コード例 #1
0
ファイル: dget31.c プロジェクト: TakuroNegishi/PDRTAM
/* Subroutine */ int dget31_(doublereal *rmax, integer *lmax, integer *ninfo,
                             integer *knt)
{
    /* Initialized data */

    static logical ltrans[2] = { FALSE_,TRUE_ };

    /* System generated locals */
    doublereal d__1, d__2, d__3, d__4, d__5, d__6, d__7, d__8, d__9, d__10,
               d__11, d__12, d__13;

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

    /* Local variables */
    doublereal a[4]	/* was [2][2] */, b[4]	/* was [2][2] */, x[4]	/*
	    was [2][2] */, d1, d2, ca;
    integer ia, ib, na;
    doublereal wi;
    integer nw;
    doublereal wr;
    integer id1, id2, ica;
    doublereal den, vab[3], vca[5], vdd[4], eps;
    integer iwi;
    doublereal res, tmp;
    integer iwr;
    doublereal vwi[4], vwr[4];
    integer info;
    doublereal unfl, smin, scale;
    integer ismin;
    doublereal vsmin[4], 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 *);
    doublereal bignum;
    integer itrans;
    doublereal smlnum;


    /*  -- LAPACK test routine (version 3.1) -- */
    /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
    /*     November 2006 */

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

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

    /*  DGET31 tests DLALN2, a routine for solving */

    /*     (ca A - w D)X = sB */

    /*  where A is an NA by NA matrix (NA=1 or 2 only), w is a real (NW=1) or */
    /*  complex (NW=2) constant, ca is a real constant, D is an NA by NA real */
    /*  diagonal matrix, and B is an NA by NW matrix (when NW=2 the second */
    /*  column of B contains the imaginary part of the solution).  The code */
    /*  returns X and s, where s is a scale factor, less than or equal to 1, */
    /*  which is chosen to avoid overflow in X. */

    /*  If any singular values of ca A-w D are less than another input */
    /*  parameter SMIN, they are perturbed up to SMIN. */

    /*  The test condition is that the scaled residual */

    /*      norm( (ca A-w D)*X - s*B ) / */
    /*            ( max( ulp*norm(ca A-w D), SMIN )*norm(X) ) */

    /*  should be on the order of 1.  Here, ulp is the machine precision. */
    /*  Also, it is verified that SCALE is less than or equal to 1, and that */
    /*  XNORM = infinity-norm(X). */

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

    /*  RMAX    (output) DOUBLE PRECISION */
    /*          Value of the largest test ratio. */

    /*  LMAX    (output) INTEGER */
    /*          Example number where largest test ratio achieved. */

    /*  NINFO   (output) INTEGER array, dimension (3) */
    /*          NINFO(1) = number of examples with INFO less than 0 */
    /*          NINFO(2) = number of examples with INFO greater than 0 */

    /*  KNT     (output) INTEGER */
    /*          Total number of examples tested. */

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

    /*     .. Parameters .. */
    /*     .. */
    /*     .. Local Scalars .. */
    /*     .. */
    /*     .. Local Arrays .. */
    /*     .. */
    /*     .. External Functions .. */
    /*     .. */
    /*     .. External Subroutines .. */
    /*     .. */
    /*     .. Intrinsic Functions .. */
    /*     .. */
    /*     .. Data statements .. */
    /* Parameter adjustments */
    --ninfo;

    /* Function Body */
    /*     .. */
    /*     .. Executable Statements .. */

    /*     Get machine parameters */

    eps = dlamch_("P");
    unfl = dlamch_("U");
    smlnum = dlamch_("S") / eps;
    bignum = 1. / smlnum;
    dlabad_(&smlnum, &bignum);

    /*     Set up test case parameters */

    vsmin[0] = smlnum;
    vsmin[1] = eps;
    vsmin[2] = .01;
    vsmin[3] = 1. / eps;
    vab[0] = sqrt(smlnum);
    vab[1] = 1.;
    vab[2] = sqrt(bignum);
    vwr[0] = 0.;
    vwr[1] = .5;
    vwr[2] = 2.;
    vwr[3] = 1.;
    vwi[0] = smlnum;
    vwi[1] = eps;
    vwi[2] = 1.;
    vwi[3] = 2.;
    vdd[0] = sqrt(smlnum);
    vdd[1] = 1.;
    vdd[2] = 2.;
    vdd[3] = sqrt(bignum);
    vca[0] = 0.;
    vca[1] = sqrt(smlnum);
    vca[2] = eps;
    vca[3] = .5;
    vca[4] = 1.;

