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authorshmel1k <shmel1k@ydb.tech>2022-09-02 12:44:59 +0300
committershmel1k <shmel1k@ydb.tech>2022-09-02 12:44:59 +0300
commit90d450f74722da7859d6f510a869f6c6908fd12f (patch)
tree538c718dedc76cdfe37ad6d01ff250dd930d9278 /contrib/libs/clapack/dgegv.c
parent01f64c1ecd0d4ffa9e3a74478335f1745f26cc75 (diff)
downloadydb-90d450f74722da7859d6f510a869f6c6908fd12f.tar.gz
[] add metering mode to CLI
Diffstat (limited to 'contrib/libs/clapack/dgegv.c')
-rw-r--r--contrib/libs/clapack/dgegv.c842
1 files changed, 842 insertions, 0 deletions
diff --git a/contrib/libs/clapack/dgegv.c b/contrib/libs/clapack/dgegv.c
new file mode 100644
index 0000000000..8551895e4c
--- /dev/null
+++ b/contrib/libs/clapack/dgegv.c
@@ -0,0 +1,842 @@
+/* dgegv.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_b27 = 1.;
+static doublereal c_b38 = 0.;
+
+/* Subroutine */ int dgegv_(char *jobvl, char *jobvr, integer *n, doublereal *
+ a, integer *lda, doublereal *b, integer *ldb, doublereal *alphar,
+ doublereal *alphai, doublereal *beta, doublereal *vl, integer *ldvl,
+ doublereal *vr, integer *ldvr, doublereal *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;
+ doublereal d__1, d__2, d__3, d__4;
+
+ /* Local variables */
+ integer jc, nb, in, jr, nb1, nb2, nb3, ihi, ilo;
+ doublereal eps;
+ logical ilv;
+ doublereal absb, anrm, bnrm;
+ integer itau;
+ doublereal temp;
+ logical ilvl, ilvr;
+ integer lopt;
+ doublereal anrm1, anrm2, bnrm1, bnrm2, absai, scale, absar, sbeta;
+ extern logical lsame_(char *, char *);
+ integer ileft, iinfo, icols, iwork, 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 *);
+ doublereal salfai;
+ 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 *);
+ doublereal salfar;
+ 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 *);
+ doublereal safmax;
+ char chtemp[1];
+ logical ldumma[1];
+ extern /* Subroutine */ int dhgeqz_(char *, char *, char *, integer *,
+ integer *, integer *, doublereal *, integer *, doublereal *,
+ integer *, doublereal *, doublereal *, doublereal *, doublereal *,
+ integer *, doublereal *, integer *, doublereal *, integer *,
+ integer *), dtgevc_(char *, char *,
+ logical *, integer *, doublereal *, integer *, doublereal *,
+ integer *, doublereal *, integer *, doublereal *, integer *,
+ integer *, integer *, doublereal *, integer *),
+ xerbla_(char *, integer *);
+ integer ijobvl, iright;
+ logical ilimit;
+ extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
+ integer *, integer *);
+ integer ijobvr;
+ extern /* Subroutine */ int dorgqr_(integer *, integer *, integer *,
+ doublereal *, integer *, doublereal *, doublereal *, integer *,
+ integer *);
+ doublereal onepls;
+ integer lwkmin;
+ extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *,
+ integer *, doublereal *, integer *, doublereal *, doublereal *,
+ integer *, doublereal *, integer *, integer *);
+ 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 DGGEV. */
+
+/* DGEGV computes the eigenvalues and, optionally, the left and/or right */
+/* eigenvectors of a real matrix pair (A,B). */
+/* Given two square matrices A and B, */
+/* the generalized nonsymmetric eigenvalue problem (GNEP) is to find the */
+/* eigenvalues lambda and corresponding (non-zero) eigenvectors x such */
+/* that */
+
+/* A*x = lambda*B*x. */
+
