPLEX*16 array, dimension (LDVSL,N)
If JOBVSL = 'V', VSL will contain the left Schur vectors.
Not referenced if JOBVSL = 'N'.
LDVSL (input) INTEGER
The leading dimension of the matrix VSL. LDVSL >= 1, and
if JOBVSL = 'V', LDVSL >= N.
VSR (output) COMPLEX*16 array, dimension (LDVSR,N)
If JOBVSR = 'V', VSR will contain the right Schur vectors.
Not referenced if JOBVSR = 'N'.
LDVSR (input) INTEGER
The leading dimension of the matrix VSR. LDVSR >= 1, and
if JOBVSR = 'V', LDVSR >= N.
WORK (workspace/output) COMPLEX*16 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(1,2*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) DOUBLE PRECISION array, dimension (8*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.
=1,...,N:
The QZ iteration failed. (A,B) are not in Schur
form, but ALPHA(j) and BETA(j) should be correct for
j=INFO+1,...,N.
> N: =N+1: other than QZ iteration failed in ZHGEQZ
=N+2: after reordering, roundoff changed values of
some complex eigenvalues so that leading
eigenvalues in the Generalized Schur form no
longer satisfy DELZTG=.TRUE. This could also
be caused due to scaling.
=N+3: reordering falied in ZTGSEN.
=====================================================================
Decode the input arguments
Parameter adjustments */
/* Table of constant values */
static doublecomplex c_b1 = {0.,0.};
static doublecomplex c_b2 = {1.,0.};
static integer c__1 = 1;
static integer c__0 = 0;
static integer c_n1 = -1;
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, vsl_dim1, vsl_offset,
vsr_dim1, vsr_offset, i__1, i__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static doublereal anrm, bnrm;
static integer idum[1], ierr, itau, iwrk;
static doublereal pvsl, pvsr;
static integer i__;
extern logical lsame_(char *, char *);
static integer ileft, icols;
static logical cursl, ilvsl, ilvsr;
static integer irwrk, irows;
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
extern doublereal dlamch_(char *);
extern /* Subroutine */ int zggbak_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublecomplex *,
integer *, integer *), zggbal_(char *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *
, integer *, doublereal *, doublereal *, doublereal *, integer *);
static logical ilascl, ilbscl;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
integer *, doublereal *);
static doublereal bignum;
static integer ijobvl, iright;
extern /* Subroutine */ int zgghrd_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *
), zlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublecomplex *,
integer *, integer *);
static integer ijobvr;
extern /* Subroutine */ int zgeqrf_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *, integer *
);
static doublereal anrmto;
static integer lwkmin;
static logical lastsl;
static doublereal bnrmto;
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *),
zlaset_(char *, integer *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *, integer *), zhgeqz_(
char *, char *, char *, integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, integer *), ztgsen_(integer
*, logical *, logical *, logical *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, integer *, doublereal *, doublereal *, doublereal *,
doublecomplex *, integer *, integer *, integer *, integer *);
static doublereal smlnum;
static logical wantst, lquery;
static integer lwkopt;
extern /* Subroutine */ int zungqr_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *), zunmqr_(char *, char *, integer *, integer
*, integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *);
static doublereal dif[2];
static integer ihi, ilo;
static doublereal eps;
#define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
#define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1
#define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)]
#define vsl_subscr(a_1,a_2) (a_2)*vsl_dim1 + a_1
#define vsl_ref(a_1,a_2) vsl[vsl_subscr(a_1,a_2)]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
--alpha;
--beta;
vsl_dim1 = *ldvsl;
vsl_offset = 1 + vsl_dim1 * 1;
vsl -= vsl_offset;
vsr_dim1 = *ldvsr;
vsr_offset = 1 + vsr_dim1 * 1;
vsr -= vsr_offset;
--work;
--rwork;
--bwork;
/* Function Body */
if (lsame_(jobvsl, "N")) {
ijobvl = 1;
ilvsl = FALSE_;
} else if (lsame_(jobvsl, "V")) {
ijobvl = 2;
ilvsl = TRUE_;
} else {
ijobvl = -1;
ilvsl = FALSE_;
}
if (lsame_(jobvsr, "N")) {
ijobvr = 1;
ilvsr = FALSE_;
} else if (lsame_(jobvsr, "V")) {
ijobvr = 2;
ilvsr = TRUE_;
} else {
ijobvr = -1;
ilvsr = FALSE_;
}
wantst = lsame_(sort, "S");
/* Test the input arguments */
*info = 0;
lquery = *lwork == -1;
if (ijobvl <= 0) {
*info = -1;
} else if (ijobvr <= 0) {
*info = -2;
} else if (! wantst && ! lsame_(sort, "N")) {
*info = -3;
} else if (*n < 0) {
*info = -5;
} else if (*lda < max(1,*n)) {
*info = -7;
} else if (*ldb < max(1,*n)) {
*info = -9;
} else if (*ldvsl < 1 || ilvsl && *ldvsl < *n) {
*info = -14;
} else if (*ldvsr < 1 || ilvsr && *ldvsr < *n) {
*info = -16;
}
/* 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.