    *knt = 0;
    ninfo[1] = 0;
    ninfo[2] = 0;
    *lmax = 0;
    *rmax = 0.;

    /*     Begin test loop */

    for (id1 = 1; id1 <= 4; ++id1) {
        d1 = vdd[id1 - 1];
        for (id2 = 1; id2 <= 4; ++id2) {
            d2 = vdd[id2 - 1];
            for (ica = 1; ica <= 5; ++ica) {
                ca = vca[ica - 1];
                for (itrans = 0; itrans <= 1; ++itrans) {
                    for (ismin = 1; ismin <= 4; ++ismin) {
                        smin = vsmin[ismin - 1];

                        na = 1;
                        nw = 1;
                        for (ia = 1; ia <= 3; ++ia) {
                            a[0] = vab[ia - 1];
                            for (ib = 1; ib <= 3; ++ib) {
                                b[0] = vab[ib - 1];
                                for (iwr = 1; iwr <= 4; ++iwr) {
                                    if (d1 == 1. && d2 == 1. && ca == 1.) {
                                        wr = vwr[iwr - 1] * a[0];
                                    } else {
                                        wr = vwr[iwr - 1];
                                    }
                                    wi = 0.;
                                    dlaln2_(&ltrans[itrans], &na, &nw, &smin,
                                            &ca, a, &c__2, &d1, &d2, b, &c__2,
                                            &wr, &wi, x, &c__2, &scale, &
                                            xnorm, &info);
                                    if (info < 0) {
                                        ++ninfo[1];
                                    }
                                    if (info > 0) {
                                        ++ninfo[2];
                                    }
                                    res = (d__1 = (ca * a[0] - wr * d1) * x[0]
                                                  - scale * b[0], abs(d__1));
                                    if (info == 0) {
                                        /* Computing MAX */
                                        d__2 = eps * (d__1 = (ca * a[0] - wr *
                                                              d1) * x[0], abs(d__1));
                                        den = max(d__2,smlnum);
                                    } else {
                                        /* Computing MAX */
                                        d__1 = smin * abs(x[0]);
                                        den = max(d__1,smlnum);
                                    }
                                    res /= den;
                                    if (abs(x[0]) < unfl && abs(b[0]) <=
                                            smlnum * (d__1 = ca * a[0] - wr *
                                                             d1, abs(d__1))) {
                                        res = 0.;
                                    }
                                    if (scale > 1.) {
                                        res += 1. / eps;
                                    }
                                    res += (d__1 = xnorm - abs(x[0]), abs(
                                                d__1)) / max(smlnum,xnorm) / eps;
                                    if (info != 0 && info != 1) {
                                        res += 1. / eps;
                                    }
                                    ++(*knt);
                                    if (res > *rmax) {
                                        *lmax = *knt;
                                        *rmax = res;
                                    }
                                    /* L10: */
                                }
                                /* L20: */
                            }
                            /* L30: */
                        }

