/* cggev.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static complex c_b1 = {0.f,0.f};
static complex c_b2 = {1.f,0.f};
static integer c__1 = 1;
static integer c__0 = 0;
static integer c_n1 = -1;
/* Subroutine */ int cggev_(char *jobvl, char *jobvr, integer *n, complex *a,
integer *lda, complex *b, integer *ldb, complex *alpha, complex *beta,
complex *vl, integer *ldvl, complex *vr, integer *ldvr, complex *
work, integer *lwork, real *rwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1,
vr_offset, i__1, i__2, i__3, i__4;
real r__1, r__2, r__3, r__4;
complex q__1;
/* Builtin functions */
double sqrt(doublereal), r_imag(complex *);
/* Local variables */
integer jc, in, jr, ihi, ilo;
real eps;
logical ilv;
real anrm, bnrm;
integer ierr, itau;
real temp;
logical ilvl, ilvr;
integer iwrk;
extern logical lsame_(char *, char *);
integer ileft, icols, irwrk, irows;
extern /* Subroutine */ int cggbak_(char *, char *, integer *, integer *,
integer *, real *, real *, integer *, complex *, integer *,
integer *), cggbal_(char *, integer *, complex *,
integer *, complex *, integer *, integer *, integer *, real *,
real *, real *, integer *), slabad_(real *, real *);
extern doublereal clange_(char *, integer *, integer *, complex *,
integer *, real *);
extern /* Subroutine */ int cgghrd_(char *, char *, integer *, integer *,
integer *, complex *, integer *, complex *, integer *, complex *,
integer *, complex *, integer *, integer *),
clascl_(char *, integer *, integer *, real *, real *, integer *,
integer *, complex *, integer *, integer *);
logical ilascl, ilbscl;
extern /* Subroutine */ int cgeqrf_(integer *, integer *, complex *,
integer *, complex *, complex *, integer *, integer *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
*, integer *, complex *, integer *), claset_(char *,
integer *, integer *, complex *, complex *, complex *, integer *), ctgevc_(char *, char *, logical *, integer *, complex *,
integer *, complex *, integer *, complex *, integer *, complex *,
integer *, integer *, integer *, complex *, real *, integer *), xerbla_(char *, integer *);
logical ldumma[1];
char chtemp[1];
real bignum;
extern /* Subroutine */ int chgeqz_(char *, char *, char *, integer *,
integer *, integer *, complex *, integer *, complex *, integer *,
complex *, complex *, complex *, integer *, complex *, integer *,
complex *, integer *, real *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
integer ijobvl, iright, ijobvr;
extern /* Subroutine */ int cungqr_(integer *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *, integer *);
real anrmto;
integer lwkmin;
real bnrmto;
extern /* Subroutine */ int cunmqr_(char *, char *, integer *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
complex *, integer *, integer *);
real smlnum;
integer lwkopt;
logical lquery;
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CGGEV computes for a pair of N-by-N complex nonsymmetric matrices */
/* (A,B), the generalized eigenvalues, and optionally, the left and/or */
/* right generalized eigenvectors. */
/* A generalized eigenvalue for a pair of matrices (A,B) is a scalar */
/* lambda or a ratio alpha/beta = lambda, such that A - lambda*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. */
/* The right generalized eigenvector v(j) corresponding to the */
/* generalized eigenvalue lambda(j) of (A,B) satisfies */
/* A * v(j) = lambda(j) * B * v(j). */
/* The left generalized eigenvector u(j) corresponding to the */
/* generalized eigenvalues lambda(j) of (A,B) satisfies */
/* u(j)**H * A = lambda(j) * u(j)**H * B */
/* where u(j)**H is the conjugate-transpose of u(j). */
/* Arguments */
/* ========= */
/* JOBVL (input) CHARACTER*1 */
/* = 'N': do not compute the left generalized eigenvectors; */
/* = 'V': compute the left generalized eigenvectors. */
/* JOBVR (input) CHARACTER*1 */
/* = 'N': do not compute the right generalized eigenvectors; */
/* = 'V': compute the right generalized eigenvectors. */
/* N (input) INTEGER */
/* The order of the matrices A, B, VL, and VR. N >= 0. */
/* A (input/output) COMPLEX array, dimension (LDA, N) */
/* On entry, the matrix A in the pair (A,B). */
