/* dgegs.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_n1 = -1;
static doublereal c_b36 = 0.;
static doublereal c_b37 = 1.;
/* Subroutine */ int dgegs_(char *jobvsl, char *jobvsr, integer *n,
doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *
alphar, doublereal *alphai, doublereal *beta, doublereal *vsl,
integer *ldvsl, doublereal *vsr, integer *ldvsr, doublereal *work,
integer *lwork, 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;
/* Local variables */
integer nb, nb1, nb2, nb3, ihi, ilo;
doublereal eps, anrm, bnrm;
integer itau, lopt;
extern logical lsame_(char *, char *);
integer ileft, iinfo, icols;
logical ilvsl;
integer iwork;
logical ilvsr;
integer irows;
extern /* Subroutine */ int dggbak_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, integer *), dggbal_(char *, integer *,
doublereal *, integer *, doublereal *, integer *, integer *,
integer *, doublereal *, doublereal *, doublereal *, integer *);
extern doublereal dlamch_(char *), dlange_(char *, integer *,
integer *, doublereal *, integer *, doublereal *);
extern /* Subroutine */ int dgghrd_(char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, integer *, integer *), dlascl_(char *, integer *, integer *, doublereal
*, doublereal *, integer *, integer *, doublereal *, integer *,
integer *);
logical ilascl, ilbscl;
extern /* Subroutine */ int dgeqrf_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *, integer *),
dlacpy_(char *, integer *, integer *, doublereal *, integer *,
doublereal *, integer *);
doublereal safmin;
extern /* Subroutine */ int dlaset_(char *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *),
xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
doublereal bignum;
extern /* Subroutine */ int dhgeqz_(char *, char *, char *, integer *,
integer *, integer *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
integer *, doublereal *, integer *, doublereal *, integer *,
integer *);
integer ijobvl, iright, ijobvr;
extern /* Subroutine */ int dorgqr_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *);
doublereal anrmto;
integer lwkmin;
doublereal bnrmto;
extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, integer *);
doublereal 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 */
/* ======= */
/* This routine is deprecated and has been replaced by routine DGGES. */
/* DGEGS computes the eigenvalues, real Schur form, and, optionally, */
/* left and or/right Schur vectors of a real matrix pair (A,B). */
/* Given two square matrices A and B, the generalized real Schur */
/* factorization has the form */
/* A = Q*S*Z**T, B = Q*T*Z**T */
/* where Q and Z are orthogonal matrices, T is upper triangular, and S */
/* is an upper quasi-triangular matrix with 1-by-1 and 2-by-2 diagonal */
/* blocks, the 2-by-2 blocks corresponding to complex conjugate pairs */
/* of eigenvalues of (A,B). The columns of Q are the left Schur vectors */
/* and the columns of Z are the right Schur vectors. */
/* If only the eigenvalues of (A,B) are needed, the driver routine */
/* DGEGV should be used instead. See DGEGV for a description of the */
/* eigenvalues of the generalized nonsymmetric eigenvalue problem */
/* (GNEP). */
/* Arguments */
/* ========= */
/* JOBVSL (input) CHARACTER*1 */
/* = 'N': do not compute the left Schur vectors; */
/* = 'V': compute the left Schur vectors (returned in VSL). */
/* JOBVSR (input) CHARACTER*1 */
/* = 'N': do not compute the right Schur vectors; */
/* = 'V': compute the right Schur vectors (returned in VSR). */
/* N (input) INTEGER */
/* The order of the matrices A, B, VSL, and VSR. N >= 0. */
/* A (input/output) DOUBLE PRECISION array, dimension (LDA, N) */
/* On entry, the matrix A. */
/* On exit, the upper quasi-triangular matrix S from the */
/* generalized real Schur factorization. */
/* LDA (input) INTEGER */
/* The leading dimension of A. LDA >= max(1,N). */
/* B (input/output) DOUBLE PRECISION array, dimension (LDB, N) */
/* On entry, the matrix B. */
/* On exit, the upper triangular matrix T from the generalized */