                        na = 1;
                        nw = 2;
                        for (ia = 1; ia <= 3; ++ia) {
                            a[0] = vab[ia - 1];
                            for (ib = 1; ib <= 3; ++ib) {
                                b[0] = vab[ib - 1];
                                b[2] = vab[ib - 1] * -.5;
                                for (iwr = 1; iwr <= 4; ++iwr) {
                                    if (d1 == 1. && d2 == 1. && ca == 1.) {
                                        wr = vwr[iwr - 1] * a[0];
                                    } else {
                                        wr = vwr[iwr - 1];
                                    }
                                    for (iwi = 1; iwi <= 4; ++iwi) {
                                        if (d1 == 1. && d2 == 1. && ca == 1.)
                                        {
                                            wi = vwi[iwi - 1] * a[0];
                                        } else {
                                            wi = vwi[iwi - 1];
                                        }
                                        dlaln2_(&ltrans[itrans], &na, &nw, &
                                                smin, &ca, a, &c__2, &d1, &d2,
                                                b, &c__2, &wr, &wi, x, &c__2,
                                                &scale, &xnorm, &info);
                                        if (info < 0) {
                                            ++ninfo[1];
                                        }
                                        if (info > 0) {
                                            ++ninfo[2];
                                        }
                                        res = (d__1 = (ca * a[0] - wr * d1) *
                                                      x[0] + wi * d1 * x[2] - scale
                                                      * b[0], abs(d__1));
                                        res += (d__1 = -wi * d1 * x[0] + (ca *
                                                                          a[0] - wr * d1) * x[2] -
                                                       scale * b[2], abs(d__1));
                                        if (info == 0) {
                                            /* Computing MAX */
                                            /* Computing MAX */
                                            d__4 = (d__1 = ca * a[0] - wr *
                                                           d1, abs(d__1)), d__5 = (
                                                                   d__2 = d1 * wi, abs(d__2))
                                                                                  ;
                                            d__3 = eps * (max(d__4,d__5) * (
                                                              abs(x[0]) + abs(x[2])));
                                            den = max(d__3,smlnum);
                                        } else {
                                            /* Computing MAX */
                                            d__1 = smin * (abs(x[0]) + abs(x[
                                                                               2]));
                                            den = max(d__1,smlnum);
                                        }
                                        res /= den;
                                        if (abs(x[0]) < unfl && abs(x[2]) <
                                                unfl && abs(b[0]) <= smlnum *
                                                (d__1 = ca * a[0] - wr * d1,
                                                 abs(d__1))) {
                                            res = 0.;
                                        }
                                        if (scale > 1.) {
                                            res += 1. / eps;
                                        }
                                        res += (d__1 = xnorm - abs(x[0]) -
                                                       abs(x[2]), abs(d__1)) / max(
                                                   smlnum,xnorm) / eps;
                                        if (info != 0 && info != 1) {
                                            res += 1. / eps;
                                        }
                                        ++(*knt);
                                        if (res > *rmax) {
                                            *lmax = *knt;
                                            *rmax = res;
                                        }
                                        /* L40: */
                                    }
                                    /* L50: */
                                }
                                /* L60: */
                            }
                            /* L70: */
                        }