NB refers to the optimal block size for the immediately
following subroutine, as returned by ILAENV.) */
lwkmin = 1;
if (*info == 0 && (*lwork >= 1 || lquery)) {
/* Computing MAX */
i__1 = 1, i__2 = *n << 1;
lwkmin = max(i__1,i__2);
lwkopt = *n + *n * ilaenv_(&c__1, "ZGEQRF", " ", n, &c__1, n, &c__0, (
ftnlen)6, (ftnlen)1);
if (ilvsl) {
/* Computing MAX */
i__1 = lwkopt, i__2 = *n + *n * ilaenv_(&c__1, "ZUNGQR", " ", n, &
c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
lwkopt = max(i__1,i__2);
}
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
}
if (*lwork < lwkmin && ! lquery) {
*info = -18;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGGES ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
if (*n == 0) {
*sdim = 0;
return 0;
}
/* Get machine constants */
eps = dlamch_("P");
smlnum = dlamch_("S");
bignum = 1. / smlnum;
dlabad_(&smlnum, &bignum);
smlnum = sqrt(smlnum) / eps;
bignum = 1. / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = zlange_("M", n, n, &a[a_offset], lda, &rwork[1]);
ilascl = FALSE_;
if (anrm > 0. && anrm < smlnum) {
anrmto = smlnum;
ilascl = TRUE_;
} else if (anrm > bignum) {
anrmto = bignum;
ilascl = TRUE_;
}
if (ilascl) {
zlascl_("G", &c__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, &
ierr);
}
/* Scale B if max element outside range [SMLNUM,BIGNUM] */
bnrm = zlange_("M", n, n, &b[b_offset], ldb, &rwork[1]);
ilbscl = FALSE_;
if (bnrm > 0. && bnrm < smlnum) {
bnrmto = smlnum;
ilbscl = TRUE_;
} else if (bnrm > bignum) {
bnrmto = bignum;
ilbscl = TRUE_;
}
if (ilbscl) {
zlascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
ierr);
}
/* Permute the matrix to make it more nearly triangular
(Real Workspace: need 6*N) */
ileft = 1;
iright = *n + 1;
irwrk = iright + *n;
zggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &rwork[
ileft], &rwork[iright], &rwork[irwrk], &ierr);
/* Reduce B to triangular form (QR decomposition of B)
(Complex Workspace: need N, prefer N*NB) */
irows = ihi + 1 - ilo;
icols = *n + 1 - ilo;
itau = 1;
iwrk = itau + irows;
i__1 = *lwork + 1 - iwrk;
zgeqrf_(&irows, &icols, &b_ref(ilo, ilo), ldb, &work[itau], &work[iwrk], &
i__1, &ierr);
/* Apply the orthogonal transformation to matrix A
(Complex Workspace: need N, prefer N*NB) */
i__1 = *lwork + 1 - iwrk;
zunmqr_("L", "C", &irows, &icols, &irows, &b_ref(ilo, ilo), ldb, &work[
itau], &a_ref(ilo, ilo), lda, &work[iwrk], &i__1, &ierr);
/* Initialize VSL
(Complex Workspace: need N, prefer N*NB) */
if (ilvsl) {
zlaset_("Full", n, n, &c_b1, &c_b2, &vsl[vsl_offset], ldvsl);
i__1 = irows - 1;
i__2 = irows - 1;
zlacpy_("L", &i__1, &i__2, &b_ref(ilo + 1, ilo), ldb, &vsl_ref(ilo +
1, ilo), ldvsl);
i__1 = *lwork + 1 - iwrk;
zungqr_(&irows, &irows, &irows, &vsl_ref(ilo, ilo), ldvsl, &work[itau]
, &work[iwrk], &i__1, &ierr);
}
/* Initialize VSR */
if (ilvsr) {
zlaset_("Full", n, n, &c_b1, &c_b2, &vsr[vsr_offset], ldvsr);
}
/* Reduce to generalized Hessenberg form
(Workspace: none needed) */
zgghrd_(jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset],
ldb, &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &ierr);
*sdim = 0;
/* Perform QZ algorithm, computing Schur vectors if desired
(Complex Workspace: need N)
(Real Workspace: need N) */
iwrk = itau;
i__1 = *lwork + 1 - iwrk;
zhgeqz_("S", jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[
b_offset], ldb, &alpha[1], &beta[1], &vsl[vsl_offset], ldvsl, &
vsr[vsr_offset], ldvsr, &work[iwrk], &i__1, &rwork[irwrk], &ierr);
if (ierr != 0) {
if (ierr > 0 && ierr <= *n) {
*info = ierr;
} else if (ierr > *n && ierr <= *n << 1) {
*info = ierr - *n;
} else {
*info = *n + 1;
}
goto L30;
}
/* Sort eigenvalues ALPHA/BETA if desired
(Workspace: none needed) */
if (wantst) {
/* Undo scaling on eigenvalues before selecting */
if (ilascl) {
zlascl_("G", &c__0, &c__0, &anrm, &anrmto, n, &c__1, &alpha[1], n,
&ierr);
}
if (ilbscl) {
zlascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, &c__1, &beta[1], n,
&ierr);
}
/* Select eigenvalues */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
bwork[i__] = (*delctg)(&alpha[i__], &beta[i__]);
/* L10: */
}
i__1 = *lwork - iwrk + 1;
ztgsen_(&c__0, &ilvsl, &ilvsr, &bwork[1], n, &a[a_offset], lda, &b[
b_offset], ldb, &alpha[1], &beta[1], &vsl[vsl_offset], ldvsl,
&vsr[vsr_offset], ldvsr, sdim, &pvsl, &pvsr, dif, &work[iwrk],
&i__1, idum, &c__1, &ierr);
if (ierr == 1) {
*info = *n + 3;
}
}
/* Apply back-permutation to VSL and VSR
(Workspace: none needed) */
if (ilvsl) {
zggbak_("P", "L", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n, &
vsl[vsl_offset], ldvsl, &ierr);
}
if (ilvsr) {
zggbak_("P", "R", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n, &
vsr[vsr_offset], ldvsr, &ierr);
}
/* Undo scaling */
if (ilascl) {
zlascl_("U", &c__0, &c__0, &anrmto, &anrm, n, n, &a[a_offset], lda, &
ierr);
zlascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alpha[1], n, &
ierr);
}
if (ilbscl) {
zlascl_("U", &c__0, &c__0, &bnrmto, &bnrm, n, n, &b[b_offset], ldb, &
ierr);
zlascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
ierr);
}
if (wantst) {
/* Check if reordering is correct */
lastsl = TRUE_;
*sdim = 0;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
cursl = (*delctg)(&alpha[i__], &beta[i__]);
if (cursl) {
++(*sdim);
}
if (cursl && ! lastsl) {
*info = *n + 2;
}
lastsl = cursl;
/* L20: */
}
}
L30:
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
return 0;
/* End of ZGGES */
} /* zgges_ */
/* Subroutine */ int zggesx_(char *jobvsl, char *jobvsr, char *sort, L_fp
