dtrevc.c

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/* dtrevc.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 logical c_false = FALSE_;
static integer c__1 = 1;
static doublereal c_b22 = 1.;
static doublereal c_b25 = 0.;
static integer c__2 = 2;
static logical c_true = TRUE_;

/* Subroutine */ int dtrevc_(char *side, char *howmny, logical *select, 
        integer *n, doublereal *t, integer *ldt, doublereal *vl, integer *
        ldvl, doublereal *vr, integer *ldvr, integer *mm, integer *m, 
        doublereal *work, integer *info)
{
    /* System generated locals */
    integer t_dim1, t_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1, 
            i__2, i__3;
    doublereal d__1, d__2, d__3, d__4;

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

    /* Local variables */
    integer i__, j, k;
    doublereal x[4]     /* was [2][2] */;
    integer j1, j2, n2, ii, ki, ip, is;
    doublereal wi, wr, rec, ulp, beta, emax;
    logical pair;
    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, 
            integer *);
    logical allv;
    integer ierr;
    doublereal unfl, ovfl, smin;
    logical over;
    doublereal vmax;
    integer jnxt;
    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, 
            integer *);
    doublereal scale;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int dgemv_(char *, integer *, integer *, 
            doublereal *, doublereal *, integer *, doublereal *, integer *, 
            doublereal *, doublereal *, integer *);
    doublereal remax;
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
            doublereal *, integer *);
    logical leftv, bothv;
    extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, 
            integer *, doublereal *, integer *);
    doublereal vcrit;
    logical somev;
    doublereal xnorm;
    extern /* Subroutine */ int dlaln2_(logical *, integer *, integer *, 
            doublereal *, doublereal *, doublereal *, integer *, doublereal *, 
             doublereal *, doublereal *, integer *, doublereal *, doublereal *
, doublereal *, integer *, doublereal *, doublereal *, integer *),
             dlabad_(doublereal *, doublereal *);
    extern doublereal dlamch_(char *);
    extern integer idamax_(integer *, doublereal *, integer *);
    extern /* Subroutine */ int xerbla_(char *, integer *);
    doublereal bignum;
    logical rightv;
    doublereal smlnum;


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

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

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

/*  DTREVC computes some or all of the right and/or left eigenvectors of */
/*  a real upper quasi-triangular matrix T. */
/*  Matrices of this type are produced by the Schur factorization of */
/*  a real general matrix:  A = Q*T*Q**T, as computed by DHSEQR. */

/*  The right eigenvector x and the left eigenvector y of T corresponding */
/*  to an eigenvalue w are defined by: */

/*     T*x = w*x,     (y**H)*T = w*(y**H) */

/*  where y**H denotes the conjugate transpose of y. */
/*  The eigenvalues are not input to this routine, but are read directly */
/*  from the diagonal blocks of T. */

/*  This routine returns the matrices X and/or Y of right and left */
/*  eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an */
/*  input matrix.  If Q is the orthogonal factor that reduces a matrix */
/*  A to Schur form T, then Q*X and Q*Y are the matrices of right and */
/*  left eigenvectors of A. */

/*  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, */
/*                  as indicated by the logical array SELECT. */

/*  SELECT  (input/output) LOGICAL array, dimension (N) */
/*          If HOWMNY = 'S', SELECT specifies the eigenvectors to be */
/*          computed. */
/*          If w(j) is a real eigenvalue, the corresponding real */
/*          eigenvector is computed if SELECT(j) is .TRUE.. */
/*          If w(j) and w(j+1) are the real and imaginary parts of a */
/*          complex eigenvalue, the corresponding complex eigenvector is */
/*          computed if either SELECT(j) or SELECT(j+1) is .TRUE., and */
/*          on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is set to */
/*          .FALSE.. */
/*          Not referenced if HOWMNY = 'A' or 'B'. */

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

/*  T       (input) DOUBLE PRECISION array, dimension (LDT,N) */
/*          The upper quasi-triangular matrix T in Schur canonical form. */

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

/*  VL      (input/output) DOUBLE PRECISION 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 orthogonal matrix Q */
/*          of Schur vectors returned by DHSEQR). */
/*          On exit, if SIDE = 'L' or 'B', VL contains: */
/*          if HOWMNY = 'A', the matrix Y of left eigenvectors of T; */
/*          if HOWMNY = 'B', the matrix Q*Y; */
/*          if HOWMNY = 'S', the left eigenvectors of T specified by */
/*                           SELECT, stored consecutively in the columns */
/*                           of VL, in the same order as their */
/*                           eigenvalues. */
/*          A complex eigenvector corresponding to a complex eigenvalue */
/*          is stored in two consecutive columns, the first holding the */
/*          real part, and the second the imaginary part. */
/*          Not referenced if SIDE = 'R'. */

