ztgevc.c

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/* ztgevc.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;

/* Subroutine */ int ztgevc_(char *side, char *howmny, logical *select, 
        integer *n, doublecomplex *s, integer *lds, doublecomplex *p, integer 
        *ldp, doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *
        ldvr, integer *mm, integer *m, doublecomplex *work, doublereal *rwork, 
         integer *info)
{
    /* System generated locals */
    integer p_dim1, p_offset, s_dim1, s_offset, vl_dim1, vl_offset, vr_dim1, 
            vr_offset, i__1, i__2, i__3, i__4, i__5;
    doublereal d__1, d__2, d__3, d__4, d__5, d__6;
    doublecomplex z__1, z__2, z__3, z__4;

    /* Builtin functions */
    double d_imag(doublecomplex *);
    void d_cnjg(doublecomplex *, doublecomplex *);

    /* Local variables */
    doublecomplex d__;
    integer i__, j;
    doublecomplex ca, cb;
    integer je, im, jr;
    doublereal big;
    logical lsa, lsb;
    doublereal ulp;
    doublecomplex sum;
    integer ibeg, ieig, iend;
    doublereal dmin__;
    integer isrc;
    doublereal temp;
    doublecomplex suma, sumb;
    doublereal xmax, scale;
    logical ilall;
    integer iside;
    doublereal sbeta;
    extern logical lsame_(char *, char *);
    doublereal small;
    logical compl;
    doublereal anorm, bnorm;
    logical compr;
    extern /* Subroutine */ int zgemv_(char *, integer *, integer *, 
            doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
            integer *, doublecomplex *, doublecomplex *, integer *), 
            dlabad_(doublereal *, doublereal *);
    logical ilbbad;
    doublereal acoefa, bcoefa, acoeff;
    doublecomplex bcoeff;
    logical ilback;
    doublereal ascale, bscale;
    extern doublereal dlamch_(char *);
    doublecomplex salpha;
    doublereal safmin;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    doublereal bignum;
    logical ilcomp;
    extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *, 
             doublecomplex *);
    integer ihwmny;


/*  -- LAPACK routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */


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

/*  ZTGEVC computes some or all of the right and/or left eigenvectors of */
/*  a pair of complex matrices (S,P), where S and P are upper triangular. */
/*  Matrix pairs of this type are produced by the generalized Schur */
/*  factorization of a complex matrix pair (A,B): */

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

/*  as computed by ZGGHRD + ZHGEQZ. */

/*  The right eigenvector x and the left eigenvector y of (S,P) */
/*  corresponding to an eigenvalue w are defined by: */

/*     S*x = w*P*x,  (y**H)*S = w*(y**H)*P, */

/*  where y**H denotes the conjugate tranpose of y. */
/*  The eigenvalues are not input to this routine, but are computed */
/*  directly from the diagonal elements of S and P. */

/*  This routine returns the matrices X and/or Y of right and left */
/*  eigenvectors of (S,P), or the products Z*X and/or Q*Y, */
/*  where Z and Q are input matrices. */
/*  If Q and Z are the unitary factors from the generalized Schur */
/*  factorization of a matrix pair (A,B), then Z*X and Q*Y */
/*  are the matrices of right and left eigenvectors of (A,B). */

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

/*  SIDE    (input) CHARACTER*1 */
/*          = 'R': compute right eigenvectors only; */
/*          = 'L': compute left eigenvectors only; */
/*          = 'B': compute both right and left eigenvectors. */

/*  HOWMNY  (input) CHARACTER*1 */
/*          = 'A': compute all right and/or left eigenvectors; */
/*          = 'B': compute all right and/or left eigenvectors, */
/*                 backtransformed by the matrices in VR and/or VL; */
/*          = 'S': compute selected right and/or left eigenvectors, */
/*                 specified by the logical array SELECT. */

/*  SELECT  (input) LOGICAL array, dimension (N) */
/*          If HOWMNY='S', SELECT specifies the eigenvectors to be */
/*          computed.  The eigenvector corresponding to the j-th */
/*          eigenvalue is computed if SELECT(j) = .TRUE.. */
/*          Not referenced if HOWMNY = 'A' or 'B'. */

/*  N       (input) INTEGER */
/*          The order of the matrices S and P.  N >= 0. */

/*  S       (input) COMPLEX*16 array, dimension (LDS,N) */
/*          The upper triangular matrix S from a generalized Schur */
/*          factorization, as computed by ZHGEQZ. */

/*  LDS     (input) INTEGER */
/*          The leading dimension of array S.  LDS >= max(1,N). */