+/* An alternate form is to find the eigenvalues mu and corresponding */
+/* eigenvectors y such that */
+
+/* mu*A*y = B*y. */
+
+/* These two forms are equivalent with mu = 1/lambda and x = y if */
+/* neither lambda nor mu is zero. In order to deal with the case that */
+/* lambda or mu is zero or small, two values alpha and beta are returned */
+/* for each eigenvalue, such that lambda = alpha/beta and */
+/* mu = beta/alpha. */
+
+/* The vectors x and y in the above equations are right eigenvectors of */
+/* the matrix pair (A,B). Vectors u and v satisfying */
+
+/* u**H*A = lambda*u**H*B or mu*v**H*A = v**H*B */
+
+/* are left eigenvectors of (A,B). */
+
+/* Note: this routine performs "full balancing" on A and B -- see */
+/* "Further Details", below. */
+
+/* Arguments */
+/* ========= */
+
+/* JOBVL (input) CHARACTER*1 */
+/* = 'N': do not compute the left generalized eigenvectors; */
+/* = 'V': compute the left generalized eigenvectors (returned */
+/* in VL). */
+
+/* JOBVR (input) CHARACTER*1 */
+/* = 'N': do not compute the right generalized eigenvectors; */
+/* = 'V': compute the right generalized eigenvectors (returned */
+/* in VR). */
+
+/* N (input) INTEGER */
+/* The order of the matrices A, B, VL, and VR. N >= 0. */
+
+/* A (input/output) DOUBLE PRECISION array, dimension (LDA, N) */
+/* On entry, the matrix A. */
+/* If JOBVL = 'V' or JOBVR = 'V', then on exit A */
+/* contains the real Schur form of A from the generalized Schur */
+/* factorization of the pair (A,B) after balancing. */
+/* If no eigenvectors were computed, then only the diagonal */
+/* blocks from the Schur form will be correct. See DGGHRD and */
+/* DHGEQZ for details. */
+
+/* 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. */
+/* If JOBVL = 'V' or JOBVR = 'V', then on exit B contains the */
+/* upper triangular matrix obtained from B in the generalized */
+/* Schur factorization of the pair (A,B) after balancing. */
+/* If no eigenvectors were computed, then only those elements of */
+/* B corresponding to the diagonal blocks from the Schur form of */
+/* A will be correct. See DGGHRD and DHGEQZ for details. */
+
+/* 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. */
+
+/* VL (output) DOUBLE PRECISION array, dimension (LDVL,N) */
+/* If JOBVL = 'V', the left eigenvectors u(j) are stored */
+/* in the columns of VL, in the same order as their eigenvalues. */
+/* If the j-th eigenvalue is real, then u(j) = VL(:,j). */
+/* If the j-th and (j+1)-st 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 that its largest component has */
+/* abs(real part) + abs(imag. part) = 1, except for eigenvectors */
+/* corresponding to an eigenvalue with alpha = beta = 0, which */
+/* are set to zero. */
+/* 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) DOUBLE PRECISION array, dimension (LDVR,N) */
+/* If JOBVR = 'V', the right eigenvectors x(j) are stored */
+/* in the columns of VR, in the same order as their eigenvalues. */
+/* If the j-th eigenvalue is real, then x(j) = VR(:,j). */
+/* If the j-th and (j+1)-st eigenvalues form a complex conjugate */
+/* pair, then */
+/* x(j) = VR(:,j) + i*VR(:,j+1) */
+/* and */
+/* x(j+1) = VR(:,j) - i*VR(:,j+1). */
+
+/* Each eigenvector is scaled so that its largest component has */
+/* abs(real part) + abs(imag. part) = 1, except for eigenvalues */