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

/*  VR      (input/output) DOUBLE PRECISION 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 orthogonal matrix Q */
/*          of Schur vectors returned by DHSEQR). */
/*          On exit, if SIDE = 'R' or 'B', VR contains: */
/*          if HOWMNY = 'A', the matrix X of right eigenvectors of T; */
/*          if HOWMNY = 'B', the matrix Q*X; */
/*          if HOWMNY = 'S', the right eigenvectors of T specified by */
/*                           SELECT, stored consecutively in the columns */
/*                           of VR, in the same order as their */
/*                           eigenvalues. */
/*          A complex eigenvector corresponding to a complex eigenvalue */
/*          is stored in two consecutive columns, the first holding the */
/*          real part and the second the imaginary part. */
/*          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 real eigenvector occupies one column and each */
/*          selected complex eigenvector occupies two columns. */

/*  WORK    (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 */

/*  Further Details */
/*  =============== */

/*  The algorithm used in this program is basically backward (forward) */
/*  substitution, with scaling to make the the code robust against */
/*  possible overflow. */

/*  Each eigenvector is normalized so that the element of largest */
/*  magnitude has magnitude 1; here the magnitude of a complex number */
/*  (x,y) is taken to be |x| + |y|. */

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

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

/*     Decode and test the input parameters */

    /* Parameter adjustments */
    --select;
    t_dim1 = *ldt;
    t_offset = 1 + t_dim1;
    t -= t_offset;
    vl_dim1 = *ldvl;
    vl_offset = 1 + vl_dim1;
    vl -= vl_offset;
    vr_dim1 = *ldvr;
    vr_offset = 1 + vr_dim1;
    vr -= vr_offset;
    --work;

    /* Function Body */
    bothv = lsame_(side, "B");
    rightv = lsame_(side, "R") || bothv;
    leftv = lsame_(side, "L") || bothv;

    allv = lsame_(howmny, "A");
    over = lsame_(howmny, "B");
    somev = lsame_(howmny, "S");

    *info = 0;
    if (! rightv && ! leftv) {
        *info = -1;
    } else if (! allv && ! over && ! somev) {
        *info = -2;
    } else if (*n < 0) {
        *info = -4;
    } else if (*ldt < max(1,*n)) {
        *info = -6;
    } else if (*ldvl < 1 || leftv && *ldvl < *n) {
        *info = -8;
    } else if (*ldvr < 1 || rightv && *ldvr < *n) {
        *info = -10;
    } else {

/*        Set M to the number of columns required to store the selected */
/*        eigenvectors, standardize the array SELECT if necessary, and */
/*        test MM. */

        if (somev) {
            *m = 0;
            pair = FALSE_;
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                if (pair) {
                    pair = FALSE_;
                    select[j] = FALSE_;
                } else {
                    if (j < *n) {
                        if (t[j + 1 + j * t_dim1] == 0.) {
                            if (select[j]) {
                                ++(*m);
                            }
                        } else {
                            pair = TRUE_;
                            if (select[j] || select[j + 1]) {
                                select[j] = TRUE_;
                                *m += 2;
                            }
                        }
                    } else {
                        if (select[*n]) {
                            ++(*m);
                        }
                    }
                }
/* L10: */
            }
        } else {
            *m = *n;
        }

        if (*mm < *m) {
            *info = -11;
        }
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DTREVC", &i__1);
        return 0;
    }

/*     Quick return if possible. */

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

/*     Set the constants to control overflow. */

    unfl = dlamch_("Safe minimum");
    ovfl = 1. / unfl;
    dlabad_(&unfl, &ovfl);
    ulp = dlamch_("Precision");
    smlnum = unfl * (*n / ulp);
    bignum = (1. - ulp) / smlnum;

/*     Compute 1-norm of each column of strictly upper triangular */
/*     part of T to control overflow in triangular solver. */

    work[1] = 0.;
    i__1 = *n;
    for (j = 2; j <= i__1; ++j) {
        work[j] = 0.;
        i__2 = j - 1;
        for (i__ = 1; i__ <= i__2; ++i__) {
            work[j] += (d__1 = t[i__ + j * t_dim1], abs(d__1));
/* L20: */
        }
/* L30: */
    }

/*     Index IP is used to specify the real or complex eigenvalue: */
/*       IP = 0, real eigenvalue, */
/*            1, first of conjugate complex pair: (wr,wi) */
/*           -1, second of conjugate complex pair: (wr,wi) */

    n2 = *n << 1;

    if (rightv) {

/*        Compute right eigenvectors. */

        ip = 0;
        is = *m;
        for (ki = *n; ki >= 1; --ki) {

            if (ip == 1) {
                goto L130;
            }
            if (ki == 1) {
                goto L40;
            }
            if (t[ki + (ki - 1) * t_dim1] == 0.) {
                goto L40;
            }
            ip = -1;

L40:
            if (somev) {
                if (ip == 0) {
                    if (! select[ki]) {
                        goto L130;
                    }
                } else {
                    if (! select[ki - 1]) {
                        goto L130;
                    }
                }
            }

/*           Compute the KI-th eigenvalue (WR,WI). */

            wr = t[ki + ki * t_dim1];
            wi = 0.;
            if (ip != 0) {
                wi = sqrt((d__1 = t[ki + (ki - 1) * t_dim1], abs(d__1))) * 
                        sqrt((d__2 = t[ki - 1 + ki * t_dim1], abs(d__2)));
            }
/* Computing MAX */
            d__1 = ulp * (abs(wr) + abs(wi));
            smin = max(d__1,smlnum);

            if (ip == 0) {

/*              Real right eigenvector */

                work[ki + *n] = 1.;