                        na = 2;
                        nw = 1;
                        for (ia = 1; ia <= 3; ++ia) {
                            a[0] = vab[ia - 1];
                            a[2] = vab[ia - 1] * -3.;
                            a[1] = vab[ia - 1] * -7.;
                            a[3] = vab[ia - 1] * 21.;
                            for (ib = 1; ib <= 3; ++ib) {
                                b[0] = vab[ib - 1];
                                b[1] = vab[ib - 1] * -2.;
                                for (iwr = 1; iwr <= 4; ++iwr) {
                                    if (d1 == 1. && d2 == 1. && ca == 1.) {
                                        wr = vwr[iwr - 1] * a[0];
                                    } else {
                                        wr = vwr[iwr - 1];
                                    }
                                    wi = 0.;
                                    dlaln2_(&ltrans[itrans], &na, &nw, &smin,
                                            &ca, a, &c__2, &d1, &d2, b, &c__2,
                                            &wr, &wi, x, &c__2, &scale, &
                                            xnorm, &info);
                                    if (info < 0) {
                                        ++ninfo[1];
                                    }
                                    if (info > 0) {
                                        ++ninfo[2];
                                    }
                                    if (itrans == 1) {
                                        tmp = a[2];
                                        a[2] = a[1];
                                        a[1] = tmp;
                                    }
                                    res = (d__1 = (ca * a[0] - wr * d1) * x[0]
                                                  + ca * a[2] * x[1] - scale * b[0]
                                                  , abs(d__1));
                                    res += (d__1 = ca * a[1] * x[0] + (ca * a[
                                                                           3] - wr * d2) * x[1] - scale * b[
                                                       1], abs(d__1));
                                    if (info == 0) {
                                        /* Computing MAX */
                                        /* Computing MAX */
                                        d__6 = (d__1 = ca * a[0] - wr * d1,
                                                abs(d__1)) + (d__2 = ca * a[2]
                                                                     , abs(d__2)), d__7 = (d__3 =
                                                                             ca * a[1], abs(d__3)) + (d__4
                                                                                     = ca * a[3] - wr * d2, abs(
                                                                                             d__4));
                                        /* Computing MAX */
                                        d__8 = abs(x[0]), d__9 = abs(x[1]);
                                        d__5 = eps * (max(d__6,d__7) * max(
                                                          d__8,d__9));
                                        den = max(d__5,smlnum);
                                    } else {
                                        /* Computing MAX */
                                        /* Computing MAX */
                                        /* Computing MAX */
                                        d__8 = (d__1 = ca * a[0] - wr * d1,
                                                abs(d__1)) + (d__2 = ca * a[2]
                                                                     , abs(d__2)), d__9 = (d__3 =
                                                                             ca * a[1], abs(d__3)) + (d__4
                                                                                     = ca * a[3] - wr * d2, abs(
                                                                                             d__4));
                                        d__6 = smin / eps, d__7 = max(d__8,
                                                                      d__9);
                                        /* Computing MAX */
                                        d__10 = abs(x[0]), d__11 = abs(x[1]);
                                        d__5 = eps * (max(d__6,d__7) * max(
                                                          d__10,d__11));
                                        den = max(d__5,smlnum);
                                    }
                                    res /= den;
                                    if (abs(x[0]) < unfl && abs(x[1]) < unfl
                                            && abs(b[0]) + abs(b[1]) <=
                                            smlnum * ((d__1 = ca * a[0] - wr *
                                                              d1, abs(d__1)) + (d__2 = ca * a[
                                                                          2], abs(d__2)) + (d__3 = ca * a[1]
                                                                                  , abs(d__3)) + (d__4 = ca * a[3]
                                                                                          - wr * d2, abs(d__4)))) {
                                        res = 0.;
                                    }
                                    if (scale > 1.) {
                                        res += 1. / eps;
                                    }
                                    /* Computing MAX */
                                    d__2 = abs(x[0]), d__3 = abs(x[1]);
                                    res += (d__1 = xnorm - max(d__2,d__3),
                                            abs(d__1)) / max(smlnum,xnorm) /
                                           eps;
                                    if (info != 0 && info != 1) {
                                        res += 1. / eps;
                                    }
                                    ++(*knt);
                                    if (res > *rmax) {
                                        *lmax = *knt;
                                        *rmax = res;
                                    }
                                    /* L80: */
                                }
                                /* L90: */
                            }
                            /* L100: */
                        }

