zggev.c

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/* zggev.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 zggev_(char *jobvl, char *jobvr, integer *n, 
        doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
        doublecomplex *alpha, doublecomplex *beta, doublecomplex *vl, integer 
        *ldvl, doublecomplex *vr, integer *ldvr, doublecomplex *work, integer 
        *lwork, doublereal *rwork, 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, i__3, i__4;
    doublereal d__1, d__2, d__3, d__4;
    doublecomplex z__1;

    /* Builtin functions */
    double sqrt(doublereal), d_imag(doublecomplex *);

    /* Local variables */
    integer jc, in, jr, ihi, ilo;
    doublereal eps;
    logical ilv;
    doublereal anrm, bnrm;
    integer ierr, itau;
    doublereal temp;
    logical ilvl, ilvr;
    integer iwrk;
    extern logical lsame_(char *, char *);
    integer ileft, icols, 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 *);
    logical ldumma[1];
    char chtemp[1];
    doublereal bignum;
    extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, 
            integer *, doublereal *);
    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 *), ztgevc_(
            char *, char *, logical *, integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *, integer *, integer *, doublecomplex *, 
             doublereal *, 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 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 */
/*  ======= */

/*  ZGGEV computes for a pair of N-by-N complex nonsymmetric matrices */
/*  (A,B), the generalized eigenvalues, and optionally, the left and/or */
/*  right generalized eigenvectors. */

/*  A generalized eigenvalue for a pair of matrices (A,B) is a scalar */
/*  lambda or a ratio alpha/beta = lambda, such that A - lambda*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. */

/*  The right generalized eigenvector v(j) corresponding to the */
/*  generalized eigenvalue lambda(j) of (A,B) satisfies */

/*               A * v(j) = lambda(j) * B * v(j). */

/*  The left generalized eigenvector u(j) corresponding to the */
/*  generalized eigenvalues lambda(j) of (A,B) satisfies */

/*               u(j)**H * A = lambda(j) * u(j)**H * B */

/*  where u(j)**H is the conjugate-transpose of u(j). */

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

/*  JOBVL   (input) CHARACTER*1 */
/*          = 'N':  do not compute the left generalized eigenvectors; */
/*          = 'V':  compute the left generalized eigenvectors. */

/*  JOBVR   (input) CHARACTER*1 */
/*          = 'N':  do not compute the right generalized eigenvectors; */
/*          = 'V':  compute the right generalized eigenvectors. */

/*  N       (input) INTEGER */
/*          The order of the matrices A, B, VL, and VR.  N >= 0. */

/*  A       (input/output) COMPLEX*16 array, dimension (LDA, N) */
/*          On entry, the matrix A in the pair (A,B). */
/*          On exit, A has been overwritten. */

/*  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 in the pair (A,B). */
/*          On exit, B has been overwritten. */

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

/*  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. */

/*          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). */

/*  VL      (output) COMPLEX*16 array, dimension (LDVL,N) */
/*          If JOBVL = 'V', the left generalized eigenvectors u(j) are */
/*          stored one after another in the columns of VL, in the same */
/*          order as their eigenvalues. */
/*          Each eigenvector is scaled so the largest component has */
/*          abs(real part) + abs(imag. part) = 1. */
/*          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) COMPLEX*16 array, dimension (LDVR,N) */
/*          If JOBVR = 'V', the right generalized eigenvectors v(j) are */
/*          stored one after another in the columns of VR, in the same */
/*          order as their eigenvalues. */
/*          Each eigenvector is scaled so the largest component has */
/*          abs(real part) + abs(imag. part) = 1. */
/*          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) 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/output) DOUBLE PRECISION array, dimension (8*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.  No eigenvectors have been */
/*                calculated, but ALPHA(j) and BETA(j) should be */
/*                correct for j=INFO+1,...,N. */
/*          > N:  =N+1: other then QZ iteration failed in DHGEQZ, */
/*                =N+2: error return from DTGEVC. */

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. Local Arrays .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Statement Functions .. */
/*     .. */
/*     .. Statement Function definitions .. */
/*     .. */
/*     .. 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;
    vl_dim1 = *ldvl;
    vl_offset = 1 + vl_dim1;
    vl -= vl_offset;
    vr_dim1 = *ldvr;
    vr_offset = 1 + vr_dim1;
    vr -= vr_offset;
    --work;
    --rwork;

    /* 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 */

    *info = 0;
    lquery = *lwork == -1;
    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 = -11;
    } else if (*ldvr < 1 || ilvr && *ldvr < *n) {
        *info = -13;
    }

/*     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. The workspace is */
/*       computed assuming ILO = 1 and IHI = N, the worst case.) */

    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__0);
        lwkopt = max(i__1,i__2);
        if (ilvl) {
/* 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 = -15;
        }
    }