/*  P       (input) COMPLEX*16 array, dimension (LDP,N) */
/*          The upper triangular matrix P from a generalized Schur */
/*          factorization, as computed by ZHGEQZ.  P must have real */
/*          diagonal elements. */

/*  LDP     (input) INTEGER */
/*          The leading dimension of array P.  LDP >= max(1,N). */

/*  VL      (input/output) COMPLEX*16 array, dimension (LDVL,MM) */
/*          On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must */
/*          contain an N-by-N matrix Q (usually the unitary matrix Q */
/*          of left Schur vectors returned by ZHGEQZ). */
/*          On exit, if SIDE = 'L' or 'B', VL contains: */
/*          if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P); */
/*          if HOWMNY = 'B', the matrix Q*Y; */
/*          if HOWMNY = 'S', the left eigenvectors of (S,P) specified by */
/*                      SELECT, stored consecutively in the columns of */
/*                      VL, in the same order as their eigenvalues. */
/*          Not referenced if SIDE = 'R'. */

/*  LDVL    (input) INTEGER */
/*          The leading dimension of array VL.  LDVL >= 1, and if */
/*          SIDE = 'L' or 'l' or 'B' or 'b', LDVL >= N. */

/*  VR      (input/output) COMPLEX*16 array, dimension (LDVR,MM) */
/*          On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must */
/*          contain an N-by-N matrix Q (usually the unitary matrix Z */
/*          of right Schur vectors returned by ZHGEQZ). */
/*          On exit, if SIDE = 'R' or 'B', VR contains: */
/*          if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P); */
/*          if HOWMNY = 'B', the matrix Z*X; */
/*          if HOWMNY = 'S', the right eigenvectors of (S,P) specified by */
/*                      SELECT, stored consecutively in the columns of */
/*                      VR, in the same order as their eigenvalues. */
/*          Not referenced if SIDE = 'L'. */

/*  LDVR    (input) INTEGER */
/*          The leading dimension of the array VR.  LDVR >= 1, and if */
/*          SIDE = 'R' or 'B', LDVR >= N. */

/*  MM      (input) INTEGER */
/*          The number of columns in the arrays VL and/or VR. MM >= M. */

/*  M       (output) INTEGER */
/*          The number of columns in the arrays VL and/or VR actually */
/*          used to store the eigenvectors.  If HOWMNY = 'A' or 'B', M */
/*          is set to N.  Each selected eigenvector occupies one column. */

/*  WORK    (workspace) COMPLEX*16 array, dimension (2*N) */

/*  RWORK   (workspace) DOUBLE PRECISION array, dimension (2*N) */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit. */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value. */

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Statement Functions .. */
/*     .. */
/*     .. Statement Function definitions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Decode and Test the input parameters */

    /* Parameter adjustments */
    --select;
    s_dim1 = *lds;
    s_offset = 1 + s_dim1;
    s -= s_offset;
    p_dim1 = *ldp;
    p_offset = 1 + p_dim1;
    p -= p_offset;
    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_(howmny, "A")) {
        ihwmny = 1;
        ilall = TRUE_;
        ilback = FALSE_;
    } else if (lsame_(howmny, "S")) {
        ihwmny = 2;
        ilall = FALSE_;
        ilback = FALSE_;
    } else if (lsame_(howmny, "B")) {
        ihwmny = 3;
        ilall = TRUE_;
        ilback = TRUE_;
    } else {
        ihwmny = -1;
    }

    if (lsame_(side, "R")) {
        iside = 1;
        compl = FALSE_;
        compr = TRUE_;
    } else if (lsame_(side, "L")) {
        iside = 2;
        compl = TRUE_;
        compr = FALSE_;
    } else if (lsame_(side, "B")) {
        iside = 3;
        compl = TRUE_;
        compr = TRUE_;
    } else {
        iside = -1;
    }

    *info = 0;
    if (iside < 0) {
        *info = -1;
    } else if (ihwmny < 0) {
        *info = -2;
    } else if (*n < 0) {
        *info = -4;
    } else if (*lds < max(1,*n)) {
        *info = -6;
    } else if (*ldp < max(1,*n)) {
        *info = -8;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("ZTGEVC", &i__1);
        return 0;
    }

/*     Count the number of eigenvectors */

    if (! ilall) {
        im = 0;
        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {
            if (select[j]) {
                ++im;
            }
/* L10: */
        }
    } else {
        im = *n;
    }