                        na = 2;
                        nw = 2;
                        for (ia = 1; ia <= 3; ++ia) {
                            a[0] = vab[ia - 1] * 2.;
                            a[2] = vab[ia - 1] * -3.;
                            a[1] = vab[ia - 1] * -7.;
                            a[3] = vab[ia - 1] * 21.;
                            for (ib = 1; ib <= 3; ++ib) {
                                b[0] = vab[ib - 1];
                                b[1] = vab[ib - 1] * -2.;
                                b[2] = vab[ib - 1] * 4.;
                                b[3] = vab[ib - 1] * -7.;
                                for (iwr = 1; iwr <= 4; ++iwr) {
                                    if (d1 == 1. && d2 == 1. && ca == 1.) {
                                        wr = vwr[iwr - 1] * a[0];
                                    } else {
                                        wr = vwr[iwr - 1];
                                    }
                                    for (iwi = 1; iwi <= 4; ++iwi) {
                                        if (d1 == 1. && d2 == 1. && ca == 1.)
                                        {
                                            wi = vwi[iwi - 1] * a[0];
                                        } else {
                                            wi = vwi[iwi - 1];
                                        }
                                        dlaln2_(&ltrans[itrans], &na, &nw, &
                                                smin, &ca, a, &c__2, &d1, &d2,
                                                b, &c__2, &wr, &wi, x, &c__2,
                                                &scale, &xnorm, &info);
                                        if (info < 0) {
                                            ++ninfo[1];
                                        }
                                        if (info > 0) {
                                            ++ninfo[2];
                                        }
                                        if (itrans == 1) {
                                            tmp = a[2];
                                            a[2] = a[1];
                                            a[1] = tmp;
                                        }
                                        res = (d__1 = (ca * a[0] - wr * d1) *
                                                      x[0] + ca * a[2] * x[1] + wi *
                                                      d1 * x[2] - scale * b[0],
                                               abs(d__1));
                                        res += (d__1 = (ca * a[0] - wr * d1) *
                                                       x[2] + ca * a[2] * x[3] - wi
                                                       * d1 * x[0] - scale * b[2],
                                                abs(d__1));
                                        res += (d__1 = ca * a[1] * x[0] + (ca
                                                                           * a[3] - wr * d2) * x[1] + wi
                                                       * d2 * x[3] - scale * b[1],
                                                abs(d__1));
                                        res += (d__1 = ca * a[1] * x[2] + (ca
                                                                           * a[3] - wr * d2) * x[3] - wi
                                                       * d2 * x[1] - scale * b[3],
                                                abs(d__1));
                                        if (info == 0) {
                                            /* Computing MAX */
                                            /* Computing MAX */
                                            d__8 = (d__1 = ca * a[0] - wr *
                                                           d1, abs(d__1)) + (d__2 =
                                                                                 ca * a[2], abs(d__2)) + (
                                                       d__3 = wi * d1, abs(d__3))
                                                   , d__9 = (d__4 = ca * a[1]
                                                                    , abs(d__4)) + (d__5 = ca
                                                                                    * a[3] - wr * d2, abs(
                                                                                            d__5)) + (d__6 = wi * d2,
                                                                                                    abs(d__6));
                                            /* Computing MAX */
                                            d__10 = abs(x[0]) + abs(x[1]),
                                            d__11 = abs(x[2]) + abs(x[
                                                                        3]);
                                            d__7 = eps * (max(d__8,d__9) *
                                                          max(d__10,d__11));
                                            den = max(d__7,smlnum);
                                        } else {
                                            /* Computing MAX */
                                            /* Computing MAX */
                                            /* Computing MAX */
                                            d__10 = (d__1 = ca * a[0] - wr *
                                                            d1, abs(d__1)) + (d__2 =
                                                                                  ca * a[2], abs(d__2)) + (
                                                        d__3 = wi * d1, abs(d__3))
                                                    , d__11 = (d__4 = ca * a[
                                                                          1], abs(d__4)) + (d__5 =
                                                                                  ca * a[3] - wr * d2, abs(
                                                                                          d__5)) + (d__6 = wi * d2,
                                                                                                  abs(d__6));
                                            d__8 = smin / eps, d__9 = max(
                                                                          d__10,d__11);
                                            /* Computing MAX */
                                            d__12 = abs(x[0]) + abs(x[1]),
                                            d__13 = abs(x[2]) + abs(x[
                                                                        3]);
                                            d__7 = eps * (max(d__8,d__9) *
                                                          max(d__12,d__13));
                                            den = max(d__7,smlnum);
                                        }
                                        res /= den;
                                        if (abs(x[0]) < unfl && abs(x[1]) <
                                                unfl && abs(x[2]) < unfl &&
                                                abs(x[3]) < unfl && abs(b[0])
                                                + abs(b[1]) <= smlnum * ((
                                                                             d__1 = ca * a[0] - wr * d1,
                                                                             abs(d__1)) + (d__2 = ca * a[2]
                                                                                     , abs(d__2)) + (d__3 = ca * a[
                                                                                             1], abs(d__3)) + (d__4 = ca *
                                                                                                     a[3] - wr * d2, abs(d__4)) + (
                                                                             d__5 = wi * d2, abs(d__5)) + (
                                                                             d__6 = wi * d1, abs(d__6)))) {
                                            res = 0.;
                                        }
                                        if (scale > 1.) {
                                            res += 1. / eps;
                                        }
                                        /* Computing MAX */
                                        d__2 = abs(x[0]) + abs(x[2]), d__3 =
                                                   abs(x[1]) + abs(x[3]);
                                        res += (d__1 = xnorm - max(d__2,d__3),
                                                abs(d__1)) / max(smlnum,
                                                                 xnorm) / eps;
                                        if (info != 0 && info != 1) {
                                            res += 1. / eps;
                                        }
                                        ++(*knt);
                                        if (res > *rmax) {
                                            *lmax = *knt;
                                            *rmax = res;
                                        }
                                        /* L110: */
                                    }
                                    /* L120: */
                                }
                                /* L130: */
                            }
                            /* L140: */
                        }
                        /* L150: */
                    }
                    /* L160: */
                }
                /* L170: */
            }
            /* L180: */
        }
        /* L190: */
    }

    return 0;