+/* corresponding to an eigenvalue with alpha = beta = 0, which */
+/* are set to zero. */
+/* 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) 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(1,8*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 + MAX( 6*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. No eigenvectors have been */
+/* calculated, 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 DTGEVC */
+/* =N+8: error return from DGGBAK (computing VL) */
+/* =N+9: error return from DGGBAK (computing VR) */
+/* =N+10: error return from DLASCL (various calls) */
+
+/* Further Details */
+/* =============== */
+
+/* Balancing */
+/* --------- */
+
+/* This driver calls DGGBAL to both permute and scale rows and columns */
+/* of A and B. The permutations PL and PR are chosen so that PL*A*PR */
+/* and PL*B*R will be upper triangular except for the diagonal blocks */
+/* A(i:j,i:j) and B(i:j,i:j), with i and j as close together as */
+/* possible. The diagonal scaling matrices DL and DR are chosen so */
+/* that the pair DL*PL*A*PR*DR, DL*PL*B*PR*DR have elements close to */
+/* one (except for the elements that start out zero.) */
+
+/* After the eigenvalues and eigenvectors of the balanced matrices */
+/* have been computed, DGGBAK transforms the eigenvectors back to what */
+/* they would have been (in perfect arithmetic) if they had not been */
+/* balanced. */
+
+/* Contents of A and B on Exit */
+/* -------- -- - --- - -- ---- */
+
+/* If any eigenvectors are computed (either JOBVL='V' or JOBVR='V' or */
+/* both), then on exit the arrays A and B will contain the real Schur */
+/* form[*] of the "balanced" versions of A and B. If no eigenvectors */
+/* are computed, then only the diagonal blocks will be correct. */
+
+/* [*] See DHGEQZ, DGEGS, or read the book "Matrix Computations", */
+/* by Golub & van Loan, pub. by Johns Hopkins U. Press. */
+
+/* ===================================================================== */
+
+/* .. 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 */
+
+/* Computing MAX */
+ i__1 = *n << 3;
+ 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 (*ldvl < 1 || ilvl && *ldvl < *n) {
+ *info = -12;
+ } else if (*ldvr < 1 || ilvr && *ldvr < *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);
+/* Computing MAX */
+ i__1 = *n * 6, i__2 = *n * (nb + 1);
+ lopt = (*n << 1) + max(i__1,i__2);
+ work[1] = (doublereal) lopt;
+ }
+
+ if (*info != 0) {
+ i__1 = -(*info);
+ xerbla_("DGEGV ", &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");
+ safmin += safmin;
+ safmax = 1. / safmin;
+ onepls = eps * 4 + 1.;
+
+/* Scale A */
+
+ anrm = dlange_("M", n, n, &a[a_offset], lda, &work[1]);
+ anrm1 = anrm;
+ anrm2 = 1.;
+ if (anrm < 1.) {
+ if (safmax * anrm < 1.) {
+ anrm1 = safmin;
+ anrm2 = safmax * anrm;
+ }
+ }
+
+ if (anrm > 0.) {
+ dlascl_("G", &c_n1, &c_n1, &anrm, &c_b27, n, n, &a[a_offset], lda, &
+ iinfo);
+ if (iinfo != 0) {
+ *info = *n + 10;
+ return 0;
+ }
+ }
+
+/* Scale B */
+
+ bnrm = dlange_("M", n, n, &b[b_offset], ldb, &work[1]);
+ bnrm1 = bnrm;
+ bnrm2 = 1.;
+ if (bnrm < 1.) {
+ if (safmax * bnrm < 1.) {
+ bnrm1 = safmin;
+ bnrm2 = safmax * bnrm;
+ }
+ }
+
+ if (bnrm > 0.) {
+ dlascl_("G", &c_n1, &c_n1, &bnrm, &c_b27, n, n, &b[b_offset], ldb, &
+ iinfo);
+ if (iinfo != 0) {
+ *info = *n + 10;
+ return 0;
+ }
+ }
+
