zgges.c

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/* zgges.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 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;

/* Subroutine */ int zgges_(char *jobvsl, char *jobvsr, char *sort, L_fp 
        selctg, 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)
{
    /* 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 dif[2];
    integer ihi, ilo;
    doublereal eps, anrm, bnrm;
    integer idum[1], ierr, itau, iwrk;
    doublereal pvsl, pvsr;
    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;
    extern /* Subroutine */ int zgeqrf_(integer *, integer *, doublecomplex *, 
             integer *, doublecomplex *, doublecomplex *, integer *, integer *
);
    doublereal anrmto;
    integer lwkmin;
    logical lastsl;
    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 *);
    doublereal smlnum;
    logical wantst, lquery;
    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 *);


/*  -- 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 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 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 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 (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 = (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 */

    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 = (doublereal) lwkopt, work[1].i = 0.;

    return 0;

/*     End of ZGGES */

} /* zgges_ */