/* On exit, A has been overwritten. */
/* LDA (input) INTEGER */
/* The leading dimension of A. LDA >= max(1,N). */
/* B (input/output) COMPLEX array, dimension (LDB, N) */
/* On entry, the matrix B in the pair (A,B). */
/* On exit, B has been overwritten. */
/* LDB (input) INTEGER */
/* The leading dimension of B. LDB >= max(1,N). */
/* ALPHA (output) COMPLEX array, dimension (N) */
/* BETA (output) COMPLEX array, dimension (N) */
/* On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the */
/* generalized eigenvalues. */
/* 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). */
/* VL (output) COMPLEX array, dimension (LDVL,N) */
/* If JOBVL = 'V', the left generalized eigenvectors u(j) are */
/* stored one after another in the columns of VL, in the same */
/* order as their eigenvalues. */
/* Each eigenvector is scaled so the largest component has */
/* abs(real part) + abs(imag. part) = 1. */
/* Not referenced if JOBVL = 'N'. */
/* LDVL (input) INTEGER */
/* The leading dimension of the matrix VL. LDVL >= 1, and */
/* if JOBVL = 'V', LDVL >= N. */
/* VR (output) COMPLEX array, dimension (LDVR,N) */
/* If JOBVR = 'V', the right generalized eigenvectors v(j) are */
/* stored one after another in the columns of VR, in the same */
/* order as their eigenvalues. */
/* Each eigenvector is scaled so the largest component has */
/* abs(real part) + abs(imag. part) = 1. */
/* Not referenced if JOBVR = 'N'. */
/* LDVR (input) INTEGER */
/* The leading dimension of the matrix VR. LDVR >= 1, and */
/* if JOBVR = 'V', LDVR >= 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/output) REAL array, dimension (8*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. No eigenvectors have been */
/* calculated, but ALPHA(j) and BETA(j) should be */
/* correct for j=INFO+1,...,N. */
/* > N: =N+1: other then QZ iteration failed in SHGEQZ, */
/* =N+2: error return from STGEVC. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. 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;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1;
vr -= vr_offset;
--work;
--rwork;
/* Function Body */
if (lsame_(jobvl, "N")) {
ijobvl = 1;
ilvl = FALSE_;
} else if (lsame_(jobvl, "V")) {
ijobvl = 2;
ilvl = TRUE_;
} else {
ijobvl = -1;
ilvl = FALSE_;
}
if (lsame_(jobvr, "N")) {
ijobvr = 1;
ilvr = FALSE_;
} else if (lsame_(jobvr, "V")) {
ijobvr = 2;
ilvr = TRUE_;
} else {
ijobvr = -1;
ilvr = FALSE_;
}
ilv = ilvl || ilvr;
/* Test the input arguments */
*info = 0;
lquery = *lwork == -1;
if (ijobvl <= 0) {
*info = -1;
} else if (ijobvr <= 0) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldb < max(1,*n)) {
*info = -7;
} else if (*ldvl < 1 || ilvl && *ldvl < *n) {
*info = -11;
} else if (*ldvr < 1 || ilvr && *ldvr < *n) {
*info = -13;
}
/* 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. The workspace is */
/* computed assuming ILO = 1 and IHI = N, the worst case.) */
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, "CGEQRF", " ", n, &c__1, n,
&c__0);
lwkopt = max(i__1,i__2);
/* Computing MAX */
i__1 = lwkopt, i__2 = *n + *n * ilaenv_(&c__1, "CUNMQR", " ", n, &
c__1, n, &c__0);
lwkopt = max(i__1,i__2);
if (ilvl) {
/* Computing MAX */
i__1 = lwkopt, i__2 = *n + *n * ilaenv_(&c__1, "CUNGQR", " ", n, &
c__1, n, &c_n1);
lwkopt = max(i__1,i__2);
}
work[1].r = (real) lwkopt, work[1].i = 0.f;
if (*lwork < lwkmin && ! lquery) {
*info = -15;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGGEV ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Get machine constants */
eps = slamch_("E") * slamch_("B");
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, &rwork[1]);
ilascl = FALSE_;
if (anrm > 0.f && anrm < smlnum) {
anrmto = smlnum;
ilascl = TRUE_;
} else if (anrm > bignum) {
anrmto = bignum;
ilascl = TRUE_;
}
if (ilascl) {
clascl_("G", &c__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, &
ierr);
}
/* Scale B if max element outside range [SMLNUM,BIGNUM] */
bnrm = clange_("M", n, n, &b[b_offset], ldb, &rwork[1]);
ilbscl = FALSE_;
if (bnrm > 0.f && bnrm < smlnum) {
bnrmto = smlnum;
ilbscl = TRUE_;
} else if (bnrm > bignum) {
bnrmto = bignum;
ilbscl = TRUE_;
}
if (ilbscl) {
clascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
ierr);
}
/* Permute the matrices A, B to isolate eigenvalues if possible */
/* (Real Workspace: need 6*N) */
ileft = 1;
iright = *n + 1;
irwrk = iright + *n;
cggbal_("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;
if (ilv) {
icols = *n + 1 - ilo;
} else {
icols = irows;
}
itau = 1;
iwrk = itau + irows;
i__1 = *lwork + 1 - iwrk;
cgeqrf_(&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;
cunmqr_("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 VL */
/* (Complex Workspace: need N, prefer N*NB) */
if (ilvl) {
claset_("Full", n, n, &c_b1, &c_b2, &vl[vl_offset], ldvl);
if (irows > 1) {
i__1 = irows - 1;
i__2 = irows - 1;
clacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vl[
ilo + 1 + ilo * vl_dim1], ldvl);
}
i__1 = *lwork + 1 - iwrk;
cungqr_(&irows, &irows, &irows, &vl[ilo + ilo * vl_dim1], ldvl, &work[
itau], &work[iwrk], &i__1, &ierr);
}
/* Initialize VR */
if (ilvr) {
claset_("Full", n, n, &c_b1, &c_b2, &vr[vr_offset], ldvr);
}
/* Reduce to generalized Hessenberg form */
if (ilv) {
/* Eigenvectors requested -- work on whole matrix. */
cgghrd_(jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset],
ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &ierr);
} else {
cgghrd_("N", "N", &irows, &c__1, &irows, &a[ilo + ilo * a_dim1], lda,
&b[ilo + ilo * b_dim1], ldb, &vl[vl_offset], ldvl, &vr[
vr_offset], ldvr, &ierr);
}
/* Perform QZ algorithm (Compute eigenvalues, and optionally, the */
/* Schur form and Schur vectors) */
/* (Complex Workspace: need N) */
/* (Real Workspace: need N) */
iwrk = itau;
if (ilv) {
*(unsigned char *)chtemp = 'S';
} else {
*(unsigned char *)chtemp = 'E';
}
i__1 = *lwork + 1 - iwrk;
chgeqz_(chtemp, jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[
b_offset], ldb, &alpha[1], &beta[1], &vl[vl_offset], ldvl, &vr[
vr_offset], ldvr, &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 L70;
}
/* Compute Eigenvectors */
/* (Real Workspace: need 2*N) */
/* (Complex Workspace: need 2*N) */
if (ilv) {
if (ilvl) {
if (ilvr) {
*(unsigned char *)chtemp = 'B';
} else {
*(unsigned char *)chtemp = 'L';
}
} else {
*(unsigned char *)chtemp = 'R';
}
ctgevc_(chtemp, "B", ldumma, n, &a[a_offset], lda, &b[b_offset], ldb,
&vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &in, &work[
iwrk], &rwork[irwrk], &ierr);
if (ierr != 0) {
*info = *n + 2;
goto L70;
}
/* Undo balancing on VL and VR and normalization */
/* (Workspace: none needed) */
if (ilvl) {
cggbak_("P", "L", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n,
&vl[vl_offset], ldvl, &ierr);
i__1 = *n;
for (jc = 1; jc <= i__1; ++jc) {
temp = 0.f;
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
i__3 = jr + jc * vl_dim1;
r__3 = temp, r__4 = (r__1 = vl[i__3].r, dabs(r__1)) + (
r__2 = r_imag(&vl[jr + jc * vl_dim1]), dabs(r__2))
;
temp = dmax(r__3,r__4);
/* L10: */
}
if (temp < smlnum) {
goto L30;
}
temp = 1.f / temp;
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
i__3 = jr + jc * vl_dim1;
i__4 = jr + jc * vl_dim1;
q__1.r = temp * vl[i__4].r, q__1.i = temp * vl[i__4].i;
vl[i__3].r = q__1.r, vl[i__3].i = q__1.i;
/* L20: */
}
L30:
;
}
}
if (ilvr) {
cggbak_("P", "R", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n,
&vr[vr_offset], ldvr, &ierr);
i__1 = *n;
for (jc = 1; jc <= i__1; ++jc) {
temp = 0.f;
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
i__3 = jr + jc * vr_dim1;
r__3 = temp, r__4 = (r__1 = vr[i__3].r, dabs(r__1)) + (
r__2 = r_imag(&vr[jr + jc * vr_dim1]), dabs(r__2))
;
temp = dmax(r__3,r__4);
/* L40: */
}
if (temp < smlnum) {
goto L60;
}
temp = 1.f / temp;
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
i__3 = jr + jc * vr_dim1;
i__4 = jr + jc * vr_dim1;
q__1.r = temp * vr[i__4].r, q__1.i = temp * vr[i__4].i;
vr[i__3].r = q__1.r, vr[i__3].i = q__1.i;
/* L50: */
}
L60:
;
}
}
}
/* Undo scaling if necessary */
if (ilascl) {
clascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alpha[1], n, &
ierr);
}
if (ilbscl) {
clascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
ierr);
}
L70:
work[1].r = (real) lwkopt, work[1].i = 0.f;
return 0;
/* End of CGGEV */
} /* cggev_ */