/* real Schur factorization. */
/* LDB (input) INTEGER */
/* The leading dimension of B. LDB >= max(1,N). */
/* ALPHAR (output) DOUBLE PRECISION array, dimension (N) */
/* The real parts of each scalar alpha defining an eigenvalue */
/* of GNEP. */
/* ALPHAI (output) DOUBLE PRECISION array, dimension (N) */
/* The imaginary parts of each scalar alpha defining an */
/* eigenvalue of GNEP. 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) = -ALPHAI(j). */
/* BETA (output) DOUBLE PRECISION array, dimension (N) */
/* The scalars beta that define the eigenvalues of GNEP. */
/* Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and */
/* beta = BETA(j) represent the j-th eigenvalue of the matrix */
/* pair (A,B), in one of the forms lambda = alpha/beta or */
/* mu = beta/alpha. Since either lambda or mu may overflow, */
/* they should not, in general, be computed. */
/* VSL (output) DOUBLE PRECISION array, dimension (LDVSL,N) */
/* If JOBVSL = 'V', the matrix of left Schur vectors Q. */
/* 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) DOUBLE PRECISION array, dimension (LDVSR,N) */
/* If JOBVSR = 'V', the matrix of right Schur vectors Z. */
/* 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) DOUBLE PRECISION 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(1,4*N). */
/* For good performance, LWORK must generally be larger. */
/* To compute the optimal value of LWORK, call ILAENV to get */
/* blocksizes (for DGEQRF, DORMQR, and DORGQR.) Then compute: */
/* NB -- MAX of the blocksizes for DGEQRF, DORMQR, and DORGQR */
/* The optimal LWORK is 2*N + N*(NB+1). */
/* 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. (A,B) are not in Schur */
/* form, but ALPHAR(j), ALPHAI(j), and BETA(j) should */
/* be correct for j=INFO+1,...,N. */
/* > N: errors that usually indicate LAPACK problems: */
/* =N+1: error return from DGGBAL */
/* =N+2: error return from DGEQRF */
/* =N+3: error return from DORMQR */
/* =N+4: error return from DORGQR */
/* =N+5: error return from DGGHRD */
/* =N+6: error return from DHGEQZ (other than failed */
/* iteration) */
/* =N+7: error return from DGGBAK (computing VSL) */
/* =N+8: error return from DGGBAK (computing VSR) */
/* =N+9: error return from DLASCL (various places) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. 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;
vsl_dim1 = *ldvsl;
vsl_offset = 1 + vsl_dim1;
vsl -= vsl_offset;
vsr_dim1 = *ldvsr;
vsr_offset = 1 + vsr_dim1;
vsr -= vsr_offset;
--work;
/* 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_;
}
/* Test the input arguments */
/* Computing MAX */
i__1 = *n << 2;
lwkmin = max(i__1,1);
lwkopt = lwkmin;
work[1] = (doublereal) lwkopt;
lquery = *lwork == -1;
*info = 0;
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 (*ldvsl < 1 || ilvsl && *ldvsl < *n) {
*info = -12;
} else if (*ldvsr < 1 || ilvsr && *ldvsr < *n) {
*info = -14;
} else if (*lwork < lwkmin && ! lquery) {
*info = -16;
}
if (*info == 0) {
nb1 = ilaenv_(&c__1, "DGEQRF", " ", n, n, &c_n1, &c_n1);
nb2 = ilaenv_(&c__1, "DORMQR", " ", n, n, n, &c_n1);
nb3 = ilaenv_(&c__1, "DORGQR", " ", n, n, n, &c_n1);
/* Computing MAX */
i__1 = max(nb1,nb2);
nb = max(i__1,nb3);
lopt = (*n << 1) + *n * (nb + 1);
work[1] = (doublereal) lopt;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DGEGS ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Get machine constants */
eps = dlamch_("E") * dlamch_("B");
safmin = dlamch_("S");
smlnum = *n * safmin / eps;
bignum = 1. / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = dlange_("M", n, n, &a[a_offset], lda, &work[1]);
ilascl = FALSE_;
if (anrm > 0. && anrm < smlnum) {
anrmto = smlnum;
ilascl = TRUE_;
} else if (anrm > bignum) {
anrmto = bignum;
ilascl = TRUE_;
}
if (ilascl) {
dlascl_("G", &c_n1, &c_n1, &anrm, &anrmto, n, n, &a[a_offset], lda, &
iinfo);
if (iinfo != 0) {
*info = *n + 9;
return 0;
}
}
/* Scale B if max element outside range [SMLNUM,BIGNUM] */