/*     Check diagonal of B */

    ilbbad = FALSE_;
    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
        if (d_imag(&p[j + j * p_dim1]) != 0.) {
            ilbbad = TRUE_;
        }
/* L20: */
    }

    if (ilbbad) {
        *info = -7;
    } else if (compl && *ldvl < *n || *ldvl < 1) {
        *info = -10;
    } else if (compr && *ldvr < *n || *ldvr < 1) {
        *info = -12;
    } else if (*mm < im) {
        *info = -13;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("ZTGEVC", &i__1);
        return 0;
    }

/*     Quick return if possible */

    *m = im;
    if (*n == 0) {
        return 0;
    }

/*     Machine Constants */

    safmin = dlamch_("Safe minimum");
    big = 1. / safmin;
    dlabad_(&safmin, &big);
    ulp = dlamch_("Epsilon") * dlamch_("Base");
    small = safmin * *n / ulp;
    big = 1. / small;
    bignum = 1. / (safmin * *n);

/*     Compute the 1-norm of each column of the strictly upper triangular */
/*     part of A and B to check for possible overflow in the triangular */
/*     solver. */

    i__1 = s_dim1 + 1;
    anorm = (d__1 = s[i__1].r, abs(d__1)) + (d__2 = d_imag(&s[s_dim1 + 1]), 
            abs(d__2));
    i__1 = p_dim1 + 1;
    bnorm = (d__1 = p[i__1].r, abs(d__1)) + (d__2 = d_imag(&p[p_dim1 + 1]), 
            abs(d__2));
    rwork[1] = 0.;
    rwork[*n + 1] = 0.;
    i__1 = *n;
    for (j = 2; j <= i__1; ++j) {
        rwork[j] = 0.;
        rwork[*n + j] = 0.;
        i__2 = j - 1;
        for (i__ = 1; i__ <= i__2; ++i__) {
            i__3 = i__ + j * s_dim1;
            rwork[j] += (d__1 = s[i__3].r, abs(d__1)) + (d__2 = d_imag(&s[i__ 
                    + j * s_dim1]), abs(d__2));
            i__3 = i__ + j * p_dim1;
            rwork[*n + j] += (d__1 = p[i__3].r, abs(d__1)) + (d__2 = d_imag(&
                    p[i__ + j * p_dim1]), abs(d__2));
/* L30: */
        }
/* Computing MAX */
        i__2 = j + j * s_dim1;
        d__3 = anorm, d__4 = rwork[j] + ((d__1 = s[i__2].r, abs(d__1)) + (
                d__2 = d_imag(&s[j + j * s_dim1]), abs(d__2)));
        anorm = max(d__3,d__4);
/* Computing MAX */
        i__2 = j + j * p_dim1;
        d__3 = bnorm, d__4 = rwork[*n + j] + ((d__1 = p[i__2].r, abs(d__1)) + 
                (d__2 = d_imag(&p[j + j * p_dim1]), abs(d__2)));
        bnorm = max(d__3,d__4);
/* L40: */
    }

    ascale = 1. / max(anorm,safmin);
    bscale = 1. / max(bnorm,safmin);

/*     Left eigenvectors */

    if (compl) {
        ieig = 0;

/*        Main loop over eigenvalues */

        i__1 = *n;
        for (je = 1; je <= i__1; ++je) {
            if (ilall) {
                ilcomp = TRUE_;
            } else {
                ilcomp = select[je];
            }
            if (ilcomp) {
                ++ieig;

                i__2 = je + je * s_dim1;
                i__3 = je + je * p_dim1;
                if ((d__2 = s[i__2].r, abs(d__2)) + (d__3 = d_imag(&s[je + je 
                        * s_dim1]), abs(d__3)) <= safmin && (d__1 = p[i__3].r,
                         abs(d__1)) <= safmin) {

/*                 Singular matrix pencil -- return unit eigenvector */

                    i__2 = *n;
                    for (jr = 1; jr <= i__2; ++jr) {
                        i__3 = jr + ieig * vl_dim1;
                        vl[i__3].r = 0., vl[i__3].i = 0.;
/* L50: */
                    }
                    i__2 = ieig + ieig * vl_dim1;
                    vl[i__2].r = 1., vl[i__2].i = 0.;
                    goto L140;
                }

/*              Non-singular eigenvalue: */
/*              Compute coefficients  a  and  b  in */
/*                   H */
/*                 y  ( a A - b B ) = 0 */

