zgeesx.c

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/* zgeesx.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;

/* Subroutine */ int zgeesx_(char *jobvs, char *sort, L_fp select, char *
        sense, integer *n, doublecomplex *a, integer *lda, integer *sdim, 
        doublecomplex *w, doublecomplex *vs, integer *ldvs, doublereal *
        rconde, doublereal *rcondv, doublecomplex *work, integer *lwork, 
        doublereal *rwork, logical *bwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, vs_dim1, vs_offset, i__1, i__2;

    /* Builtin functions */
    double sqrt(doublereal);

    /* Local variables */
    integer i__, ihi, ilo;
    doublereal dum[1], eps;
    integer ibal;
    doublereal anrm;
    integer ierr, itau, iwrk, lwrk, icond, ieval;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
    logical scalea;
    extern doublereal dlamch_(char *);
    doublereal cscale;
    extern /* Subroutine */ int dlascl_(char *, integer *, integer *, 
            doublereal *, doublereal *, integer *, integer *, doublereal *, 
            integer *, integer *), zgebak_(char *, char *, integer *, 
            integer *, integer *, doublereal *, integer *, doublecomplex *, 
            integer *, integer *), zgebal_(char *, integer *, 
            doublecomplex *, integer *, integer *, integer *, doublereal *, 
            integer *), xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *);
    extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, 
            integer *, doublereal *);
    doublereal bignum;
    extern /* Subroutine */ int zgehrd_(integer *, integer *, integer *, 
            doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
            integer *, integer *), zlascl_(char *, integer *, integer *, 
            doublereal *, doublereal *, integer *, integer *, doublecomplex *, 
             integer *, integer *);
    logical wantsb, wantse;
    extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *);
    integer minwrk, maxwrk;
    logical wantsn;
    doublereal smlnum;
    extern /* Subroutine */ int zhseqr_(char *, char *, integer *, integer *, 
            integer *, doublecomplex *, integer *, doublecomplex *, 
            doublecomplex *, integer *, doublecomplex *, integer *, integer *);
    integer hswork;
    extern /* Subroutine */ int zunghr_(integer *, integer *, integer *, 
            doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
            integer *, integer *);
    logical wantst, wantsv, wantvs;
    extern /* Subroutine */ int ztrsen_(char *, char *, logical *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *, doublereal *, doublereal *, 
            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 */
/*  ======= */

/*  ZGEESX computes for an N-by-N complex nonsymmetric matrix A, the */
/*  eigenvalues, the Schur form T, and, optionally, the matrix of Schur */
/*  vectors Z.  This gives the Schur factorization A = Z*T*(Z**H). */

/*  Optionally, it also orders the eigenvalues on the diagonal of the */
/*  Schur form so that selected eigenvalues are at the top left; */
/*  computes a reciprocal condition number for the average of the */
/*  selected eigenvalues (RCONDE); and computes a reciprocal condition */
/*  number for the right invariant subspace corresponding to the */
/*  selected eigenvalues (RCONDV).  The leading columns of Z form an */
/*  orthonormal basis for this invariant subspace. */

/*  For further explanation of the reciprocal condition numbers RCONDE */
/*  and RCONDV, see Section 4.10 of the LAPACK Users' Guide (where */
/*  these quantities are called s and sep respectively). */

/*  A complex matrix is in Schur form if it is upper triangular. */

/*  Arguments */
/*  ========= */

/*  JOBVS   (input) CHARACTER*1 */
/*          = 'N': Schur vectors are not computed; */
/*          = 'V': Schur vectors are computed. */

/*  SORT    (input) CHARACTER*1 */
/*          Specifies whether or not to order the eigenvalues on the */
/*          diagonal of the Schur form. */
/*          = 'N': Eigenvalues are not ordered; */
/*          = 'S': Eigenvalues are ordered (see SELECT). */

/*  SELECT  (external procedure) LOGICAL FUNCTION of one COMPLEX*16 argument */
/*          SELECT must be declared EXTERNAL in the calling subroutine. */
/*          If SORT = 'S', SELECT is used to select eigenvalues to order */
/*          to the top left of the Schur form. */
/*          If SORT = 'N', SELECT is not referenced. */
/*          An eigenvalue W(j) is selected if SELECT(W(j)) is true. */

/*  SENSE   (input) CHARACTER*1 */
/*          Determines which reciprocal condition numbers are computed. */
/*          = 'N': None are computed; */
/*          = 'E': Computed for average of selected eigenvalues only; */
/*          = 'V': Computed for selected right invariant subspace only; */
/*          = 'B': Computed for both. */
/*          If SENSE = 'E', 'V' or 'B', SORT must equal 'S'. */

/*  N       (input) INTEGER */
/*          The order of the matrix A. N >= 0. */

/*  A       (input/output) COMPLEX*16 array, dimension (LDA, N) */
/*          On entry, the N-by-N matrix A. */
/*          On exit, A is overwritten by its Schur form T. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A.  LDA >= max(1,N). */