/*              Form right-hand side */

                i__1 = ki - 1;
                for (k = 1; k <= i__1; ++k) {
                    work[k + *n] = -t[k + ki * t_dim1];
/* L50: */
                }

/*              Solve the upper quasi-triangular system: */
/*                 (T(1:KI-1,1:KI-1) - WR)*X = SCALE*WORK. */

                jnxt = ki - 1;
                for (j = ki - 1; j >= 1; --j) {
                    if (j > jnxt) {
                        goto L60;
                    }
                    j1 = j;
                    j2 = j;
                    jnxt = j - 1;
                    if (j > 1) {
                        if (t[j + (j - 1) * t_dim1] != 0.) {
                            j1 = j - 1;
                            jnxt = j - 2;
                        }
                    }

                    if (j1 == j2) {

/*                    1-by-1 diagonal block */

                        dlaln2_(&c_false, &c__1, &c__1, &smin, &c_b22, &t[j + 
                                j * t_dim1], ldt, &c_b22, &c_b22, &work[j + *
                                n], n, &wr, &c_b25, x, &c__2, &scale, &xnorm, 
                                &ierr);

/*                    Scale X(1,1) to avoid overflow when updating */
/*                    the right-hand side. */

                        if (xnorm > 1.) {
                            if (work[j] > bignum / xnorm) {
                                x[0] /= xnorm;
                                scale /= xnorm;
                            }
                        }

/*                    Scale if necessary */

                        if (scale != 1.) {
                            dscal_(&ki, &scale, &work[*n + 1], &c__1);
                        }
                        work[j + *n] = x[0];

/*                    Update right-hand side */

                        i__1 = j - 1;
                        d__1 = -x[0];
                        daxpy_(&i__1, &d__1, &t[j * t_dim1 + 1], &c__1, &work[
                                *n + 1], &c__1);

                    } else {

/*                    2-by-2 diagonal block */

                        dlaln2_(&c_false, &c__2, &c__1, &smin, &c_b22, &t[j - 
                                1 + (j - 1) * t_dim1], ldt, &c_b22, &c_b22, &
                                work[j - 1 + *n], n, &wr, &c_b25, x, &c__2, &
                                scale, &xnorm, &ierr);

/*                    Scale X(1,1) and X(2,1) to avoid overflow when */
/*                    updating the right-hand side. */

                        if (xnorm > 1.) {
/* Computing MAX */
                            d__1 = work[j - 1], d__2 = work[j];
                            beta = max(d__1,d__2);
                            if (beta > bignum / xnorm) {
                                x[0] /= xnorm;
                                x[1] /= xnorm;
                                scale /= xnorm;
                            }
                        }

/*                    Scale if necessary */

                        if (scale != 1.) {
                            dscal_(&ki, &scale, &work[*n + 1], &c__1);
                        }
                        work[j - 1 + *n] = x[0];
                        work[j + *n] = x[1];

/*                    Update right-hand side */

                        i__1 = j - 2;
                        d__1 = -x[0];
                        daxpy_(&i__1, &d__1, &t[(j - 1) * t_dim1 + 1], &c__1, 
                                &work[*n + 1], &c__1);
                        i__1 = j - 2;
                        d__1 = -x[1];
                        daxpy_(&i__1, &d__1, &t[j * t_dim1 + 1], &c__1, &work[
                                *n + 1], &c__1);
                    }
L60:
                    ;
                }

/*              Copy the vector x or Q*x to VR and normalize. */

                if (! over) {
                    dcopy_(&ki, &work[*n + 1], &c__1, &vr[is * vr_dim1 + 1], &
                            c__1);

                    ii = idamax_(&ki, &vr[is * vr_dim1 + 1], &c__1);
                    remax = 1. / (d__1 = vr[ii + is * vr_dim1], abs(d__1));
                    dscal_(&ki, &remax, &vr[is * vr_dim1 + 1], &c__1);

                    i__1 = *n;
                    for (k = ki + 1; k <= i__1; ++k) {
                        vr[k + is * vr_dim1] = 0.;
/* L70: */
                    }
                } else {
                    if (ki > 1) {
                        i__1 = ki - 1;
                        dgemv_("N", n, &i__1, &c_b22, &vr[vr_offset], ldvr, &
                                work[*n + 1], &c__1, &work[ki + *n], &vr[ki * 
                                vr_dim1 + 1], &c__1);
                    }

                    ii = idamax_(n, &vr[ki * vr_dim1 + 1], &c__1);
                    remax = 1. / (d__1 = vr[ii + ki * vr_dim1], abs(d__1));
                    dscal_(n, &remax, &vr[ki * vr_dim1 + 1], &c__1);
                }