delctg, char *sense, integer *n, doublecomplex *a, integer *lda,
doublecomplex *b, integer *ldb, integer *sdim, doublecomplex *alpha,
doublecomplex *beta, doublecomplex *vsl, integer *ldvsl,
doublecomplex *vsr, integer *ldvsr, doublereal *rconde, doublereal *
rcondv, doublecomplex *work, integer *lwork, doublereal *rwork,
integer *iwork, integer *liwork, logical *bwork, integer *info,
ftnlen jobvsl_len, ftnlen jobvsr_len, ftnlen sort_len, ftnlen
sense_len)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, vsl_dim1, vsl_offset,
vsr_dim1, vsr_offset, i__1, i__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static integer i__;
static doublereal pl, pr, dif[2];
static integer ihi, ilo;
static doublereal eps;
static integer ijob;
static doublereal anrm, bnrm;
static integer ierr, itau, iwrk;
extern logical lsame_(char *, char *, ftnlen, ftnlen);
static integer ileft, icols;
static logical cursl, ilvsl, ilvsr;
static integer irwrk, irows;
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
extern doublereal dlamch_(char *, ftnlen);
extern /* Subroutine */ int zggbak_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublecomplex *,
integer *, integer *, ftnlen, ftnlen), zggbal_(char *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *
, integer *, doublereal *, doublereal *, doublereal *, integer *,
ftnlen);
static logical ilascl, ilbscl;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
integer *, doublereal *, ftnlen);
static doublereal bignum;
static integer ijobvl, iright;
extern /* Subroutine */ int zgghrd_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *
, ftnlen, ftnlen), zlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublecomplex *,
integer *, integer *, ftnlen);
static integer ijobvr;
static logical wantsb;
static integer liwmin;
static logical wantse, lastsl;
static doublereal anrmto, bnrmto;
extern /* Subroutine */ int zgeqrf_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *, integer *
);
static integer maxwrk;
static logical wantsn;
static integer minwrk;
static doublereal smlnum;
extern /* Subroutine */ int zhgeqz_(char *, char *, char *, integer *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, integer *, ftnlen, ftnlen, ftnlen), zlacpy_(char *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *
, integer *, ftnlen), zlaset_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *,
ftnlen);
static logical wantst;
extern /* Subroutine */ int ztgsen_(integer *, logical *, logical *,
logical *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *, integer *, integer *, doublereal *,
doublereal *, doublereal *, doublecomplex *, integer *, integer *,
integer *, integer *);
static logical wantsv;
extern /* Subroutine */ int zungqr_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *), zunmqr_(char *, char *, integer *, integer
*, integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *,
ftnlen, ftnlen);
/* -- LAPACK driver routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* June 30, 1999 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* .. Function Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGGESX computes for a pair of N-by-N complex nonsymmetric matrices */
/* (A,B), the generalized eigenvalues, the complex Schur form (S,T), */
/* and, optionally, the left and/or right matrices of Schur vectors (VSL */
/* and VSR). This gives the generalized Schur factorization */
/* (A,B) = ( (VSL) S (VSR)**H, (VSL) T (VSR)**H ) */
/* where (VSR)**H is the conjugate-transpose of VSR. */
/* Optionally, it also orders the eigenvalues so that a selected cluster */
/* of eigenvalues appears in the leading diagonal blocks of the upper */
/* triangular matrix S and the upper triangular matrix T; computes */
/* a reciprocal condition number for the average of the selected */
/* eigenvalues (RCONDE); and computes a reciprocal condition number for */
/* the right and left deflating subspaces corresponding to the selected */
/* eigenvalues (RCONDV). The leading columns of VSL and VSR then form */
/* an orthonormal basis for the corresponding left and right eigenspaces */
/* (deflating subspaces). */
/* A generalized eigenvalue for a pair of matrices (A,B) is a scalar w */
/* or a ratio alpha/beta = w, such that A - w*B is singular. It is */
/* usually represented as the pair (alpha,beta), as there is a */
/* reasonable interpretation for beta=0 or for both being zero. */
/* A pair of matrices (S,T) is in generalized complex Schur form if T is */
/* upper triangular with non-negative diagonal and S is upper */
/* triangular. */
/* Arguments */
/* ========= */
/* JOBVSL (input) CHARACTER*1 */
/* = 'N': do not compute the left Schur vectors; */
/* = 'V': compute the left Schur vectors. */
/* JOBVSR (input) CHARACTER*1 */
/* = 'N': do not compute the right Schur vectors; */
/* = 'V': compute the right Schur vectors. */
/* SORT (input) CHARACTER*1 */
/* Specifies whether or not to order the eigenvalues on the */
/* diagonal of the generalized Schur form. */
/* = 'N': Eigenvalues are not ordered; */
/* = 'S': Eigenvalues are ordered (see DELZTG). */
/* DELZTG (input) LOGICAL FUNCTION of two COMPLEX*16 arguments */
/* DELZTG must be declared EXTERNAL in the calling subroutine. */
/* If SORT = 'N', DELZTG is not referenced. */
/* If SORT = 'S', DELZTG is used to select eigenvalues to sort */
/* to the top left of the Schur form. */
/* Note that a selected complex eigenvalue may no longer satisfy */
/* DELZTG(ALPHA(j),BETA(j)) = .TRUE. after ordering, since */