/*  SDIM    (output) INTEGER */
/*          If SORT = 'N', SDIM = 0. */
/*          If SORT = 'S', SDIM = number of eigenvalues for which */
/*                         SELECT is true. */

/*  W       (output) COMPLEX*16 array, dimension (N) */
/*          W contains the computed eigenvalues, in the same order */
/*          that they appear on the diagonal of the output Schur form T. */

/*  VS      (output) COMPLEX*16 array, dimension (LDVS,N) */
/*          If JOBVS = 'V', VS contains the unitary matrix Z of Schur */
/*          vectors. */
/*          If JOBVS = 'N', VS is not referenced. */

/*  LDVS    (input) INTEGER */
/*          The leading dimension of the array VS.  LDVS >= 1, and if */
/*          JOBVS = 'V', LDVS >= N. */

/*  RCONDE  (output) DOUBLE PRECISION */
/*          If SENSE = 'E' or 'B', RCONDE contains the reciprocal */
/*          condition number for the average of the selected eigenvalues. */
/*          Not referenced if SENSE = 'N' or 'V'. */

/*  RCONDV  (output) DOUBLE PRECISION */
/*          If SENSE = 'V' or 'B', RCONDV contains the reciprocal */
/*          condition number for the selected right invariant subspace. */
/*          Not referenced if SENSE = 'N' or 'E'. */

/*  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). */
/*          Also, if SENSE = 'E' or 'V' or 'B', LWORK >= 2*SDIM*(N-SDIM), */
/*          where SDIM is the number of selected eigenvalues computed by */
/*          this routine.  Note that 2*SDIM*(N-SDIM) <= N*N/2. Note also */
/*          that an error is only returned if LWORK < max(1,2*N), but if */
/*          SENSE = 'E' or 'V' or 'B' this may not be large enough. */
/*          For good performance, LWORK must generally be larger. */

/*          If LWORK = -1, then a workspace query is assumed; the routine */
/*          only calculates upper bound on the optimal size of the */
/*          array WORK, 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 (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. */
/*          > 0: if INFO = i, and i is */
/*             <= N: the QR algorithm failed to compute all the */
/*                   eigenvalues; elements 1:ILO-1 and i+1:N of W */
/*                   contain those eigenvalues which have converged; if */
/*                   JOBVS = 'V', VS contains the transformation which */
/*                   reduces A to its partially converged Schur form. */
/*             = N+1: the eigenvalues could not be reordered because some */
/*                   eigenvalues were too close to separate (the problem */
/*                   is very ill-conditioned); */
/*             = N+2: after reordering, roundoff changed values of some */
/*                   complex eigenvalues so that leading eigenvalues in */
/*                   the Schur form no longer satisfy SELECT=.TRUE.  This */
/*                   could also be caused by underflow due to scaling. */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. Local Arrays .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input arguments */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --w;
    vs_dim1 = *ldvs;
    vs_offset = 1 + vs_dim1;
    vs -= vs_offset;
    --work;
    --rwork;
    --bwork;

    /* Function Body */
    *info = 0;
    wantvs = lsame_(jobvs, "V");
    wantst = lsame_(sort, "S");
    wantsn = lsame_(sense, "N");
    wantse = lsame_(sense, "E");
    wantsv = lsame_(sense, "V");
    wantsb = lsame_(sense, "B");
    if (! wantvs && ! lsame_(jobvs, "N")) {
        *info = -1;
    } else if (! wantst && ! lsame_(sort, "N")) {
        *info = -2;
    } else if (! (wantsn || wantse || wantsv || wantsb) || ! wantst && ! 
            wantsn) {
        *info = -4;
    } else if (*n < 0) {
        *info = -5;
    } else if (*lda < max(1,*n)) {
        *info = -7;
    } else if (*ldvs < 1 || wantvs && *ldvs < *n) {
        *info = -11;
    }

/*     Compute workspace */
/*      (Note: Comments in the code beginning "Workspace:" describe the */
/*       minimal amount of real workspace needed at that point in the */
/*       code, as well as the preferred amount for good performance. */
/*       CWorkspace refers to complex workspace, and RWorkspace to real */
/*       workspace. NB refers to the optimal block size for the */
/*       immediately following subroutine, as returned by ILAENV. */
/*       HSWORK refers to the workspace preferred by ZHSEQR, as */
/*       calculated below. HSWORK is computed assuming ILO=1 and IHI=N, */
/*       the worst case. */
/*       If SENSE = 'E', 'V' or 'B', then the amount of workspace needed */
/*       depends on SDIM, which is computed by the routine ZTRSEN later */
/*       in the code.) */

    if (*info == 0) {
        if (*n == 0) {
            minwrk = 1;
            lwrk = 1;
        } else {
            maxwrk = *n + *n * ilaenv_(&c__1, "ZGEHRD", " ", n, &c__1, n, &
                    c__0);
            minwrk = *n << 1;