/* Computing MAX */
                i__2 = je + je * s_dim1;
                i__3 = je + je * p_dim1;
                d__4 = ((d__2 = s[i__2].r, abs(d__2)) + (d__3 = d_imag(&s[je 
                        + je * s_dim1]), abs(d__3))) * ascale, d__5 = (d__1 = 
                        p[i__3].r, abs(d__1)) * bscale, d__4 = max(d__4,d__5);
                temp = 1. / max(d__4,safmin);
                i__2 = je + je * s_dim1;
                z__2.r = temp * s[i__2].r, z__2.i = temp * s[i__2].i;
                z__1.r = ascale * z__2.r, z__1.i = ascale * z__2.i;
                salpha.r = z__1.r, salpha.i = z__1.i;
                i__2 = je + je * p_dim1;
                sbeta = temp * p[i__2].r * bscale;
                acoeff = sbeta * ascale;
                z__1.r = bscale * salpha.r, z__1.i = bscale * salpha.i;
                bcoeff.r = z__1.r, bcoeff.i = z__1.i;

/*              Scale to avoid underflow */

                lsa = abs(sbeta) >= safmin && abs(acoeff) < small;
                lsb = (d__1 = salpha.r, abs(d__1)) + (d__2 = d_imag(&salpha), 
                        abs(d__2)) >= safmin && (d__3 = bcoeff.r, abs(d__3)) 
                        + (d__4 = d_imag(&bcoeff), abs(d__4)) < small;

                scale = 1.;
                if (lsa) {
                    scale = small / abs(sbeta) * min(anorm,big);
                }
                if (lsb) {
/* Computing MAX */
                    d__3 = scale, d__4 = small / ((d__1 = salpha.r, abs(d__1))
                             + (d__2 = d_imag(&salpha), abs(d__2))) * min(
                            bnorm,big);
                    scale = max(d__3,d__4);
                }
                if (lsa || lsb) {
/* Computing MIN */
/* Computing MAX */
                    d__5 = 1., d__6 = abs(acoeff), d__5 = max(d__5,d__6), 
                            d__6 = (d__1 = bcoeff.r, abs(d__1)) + (d__2 = 
                            d_imag(&bcoeff), abs(d__2));
                    d__3 = scale, d__4 = 1. / (safmin * max(d__5,d__6));
                    scale = min(d__3,d__4);
                    if (lsa) {
                        acoeff = ascale * (scale * sbeta);
                    } else {
                        acoeff = scale * acoeff;
                    }
                    if (lsb) {
                        z__2.r = scale * salpha.r, z__2.i = scale * salpha.i;
                        z__1.r = bscale * z__2.r, z__1.i = bscale * z__2.i;
                        bcoeff.r = z__1.r, bcoeff.i = z__1.i;
                    } else {
                        z__1.r = scale * bcoeff.r, z__1.i = scale * bcoeff.i;
                        bcoeff.r = z__1.r, bcoeff.i = z__1.i;
                    }
                }

                acoefa = abs(acoeff);
                bcoefa = (d__1 = bcoeff.r, abs(d__1)) + (d__2 = d_imag(&
                        bcoeff), abs(d__2));
                xmax = 1.;
                i__2 = *n;
                for (jr = 1; jr <= i__2; ++jr) {
                    i__3 = jr;
                    work[i__3].r = 0., work[i__3].i = 0.;
/* L60: */
                }
                i__2 = je;
                work[i__2].r = 1., work[i__2].i = 0.;
/* Computing MAX */
                d__1 = ulp * acoefa * anorm, d__2 = ulp * bcoefa * bnorm, 
                        d__1 = max(d__1,d__2);
                dmin__ = max(d__1,safmin);

/*                                              H */
/*              Triangular solve of  (a A - b B)  y = 0 */

/*                                      H */
/*              (rowwise in  (a A - b B) , or columnwise in a A - b B) */

                i__2 = *n;
                for (j = je + 1; j <= i__2; ++j) {

/*                 Compute */
/*                       j-1 */
/*                 SUM = sum  conjg( a*S(k,j) - b*P(k,j) )*x(k) */
/*                       k=je */
/*                 (Scale if necessary) */

                    temp = 1. / xmax;
                    if (acoefa * rwork[j] + bcoefa * rwork[*n + j] > bignum * 
                            temp) {
                        i__3 = j - 1;
                        for (jr = je; jr <= i__3; ++jr) {
                            i__4 = jr;
                            i__5 = jr;
                            z__1.r = temp * work[i__5].r, z__1.i = temp * 
                                    work[i__5].i;
                            work[i__4].r = z__1.r, work[i__4].i = z__1.i;
/* L70: */
                        }
                        xmax = 1.;
                    }
                    suma.r = 0., suma.i = 0.;
                    sumb.r = 0., sumb.i = 0.;