    /*     End of DGET31 */

} /* dget31_ */
コード例 #2
0
ファイル: dlaqtr.c プロジェクト: Ayato-Harashima/Bundler
/* Subroutine */ int dlaqtr_(logical *ltran, logical *lreal, integer *n, 
	doublereal *t, integer *ldt, doublereal *b, doublereal *w, doublereal 
	*scale, doublereal *x, doublereal *work, integer *info)
{
    /* System generated locals */
    integer t_dim1, t_offset, i__1, i__2;
    doublereal d__1, d__2, d__3, d__4, d__5, d__6;

    /* Local variables */
    doublereal d__[4]	/* was [2][2] */;
    integer i__, j, k;
    doublereal v[4]	/* was [2][2] */, z__;
    integer j1, j2, n1, n2;
    doublereal si, xj, sr, rec, eps, tjj, tmp;
    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, 
	    integer *);
    integer ierr;
    doublereal smin, xmax;
    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, 
	    integer *);
    extern doublereal dasum_(integer *, doublereal *, integer *);
    extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, 
	    integer *, doublereal *, integer *);
    integer jnext;
    doublereal sminw, xnorm;
    extern /* Subroutine */ int dlaln2_(logical *, integer *, integer *, 
	    doublereal *, doublereal *, doublereal *, integer *, doublereal *, 
	     doublereal *, doublereal *, integer *, doublereal *, doublereal *
, doublereal *, integer *, doublereal *, doublereal *, integer *);
    extern doublereal dlamch_(char *), dlange_(char *, integer *, 
	    integer *, doublereal *, integer *, doublereal *);
    extern integer idamax_(integer *, doublereal *, integer *);
    doublereal scaloc;
    extern /* Subroutine */ int dladiv_(doublereal *, doublereal *, 
	    doublereal *, doublereal *, doublereal *, doublereal *);
    doublereal bignum;
    logical notran;
    doublereal smlnum;


/*  -- LAPACK auxiliary routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*  DLAQTR solves the real quasi-triangular system */

/*               op(T)*p = scale*c,               if LREAL = .TRUE. */

/*  or the complex quasi-triangular systems */

/*             op(T + iB)*(p+iq) = scale*(c+id),  if LREAL = .FALSE. */

/*  in real arithmetic, where T is upper quasi-triangular. */
/*  If LREAL = .FALSE., then the first diagonal block of T must be */
/*  1 by 1, B is the specially structured matrix */

/*                 B = [ b(1) b(2) ... b(n) ] */
/*                     [       w            ] */
/*                     [           w        ] */
/*                     [              .     ] */
/*                     [                 w  ] */

/*  op(A) = A or A', A' denotes the conjugate transpose of */
/*  matrix A. */

/*  On input, X = [ c ].  On output, X = [ p ]. */
/*                [ d ]                  [ q ] */

/*  This subroutine is designed for the condition number estimation */
/*  in routine DTRSNA. */

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

/*  LTRAN   (input) LOGICAL */
/*          On entry, LTRAN specifies the option of conjugate transpose: */
/*             = .FALSE.,    op(T+i*B) = T+i*B, */
/*             = .TRUE.,     op(T+i*B) = (T+i*B)'. */

/*  LREAL   (input) LOGICAL */
/*          On entry, LREAL specifies the input matrix structure: */
/*             = .FALSE.,    the input is complex */
/*             = .TRUE.,     the input is real */

/*  N       (input) INTEGER */
/*          On entry, N specifies the order of T+i*B. N >= 0. */

/*  T       (input) DOUBLE PRECISION array, dimension (LDT,N) */
/*          On entry, T contains a matrix in Schur canonical form. */
/*          If LREAL = .FALSE., then the first diagonal block of T mu */
/*          be 1 by 1. */

