zgegs.c

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/* zgegs.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_n1 = -1;

/* Subroutine */ int zgegs_(char *jobvsl, char *jobvsr, integer *n, 
        doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
        doublecomplex *alpha, doublecomplex *beta, doublecomplex *vsl, 
        integer *ldvsl, doublecomplex *vsr, integer *ldvsr, doublecomplex *
        work, integer *lwork, doublereal *rwork, 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, i__3;

    /* 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 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;
    doublereal safmin;
    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;
    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 *);
    doublereal smlnum;
    integer irwork, lwkopt;
    logical lquery;
    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 .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  This routine is deprecated and has been replaced by routine ZGGES. */

/*  ZGEGS computes the eigenvalues, Schur form, and, optionally, the */
/*  left and or/right Schur vectors of a complex matrix pair (A,B). */
/*  Given two square matrices A and B, the generalized Schur */
/*  factorization has the form */

/*     A = Q*S*Z**H,  B = Q*T*Z**H */

/*  where Q and Z are unitary matrices and S and T are upper triangular. */
/*  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 */
/*  ZGEGV should be used instead.  See ZGEGV 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) COMPLEX*16 array, dimension (LDA, N) */
/*          On entry, the matrix A. */
/*          On exit, the upper triangular matrix S from the generalized */
/*          Schur factorization. */

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

/*  B       (input/output) COMPLEX*16 array, dimension (LDB, N) */
/*          On entry, the matrix B. */
/*          On exit, the upper triangular matrix T from the generalized */
/*          Schur factorization. */

/*  LDB     (input) INTEGER */
/*          The leading dimension of B.  LDB >= max(1,N). */

/*  ALPHA   (output) COMPLEX*16 array, dimension (N) */
/*          The complex scalars alpha that define the eigenvalues of */
/*          GNEP.  ALPHA(j) = S(j,j), the diagonal element of the Schur */
/*          form of A. */

/*  BETA    (output) COMPLEX*16 array, dimension (N) */
/*          The non-negative real scalars beta that define the */
/*          eigenvalues of GNEP.  BETA(j) = T(j,j), the diagonal element */
/*          of the triangular factor T. */

/*          Together, the quantities alpha = ALPHA(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) COMPLEX*16 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) COMPLEX*16 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) 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. */
/*          To compute the optimal value of LWORK, call ILAENV to get */
/*          blocksizes (for ZGEQRF, ZUNMQR, and CUNGQR.)  Then compute: */
/*          NB  -- MAX of the blocksizes for ZGEQRF, ZUNMQR, and CUNGQR; */
/*          the optimal LWORK is 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. */

/*  RWORK   (workspace) DOUBLE PRECISION array, dimension (3*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:  errors that usually indicate LAPACK problems: */
/*                =N+1: error return from ZGGBAL */
/*                =N+2: error return from ZGEQRF */
/*                =N+3: error return from ZUNMQR */
/*                =N+4: error return from ZUNGQR */
/*                =N+5: error return from ZGGHRD */
/*                =N+6: error return from ZHGEQZ (other than failed */
/*                                               iteration) */
/*                =N+7: error return from ZGGBAK (computing VSL) */
/*                =N+8: error return from ZGGBAK (computing VSR) */
/*                =N+9: error return from ZLASCL (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;
    --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;

    /* 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 << 1;
    lwkmin = max(i__1,1);
    lwkopt = lwkmin;
    work[1].r = (doublereal) lwkopt, work[1].i = 0.;
    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 = -11;
    } else if (*ldvsr < 1 || ilvsr && *ldvsr < *n) {
        *info = -13;
    } else if (*lwork < lwkmin && ! lquery) {
        *info = -15;
    }

    if (*info == 0) {
        nb1 = ilaenv_(&c__1, "ZGEQRF", " ", n, n, &c_n1, &c_n1);
        nb2 = ilaenv_(&c__1, "ZUNMQR", " ", n, n, n, &c_n1);
        nb3 = ilaenv_(&c__1, "ZUNGQR", " ", n, n, n, &c_n1);
/* Computing MAX */
        i__1 = max(nb1,nb2);
        nb = max(i__1,nb3);
        lopt = *n * (nb + 1);
        work[1].r = (doublereal) lopt, work[1].i = 0.;
    }