+/* Permute the matrix to make it more nearly triangular */
+/* Workspace layout: (8*N words -- "work" requires 6*N words) */
+/* 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 L120;
+ }
+
+/* Reduce B to triangular form, and initialize VL and/or VR */
+/* Workspace layout: ("work..." must have at least N words) */
+/* left_permutation, right_permutation, tau, work... */
+
+ irows = ihi + 1 - ilo;
+ if (ilv) {
+ icols = *n + 1 - ilo;
+ } else {
+ icols = irows;
+ }
+ 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 L120;
+ }
+
+ 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 L120;
+ }
+
+ if (ilvl) {
+ dlaset_("Full", n, n, &c_b38, &c_b27, &vl[vl_offset], ldvl)
+ ;
+ i__1 = irows - 1;
+ i__2 = irows - 1;
+ dlacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vl[ilo +
+ 1 + ilo * vl_dim1], ldvl);
+ i__1 = *lwork + 1 - iwork;
+ dorgqr_(&irows, &irows, &irows, &vl[ilo + ilo * vl_dim1], ldvl, &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 L120;
+ }
+ }
+
+ if (ilvr) {
+ dlaset_("Full", n, n, &c_b38, &c_b27, &vr[vr_offset], ldvr)
+ ;
+ }
+
+/* Reduce to generalized Hessenberg form */
+
+ if (ilv) {
+
+/* Eigenvectors requested -- work on whole matrix. */
+
+ dgghrd_(jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset],
+ ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &iinfo);
+ } else {
+ dgghrd_("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, &iinfo);
+ }
+ if (iinfo != 0) {
+ *info = *n + 5;
+ goto L120;
+ }
+
+/* Perform QZ algorithm */
+/* Workspace layout: ("work..." must have at least 1 word) */
+/* left_permutation, right_permutation, work... */
+
+ iwork = itau;
+ if (ilv) {
+ *(unsigned char *)chtemp = 'S';
+ } else {
+ *(unsigned char *)chtemp = 'E';
+ }
+ i__1 = *lwork + 1 - iwork;
+ dhgeqz_(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[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 L120;
+ }
+
+ if (ilv) {
+
+/* Compute Eigenvectors (DTGEVC requires 6*N words of workspace) */
+
+ if (ilvl) {
+ if (ilvr) {
+ *(unsigned char *)chtemp = 'B';
+ } else {
+ *(unsigned char *)chtemp = 'L';
+ }
+ } else {
+ *(unsigned char *)chtemp = 'R';
+ }
+
+ dtgevc_(chtemp, "B", ldumma, n, &a[a_offset], lda, &b[b_offset], ldb,
+ &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &in, &work[
+ iwork], &iinfo);
+ if (iinfo != 0) {
+ *info = *n + 7;
+ goto L120;
+ }
+
+/* Undo balancing on VL and VR, rescale */
+
+ if (ilvl) {
+ dggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &
+ vl[vl_offset], ldvl, &iinfo);
+ if (iinfo != 0) {
+ *info = *n + 8;
+ goto L120;
+ }
+ i__1 = *n;
+ for (jc = 1; jc <= i__1; ++jc) {
+ if (alphai[jc] < 0.) {
+ goto L50;
+ }
+ temp = 0.;
+ if (alphai[jc] == 0.) {
+ i__2 = *n;
+ for (jr = 1; jr <= i__2; ++jr) {
+/* Computing MAX */
+ d__2 = temp, d__3 = (d__1 = vl[jr + jc * vl_dim1],
+ abs(d__1));
+ temp = max(d__2,d__3);
+/* L10: */
+ }
+ } else {
+ i__2 = *n;
+ for (jr = 1; jr <= i__2; ++jr) {
+/* Computing MAX */
+ d__3 = temp, d__4 = (d__1 = vl[jr + jc * vl_dim1],
+ abs(d__1)) + (d__2 = vl[jr + (jc + 1) *
+ vl_dim1], abs(d__2));
+ temp = max(d__3,d__4);
+/* L20: */
+ }
+ }
+ if (temp < safmin) {
+ goto L50;
+ }
+ temp = 1. / temp;
+ if (alphai[jc] == 0.) {
+ 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) {
+ dggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, &
+ vr[vr_offset], ldvr, &iinfo);
+ if (iinfo != 0) {