    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("ZGGEV ", &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");
    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 matrices A, B to isolate eigenvalues if possible */
/*     (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;
    if (ilv) {
        icols = *n + 1 - ilo;
    } else {
        icols = irows;
    }
    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 VL */
/*     (Complex Workspace: need N, prefer N*NB) */

    if (ilvl) {
        zlaset_("Full", n, n, &c_b1, &c_b2, &vl[vl_offset], ldvl);
        if (irows > 1) {
            i__1 = irows - 1;
            i__2 = irows - 1;
            zlacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vl[
                    ilo + 1 + ilo * vl_dim1], ldvl);
        }
        i__1 = *lwork + 1 - iwrk;
        zungqr_(&irows, &irows, &irows, &vl[ilo + ilo * vl_dim1], ldvl, &work[
                itau], &work[iwrk], &i__1, &ierr);
    }

/*     Initialize VR */

    if (ilvr) {
        zlaset_("Full", n, n, &c_b1, &c_b2, &vr[vr_offset], ldvr);
    }

/*     Reduce to generalized Hessenberg form */

    if (ilv) {

/*        Eigenvectors requested -- work on whole matrix. */

        zgghrd_(jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset], 
                ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &ierr);
    } else {
        zgghrd_("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, &ierr);
    }

/*     Perform QZ algorithm (Compute eigenvalues, and optionally, the */
/*     Schur form and Schur vectors) */
/*     (Complex Workspace: need N) */
/*     (Real Workspace: need N) */

    iwrk = itau;
    if (ilv) {
        *(unsigned char *)chtemp = 'S';
    } else {
        *(unsigned char *)chtemp = 'E';
    }
    i__1 = *lwork + 1 - iwrk;
    zhgeqz_(chtemp, jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[
            b_offset], ldb, &alpha[1], &beta[1], &vl[vl_offset], ldvl, &vr[
            vr_offset], ldvr, &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 L70;
    }

/*     Compute Eigenvectors */
/*     (Real Workspace: need 2*N) */
/*     (Complex Workspace: need 2*N) */

    if (ilv) {
        if (ilvl) {
            if (ilvr) {
                *(unsigned char *)chtemp = 'B';
            } else {
                *(unsigned char *)chtemp = 'L';
            }
        } else {
            *(unsigned char *)chtemp = 'R';
        }

        ztgevc_(chtemp, "B", ldumma, n, &a[a_offset], lda, &b[b_offset], ldb, 
                &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &in, &work[
                iwrk], &rwork[irwrk], &ierr);
        if (ierr != 0) {
            *info = *n + 2;
            goto L70;
        }

/*        Undo balancing on VL and VR and normalization */
/*        (Workspace: none needed) */

        if (ilvl) {
            zggbak_("P", "L", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n, 
                     &vl[vl_offset], ldvl, &ierr);
            i__1 = *n;
            for (jc = 1; jc <= i__1; ++jc) {
                temp = 0.;
                i__2 = *n;
                for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
                    i__3 = jr + jc * vl_dim1;
                    d__3 = temp, d__4 = (d__1 = vl[i__3].r, abs(d__1)) + (
                            d__2 = d_imag(&vl[jr + jc * vl_dim1]), abs(d__2));
                    temp = max(d__3,d__4);
/* L10: */
                }
                if (temp < smlnum) {
                    goto L30;
                }
                temp = 1. / temp;
                i__2 = *n;
                for (jr = 1; jr <= i__2; ++jr) {
                    i__3 = jr + jc * vl_dim1;
                    i__4 = jr + jc * vl_dim1;
                    z__1.r = temp * vl[i__4].r, z__1.i = temp * vl[i__4].i;
                    vl[i__3].r = z__1.r, vl[i__3].i = z__1.i;
/* L20: */
                }
L30:
                ;
            }
        }
        if (ilvr) {
            zggbak_("P", "R", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n, 
                     &vr[vr_offset], ldvr, &ierr);
            i__1 = *n;
            for (jc = 1; jc <= i__1; ++jc) {
                temp = 0.;
                i__2 = *n;
                for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
                    i__3 = jr + jc * vr_dim1;
                    d__3 = temp, d__4 = (d__1 = vr[i__3].r, abs(d__1)) + (
                            d__2 = d_imag(&vr[jr + jc * vr_dim1]), abs(d__2));
                    temp = max(d__3,d__4);
/* L40: */
                }
                if (temp < smlnum) {
                    goto L60;
                }
                temp = 1. / temp;
                i__2 = *n;
                for (jr = 1; jr <= i__2; ++jr) {
                    i__3 = jr + jc * vr_dim1;
                    i__4 = jr + jc * vr_dim1;
                    z__1.r = temp * vr[i__4].r, z__1.i = temp * vr[i__4].i;
                    vr[i__3].r = z__1.r, vr[i__3].i = z__1.i;
/* L50: */
                }
L60:
                ;
            }
        }
    }

/*     Undo scaling if necessary */

    if (ilascl) {
        zlascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alpha[1], n, &
                ierr);
    }

    if (ilbscl) {
        zlascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
                ierr);
    }

L70:
    work[1].r = (doublereal) lwkopt, work[1].i = 0.;

    return 0;

/*     End of ZGGEV */

} /* zggev_ */