            } else {

/*              Complex right eigenvector. */

/*              Initial solve */
/*                [ (T(KI-1,KI-1) T(KI-1,KI) ) - (WR + I* WI)]*X = 0. */
/*                [ (T(KI,KI-1)   T(KI,KI)   )               ] */

                if ((d__1 = t[ki - 1 + ki * t_dim1], abs(d__1)) >= (d__2 = t[
                        ki + (ki - 1) * t_dim1], abs(d__2))) {
                    work[ki - 1 + *n] = 1.;
                    work[ki + n2] = wi / t[ki - 1 + ki * t_dim1];
                } else {
                    work[ki - 1 + *n] = -wi / t[ki + (ki - 1) * t_dim1];
                    work[ki + n2] = 1.;
                }
                work[ki + *n] = 0.;
                work[ki - 1 + n2] = 0.;

/*              Form right-hand side */

                i__1 = ki - 2;
                for (k = 1; k <= i__1; ++k) {
                    work[k + *n] = -work[ki - 1 + *n] * t[k + (ki - 1) * 
                            t_dim1];
                    work[k + n2] = -work[ki + n2] * t[k + ki * t_dim1];
/* L80: */
                }

/*              Solve upper quasi-triangular system: */
/*              (T(1:KI-2,1:KI-2) - (WR+i*WI))*X = SCALE*(WORK+i*WORK2) */

                jnxt = ki - 2;
                for (j = ki - 2; j >= 1; --j) {
                    if (j > jnxt) {
                        goto L90;
                    }
                    j1 = j;
                    j2 = j;
                    jnxt = j - 1;
                    if (j > 1) {
                        if (t[j + (j - 1) * t_dim1] != 0.) {
                            j1 = j - 1;
                            jnxt = j - 2;
                        }
                    }

                    if (j1 == j2) {

/*                    1-by-1 diagonal block */

                        dlaln2_(&c_false, &c__1, &c__2, &smin, &c_b22, &t[j + 
                                j * t_dim1], ldt, &c_b22, &c_b22, &work[j + *
                                n], n, &wr, &wi, x, &c__2, &scale, &xnorm, &
                                ierr);

/*                    Scale X(1,1) and X(1,2) to avoid overflow when */
/*                    updating the right-hand side. */

                        if (xnorm > 1.) {
                            if (work[j] > bignum / xnorm) {
                                x[0] /= xnorm;
                                x[2] /= xnorm;
                                scale /= xnorm;
                            }
                        }

/*                    Scale if necessary */

                        if (scale != 1.) {
                            dscal_(&ki, &scale, &work[*n + 1], &c__1);
                            dscal_(&ki, &scale, &work[n2 + 1], &c__1);
                        }
                        work[j + *n] = x[0];
                        work[j + n2] = x[2];

/*                    Update the right-hand side */

                        i__1 = j - 1;
                        d__1 = -x[0];
                        daxpy_(&i__1, &d__1, &t[j * t_dim1 + 1], &c__1, &work[
                                *n + 1], &c__1);
                        i__1 = j - 1;
                        d__1 = -x[2];
                        daxpy_(&i__1, &d__1, &t[j * t_dim1 + 1], &c__1, &work[
                                n2 + 1], &c__1);

                    } else {

/*                    2-by-2 diagonal block */

                        dlaln2_(&c_false, &c__2, &c__2, &smin, &c_b22, &t[j - 
                                1 + (j - 1) * t_dim1], ldt, &c_b22, &c_b22, &
                                work[j - 1 + *n], n, &wr, &wi, x, &c__2, &
                                scale, &xnorm, &ierr);

/*                    Scale X to avoid overflow when updating */
/*                    the right-hand side. */

                        if (xnorm > 1.) {
/* Computing MAX */
                            d__1 = work[j - 1], d__2 = work[j];
                            beta = max(d__1,d__2);
                            if (beta > bignum / xnorm) {
                                rec = 1. / xnorm;
                                x[0] *= rec;
                                x[2] *= rec;
                                x[1] *= rec;
                                x[3] *= rec;
                                scale *= rec;
                            }
                        }

/*                    Scale if necessary */

                        if (scale != 1.) {
                            dscal_(&ki, &scale, &work[*n + 1], &c__1);
                            dscal_(&ki, &scale, &work[n2 + 1], &c__1);
                        }
                        work[j - 1 + *n] = x[0];
                        work[j + *n] = x[1];
                        work[j - 1 + n2] = x[2];
                        work[j + n2] = x[3];

/*                    Update the right-hand side */

                        i__1 = j - 2;
                        d__1 = -x[0];
                        daxpy_(&i__1, &d__1, &t[(j - 1) * t_dim1 + 1], &c__1, 
                                &work[*n + 1], &c__1);
                        i__1 = j - 2;
                        d__1 = -x[1];
                        daxpy_(&i__1, &d__1, &t[j * t_dim1 + 1], &c__1, &work[
                                *n + 1], &c__1);
                        i__1 = j - 2;
                        d__1 = -x[2];
                        daxpy_(&i__1, &d__1, &t[(j - 1) * t_dim1 + 1], &c__1, 
                                &work[n2 + 1], &c__1);
                        i__1 = j - 2;
                        d__1 = -x[3];
                        daxpy_(&i__1, &d__1, &t[j * t_dim1 + 1], &c__1, &work[
                                n2 + 1], &c__1);
                    }
L90:
                    ;
                }