+ *info = *n + 9;
+ goto L120;
+ }
+ i__1 = *n;
+ for (jc = 1; jc <= i__1; ++jc) {
+ if (alphai[jc] < 0.) {
+ goto L100;
+ }
+ temp = 0.;
+ if (alphai[jc] == 0.) {
+ i__2 = *n;
+ for (jr = 1; jr <= i__2; ++jr) {
+/* Computing MAX */
+ d__2 = temp, d__3 = (d__1 = vr[jr + jc * vr_dim1],
+ abs(d__1));
+ temp = max(d__2,d__3);
+/* L60: */
+ }
+ } else {
+ i__2 = *n;
+ for (jr = 1; jr <= i__2; ++jr) {
+/* Computing MAX */
+ d__3 = temp, d__4 = (d__1 = vr[jr + jc * vr_dim1],
+ abs(d__1)) + (d__2 = vr[jr + (jc + 1) *
+ vr_dim1], abs(d__2));
+ temp = max(d__3,d__4);
+/* L70: */
+ }
+ }
+ if (temp < safmin) {
+ goto L100;
+ }
+ temp = 1. / temp;
+ if (alphai[jc] == 0.) {
+ 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 in alpha, beta */
+
+/* Note: this does not give the alpha and beta for the unscaled */
+/* problem. */
+
+/* Un-scaling is limited to avoid underflow in alpha and beta */
+/* if they are significant. */
+
+ i__1 = *n;
+ for (jc = 1; jc <= i__1; ++jc) {
+ absar = (d__1 = alphar[jc], abs(d__1));
+ absai = (d__1 = alphai[jc], abs(d__1));
+ absb = (d__1 = beta[jc], abs(d__1));
+ salfar = anrm * alphar[jc];
+ salfai = anrm * alphai[jc];
+ sbeta = bnrm * beta[jc];
+ ilimit = FALSE_;
+ scale = 1.;
+
+/* Check for significant underflow in ALPHAI */
+
+/* Computing MAX */
+ d__1 = safmin, d__2 = eps * absar, d__1 = max(d__1,d__2), d__2 = eps *
+ absb;
+ if (abs(salfai) < safmin && absai >= max(d__1,d__2)) {
+ ilimit = TRUE_;
+/* Computing MAX */
+ d__1 = onepls * safmin, d__2 = anrm2 * absai;
+ scale = onepls * safmin / anrm1 / max(d__1,d__2);
+
+ } else if (salfai == 0.) {
+
+/* If insignificant underflow in ALPHAI, then make the */
+/* conjugate eigenvalue real. */
+
+ if (alphai[jc] < 0. && jc > 1) {
+ alphai[jc - 1] = 0.;
+ } else if (alphai[jc] > 0. && jc < *n) {
+ alphai[jc + 1] = 0.;
+ }
+ }
+
+/* Check for significant underflow in ALPHAR */
+
+/* Computing MAX */
+ d__1 = safmin, d__2 = eps * absai, d__1 = max(d__1,d__2), d__2 = eps *
+ absb;
+ if (abs(salfar) < safmin && absar >= max(d__1,d__2)) {
+ ilimit = TRUE_;
+/* Computing MAX */
+/* Computing MAX */
+ d__3 = onepls * safmin, d__4 = anrm2 * absar;
+ d__1 = scale, d__2 = onepls * safmin / anrm1 / max(d__3,d__4);
+ scale = max(d__1,d__2);
+ }
+
+/* Check for significant underflow in BETA */
+
+/* Computing MAX */
+ d__1 = safmin, d__2 = eps * absar, d__1 = max(d__1,d__2), d__2 = eps *
+ absai;
+ if (abs(sbeta) < safmin && absb >= max(d__1,d__2)) {
+ ilimit = TRUE_;
+/* Computing MAX */
+/* Computing MAX */
+ d__3 = onepls * safmin, d__4 = bnrm2 * absb;
+ d__1 = scale, d__2 = onepls * safmin / bnrm1 / max(d__3,d__4);
+ scale = max(d__1,d__2);
+ }
+
+/* Check for possible overflow when limiting scaling */
+
+ if (ilimit) {
+/* Computing MAX */
+ d__1 = abs(salfar), d__2 = abs(salfai), d__1 = max(d__1,d__2),
+ d__2 = abs(sbeta);
+ temp = scale * safmin * max(d__1,d__2);
+ if (temp > 1.) {
+ scale /= temp;
+ }
+ if (scale < 1.) {
+ ilimit = FALSE_;
+ }
+ }
+
+/* Recompute un-scaled ALPHAR, ALPHAI, BETA if necessary. */
+
+ if (ilimit) {
+ salfar = scale * alphar[jc] * anrm;
+ salfai = scale * alphai[jc] * anrm;
+ sbeta = scale * beta[jc] * bnrm;
+ }
+ alphar[jc] = salfar;
+ alphai[jc] = salfai;
+ beta[jc] = sbeta;
+/* L110: */
+ }
+
+L120:
+ work[1] = (doublereal) lwkopt;
+
+ return 0;
+
+/* End of DGEGV */
+
+} /* dgegv_ */