/* sggev.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 integer c__1 = 1;
static integer c__0 = 0;
static integer c_n1 = -1;
static real c_b36 = 0.f;
static real c_b37 = 1.f;
/* Subroutine */ int sggev_(char *jobvl, char *jobvr, integer *n, real *a,
integer *lda, real *b, integer *ldb, real *alphar, real *alphai, real
*beta, real *vl, integer *ldvl, real *vr, integer *ldvr, real *work,
integer *lwork, 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;
real r__1, r__2, r__3, r__4;
/* Builtin functions */
double sqrt(doublereal);
/* 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, irows;
extern /* Subroutine */ int slabad_(real *, real *), sggbak_(char *, char
*, integer *, integer *, integer *, real *, real *, integer *,
real *, integer *, integer *), sggbal_(char *,
integer *, real *, integer *, real *, integer *, integer *,
integer *, real *, real *, real *, integer *);
logical ilascl, ilbscl;
extern doublereal slamch_(char *), slange_(char *, integer *,
integer *, real *, integer *, real *);
extern /* Subroutine */ int xerbla_(char *, integer *), sgghrd_(
char *, char *, integer *, integer *, integer *, real *, integer *
, real *, integer *, real *, integer *, real *, integer *,
integer *);
logical ldumma[1];
char chtemp[1];
real bignum;
extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, real *, integer *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
integer ijobvl, iright;
extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer
*, real *, real *, integer *, integer *);
integer ijobvr;
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *), slaset_(char *, integer *,
integer *, real *, real *, real *, integer *), stgevc_(
char *, char *, logical *, integer *, real *, integer *, real *,
integer *, real *, integer *, real *, integer *, integer *,
integer *, real *, integer *);
real anrmto, bnrmto;
extern /* Subroutine */ int shgeqz_(char *, char *, char *, integer *,
integer *, integer *, real *, integer *, real *, integer *, real *
, real *, real *, real *, integer *, real *, integer *, real *,
integer *, integer *);
integer minwrk, maxwrk;
real smlnum;
extern /* Subroutine */ int sorgqr_(integer *, integer *, integer *, real
*, integer *, real *, real *, integer *, integer *);
logical lquery;
extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SGGEV computes for a pair of N-by-N real 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 eigenvector v(j) corresponding to the eigenvalue lambda(j) */
/* of (A,B) satisfies */
/* A * v(j) = lambda(j) * B * v(j). */
/* The left eigenvector u(j) corresponding to the eigenvalue 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) REAL 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) REAL 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). */
/* ALPHAR (output) REAL array, dimension (N) */
/* ALPHAI (output) REAL array, dimension (N) */
/* BETA (output) REAL array, dimension (N) */
/* On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will */
/* be the generalized eigenvalues. If ALPHAI(j) is zero, then */
/* the j-th eigenvalue is real; if positive, then the j-th and */
/* (j+1)-st eigenvalues are a complex conjugate pair, with */
/* ALPHAI(j+1) negative. */
/* Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(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, ALPHAR and ALPHAI 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) REAL array, dimension (LDVL,N) */
/* If JOBVL = 'V', the left eigenvectors u(j) are stored one */
/* after another in the columns of VL, in the same order as */
/* their eigenvalues. If the j-th eigenvalue is real, then */
/* u(j) = VL(:,j), the j-th column of VL. If the j-th and */
/* (j+1)-th eigenvalues form a complex conjugate pair, then */
/* u(j) = VL(:,j)+i*VL(:,j+1) and u(j+1) = VL(:,j)-i*VL(:,j+1). */
/* 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) REAL array, dimension (LDVR,N) */
/* If JOBVR = 'V', the right eigenvectors v(j) are stored one */
/* after another in the columns of VR, in the same order as */
/* their eigenvalues. If the j-th eigenvalue is real, then */
/* v(j) = VR(:,j), the j-th column of VR. If the j-th and */
/* (j+1)-th eigenvalues form a complex conjugate pair, then */
/* v(j) = VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1). */
/* 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) REAL 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(1,8*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. */
/* 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 ALPHAR(j), ALPHAI(j), and BETA(j) */
/* should be correct for j=INFO+1,...,N. */
/* > N: =N+1: other than QZ iteration failed in SHGEQZ. */
/* =N+2: error return from STGEVC. */
/* ===================================================================== */
/* .. 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;
--alphar;
--alphai;
--beta;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1;
vr -= vr_offset;
--work;
/* 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 = -12;
} else if (*ldvr < 1 || ilvr && *ldvr < *n) {
*info = -14;
}
/* 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 << 3;
minwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = 1, i__2 = *n * (ilaenv_(&c__1, "SGEQRF", " ", n, &c__1, n, &
c__0) + 7);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * (ilaenv_(&c__1, "SORMQR", " ", n, &c__1, n,
&c__0) + 7);
maxwrk = max(i__1,i__2);
if (ilvl) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * (ilaenv_(&c__1, "SORGQR", " ", n, &
c__1, n, &c_n1) + 7);
maxwrk = max(i__1,i__2);