/*              Copy the vector x or Q*x to VR and normalize. */

                if (! over) {
                    dcopy_(&ki, &work[*n + 1], &c__1, &vr[(is - 1) * vr_dim1 
                            + 1], &c__1);
                    dcopy_(&ki, &work[n2 + 1], &c__1, &vr[is * vr_dim1 + 1], &
                            c__1);

                    emax = 0.;
                    i__1 = ki;
                    for (k = 1; k <= i__1; ++k) {
/* Computing MAX */
                        d__3 = emax, d__4 = (d__1 = vr[k + (is - 1) * vr_dim1]
                                , abs(d__1)) + (d__2 = vr[k + is * vr_dim1], 
                                abs(d__2));
                        emax = max(d__3,d__4);
/* L100: */
                    }

                    remax = 1. / emax;
                    dscal_(&ki, &remax, &vr[(is - 1) * vr_dim1 + 1], &c__1);
                    dscal_(&ki, &remax, &vr[is * vr_dim1 + 1], &c__1);

                    i__1 = *n;
                    for (k = ki + 1; k <= i__1; ++k) {
                        vr[k + (is - 1) * vr_dim1] = 0.;
                        vr[k + is * vr_dim1] = 0.;
/* L110: */
                    }

                } else {

                    if (ki > 2) {
                        i__1 = ki - 2;
                        dgemv_("N", n, &i__1, &c_b22, &vr[vr_offset], ldvr, &
                                work[*n + 1], &c__1, &work[ki - 1 + *n], &vr[(
                                ki - 1) * vr_dim1 + 1], &c__1);
                        i__1 = ki - 2;
                        dgemv_("N", n, &i__1, &c_b22, &vr[vr_offset], ldvr, &
                                work[n2 + 1], &c__1, &work[ki + n2], &vr[ki * 
                                vr_dim1 + 1], &c__1);
                    } else {
                        dscal_(n, &work[ki - 1 + *n], &vr[(ki - 1) * vr_dim1 
                                + 1], &c__1);
                        dscal_(n, &work[ki + n2], &vr[ki * vr_dim1 + 1], &
                                c__1);
                    }

                    emax = 0.;
                    i__1 = *n;
                    for (k = 1; k <= i__1; ++k) {
/* Computing MAX */
                        d__3 = emax, d__4 = (d__1 = vr[k + (ki - 1) * vr_dim1]
                                , abs(d__1)) + (d__2 = vr[k + ki * vr_dim1], 
                                abs(d__2));
                        emax = max(d__3,d__4);
/* L120: */
                    }
                    remax = 1. / emax;
                    dscal_(n, &remax, &vr[(ki - 1) * vr_dim1 + 1], &c__1);
                    dscal_(n, &remax, &vr[ki * vr_dim1 + 1], &c__1);
                }
            }

            --is;
            if (ip != 0) {
                --is;
            }
L130:
            if (ip == 1) {
                ip = 0;
            }
            if (ip == -1) {
                ip = 1;
            }
/* L140: */
        }
    }

    if (leftv) {

/*        Compute left eigenvectors. */

        ip = 0;
        is = 1;
        i__1 = *n;
        for (ki = 1; ki <= i__1; ++ki) {

            if (ip == -1) {
                goto L250;
            }
            if (ki == *n) {
                goto L150;
            }
            if (t[ki + 1 + ki * t_dim1] == 0.) {
                goto L150;
            }
            ip = 1;

L150:
            if (somev) {
                if (! select[ki]) {
                    goto L250;
                }
            }

/*           Compute the KI-th eigenvalue (WR,WI). */

            wr = t[ki + ki * t_dim1];
            wi = 0.;
            if (ip != 0) {
                wi = sqrt((d__1 = t[ki + (ki + 1) * t_dim1], abs(d__1))) * 
                        sqrt((d__2 = t[ki + 1 + ki * t_dim1], abs(d__2)));
            }
/* Computing MAX */
            d__1 = ulp * (abs(wr) + abs(wi));
            smin = max(d__1,smlnum);

            if (ip == 0) {

/*              Real left eigenvector. */

                work[ki + *n] = 1.;

/*              Form right-hand side */

                i__2 = *n;
                for (k = ki + 1; k <= i__2; ++k) {
                    work[k + *n] = -t[ki + k * t_dim1];
/* L160: */
                }

/*              Solve the quasi-triangular system: */
/*                 (T(KI+1:N,KI+1:N) - WR)'*X = SCALE*WORK */

                vmax = 1.;
                vcrit = bignum;

                jnxt = ki + 1;
                i__2 = *n;
                for (j = ki + 1; j <= i__2; ++j) {
                    if (j < jnxt) {
                        goto L170;
                    }
                    j1 = j;
                    j2 = j;
                    jnxt = j + 1;
                    if (j < *n) {
                        if (t[j + 1 + j * t_dim1] != 0.) {
                            j2 = j + 1;
                            jnxt = j + 2;
                        }
                    }

                    if (j1 == j2) {

/*                    1-by-1 diagonal block */

/*                    Scale if necessary to avoid overflow when forming */
/*                    the right-hand side. */