/* ordering may change the value of complex eigenvalues */
/* (especially if the eigenvalue is ill-conditioned), in this */
/* case INFO is set to N+3 see INFO below). */
/* SENSE (input) CHARACTER */
/* Determines which reciprocal condition numbers are computed. */
/* = 'N' : None are computed; */
/* = 'E' : Computed for average of selected eigenvalues only; */
/* = 'V' : Computed for selected deflating subspaces only; */
/* = 'B' : Computed for both. */
/* If SENSE = 'E', 'V', or 'B', SORT must equal 'S'. */
/* N (input) INTEGER */
/* The order of the matrices A, B, VSL, and VSR. N >= 0. */
/* A (input/output) COMPLEX*16 array, dimension (LDA, N) */
/* On entry, the first of the pair of matrices. */
/* On exit, A has been overwritten by its generalized Schur */
/* form S. */
/* LDA (input) INTEGER */
/* The leading dimension of A. LDA >= max(1,N). */
/* B (input/output) COMPLEX*16 array, dimension (LDB, N) */
/* On entry, the second of the pair of matrices. */
/* On exit, B has been overwritten by its generalized Schur */
/* form T. */
/* LDB (input) INTEGER */
/* The leading dimension of B. LDB >= max(1,N). */
/* SDIM (output) INTEGER */
/* If SORT = 'N', SDIM = 0. */
/* If SORT = 'S', SDIM = number of eigenvalues (after sorting) */
/* for which DELZTG is true. */
/* ALPHA (output) COMPLEX*16 array, dimension (N) */
/* BETA (output) COMPLEX*16 array, dimension (N) */
/* On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the */
/* generalized eigenvalues. ALPHA(j) and BETA(j),j=1,...,N are */
/* the diagonals of the complex Schur form (S,T). BETA(j) will */
/* be non-negative real. */
/* Note: the quotients ALPHA(j)/BETA(j) may easily over- or */
/* underflow, and BETA(j) may even be zero. Thus, the user */
/* should avoid naively computing the ratio alpha/beta. */
/* However, ALPHA will be always less than and usually */
/* comparable with norm(A) in magnitude, and BETA always less */
/* than and usually comparable with norm(B). */
/* VSL (output) COMPLEX*16 array, dimension (LDVSL,N) */
/* If JOBVSL = 'V', VSL will contain the left Schur vectors. */
/* Not referenced if JOBVSL = 'N'. */
/* LDVSL (input) INTEGER */
/* The leading dimension of the matrix VSL. LDVSL >=1, and */
/* if JOBVSL = 'V', LDVSL >= N. */
/* VSR (output) COMPLEX*16 array, dimension (LDVSR,N) */
/* If JOBVSR = 'V', VSR will contain the right Schur vectors. */
/* Not referenced if JOBVSR = 'N'. */
/* LDVSR (input) INTEGER */
/* The leading dimension of the matrix VSR. LDVSR >= 1, and */
/* if JOBVSR = 'V', LDVSR >= N. */
/* RCONDE (output) DOUBLE PRECISION array, dimension ( 2 ) */
/* If SENSE = 'E' or 'B', RCONDE(1) and RCONDE(2) contain the */
/* reciprocal condition numbers for the average of the selected */
/* eigenvalues. */
/* Not referenced if SENSE = 'N' or 'V'. */
/* RCONDV (output) DOUBLE PRECISION array, dimension ( 2 ) */
/* If SENSE = 'V' or 'B', RCONDV(1) and RCONDV(2) contain the */
/* reciprocal condition number for the selected deflating */
/* subspaces. */
/* Not referenced if SENSE = 'N' or 'E'. */
/* WORK (workspace/output) COMPLEX*16 array, dimension (LWORK) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= 2*N. */
/* If SENSE = 'E', 'V', or 'B', */
/* LWORK >= MAX(2*N, 2*SDIM*(N-SDIM)). */
/* RWORK (workspace) DOUBLE PRECISION array, dimension ( 8*N ) */
/* Real workspace. */
/* IWORK (workspace/output) INTEGER array, dimension (LIWORK) */
/* Not referenced if SENSE = 'N'. */
/* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */
/* LIWORK (input) INTEGER */
/* The dimension of the array WORK. LIWORK >= N+2. */
/* 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. */
/* = 1,...,N: */
/* The QZ iteration failed. (A,B) are not in Schur */
/* form, but ALPHA(j) and BETA(j) should be correct for */
/* j=INFO+1,...,N. */
/* > N: =N+1: other than QZ iteration failed in ZHGEQZ */
/* =N+2: after reordering, roundoff changed values of */
/* some complex eigenvalues so that leading */
/* eigenvalues in the Generalized Schur form no */
/* longer satisfy DELZTG=.TRUE. This could also */
/* be caused due to scaling. */
/* =N+3: reordering failed in ZTGSEN. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Decode the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--alpha;
--beta;
vsl_dim1 = *ldvsl;
vsl_offset = 1 + vsl_dim1;
vsl -= vsl_offset;
vsr_dim1 = *ldvsr;
vsr_offset = 1 + vsr_dim1;
vsr -= vsr_offset;
--rconde;
--rcondv;
--work;
--rwork;
--iwork;
--bwork;
/* Function Body */
if (lsame_(jobvsl, "N", (ftnlen)1, (ftnlen)1)) {
ijobvl = 1;
ilvsl = FALSE_;
} else if (lsame_(jobvsl, "V", (ftnlen)1, (ftnlen)1)) {
ijobvl = 2;
ilvsl = TRUE_;
} else {
ijobvl = -1;
ilvsl = FALSE_;
}
if (lsame_(jobvsr, "N", (ftnlen)1, (ftnlen)1)) {
ijobvr = 1;
ilvsr = FALSE_;
} else if (lsame_(jobvsr, "V", (ftnlen)1, (ftnlen)1)) {
ijobvr = 2;
ilvsr = TRUE_;
} else {
ijobvr = -1;
ilvsr = FALSE_;
}
wantst = lsame_(sort, "S", (ftnlen)1, (ftnlen)1);
wantsn = lsame_(sense, "N", (ftnlen)1, (ftnlen)1);
wantse = lsame_(sense, "E", (ftnlen)1, (ftnlen)1);
wantsv = lsame_(sense, "V", (ftnlen)1, (ftnlen)1);
wantsb = lsame_(sense, "B", (ftnlen)1, (ftnlen)1);
if (wantsn) {
ijob = 0;
iwork[1] = 1;
} else if (wantse) {
ijob = 1;
} else if (wantsv) {
ijob = 2;
} else if (wantsb) {
ijob = 4;
}
/* Test the input arguments */
*info = 0;
if (ijobvl <= 0) {
*info = -1;
} else if (ijobvr <= 0) {
*info = -2;
} else if (! wantst && ! lsame_(sort, "N", (ftnlen)1, (ftnlen)1)) {
*info = -3;
} else if (! (wantsn || wantse || wantsv || wantsb) || ! wantst && !