bnrm = dlange_("M", n, n, &b[b_offset], ldb, &work[1]);
ilbscl = FALSE_;
if (bnrm > 0. && bnrm < smlnum) {
bnrmto = smlnum;
ilbscl = TRUE_;
} else if (bnrm > bignum) {
bnrmto = bignum;
ilbscl = TRUE_;
}
if (ilbscl) {
dlascl_("G", &c_n1, &c_n1, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
iinfo);
if (iinfo != 0) {
*info = *n + 9;
return 0;
}
}
/* Permute the matrix to make it more nearly triangular */
/* Workspace layout: (2*N words -- "work..." not actually used) */
/* left_permutation, right_permutation, work... */
ileft = 1;
iright = *n + 1;
iwork = iright + *n;
dggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[
ileft], &work[iright], &work[iwork], &iinfo);
if (iinfo != 0) {
*info = *n + 1;
goto L10;
}
/* Reduce B to triangular form, and initialize VSL and/or VSR */
/* Workspace layout: ("work..." must have at least N words) */
/* left_permutation, right_permutation, tau, work... */
irows = ihi + 1 - ilo;
icols = *n + 1 - ilo;
itau = iwork;
iwork = itau + irows;
i__1 = *lwork + 1 - iwork;
dgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
iwork], &i__1, &iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = max(i__1,i__2);
}
if (iinfo != 0) {
*info = *n + 2;
goto L10;
}
i__1 = *lwork + 1 - iwork;
dormqr_("L", "T", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, &
work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwork], &i__1, &
iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = max(i__1,i__2);
}
if (iinfo != 0) {
*info = *n + 3;
goto L10;
}
if (ilvsl) {
dlaset_("Full", n, n, &c_b36, &c_b37, &vsl[vsl_offset], ldvsl);
i__1 = irows - 1;
i__2 = irows - 1;
dlacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vsl[ilo
+ 1 + ilo * vsl_dim1], ldvsl);
i__1 = *lwork + 1 - iwork;
dorgqr_(&irows, &irows, &irows, &vsl[ilo + ilo * vsl_dim1], ldvsl, &
work[itau], &work[iwork], &i__1, &iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = max(i__1,i__2);
}
if (iinfo != 0) {
*info = *n + 4;
goto L10;
}
}
if (ilvsr) {
dlaset_("Full", n, n, &c_b36, &c_b37, &vsr[vsr_offset], ldvsr);
}
/* Reduce to generalized Hessenberg form */
dgghrd_(jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset],
ldb, &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &iinfo);
if (iinfo != 0) {
*info = *n + 5;
goto L10;
}
/* Perform QZ algorithm, computing Schur vectors if desired */
/* Workspace layout: ("work..." must have at least 1 word) */
/* left_permutation, right_permutation, work... */
iwork = itau;
i__1 = *lwork + 1 - iwork;
dhgeqz_("S", jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[
b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vsl[vsl_offset]
, ldvsl, &vsr[vsr_offset], ldvsr, &work[iwork], &i__1, &iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = max(i__1,i__2);
}
if (iinfo != 0) {
if (iinfo > 0 && iinfo <= *n) {
*info = iinfo;
} else if (iinfo > *n && iinfo <= *n << 1) {
*info = iinfo - *n;
} else {
*info = *n + 6;
}
goto L10;
}
/* Apply permutation to VSL and VSR */
if (ilvsl) {
dggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsl[
vsl_offset], ldvsl, &iinfo);
if (iinfo != 0) {
*info = *n + 7;
goto L10;
}
}
if (ilvsr) {
dggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsr[
vsr_offset], ldvsr, &iinfo);
if (iinfo != 0) {
*info = *n + 8;
goto L10;
}
}
/* Undo scaling */
if (ilascl) {
dlascl_("H", &c_n1, &c_n1, &anrmto, &anrm, n, n, &a[a_offset], lda, &
iinfo);
if (iinfo != 0) {
*info = *n + 9;
return 0;
}
dlascl_("G", &c_n1, &c_n1, &anrmto, &anrm, n, &c__1, &alphar[1], n, &
iinfo);
if (iinfo != 0) {
*info = *n + 9;
return 0;
}
dlascl_("G", &c_n1, &c_n1, &anrmto, &anrm, n, &c__1, &alphai[1], n, &
iinfo);
if (iinfo != 0) {
*info = *n + 9;
return 0;
}
}
if (ilbscl) {
dlascl_("U", &c_n1, &c_n1, &bnrmto, &bnrm, n, n, &b[b_offset], ldb, &
iinfo);
if (iinfo != 0) {
*info = *n + 9;
return 0;
}
dlascl_("G", &c_n1, &c_n1, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
iinfo);
if (iinfo != 0) {
*info = *n + 9;
return 0;
}
}
L10:
work[1] = (doublereal) lwkopt;
return 0;
/* End of DGEGS */
} /* dgegs_ */