                        if (work[j] > vcrit) {
                            rec = 1. / vmax;
                            i__3 = *n - ki + 1;
                            dscal_(&i__3, &rec, &work[ki + *n], &c__1);
                            vmax = 1.;
                            vcrit = bignum;
                        }

                        i__3 = j - ki - 1;
                        work[j + *n] -= ddot_(&i__3, &t[ki + 1 + j * t_dim1], 
                                &c__1, &work[ki + 1 + *n], &c__1);

/*                    Solve (T(J,J)-WR)'*X = WORK */

                        dlaln2_(&c_false, &c__1, &c__1, &smin, &c_b22, &t[j + 
                                j * t_dim1], ldt, &c_b22, &c_b22, &work[j + *
                                n], n, &wr, &c_b25, x, &c__2, &scale, &xnorm, 
                                &ierr);

/*                    Scale if necessary */

                        if (scale != 1.) {
                            i__3 = *n - ki + 1;
                            dscal_(&i__3, &scale, &work[ki + *n], &c__1);
                        }
                        work[j + *n] = x[0];
/* Computing MAX */
                        d__2 = (d__1 = work[j + *n], abs(d__1));
                        vmax = max(d__2,vmax);
                        vcrit = bignum / vmax;

                    } else {

/*                    2-by-2 diagonal block */

/*                    Scale if necessary to avoid overflow when forming */
/*                    the right-hand side. */

/* Computing MAX */
                        d__1 = work[j], d__2 = work[j + 1];
                        beta = max(d__1,d__2);
                        if (beta > vcrit) {
                            rec = 1. / vmax;
                            i__3 = *n - ki + 1;
                            dscal_(&i__3, &rec, &work[ki + *n], &c__1);
                            vmax = 1.;
                            vcrit = bignum;
                        }

                        i__3 = j - ki - 1;
                        work[j + *n] -= ddot_(&i__3, &t[ki + 1 + j * t_dim1], 
                                &c__1, &work[ki + 1 + *n], &c__1);

                        i__3 = j - ki - 1;
                        work[j + 1 + *n] -= ddot_(&i__3, &t[ki + 1 + (j + 1) *
                                 t_dim1], &c__1, &work[ki + 1 + *n], &c__1);

/*                    Solve */
/*                      [T(J,J)-WR   T(J,J+1)     ]'* X = SCALE*( WORK1 ) */
/*                      [T(J+1,J)    T(J+1,J+1)-WR]             ( WORK2 ) */

                        dlaln2_(&c_true, &c__2, &c__1, &smin, &c_b22, &t[j + 
                                j * t_dim1], ldt, &c_b22, &c_b22, &work[j + *
                                n], n, &wr, &c_b25, x, &c__2, &scale, &xnorm, 
                                &ierr);

/*                    Scale if necessary */

                        if (scale != 1.) {
                            i__3 = *n - ki + 1;
                            dscal_(&i__3, &scale, &work[ki + *n], &c__1);
                        }
                        work[j + *n] = x[0];
                        work[j + 1 + *n] = x[1];

/* Computing MAX */
                        d__3 = (d__1 = work[j + *n], abs(d__1)), d__4 = (d__2 
                                = work[j + 1 + *n], abs(d__2)), d__3 = max(
                                d__3,d__4);
                        vmax = max(d__3,vmax);
                        vcrit = bignum / vmax;

                    }
L170:
                    ;
                }

/*              Copy the vector x or Q*x to VL and normalize. */

                if (! over) {
                    i__2 = *n - ki + 1;
                    dcopy_(&i__2, &work[ki + *n], &c__1, &vl[ki + is * 
                            vl_dim1], &c__1);

                    i__2 = *n - ki + 1;
                    ii = idamax_(&i__2, &vl[ki + is * vl_dim1], &c__1) + ki - 
                            1;
                    remax = 1. / (d__1 = vl[ii + is * vl_dim1], abs(d__1));
                    i__2 = *n - ki + 1;
                    dscal_(&i__2, &remax, &vl[ki + is * vl_dim1], &c__1);

                    i__2 = ki - 1;
                    for (k = 1; k <= i__2; ++k) {
                        vl[k + is * vl_dim1] = 0.;
/* L180: */
                    }

                } else {

                    if (ki < *n) {
                        i__2 = *n - ki;
                        dgemv_("N", n, &i__2, &c_b22, &vl[(ki + 1) * vl_dim1 
                                + 1], ldvl, &work[ki + 1 + *n], &c__1, &work[
                                ki + *n], &vl[ki * vl_dim1 + 1], &c__1);
                    }

                    ii = idamax_(n, &vl[ki * vl_dim1 + 1], &c__1);
                    remax = 1. / (d__1 = vl[ii + ki * vl_dim1], abs(d__1));
                    dscal_(n, &remax, &vl[ki * vl_dim1 + 1], &c__1);