wantsn) {
*info = -5;
} else if (*n < 0) {
*info = -6;
} else if (*lda < max(1,*n)) {
*info = -8;
} else if (*ldb < max(1,*n)) {
*info = -10;
} else if (*ldvsl < 1 || ilvsl && *ldvsl < *n) {
*info = -15;
} else if (*ldvsr < 1 || ilvsr && *ldvsr < *n) {
*info = -17;
}
/* 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. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV.) */
minwrk = 1;
if (*info == 0 && *lwork >= 1) {
/* Computing MAX */
i__1 = 1, i__2 = *n << 1;
minwrk = max(i__1,i__2);
maxwrk = *n + *n * ilaenv_(&c__1, "ZGEQRF", " ", n, &c__1, n, &c__0, (
ftnlen)6, (ftnlen)1);
if (ilvsl) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "ZUNGQR", " ", n, &
c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = max(i__1,i__2);
}
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
}
if (! wantsn) {
liwmin = *n + 2;
} else {
liwmin = 1;
}
iwork[1] = liwmin;
if (*info == 0 && *lwork < minwrk) {
*info = -21;
} else if (*info == 0 && ijob >= 1) {
if (*liwork < liwmin) {
*info = -24;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGGESX", &i__1, (ftnlen)6);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
*sdim = 0;
return 0;
}
/* Get machine constants */
eps = dlamch_("P", (ftnlen)1);
smlnum = dlamch_("S", (ftnlen)1);
bignum = 1. / smlnum;
dlabad_(&smlnum, &bignum);
smlnum = sqrt(smlnum) / eps;
bignum = 1. / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = zlange_("M", n, n, &a[a_offset], lda, &rwork[1], (ftnlen)1);
ilascl = FALSE_;
if (anrm > 0. && anrm < smlnum) {
anrmto = smlnum;
ilascl = TRUE_;
} else if (anrm > bignum) {
anrmto = bignum;
ilascl = TRUE_;
}
if (ilascl) {
zlascl_("G", &c__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, &
ierr, (ftnlen)1);
}
/* Scale B if max element outside range [SMLNUM,BIGNUM] */
bnrm = zlange_("M", n, n, &b[b_offset], ldb, &rwork[1], (ftnlen)1);
ilbscl = FALSE_;
if (bnrm > 0. && bnrm < smlnum) {
bnrmto = smlnum;
ilbscl = TRUE_;
} else if (bnrm > bignum) {
bnrmto = bignum;
ilbscl = TRUE_;
}
if (ilbscl) {
zlascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
ierr, (ftnlen)1);
}
/* Permute the matrix to make it more nearly triangular */
/* (Real Workspace: need 6*N) */
ileft = 1;
iright = *n + 1;
irwrk = iright + *n;
zggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &rwork[
ileft], &rwork[iright], &rwork[irwrk], &ierr, (ftnlen)1);
/* Reduce B to triangular form (QR decomposition of B) */
/* (Complex Workspace: need N, prefer N*NB) */
irows = ihi + 1 - ilo;
icols = *n + 1 - ilo;
itau = 1;
iwrk = itau + irows;
i__1 = *lwork + 1 - iwrk;
zgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
iwrk], &i__1, &ierr);
/* Apply the unitary transformation to matrix A */
/* (Complex Workspace: need N, prefer N*NB) */
i__1 = *lwork + 1 - iwrk;
zunmqr_("L", "C", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, &
work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwrk], &i__1, &
ierr, (ftnlen)1, (ftnlen)1);
/* Initialize VSL */
/* (Complex Workspace: need N, prefer N*NB) */
if (ilvsl) {
zlaset_("Full", n, n, &c_b1, &c_b2, &vsl[vsl_offset], ldvsl, (ftnlen)
4);
i__1 = irows - 1;
i__2 = irows - 1;
zlacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vsl[ilo
+ 1 + ilo * vsl_dim1], ldvsl, (ftnlen)1);
i__1 = *lwork + 1 - iwrk;
zungqr_(&irows, &irows, &irows, &vsl[ilo + ilo * vsl_dim1], ldvsl, &
work[itau], &work[iwrk], &i__1, &ierr);
}
/* Initialize VSR */
if (ilvsr) {
zlaset_("Full", n, n, &c_b1, &c_b2, &vsr[vsr_offset], ldvsr, (ftnlen)
4);
}
/* Reduce to generalized Hessenberg form */
/* (Workspace: none needed) */
zgghrd_(jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset],
ldb, &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &ierr, (
ftnlen)1, (ftnlen)1);
*sdim = 0;
/* Perform QZ algorithm, computing Schur vectors if desired */
/* (Complex Workspace: need N) */
/* (Real Workspace: need N) */
iwrk = itau;
i__1 = *lwork + 1 - iwrk;
zhgeqz_("S", jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[
b_offset], ldb, &alpha[1], &beta[1], &vsl[vsl_offset], ldvsl, &
vsr[vsr_offset], ldvsr, &work[iwrk], &i__1, &rwork[irwrk], &ierr,
(ftnlen)1, (ftnlen)1, (ftnlen)1);
if (ierr != 0) {
if (ierr > 0 && ierr <= *n) {
*info = ierr;
} else if (ierr > *n && ierr <= *n << 1) {
*info = ierr - *n;
} else {
*info = *n + 1;
}
goto L40;
}
/* Sort eigenvalues ALPHA/BETA and compute the reciprocal of */