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

/*  B       (input) DOUBLE PRECISION array, dimension (N) */
/*          On entry, B contains the elements to form the matrix */
/*          B as described above. */
/*          If LREAL = .TRUE., B is not referenced. */

/*  W       (input) DOUBLE PRECISION */
/*          On entry, W is the diagonal element of the matrix B. */
/*          If LREAL = .TRUE., W is not referenced. */

/*  SCALE   (output) DOUBLE PRECISION */
/*          On exit, SCALE is the scale factor. */

/*  X       (input/output) DOUBLE PRECISION array, dimension (2*N) */
/*          On entry, X contains the right hand side of the system. */
/*          On exit, X is overwritten by the solution. */

/*  WORK    (workspace) DOUBLE PRECISION array, dimension (N) */

/*  INFO    (output) INTEGER */
/*          On exit, INFO is set to */
/*             0: successful exit. */
/*               1: the some diagonal 1 by 1 block has been perturbed by */
/*                  a small number SMIN to keep nonsingularity. */
/*               2: the some diagonal 2 by 2 block has been perturbed by */
/*                  a small number in DLALN2 to keep nonsingularity. */
/*          NOTE: In the interests of speed, this routine does not */
/*                check the inputs for errors. */

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

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

/*     Do not test the input parameters for errors */

    /* Parameter adjustments */
    t_dim1 = *ldt;
    t_offset = 1 + t_dim1;
    t -= t_offset;
    --b;
    --x;
    --work;

    /* Function Body */
    notran = ! (*ltran);
    *info = 0;

/*     Quick return if possible */

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

/*     Set constants to control overflow */

    eps = dlamch_("P");
    smlnum = dlamch_("S") / eps;
    bignum = 1. / smlnum;

    xnorm = dlange_("M", n, n, &t[t_offset], ldt, d__);
    if (! (*lreal)) {
/* Computing MAX */
	d__1 = xnorm, d__2 = abs(*w), d__1 = max(d__1,d__2), d__2 = dlange_(
		"M", n, &c__1, &b[1], n, d__);
	xnorm = max(d__1,d__2);
    }
/* Computing MAX */
    d__1 = smlnum, d__2 = eps * xnorm;
    smin = max(d__1,d__2);

/*     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) {
	i__2 = j - 1;
	work[j] = dasum_(&i__2, &t[j * t_dim1 + 1], &c__1);
/* L10: */
    }

    if (! (*lreal)) {
	i__1 = *n;
	for (i__ = 2; i__ <= i__1; ++i__) {
	    work[i__] += (d__1 = b[i__], abs(d__1));
/* L20: */
	}
    }

    n2 = *n << 1;
    n1 = *n;
    if (! (*lreal)) {
	n1 = n2;
    }
    k = idamax_(&n1, &x[1], &c__1);
    xmax = (d__1 = x[k], abs(d__1));
    *scale = 1.;

    if (xmax > bignum) {
	*scale = bignum / xmax;
	dscal_(&n1, scale, &x[1], &c__1);
	xmax = bignum;
    }

    if (*lreal) {

	if (notran) {

/*           Solve T*p = scale*c */

	    jnext = *n;
	    for (j = *n; j >= 1; --j) {
		if (j > jnext) {
		    goto L30;
		}
		j1 = j;
		j2 = j;
		jnext = j - 1;
		if (j > 1) {
		    if (t[j + (j - 1) * t_dim1] != 0.) {
			j1 = j - 1;
			jnext = j - 2;
		    }
		}

		if (j1 == j2) {

/*                 Meet 1 by 1 diagonal block */

/*                 Scale to avoid overflow when computing */
/*                     x(j) = b(j)/T(j,j) */

		    xj = (d__1 = x[j1], abs(d__1));
		    tjj = (d__1 = t[j1 + j1 * t_dim1], abs(d__1));
		    tmp = t[j1 + j1 * t_dim1];
		    if (tjj < smin) {
			tmp = smin;
			tjj = smin;
			*info = 1;
		    }

		    if (xj == 0.) {
			goto L30;
		    }

		    if (tjj < 1.) {
			if (xj > bignum * tjj) {
			    rec = 1. / xj;
			    dscal_(n, &rec, &x[1], &c__1);
			    *scale *= rec;
			    xmax *= rec;
			}
		    }
		    x[j1] /= tmp;
		    xj = (d__1 = x[j1], abs(d__1));