            zhseqr_("S", jobvs, n, &c__1, n, &a[a_offset], lda, &w[1], &vs[
                    vs_offset], ldvs, &work[1], &c_n1, &ieval);
            hswork = (integer) work[1].r;

            if (! wantvs) {
                maxwrk = max(maxwrk,hswork);
            } else {
/* Computing MAX */
                i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "ZUNGHR", 
                         " ", n, &c__1, n, &c_n1);
                maxwrk = max(i__1,i__2);
                maxwrk = max(maxwrk,hswork);
            }
            lwrk = maxwrk;
            if (! wantsn) {
/* Computing MAX */
                i__1 = lwrk, i__2 = *n * *n / 2;
                lwrk = max(i__1,i__2);
            }
        }
        work[1].r = (doublereal) lwrk, work[1].i = 0.;

        if (*lwork < minwrk) {
            *info = -15;
        }
    }

    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("ZGEESX", &i__1);
        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, dum);
    scalea = FALSE_;
    if (anrm > 0. && anrm < smlnum) {
        scalea = TRUE_;
        cscale = smlnum;
    } else if (anrm > bignum) {
        scalea = TRUE_;
        cscale = bignum;
    }
    if (scalea) {
        zlascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
                ierr);
    }


/*     Permute the matrix to make it more nearly triangular */
/*     (CWorkspace: none) */
/*     (RWorkspace: need N) */

    ibal = 1;
    zgebal_("P", n, &a[a_offset], lda, &ilo, &ihi, &rwork[ibal], &ierr);

/*     Reduce to upper Hessenberg form */
/*     (CWorkspace: need 2*N, prefer N+N*NB) */
/*     (RWorkspace: none) */

    itau = 1;
    iwrk = *n + itau;
    i__1 = *lwork - iwrk + 1;
    zgehrd_(n, &ilo, &ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1, 
             &ierr);

    if (wantvs) {

/*        Copy Householder vectors to VS */

        zlacpy_("L", n, n, &a[a_offset], lda, &vs[vs_offset], ldvs)
                ;

/*        Generate unitary matrix in VS */
/*        (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
/*        (RWorkspace: none) */

        i__1 = *lwork - iwrk + 1;
        zunghr_(n, &ilo, &ihi, &vs[vs_offset], ldvs, &work[itau], &work[iwrk], 
                 &i__1, &ierr);
    }

    *sdim = 0;

/*     Perform QR iteration, accumulating Schur vectors in VS if desired */
/*     (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/*     (RWorkspace: none) */

    iwrk = itau;
    i__1 = *lwork - iwrk + 1;
    zhseqr_("S", jobvs, n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vs[
            vs_offset], ldvs, &work[iwrk], &i__1, &ieval);
    if (ieval > 0) {
        *info = ieval;
    }

/*     Sort eigenvalues if desired */

    if (wantst && *info == 0) {
        if (scalea) {
            zlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &w[1], n, &
                    ierr);
        }
        i__1 = *n;
        for (i__ = 1; i__ <= i__1; ++i__) {
            bwork[i__] = (*select)(&w[i__]);
/* L10: */
        }

/*        Reorder eigenvalues, transform Schur vectors, and compute */
/*        reciprocal condition numbers */
/*        (CWorkspace: if SENSE is not 'N', need 2*SDIM*(N-SDIM) */
/*                     otherwise, need none ) */
/*        (RWorkspace: none) */

        i__1 = *lwork - iwrk + 1;
        ztrsen_(sense, jobvs, &bwork[1], n, &a[a_offset], lda, &vs[vs_offset], 
                 ldvs, &w[1], sdim, rconde, rcondv, &work[iwrk], &i__1, &
                icond);
        if (! wantsn) {
/* Computing MAX */
            i__1 = maxwrk, i__2 = (*sdim << 1) * (*n - *sdim);
            maxwrk = max(i__1,i__2);
        }
        if (icond == -14) {

/*           Not enough complex workspace */

            *info = -15;
        }
    }

    if (wantvs) {

/*        Undo balancing */
/*        (CWorkspace: none) */
/*        (RWorkspace: need N) */

        zgebak_("P", "R", n, &ilo, &ihi, &rwork[ibal], n, &vs[vs_offset], 
                ldvs, &ierr);
    }

    if (scalea) {

/*        Undo scaling for the Schur form of A */

        zlascl_("U", &c__0, &c__0, &cscale, &anrm, n, n, &a[a_offset], lda, &
                ierr);
        i__1 = *lda + 1;
        zcopy_(n, &a[a_offset], &i__1, &w[1], &c__1);
        if ((wantsv || wantsb) && *info == 0) {
            dum[0] = *rcondv;
            dlascl_("G", &c__0, &c__0, &cscale, &anrm, &c__1, &c__1, dum, &
                    c__1, &ierr);
            *rcondv = dum[0];
        }
    }

    work[1].r = (doublereal) maxwrk, work[1].i = 0.;
    return 0;

/*     End of ZGEESX */

} /* zgeesx_ */