/* condition number(s) */
if (wantst) {
/* Undo scaling on eigenvalues before DELZTGing */
if (ilascl) {
zlascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alpha[1], n,
&ierr, (ftnlen)1);
}
if (ilbscl) {
zlascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n,
&ierr, (ftnlen)1);
}
/* Select eigenvalues */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
bwork[i__] = (*delctg)(&alpha[i__], &beta[i__]);
/* L10: */
}
/* Reorder eigenvalues, transform Generalized Schur vectors, and */
/* compute reciprocal condition numbers */
/* (Complex Workspace: If IJOB >= 1, need MAX(1, 2*SDIM*(N-SDIM)) */
/* otherwise, need 1 ) */
i__1 = *lwork - iwrk + 1;
ztgsen_(&ijob, &ilvsl, &ilvsr, &bwork[1], n, &a[a_offset], lda, &b[
b_offset], ldb, &alpha[1], &beta[1], &vsl[vsl_offset], ldvsl,
&vsr[vsr_offset], ldvsr, sdim, &pl, &pr, dif, &work[iwrk], &
i__1, &iwork[1], liwork, &ierr);
if (ijob >= 1) {
/* Computing MAX */
i__1 = maxwrk, i__2 = (*sdim << 1) * (*n - *sdim);
maxwrk = max(i__1,i__2);
}
if (ierr == -21) {
/* not enough complex workspace */
*info = -21;
} else {
rconde[1] = pl;
rconde[2] = pl;
rcondv[1] = dif[0];
rcondv[2] = dif[1];
if (ierr == 1) {
*info = *n + 3;
}
}
}
/* Apply permutation to VSL and VSR */
/* (Workspace: none needed) */
if (ilvsl) {
zggbak_("P", "L", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n, &
vsl[vsl_offset], ldvsl, &ierr, (ftnlen)1, (ftnlen)1);
}
if (ilvsr) {
zggbak_("P", "R", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n, &
vsr[vsr_offset], ldvsr, &ierr, (ftnlen)1, (ftnlen)1);
}
/* Undo scaling */
if (ilascl) {
zlascl_("U", &c__0, &c__0, &anrmto, &anrm, n, n, &a[a_offset], lda, &
ierr, (ftnlen)1);
zlascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alpha[1], n, &
ierr, (ftnlen)1);
}
if (ilbscl) {
zlascl_("U", &c__0, &c__0, &bnrmto, &bnrm, n, n, &b[b_offset], ldb, &
ierr, (ftnlen)1);
zlascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
ierr, (ftnlen)1);
}
/* L20: */
if (wantst) {
/* Check if reordering is correct */
lastsl = TRUE_;
*sdim = 0;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
cursl = (*delctg)(&alpha[i__], &beta[i__]);
if (cursl) {
++(*sdim);
}
if (cursl && ! lastsl) {
*info = *n + 2;
}
lastsl = cursl;
/* L30: */
}
}
L40:
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
iwork[1] = liwmin;
return 0;
/* End of ZGGESX */
} /* zggesx_ */
/* Subroutine */
int zggesx_(char *jobvsl, char *jobvsr, char *sort, L_fp selctg, char *sense, integer *n, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, integer *sdim, doublecomplex *alpha, doublecomplex *beta, doublecomplex *vsl, integer *ldvsl, doublecomplex *vsr, integer *ldvsr, doublereal *rconde, doublereal * rcondv, doublecomplex *work, integer *lwork, doublereal *rwork, integer *iwork, integer *liwork, logical *bwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, vsl_dim1, vsl_offset, vsr_dim1, vsr_offset, i__1, i__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__;
doublereal pl, pr, dif[2];
integer ihi, ilo;
doublereal eps;
integer ijob;
doublereal anrm, bnrm;
integer ierr, itau, iwrk, lwrk;
extern logical lsame_(char *, char *);
integer ileft, icols;
logical cursl, ilvsl, ilvsr;
integer irwrk, irows;
extern /* Subroutine */
int dlabad_(doublereal *, doublereal *);
extern doublereal dlamch_(char *);
extern /* Subroutine */
int zggbak_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, integer *, doublecomplex *, integer *, integer *), zggbal_(char *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer * , integer *, doublereal *, doublereal *, doublereal *, integer *);
logical ilascl, ilbscl;
extern /* Subroutine */
int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *);
doublereal bignum;
integer ijobvl, iright;
extern /* Subroutine */
int zgghrd_(char *, char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer * ), zlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublecomplex *, integer *, integer *);
integer ijobvr;
logical wantsb;
integer liwmin;
logical wantse, lastsl;
doublereal anrmto, bnrmto;
extern /* Subroutine */
int zgeqrf_(integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer * );
integer maxwrk;
logical wantsn;
integer minwrk;
doublereal smlnum;
extern /* Subroutine */