                }

            } else {

/*              Complex left eigenvector. */

/*               Initial solve: */
/*                 ((T(KI,KI)    T(KI,KI+1) )' - (WR - I* WI))*X = 0. */
/*                 ((T(KI+1,KI) T(KI+1,KI+1))                ) */

                if ((d__1 = t[ki + (ki + 1) * t_dim1], abs(d__1)) >= (d__2 = 
                        t[ki + 1 + ki * t_dim1], abs(d__2))) {
                    work[ki + *n] = wi / t[ki + (ki + 1) * t_dim1];
                    work[ki + 1 + n2] = 1.;
                } else {
                    work[ki + *n] = 1.;
                    work[ki + 1 + n2] = -wi / t[ki + 1 + ki * t_dim1];
                }
                work[ki + 1 + *n] = 0.;
                work[ki + n2] = 0.;

/*              Form right-hand side */

                i__2 = *n;
                for (k = ki + 2; k <= i__2; ++k) {
                    work[k + *n] = -work[ki + *n] * t[ki + k * t_dim1];
                    work[k + n2] = -work[ki + 1 + n2] * t[ki + 1 + k * t_dim1]
                            ;
/* L190: */
                }

/*              Solve complex quasi-triangular system: */
/*              ( T(KI+2,N:KI+2,N) - (WR-i*WI) )*X = WORK1+i*WORK2 */

                vmax = 1.;
                vcrit = bignum;

                jnxt = ki + 2;
                i__2 = *n;
                for (j = ki + 2; j <= i__2; ++j) {
                    if (j < jnxt) {
                        goto L200;
                    }
                    j1 = j;
                    j2 = j;
                    jnxt = j + 1;
                    if (j < *n) {
                        if (t[j + 1 + j * t_dim1] != 0.) {
                            j2 = j + 1;
                            jnxt = j + 2;
                        }
                    }

                    if (j1 == j2) {

/*                    1-by-1 diagonal block */

/*                    Scale if necessary to avoid overflow when */
/*                    forming the right-hand side elements. */

                        if (work[j] > vcrit) {
                            rec = 1. / vmax;
                            i__3 = *n - ki + 1;
                            dscal_(&i__3, &rec, &work[ki + *n], &c__1);
                            i__3 = *n - ki + 1;
                            dscal_(&i__3, &rec, &work[ki + n2], &c__1);
                            vmax = 1.;
                            vcrit = bignum;
                        }

                        i__3 = j - ki - 2;
                        work[j + *n] -= ddot_(&i__3, &t[ki + 2 + j * t_dim1], 
                                &c__1, &work[ki + 2 + *n], &c__1);
                        i__3 = j - ki - 2;
                        work[j + n2] -= ddot_(&i__3, &t[ki + 2 + j * t_dim1], 
                                &c__1, &work[ki + 2 + n2], &c__1);

/*                    Solve (T(J,J)-(WR-i*WI))*(X11+i*X12)= WK+I*WK2 */

                        d__1 = -wi;
                        dlaln2_(&c_false, &c__1, &c__2, &smin, &c_b22, &t[j + 
                                j * t_dim1], ldt, &c_b22, &c_b22, &work[j + *
                                n], n, &wr, &d__1, x, &c__2, &scale, &xnorm, &
                                ierr);

/*                    Scale if necessary */

                        if (scale != 1.) {
                            i__3 = *n - ki + 1;
                            dscal_(&i__3, &scale, &work[ki + *n], &c__1);
                            i__3 = *n - ki + 1;
                            dscal_(&i__3, &scale, &work[ki + n2], &c__1);
                        }
                        work[j + *n] = x[0];
                        work[j + n2] = x[2];
/* Computing MAX */
                        d__3 = (d__1 = work[j + *n], abs(d__1)), d__4 = (d__2 
                                = work[j + n2], abs(d__2)), d__3 = max(d__3,
                                d__4);
                        vmax = max(d__3,vmax);
                        vcrit = bignum / vmax;

                    } else {

/*                    2-by-2 diagonal block */

/*                    Scale if necessary to avoid overflow when forming */
/*                    the right-hand side elements. */

/* Computing MAX */
                        d__1 = work[j], d__2 = work[j + 1];
                        beta = max(d__1,d__2);
                        if (beta > vcrit) {
                            rec = 1. / vmax;
                            i__3 = *n - ki + 1;
                            dscal_(&i__3, &rec, &work[ki + *n], &c__1);
                            i__3 = *n - ki + 1;
                            dscal_(&i__3, &rec, &work[ki + n2], &c__1);
                            vmax = 1.;
                            vcrit = bignum;
                        }

                        i__3 = j - ki - 2;
                        work[j + *n] -= ddot_(&i__3, &t[ki + 2 + j * t_dim1], 
                                &c__1, &work[ki + 2 + *n], &c__1);

                        i__3 = j - ki - 2;
                        work[j + n2] -= ddot_(&i__3, &t[ki + 2 + j * t_dim1], 
                                &c__1, &work[ki + 2 + n2], &c__1);

                        i__3 = j - ki - 2;
                        work[j + 1 + *n] -= ddot_(&i__3, &t[ki + 2 + (j + 1) *
                                 t_dim1], &c__1, &work[ki + 2 + *n], &c__1);