                    i__3 = j - 1;
                    for (jr = je; jr <= i__3; ++jr) {
                        d_cnjg(&z__3, &s[jr + j * s_dim1]);
                        i__4 = jr;
                        z__2.r = z__3.r * work[i__4].r - z__3.i * work[i__4]
                                .i, z__2.i = z__3.r * work[i__4].i + z__3.i * 
                                work[i__4].r;
                        z__1.r = suma.r + z__2.r, z__1.i = suma.i + z__2.i;
                        suma.r = z__1.r, suma.i = z__1.i;
                        d_cnjg(&z__3, &p[jr + j * p_dim1]);
                        i__4 = jr;
                        z__2.r = z__3.r * work[i__4].r - z__3.i * work[i__4]
                                .i, z__2.i = z__3.r * work[i__4].i + z__3.i * 
                                work[i__4].r;
                        z__1.r = sumb.r + z__2.r, z__1.i = sumb.i + z__2.i;
                        sumb.r = z__1.r, sumb.i = z__1.i;
/* L80: */
                    }
                    z__2.r = acoeff * suma.r, z__2.i = acoeff * suma.i;
                    d_cnjg(&z__4, &bcoeff);
                    z__3.r = z__4.r * sumb.r - z__4.i * sumb.i, z__3.i = 
                            z__4.r * sumb.i + z__4.i * sumb.r;
                    z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
                    sum.r = z__1.r, sum.i = z__1.i;

/*                 Form x(j) = - SUM / conjg( a*S(j,j) - b*P(j,j) ) */

/*                 with scaling and perturbation of the denominator */

                    i__3 = j + j * s_dim1;
                    z__3.r = acoeff * s[i__3].r, z__3.i = acoeff * s[i__3].i;
                    i__4 = j + j * p_dim1;
                    z__4.r = bcoeff.r * p[i__4].r - bcoeff.i * p[i__4].i, 
                            z__4.i = bcoeff.r * p[i__4].i + bcoeff.i * p[i__4]
                            .r;
                    z__2.r = z__3.r - z__4.r, z__2.i = z__3.i - z__4.i;
                    d_cnjg(&z__1, &z__2);
                    d__.r = z__1.r, d__.i = z__1.i;
                    if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs(
                            d__2)) <= dmin__) {
                        z__1.r = dmin__, z__1.i = 0.;
                        d__.r = z__1.r, d__.i = z__1.i;
                    }

                    if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs(
                            d__2)) < 1.) {
                        if ((d__1 = sum.r, abs(d__1)) + (d__2 = d_imag(&sum), 
                                abs(d__2)) >= bignum * ((d__3 = d__.r, abs(
                                d__3)) + (d__4 = d_imag(&d__), abs(d__4)))) {
                            temp = 1. / ((d__1 = sum.r, abs(d__1)) + (d__2 = 
                                    d_imag(&sum), abs(d__2)));
                            i__3 = j - 1;
                            for (jr = je; jr <= i__3; ++jr) {
                                i__4 = jr;
                                i__5 = jr;
                                z__1.r = temp * work[i__5].r, z__1.i = temp * 
                                        work[i__5].i;
                                work[i__4].r = z__1.r, work[i__4].i = z__1.i;
/* L90: */
                            }
                            xmax = temp * xmax;
                            z__1.r = temp * sum.r, z__1.i = temp * sum.i;
                            sum.r = z__1.r, sum.i = z__1.i;
                        }
                    }
                    i__3 = j;
                    z__2.r = -sum.r, z__2.i = -sum.i;
                    zladiv_(&z__1, &z__2, &d__);
                    work[i__3].r = z__1.r, work[i__3].i = z__1.i;
/* Computing MAX */
                    i__3 = j;
                    d__3 = xmax, d__4 = (d__1 = work[i__3].r, abs(d__1)) + (
                            d__2 = d_imag(&work[j]), abs(d__2));
                    xmax = max(d__3,d__4);
/* L100: */
                }

/*              Back transform eigenvector if HOWMNY='B'. */

                if (ilback) {
                    i__2 = *n + 1 - je;
                    zgemv_("N", n, &i__2, &c_b2, &vl[je * vl_dim1 + 1], ldvl, 
                            &work[je], &c__1, &c_b1, &work[*n + 1], &c__1);
                    isrc = 2;
                    ibeg = 1;
                } else {
                    isrc = 1;
                    ibeg = je;
                }