int zhgeqz_(char *, char *, char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex * , integer *), zlaset_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *);
logical wantst, lquery, wantsv;
extern /* Subroutine */
int ztgsen_(integer *, logical *, logical *, logical *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, doublereal *, doublereal *, doublereal *, doublecomplex *, integer *, integer *, integer *, integer *), zungqr_(integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer *), zunmqr_(char *, char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, integer *);
/* -- LAPACK driver routine (version 3.4.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2011 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* .. Function Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Decode the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--alpha;
--beta;
vsl_dim1 = *ldvsl;
vsl_offset = 1 + vsl_dim1;
vsl -= vsl_offset;
vsr_dim1 = *ldvsr;
vsr_offset = 1 + vsr_dim1;
vsr -= vsr_offset;
--rconde;
--rcondv;
--work;
--rwork;
--iwork;
--bwork;
/* Function Body */
if (lsame_(jobvsl, "N"))
{
ijobvl = 1;
ilvsl = FALSE_;
}
else if (lsame_(jobvsl, "V"))
{
ijobvl = 2;
ilvsl = TRUE_;
}
else
{
ijobvl = -1;
ilvsl = FALSE_;
}
if (lsame_(jobvsr, "N"))
{
ijobvr = 1;
ilvsr = FALSE_;
}
else if (lsame_(jobvsr, "V"))
{
ijobvr = 2;
ilvsr = TRUE_;
}
else
{
ijobvr = -1;
ilvsr = FALSE_;
}
wantst = lsame_(sort, "S");
wantsn = lsame_(sense, "N");
wantse = lsame_(sense, "E");
wantsv = lsame_(sense, "V");
wantsb = lsame_(sense, "B");
lquery = *lwork == -1 || *liwork == -1;
if (wantsn)
{
ijob = 0;
}
else if (wantse)
{
ijob = 1;
}
else if (wantsv)
{
ijob = 2;
}
else if (wantsb)
{
ijob = 4;
}
/* Test the input arguments */
*info = 0;
if (ijobvl <= 0)
{
*info = -1;
}
else if (ijobvr <= 0)
{
*info = -2;
}
else if (! wantst && ! lsame_(sort, "N"))
{
*info = -3;
}
else if (! (wantsn || wantse || wantsv || wantsb) || ! wantst && ! wantsn)
{
*info = -5;
}
else if (*n < 0)
{
*info = -6;
}
else if (*lda < max(1,*n))
{
*info = -8;
}
else if (*ldb < max(1,*n))
{
*info = -10;
}
else if (*ldvsl < 1 || ilvsl && *ldvsl < *n)
{
*info = -15;
}
else if (*ldvsr < 1 || ilvsr && *ldvsr < *n)
{
*info = -17;
}
/* 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. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV.) */
if (*info == 0)
{
if (*n > 0)
{
minwrk = *n << 1;
maxwrk = *n * (ilaenv_(&c__1, "ZGEQRF", " ", n, &c__1, n, &c__0) + 1);
/* Computing MAX */
i__1 = maxwrk;
i__2 = *n * (ilaenv_(&c__1, "ZUNMQR", " ", n, & c__1, n, &c_n1) + 1); // , expr subst
maxwrk = max(i__1,i__2);
if (ilvsl)
{
/* Computing MAX */
i__1 = maxwrk;
i__2 = *n * (ilaenv_(&c__1, "ZUNGQR", " ", n, & c__1, n, &c_n1) + 1); // , expr subst
maxwrk = max(i__1,i__2);
}
lwrk = maxwrk;
if (ijob >= 1)
{
/* Computing MAX */
i__1 = lwrk;
i__2 = *n * *n / 2; // , expr subst
lwrk = max(i__1,i__2);
}
}
else
{
minwrk = 1;
maxwrk = 1;
lwrk = 1;
}
work[1].r = (doublereal) lwrk;
work[1].i = 0.; // , expr subst
if (wantsn || *n == 0)
{
liwmin = 1;
}
else
{
liwmin = *n + 2;
}
iwork[1] = liwmin;
if (*lwork < minwrk && ! lquery)
{
*info = -21;
}
else if (*liwork < liwmin && ! lquery)
{
*info = -24;
}
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("ZGGESX", &i__1);
return 0;
}
else if (lquery)
{
return 0;
}
/* Quick return if possible */
if (*n == 0)
{
*sdim = 0;
return 0;
}
/* Get machine constants */
eps = dlamch_("P");
smlnum = dlamch_("S");
bignum = 1. / smlnum;
dlabad_(&smlnum, &bignum);
smlnum = sqrt(smlnum) / eps;
bignum = 1. / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = zlange_("M", n, n, &a[a_offset], lda, &rwork[1]);
ilascl = FALSE_;
if (anrm > 0. && anrm < smlnum)
{
anrmto = smlnum;
ilascl = TRUE_;
}
else if (anrm > bignum)
{
anrmto = bignum;
ilascl = TRUE_;
}
if (ilascl)
{
zlascl_("G", &c__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, & ierr);
}
/* Scale B if max element outside range [SMLNUM,BIGNUM] */
bnrm = zlange_("M", n, n, &b[b_offset], ldb, &rwork[1]);
ilbscl = FALSE_;
if (bnrm > 0. && bnrm < smlnum)
{
bnrmto = smlnum;
ilbscl = TRUE_;
}
else if (bnrm > bignum)
{
bnrmto = bignum;
ilbscl = TRUE_;
}
if (ilbscl)
{
zlascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, & ierr);
}
/* Permute the matrix to make it more nearly triangular */
/* (Real Workspace: need 6*N) */
ileft = 1;
iright = *n + 1;
irwrk = iright + *n;
zggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &rwork[ ileft], &rwork[iright], &rwork[irwrk], &ierr);
/* Reduce B to triangular form (QR decomposition of B) */
/* (Complex Workspace: need N, prefer N*NB) */
irows = ihi + 1 - ilo;
icols = *n + 1 - ilo;
itau = 1;
iwrk = itau + irows;
i__1 = *lwork + 1 - iwrk;
zgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[ iwrk], &i__1, &ierr);
/* Apply the unitary transformation to matrix A */
/* (Complex Workspace: need N, prefer N*NB) */
i__1 = *lwork + 1 - iwrk;
zunmqr_("L", "C", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, & work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwrk], &i__1, & ierr);
/* Initialize VSL */
/* (Complex Workspace: need N, prefer N*NB) */
if (ilvsl)
{
zlaset_("Full", n, n, &c_b1, &c_b2, &vsl[vsl_offset], ldvsl);
if (irows > 1)
{
i__1 = irows - 1;
i__2 = irows - 1;
zlacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vsl[ ilo + 1 + ilo * vsl_dim1], ldvsl);
}
i__1 = *lwork + 1 - iwrk;
zungqr_(&irows, &irows, &irows, &vsl[ilo + ilo * vsl_dim1], ldvsl, & work[itau], &work[iwrk], &i__1, &ierr);
}
/* Initialize VSR */
if (ilvsr)
{
zlaset_("Full", n, n, &c_b1, &c_b2, &vsr[vsr_offset], ldvsr);
}
/* Reduce to generalized Hessenberg form */
/* (Workspace: none needed) */
zgghrd_(jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset], ldb, &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &ierr);
*sdim = 0;
/* Perform QZ algorithm, computing Schur vectors if desired */
/* (Complex Workspace: need N) */
/* (Real Workspace: need N) */
iwrk = itau;
i__1 = *lwork + 1 - iwrk;
zhgeqz_("S", jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[ b_offset], ldb, &alpha[1], &beta[1], &vsl[vsl_offset], ldvsl, & vsr[vsr_offset], ldvsr, &work[iwrk], &i__1, &rwork[irwrk], &ierr);
if (ierr != 0)
{
if (ierr > 0 && ierr <= *n)
{
*info = ierr;
}
else if (ierr > *n && ierr <= *n << 1)
{
*info = ierr - *n;
}
else
{
*info = *n + 1;
}
goto L40;
}
/* Sort eigenvalues ALPHA/BETA and compute the reciprocal of */
/* condition number(s) */
if (wantst)
{
/* Undo scaling on eigenvalues before SELCTGing */
if (ilascl)
{
zlascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alpha[1], n, &ierr);
}
if (ilbscl)
{
zlascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &ierr);
}
/* Select eigenvalues */
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
bwork[i__] = (*selctg)(&alpha[i__], &beta[i__]);
/* L10: */
}
/* Reorder eigenvalues, transform Generalized Schur vectors, and */
/* compute reciprocal condition numbers */
/* (Complex Workspace: If IJOB >= 1, need MAX(1, 2*SDIM*(N-SDIM)) */
/* otherwise, need 1 ) */
i__1 = *lwork - iwrk + 1;
ztgsen_(&ijob, &ilvsl, &ilvsr, &bwork[1], n, &a[a_offset], lda, &b[ b_offset], ldb, &alpha[1], &beta[1], &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, sdim, &pl, &pr, dif, &work[iwrk], & i__1, &iwork[1], liwork, &ierr);
if (ijob >= 1)
{
/* Computing MAX */
i__1 = maxwrk;
i__2 = (*sdim << 1) * (*n - *sdim); // , expr subst
maxwrk = max(i__1,i__2);
}
if (ierr == -21)
{
/* not enough complex workspace */
*info = -21;
}
else
{
if (ijob == 1 || ijob == 4)
{
rconde[1] = pl;
rconde[2] = pr;
}
if (ijob == 2 || ijob == 4)
{
rcondv[1] = dif[0];
rcondv[2] = dif[1];
}
if (ierr == 1)
{
*info = *n + 3;
}
}
}
/* Apply permutation to VSL and VSR */
/* (Workspace: none needed) */
if (ilvsl)
{
zggbak_("P", "L", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n, & vsl[vsl_offset], ldvsl, &ierr);
}
if (ilvsr)
{
zggbak_("P", "R", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n, & vsr[vsr_offset], ldvsr, &ierr);
}
/* Undo scaling */
if (ilascl)
{
zlascl_("U", &c__0, &c__0, &anrmto, &anrm, n, n, &a[a_offset], lda, & ierr);
zlascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alpha[1], n, & ierr);
}
if (ilbscl)
{
zlascl_("U", &c__0, &c__0, &bnrmto, &bnrm, n, n, &b[b_offset], ldb, & ierr);
zlascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, & ierr);
}
if (wantst)
{
/* Check if reordering is correct */
lastsl = TRUE_;
*sdim = 0;
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
cursl = (*selctg)(&alpha[i__], &beta[i__]);
if (cursl)
{
++(*sdim);
}
if (cursl && ! lastsl)
{
*info = *n + 2;
}
lastsl = cursl;
/* L30: */
}
}
L40:
work[1].r = (doublereal) maxwrk;
work[1].i = 0.; // , expr subst
iwork[1] = liwmin;
return 0;
/* End of ZGGESX */
}