    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("ZGEGS ", &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 = 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_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 = 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_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 */

    ileft = 1;
    iright = *n + 1;
    irwork = iright + *n;
    iwork = 1;
    zggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &rwork[
            ileft], &rwork[iright], &rwork[irwork], &iinfo);
    if (iinfo != 0) {
        *info = *n + 1;
        goto L10;
    }

/*     Reduce B to triangular form, and initialize VSL and/or VSR */

    irows = ihi + 1 - ilo;
    icols = *n + 1 - ilo;
    itau = iwork;
    iwork = itau + irows;
    i__1 = *lwork + 1 - iwork;
    zgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
            iwork], &i__1, &iinfo);
    if (iinfo >= 0) {
/* Computing MAX */
        i__3 = iwork;
        i__1 = lwkopt, i__2 = (integer) work[i__3].r + iwork - 1;
        lwkopt = max(i__1,i__2);
    }
    if (iinfo != 0) {
        *info = *n + 2;
        goto L10;
    }

    i__1 = *lwork + 1 - iwork;
    zunmqr_("L", "C", &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__3 = iwork;
        i__1 = lwkopt, i__2 = (integer) work[i__3].r + iwork - 1;
        lwkopt = max(i__1,i__2);
    }
    if (iinfo != 0) {
        *info = *n + 3;
        goto L10;
    }

    if (ilvsl) {
        zlaset_("Full", n, n, &c_b1, &c_b2, &vsl[vsl_offset], ldvsl);
        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 - iwork;
        zungqr_(&irows, &irows, &irows, &vsl[ilo + ilo * vsl_dim1], ldvsl, &
                work[itau], &work[iwork], &i__1, &iinfo);
        if (iinfo >= 0) {
/* Computing MAX */
            i__3 = iwork;
            i__1 = lwkopt, i__2 = (integer) work[i__3].r + iwork - 1;
            lwkopt = max(i__1,i__2);
        }
        if (iinfo != 0) {
            *info = *n + 4;
            goto L10;
        }
    }

    if (ilvsr) {
        zlaset_("Full", n, n, &c_b1, &c_b2, &vsr[vsr_offset], ldvsr);
    }

/*     Reduce to generalized Hessenberg form */

    zgghrd_(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 */

    iwork = itau;
    i__1 = *lwork + 1 - iwork;
    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[iwork], &i__1, &rwork[irwork], &
            iinfo);
    if (iinfo >= 0) {
/* Computing MAX */
        i__3 = iwork;
        i__1 = lwkopt, i__2 = (integer) work[i__3].r + 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) {
        zggbak_("P", "L", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n, &
                vsl[vsl_offset], ldvsl, &iinfo);
        if (iinfo != 0) {
            *info = *n + 7;
            goto L10;
        }
    }
    if (ilvsr) {
        zggbak_("P", "R", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n, &
                vsr[vsr_offset], ldvsr, &iinfo);
        if (iinfo != 0) {
            *info = *n + 8;
            goto L10;
        }
    }

/*     Undo scaling */

    if (ilascl) {
        zlascl_("U", &c_n1, &c_n1, &anrmto, &anrm, n, n, &a[a_offset], lda, &
                iinfo);
        if (iinfo != 0) {
            *info = *n + 9;
            return 0;
        }
        zlascl_("G", &c_n1, &c_n1, &anrmto, &anrm, n, &c__1, &alpha[1], n, &
                iinfo);
        if (iinfo != 0) {
            *info = *n + 9;
            return 0;
        }
    }

    if (ilbscl) {
        zlascl_("U", &c_n1, &c_n1, &bnrmto, &bnrm, n, n, &b[b_offset], ldb, &
                iinfo);
        if (iinfo != 0) {
            *info = *n + 9;
            return 0;
        }
        zlascl_("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].r = (doublereal) lwkopt, work[1].i = 0.;

    return 0;

/*     End of ZGEGS */

} /* zgegs_ */