/*              Copy and scale eigenvector into column of VL */

                xmax = 0.;
                i__2 = *n;
                for (jr = ibeg; jr <= i__2; ++jr) {
/* Computing MAX */
                    i__3 = (isrc - 1) * *n + jr;
                    d__3 = xmax, d__4 = (d__1 = work[i__3].r, abs(d__1)) + (
                            d__2 = d_imag(&work[(isrc - 1) * *n + jr]), abs(
                            d__2));
                    xmax = max(d__3,d__4);
/* L110: */
                }

                if (xmax > safmin) {
                    temp = 1. / xmax;
                    i__2 = *n;
                    for (jr = ibeg; jr <= i__2; ++jr) {
                        i__3 = jr + ieig * vl_dim1;
                        i__4 = (isrc - 1) * *n + jr;
                        z__1.r = temp * work[i__4].r, z__1.i = temp * work[
                                i__4].i;
                        vl[i__3].r = z__1.r, vl[i__3].i = z__1.i;
/* L120: */
                    }
                } else {
                    ibeg = *n + 1;
                }

                i__2 = ibeg - 1;
                for (jr = 1; jr <= i__2; ++jr) {
                    i__3 = jr + ieig * vl_dim1;
                    vl[i__3].r = 0., vl[i__3].i = 0.;
/* L130: */
                }

            }
L140:
            ;
        }
    }

/*     Right eigenvectors */

    if (compr) {
        ieig = im + 1;

/*        Main loop over eigenvalues */

        for (je = *n; je >= 1; --je) {
            if (ilall) {
                ilcomp = TRUE_;
            } else {
                ilcomp = select[je];
            }
            if (ilcomp) {
                --ieig;

                i__1 = je + je * s_dim1;
                i__2 = je + je * p_dim1;
                if ((d__2 = s[i__1].r, abs(d__2)) + (d__3 = d_imag(&s[je + je 
                        * s_dim1]), abs(d__3)) <= safmin && (d__1 = p[i__2].r,
                         abs(d__1)) <= safmin) {

/*                 Singular matrix pencil -- return unit eigenvector */

                    i__1 = *n;
                    for (jr = 1; jr <= i__1; ++jr) {
                        i__2 = jr + ieig * vr_dim1;
                        vr[i__2].r = 0., vr[i__2].i = 0.;
/* L150: */
                    }
                    i__1 = ieig + ieig * vr_dim1;
                    vr[i__1].r = 1., vr[i__1].i = 0.;
                    goto L250;
                }

/*              Non-singular eigenvalue: */
/*              Compute coefficients  a  and  b  in */

/*              ( a A - b B ) x  = 0 */

/* Computing MAX */
                i__1 = je + je * s_dim1;
                i__2 = je + je * p_dim1;
                d__4 = ((d__2 = s[i__1].r, abs(d__2)) + (d__3 = d_imag(&s[je 
                        + je * s_dim1]), abs(d__3))) * ascale, d__5 = (d__1 = 
                        p[i__2].r, abs(d__1)) * bscale, d__4 = max(d__4,d__5);
                temp = 1. / max(d__4,safmin);
                i__1 = je + je * s_dim1;
                z__2.r = temp * s[i__1].r, z__2.i = temp * s[i__1].i;
                z__1.r = ascale * z__2.r, z__1.i = ascale * z__2.i;
                salpha.r = z__1.r, salpha.i = z__1.i;
                i__1 = je + je * p_dim1;
                sbeta = temp * p[i__1].r * bscale;
                acoeff = sbeta * ascale;
                z__1.r = bscale * salpha.r, z__1.i = bscale * salpha.i;
                bcoeff.r = z__1.r, bcoeff.i = z__1.i;

/*              Scale to avoid underflow */

                lsa = abs(sbeta) >= safmin && abs(acoeff) < small;
                lsb = (d__1 = salpha.r, abs(d__1)) + (d__2 = d_imag(&salpha), 
                        abs(d__2)) >= safmin && (d__3 = bcoeff.r, abs(d__3)) 
                        + (d__4 = d_imag(&bcoeff), abs(d__4)) < small;