                        i__3 = j - ki - 2;
                        work[j + 1 + n2] -= ddot_(&i__3, &t[ki + 2 + (j + 1) *
                                 t_dim1], &c__1, &work[ki + 2 + n2], &c__1);

/*                    Solve 2-by-2 complex linear equation */
/*                      ([T(j,j)   T(j,j+1)  ]'-(wr-i*wi)*I)*X = SCALE*B */
/*                      ([T(j+1,j) T(j+1,j+1)]             ) */

                        d__1 = -wi;
                        dlaln2_(&c_true, &c__2, &c__2, &smin, &c_b22, &t[j + 
                                j * t_dim1], ldt, &c_b22, &c_b22, &work[j + *
                                n], n, &wr, &d__1, x, &c__2, &scale, &xnorm, &
                                ierr);

/*                    Scale if necessary */

                        if (scale != 1.) {
                            i__3 = *n - ki + 1;
                            dscal_(&i__3, &scale, &work[ki + *n], &c__1);
                            i__3 = *n - ki + 1;
                            dscal_(&i__3, &scale, &work[ki + n2], &c__1);
                        }
                        work[j + *n] = x[0];
                        work[j + n2] = x[2];
                        work[j + 1 + *n] = x[1];
                        work[j + 1 + n2] = x[3];
/* Computing MAX */
                        d__1 = abs(x[0]), d__2 = abs(x[2]), d__1 = max(d__1,
                                d__2), d__2 = abs(x[1]), d__1 = max(d__1,d__2)
                                , d__2 = abs(x[3]), d__1 = max(d__1,d__2);
                        vmax = max(d__1,vmax);
                        vcrit = bignum / vmax;

                    }
L200:
                    ;
                }

/*              Copy the vector x or Q*x to VL and normalize. */

                if (! over) {
                    i__2 = *n - ki + 1;
                    dcopy_(&i__2, &work[ki + *n], &c__1, &vl[ki + is * 
                            vl_dim1], &c__1);
                    i__2 = *n - ki + 1;
                    dcopy_(&i__2, &work[ki + n2], &c__1, &vl[ki + (is + 1) * 
                            vl_dim1], &c__1);

                    emax = 0.;
                    i__2 = *n;
                    for (k = ki; k <= i__2; ++k) {
/* Computing MAX */
                        d__3 = emax, d__4 = (d__1 = vl[k + is * vl_dim1], abs(
                                d__1)) + (d__2 = vl[k + (is + 1) * vl_dim1], 
                                abs(d__2));
                        emax = max(d__3,d__4);
/* L220: */
                    }
                    remax = 1. / emax;
                    i__2 = *n - ki + 1;
                    dscal_(&i__2, &remax, &vl[ki + is * vl_dim1], &c__1);
                    i__2 = *n - ki + 1;
                    dscal_(&i__2, &remax, &vl[ki + (is + 1) * vl_dim1], &c__1)
                            ;

                    i__2 = ki - 1;
                    for (k = 1; k <= i__2; ++k) {
                        vl[k + is * vl_dim1] = 0.;
                        vl[k + (is + 1) * vl_dim1] = 0.;
/* L230: */
                    }
                } else {
                    if (ki < *n - 1) {
                        i__2 = *n - ki - 1;
                        dgemv_("N", n, &i__2, &c_b22, &vl[(ki + 2) * vl_dim1 
                                + 1], ldvl, &work[ki + 2 + *n], &c__1, &work[
                                ki + *n], &vl[ki * vl_dim1 + 1], &c__1);
                        i__2 = *n - ki - 1;
                        dgemv_("N", n, &i__2, &c_b22, &vl[(ki + 2) * vl_dim1 
                                + 1], ldvl, &work[ki + 2 + n2], &c__1, &work[
                                ki + 1 + n2], &vl[(ki + 1) * vl_dim1 + 1], &
                                c__1);
                    } else {
                        dscal_(n, &work[ki + *n], &vl[ki * vl_dim1 + 1], &
                                c__1);
                        dscal_(n, &work[ki + 1 + n2], &vl[(ki + 1) * vl_dim1 
                                + 1], &c__1);
                    }

                    emax = 0.;
                    i__2 = *n;
                    for (k = 1; k <= i__2; ++k) {
/* Computing MAX */
                        d__3 = emax, d__4 = (d__1 = vl[k + ki * vl_dim1], abs(
                                d__1)) + (d__2 = vl[k + (ki + 1) * vl_dim1], 
                                abs(d__2));
                        emax = max(d__3,d__4);
/* L240: */
                    }
                    remax = 1. / emax;
                    dscal_(n, &remax, &vl[ki * vl_dim1 + 1], &c__1);
                    dscal_(n, &remax, &vl[(ki + 1) * vl_dim1 + 1], &c__1);

                }

            }

            ++is;
            if (ip != 0) {
                ++is;
            }
L250:
            if (ip == -1) {
                ip = 0;
            }
            if (ip == 1) {
                ip = -1;
            }

/* L260: */
        }

    }

    return 0;

/*     End of DTREVC */

} /* dtrevc_ */