}
work[1] = (real) maxwrk;
if (*lwork < minwrk && ! lquery) {
*info = -16;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGGEV ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 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 = slange_("M", n, n, &a[a_offset], lda, &work[1]);
ilascl = FALSE_;
if (anrm > 0.f && anrm < smlnum) {
anrmto = smlnum;
ilascl = TRUE_;
} else if (anrm > bignum) {
anrmto = bignum;
ilascl = TRUE_;
}
if (ilascl) {
slascl_("G", &c__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, &
ierr);
}
/* Scale B if max element outside range [SMLNUM,BIGNUM] */
bnrm = slange_("M", n, n, &b[b_offset], ldb, &work[1]);
ilbscl = FALSE_;
if (bnrm > 0.f && bnrm < smlnum) {
bnrmto = smlnum;
ilbscl = TRUE_;
} else if (bnrm > bignum) {
bnrmto = bignum;
ilbscl = TRUE_;
}
if (ilbscl) {
slascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
ierr);
}
/* Permute the matrices A, B to isolate eigenvalues if possible */
/* (Workspace: need 6*N) */
ileft = 1;
iright = *n + 1;
iwrk = iright + *n;
sggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[
ileft], &work[iright], &work[iwrk], &ierr);
/* Reduce B to triangular form (QR decomposition of B) */
/* (Workspace: need N, prefer N*NB) */
irows = ihi + 1 - ilo;
if (ilv) {
icols = *n + 1 - ilo;
} else {
icols = irows;
}
itau = iwrk;
iwrk = itau + irows;
i__1 = *lwork + 1 - iwrk;
sgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
iwrk], &i__1, &ierr);
/* Apply the orthogonal transformation to matrix A */
/* (Workspace: need N, prefer N*NB) */
i__1 = *lwork + 1 - iwrk;
sormqr_("L", "T", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, &
work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwrk], &i__1, &
ierr);
/* Initialize VL */
/* (Workspace: need N, prefer N*NB) */
if (ilvl) {
slaset_("Full", n, n, &c_b36, &c_b37, &vl[vl_offset], ldvl)
;
if (irows > 1) {
i__1 = irows - 1;
i__2 = irows - 1;
slacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vl[
ilo + 1 + ilo * vl_dim1], ldvl);
}
i__1 = *lwork + 1 - iwrk;
sorgqr_(&irows, &irows, &irows, &vl[ilo + ilo * vl_dim1], ldvl, &work[
itau], &work[iwrk], &i__1, &ierr);
}
/* Initialize VR */
if (ilvr) {
slaset_("Full", n, n, &c_b36, &c_b37, &vr[vr_offset], ldvr)
;
}
/* Reduce to generalized Hessenberg form */
/* (Workspace: none needed) */
if (ilv) {
/* Eigenvectors requested -- work on whole matrix. */
sgghrd_(jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset],
ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &ierr);
} else {
sgghrd_("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 forms and Schur vectors) */
/* (Workspace: need N) */
iwrk = itau;
if (ilv) {
*(unsigned char *)chtemp = 'S';
} else {
*(unsigned char *)chtemp = 'E';
}
i__1 = *lwork + 1 - iwrk;
shgeqz_(chtemp, jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[
b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vl[vl_offset],
ldvl, &vr[vr_offset], ldvr, &work[iwrk], &i__1, &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 L110;
}
/* Compute Eigenvectors */
/* (Workspace: need 6*N) */
if (ilv) {
if (ilvl) {
if (ilvr) {
*(unsigned char *)chtemp = 'B';
} else {
*(unsigned char *)chtemp = 'L';
}
} else {
*(unsigned char *)chtemp = 'R';
}
stgevc_(chtemp, "B", ldumma, n, &a[a_offset], lda, &b[b_offset], ldb,
&vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &in, &work[
iwrk], &ierr);
if (ierr != 0) {
*info = *n + 2;
goto L110;
}
/* Undo balancing on VL and VR and normalization */
/* (Workspace: none needed) */
if (ilvl) {
sggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &
vl[vl_offset], ldvl, &ierr);
i__1 = *n;
for (jc = 1; jc <= i__1; ++jc) {
if (alphai[jc] < 0.f) {
goto L50;
}
temp = 0.f;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__2 = temp, r__3 = (r__1 = vl[jr + jc * vl_dim1],
dabs(r__1));
temp = dmax(r__2,r__3);
/* L10: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__3 = temp, r__4 = (r__1 = vl[jr + jc * vl_dim1],
dabs(r__1)) + (r__2 = vl[jr + (jc + 1) *
vl_dim1], dabs(r__2));
temp = dmax(r__3,r__4);
/* L20: */
}
}
if (temp < smlnum) {
goto L50;
}
temp = 1.f / temp;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vl[jr + jc * vl_dim1] *= temp;
/* L30: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vl[jr + jc * vl_dim1] *= temp;
vl[jr + (jc + 1) * vl_dim1] *= temp;
/* L40: */
}
}
L50:
;
}
}
if (ilvr) {
sggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, &
vr[vr_offset], ldvr, &ierr);
i__1 = *n;
for (jc = 1; jc <= i__1; ++jc) {
if (alphai[jc] < 0.f) {
goto L100;
}
temp = 0.f;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__2 = temp, r__3 = (r__1 = vr[jr + jc * vr_dim1],
dabs(r__1));
temp = dmax(r__2,r__3);
/* L60: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__3 = temp, r__4 = (r__1 = vr[jr + jc * vr_dim1],
dabs(r__1)) + (r__2 = vr[jr + (jc + 1) *
vr_dim1], dabs(r__2));
temp = dmax(r__3,r__4);
/* L70: */
}
}
if (temp < smlnum) {
goto L100;
}
temp = 1.f / temp;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vr[jr + jc * vr_dim1] *= temp;
/* L80: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vr[jr + jc * vr_dim1] *= temp;
vr[jr + (jc + 1) * vr_dim1] *= temp;
/* L90: */
}
}
L100:
;
}
}
/* End of eigenvector calculation */
}
/* Undo scaling if necessary */
if (ilascl) {
slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphar[1], n, &
ierr);
slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphai[1], n, &
ierr);
}
if (ilbscl) {
slascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
ierr);
}
L110:
work[1] = (real) maxwrk;
return 0;
/* End of SGGEV */
} /* sggev_ */