                scale = 1.;
                if (lsa) {
                    scale = small / abs(sbeta) * min(anorm,big);
                }
                if (lsb) {
/* Computing MAX */
                    d__3 = scale, d__4 = small / ((d__1 = salpha.r, abs(d__1))
                             + (d__2 = d_imag(&salpha), abs(d__2))) * min(
                            bnorm,big);
                    scale = max(d__3,d__4);
                }
                if (lsa || lsb) {
/* Computing MIN */
/* Computing MAX */
                    d__5 = 1., d__6 = abs(acoeff), d__5 = max(d__5,d__6), 
                            d__6 = (d__1 = bcoeff.r, abs(d__1)) + (d__2 = 
                            d_imag(&bcoeff), abs(d__2));
                    d__3 = scale, d__4 = 1. / (safmin * max(d__5,d__6));
                    scale = min(d__3,d__4);
                    if (lsa) {
                        acoeff = ascale * (scale * sbeta);
                    } else {
                        acoeff = scale * acoeff;
                    }
                    if (lsb) {
                        z__2.r = scale * salpha.r, z__2.i = scale * salpha.i;
                        z__1.r = bscale * z__2.r, z__1.i = bscale * z__2.i;
                        bcoeff.r = z__1.r, bcoeff.i = z__1.i;
                    } else {
                        z__1.r = scale * bcoeff.r, z__1.i = scale * bcoeff.i;
                        bcoeff.r = z__1.r, bcoeff.i = z__1.i;
                    }
                }

                acoefa = abs(acoeff);
                bcoefa = (d__1 = bcoeff.r, abs(d__1)) + (d__2 = d_imag(&
                        bcoeff), abs(d__2));
                xmax = 1.;
                i__1 = *n;
                for (jr = 1; jr <= i__1; ++jr) {
                    i__2 = jr;
                    work[i__2].r = 0., work[i__2].i = 0.;
/* L160: */
                }
                i__1 = je;
                work[i__1].r = 1., work[i__1].i = 0.;
/* Computing MAX */
                d__1 = ulp * acoefa * anorm, d__2 = ulp * bcoefa * bnorm, 
                        d__1 = max(d__1,d__2);
                dmin__ = max(d__1,safmin);

/*              Triangular solve of  (a A - b B) x = 0  (columnwise) */

/*              WORK(1:j-1) contains sums w, */
/*              WORK(j+1:JE) contains x */

                i__1 = je - 1;
                for (jr = 1; jr <= i__1; ++jr) {
                    i__2 = jr;
                    i__3 = jr + je * s_dim1;
                    z__2.r = acoeff * s[i__3].r, z__2.i = acoeff * s[i__3].i;
                    i__4 = jr + je * p_dim1;
                    z__3.r = bcoeff.r * p[i__4].r - bcoeff.i * p[i__4].i, 
                            z__3.i = bcoeff.r * p[i__4].i + bcoeff.i * p[i__4]
                            .r;
                    z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
                    work[i__2].r = z__1.r, work[i__2].i = z__1.i;
/* L170: */
                }
                i__1 = je;
                work[i__1].r = 1., work[i__1].i = 0.;

                for (j = je - 1; j >= 1; --j) {

/*                 Form x(j) := - w(j) / d */
/*                 with scaling and perturbation of the denominator */

                    i__1 = j + j * s_dim1;
                    z__2.r = acoeff * s[i__1].r, z__2.i = acoeff * s[i__1].i;
                    i__2 = j + j * p_dim1;
                    z__3.r = bcoeff.r * p[i__2].r - bcoeff.i * p[i__2].i, 
                            z__3.i = bcoeff.r * p[i__2].i + bcoeff.i * p[i__2]
                            .r;
                    z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
                    d__.r = z__1.r, d__.i = z__1.i;
                    if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs(
                            d__2)) <= dmin__) {
                        z__1.r = dmin__, z__1.i = 0.;
                        d__.r = z__1.r, d__.i = z__1.i;
                    }

                    if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs(
                            d__2)) < 1.) {
                        i__1 = j;
                        if ((d__1 = work[i__1].r, abs(d__1)) + (d__2 = d_imag(
                                &work[j]), abs(d__2)) >= bignum * ((d__3 = 
                                d__.r, abs(d__3)) + (d__4 = d_imag(&d__), abs(
                                d__4)))) {
                            i__1 = j;
                            temp = 1. / ((d__1 = work[i__1].r, abs(d__1)) + (
                                    d__2 = d_imag(&work[j]), abs(d__2)));
                            i__1 = je;
                            for (jr = 1; jr <= i__1; ++jr) {
                                i__2 = jr;
                                i__3 = jr;
                                z__1.r = temp * work[i__3].r, z__1.i = temp * 
                                        work[i__3].i;
                                work[i__2].r = z__1.r, work[i__2].i = z__1.i;
/* L180: */
                            }
                        }
                    }

                    i__1 = j;
                    i__2 = j;
                    z__2.r = -work[i__2].r, z__2.i = -work[i__2].i;
                    zladiv_(&z__1, &z__2, &d__);
                    work[i__1].r = z__1.r, work[i__1].i = z__1.i;

                    if (j > 1) {

/*                    w = w + x(j)*(a S(*,j) - b P(*,j) ) with scaling */

                        i__1 = j;
                        if ((d__1 = work[i__1].r, abs(d__1)) + (d__2 = d_imag(
                                &work[j]), abs(d__2)) > 1.) {
                            i__1 = j;
                            temp = 1. / ((d__1 = work[i__1].r, abs(d__1)) + (
                                    d__2 = d_imag(&work[j]), abs(d__2)));
                            if (acoefa * rwork[j] + bcoefa * rwork[*n + j] >= 
                                    bignum * temp) {
                                i__1 = je;
                                for (jr = 1; jr <= i__1; ++jr) {
                                    i__2 = jr;
                                    i__3 = jr;
                                    z__1.r = temp * work[i__3].r, z__1.i = 
                                            temp * work[i__3].i;
                                    work[i__2].r = z__1.r, work[i__2].i = 
                                            z__1.i;
/* L190: */
                                }
                            }
                        }

                        i__1 = j;
                        z__1.r = acoeff * work[i__1].r, z__1.i = acoeff * 
                                work[i__1].i;
                        ca.r = z__1.r, ca.i = z__1.i;
                        i__1 = j;
                        z__1.r = bcoeff.r * work[i__1].r - bcoeff.i * work[
                                i__1].i, z__1.i = bcoeff.r * work[i__1].i + 
                                bcoeff.i * work[i__1].r;
                        cb.r = z__1.r, cb.i = z__1.i;
                        i__1 = j - 1;
                        for (jr = 1; jr <= i__1; ++jr) {
                            i__2 = jr;
                            i__3 = jr;
                            i__4 = jr + j * s_dim1;
                            z__3.r = ca.r * s[i__4].r - ca.i * s[i__4].i, 
                                    z__3.i = ca.r * s[i__4].i + ca.i * s[i__4]
                                    .r;
                            z__2.r = work[i__3].r + z__3.r, z__2.i = work[
                                    i__3].i + z__3.i;
                            i__5 = jr + j * p_dim1;
                            z__4.r = cb.r * p[i__5].r - cb.i * p[i__5].i, 
                                    z__4.i = cb.r * p[i__5].i + cb.i * p[i__5]
                                    .r;
                            z__1.r = z__2.r - z__4.r, z__1.i = z__2.i - 
                                    z__4.i;
                            work[i__2].r = z__1.r, work[i__2].i = z__1.i;
/* L200: */
                        }
                    }
/* L210: */
                }

/*              Back transform eigenvector if HOWMNY='B'. */

                if (ilback) {
                    zgemv_("N", n, &je, &c_b2, &vr[vr_offset], ldvr, &work[1], 
                             &c__1, &c_b1, &work[*n + 1], &c__1);
                    isrc = 2;
                    iend = *n;
                } else {
                    isrc = 1;
                    iend = je;
                }

/*              Copy and scale eigenvector into column of VR */

                xmax = 0.;
                i__1 = iend;
                for (jr = 1; jr <= i__1; ++jr) {
/* Computing MAX */
                    i__2 = (isrc - 1) * *n + jr;
                    d__3 = xmax, d__4 = (d__1 = work[i__2].r, abs(d__1)) + (
                            d__2 = d_imag(&work[(isrc - 1) * *n + jr]), abs(
                            d__2));
                    xmax = max(d__3,d__4);
/* L220: */
                }

                if (xmax > safmin) {
                    temp = 1. / xmax;
                    i__1 = iend;
                    for (jr = 1; jr <= i__1; ++jr) {
                        i__2 = jr + ieig * vr_dim1;
                        i__3 = (isrc - 1) * *n + jr;
                        z__1.r = temp * work[i__3].r, z__1.i = temp * work[
                                i__3].i;
                        vr[i__2].r = z__1.r, vr[i__2].i = z__1.i;
/* L230: */
                    }
                } else {
                    iend = 0;
                }

                i__1 = *n;
                for (jr = iend + 1; jr <= i__1; ++jr) {
                    i__2 = jr + ieig * vr_dim1;
                    vr[i__2].r = 0., vr[i__2].i = 0.;
/* L240: */
                }

            }
L250:
            ;
        }
    }

    return 0;

/*     End of ZTGEVC */

} /* ztgevc_ */