/*                 Scale x if necessary to avoid overflow when adding a */
/*                 multiple of column j1 of T. */

		    if (xj > 1.) {
			rec = 1. / xj;
			if (work[j1] > (bignum - xmax) * rec) {
			    dscal_(n, &rec, &x[1], &c__1);
			    *scale *= rec;
			}
		    }
		    if (j1 > 1) {
			i__1 = j1 - 1;
			d__1 = -x[j1];
			daxpy_(&i__1, &d__1, &t[j1 * t_dim1 + 1], &c__1, &x[1]
, &c__1);
			i__1 = j1 - 1;
			k = idamax_(&i__1, &x[1], &c__1);
			xmax = (d__1 = x[k], abs(d__1));
		    }

		} else {

/*                 Meet 2 by 2 diagonal block */

/*                 Call 2 by 2 linear system solve, to take */
/*                 care of possible overflow by scaling factor. */

		    d__[0] = x[j1];
		    d__[1] = x[j2];
		    dlaln2_(&c_false, &c__2, &c__1, &smin, &c_b21, &t[j1 + j1 
			    * t_dim1], ldt, &c_b21, &c_b21, d__, &c__2, &
			    c_b25, &c_b25, v, &c__2, &scaloc, &xnorm, &ierr);
		    if (ierr != 0) {
			*info = 2;
		    }

		    if (scaloc != 1.) {
			dscal_(n, &scaloc, &x[1], &c__1);
			*scale *= scaloc;
		    }
		    x[j1] = v[0];
		    x[j2] = v[1];

/*                 Scale V(1,1) (= X(J1)) and/or V(2,1) (=X(J2)) */
/*                 to avoid overflow in updating right-hand side. */

/* Computing MAX */
		    d__1 = abs(v[0]), d__2 = abs(v[1]);
		    xj = max(d__1,d__2);
		    if (xj > 1.) {
			rec = 1. / xj;
/* Computing MAX */
			d__1 = work[j1], d__2 = work[j2];
			if (max(d__1,d__2) > (bignum - xmax) * rec) {
			    dscal_(n, &rec, &x[1], &c__1);
			    *scale *= rec;
			}
		    }

/*                 Update right-hand side */

		    if (j1 > 1) {
			i__1 = j1 - 1;
			d__1 = -x[j1];
			daxpy_(&i__1, &d__1, &t[j1 * t_dim1 + 1], &c__1, &x[1]
, &c__1);
			i__1 = j1 - 1;
			d__1 = -x[j2];
			daxpy_(&i__1, &d__1, &t[j2 * t_dim1 + 1], &c__1, &x[1]
, &c__1);
			i__1 = j1 - 1;
			k = idamax_(&i__1, &x[1], &c__1);
			xmax = (d__1 = x[k], abs(d__1));
		    }

		}

L30:
		;
	    }

	} else {

/*           Solve T'*p = scale*c */

	    jnext = 1;
	    i__1 = *n;
	    for (j = 1; j <= i__1; ++j) {
		if (j < jnext) {
		    goto L40;
		}
		j1 = j;
		j2 = j;
		jnext = j + 1;
		if (j < *n) {
		    if (t[j + 1 + j * t_dim1] != 0.) {
			j2 = j + 1;
			jnext = j + 2;
		    }
		}

		if (j1 == j2) {

/*                 1 by 1 diagonal block */

/*                 Scale if necessary to avoid overflow in forming the */
/*                 right-hand side element by inner product. */

		    xj = (d__1 = x[j1], abs(d__1));
		    if (xmax > 1.) {
			rec = 1. / xmax;
			if (work[j1] > (bignum - xj) * rec) {
			    dscal_(n, &rec, &x[1], &c__1);
			    *scale *= rec;
			    xmax *= rec;
			}
		    }

		    i__2 = j1 - 1;
		    x[j1] -= ddot_(&i__2, &t[j1 * t_dim1 + 1], &c__1, &x[1], &
			    c__1);

		    xj = (d__1 = x[j1], abs(d__1));
		    tjj = (d__1 = t[j1 + j1 * t_dim1], abs(d__1));
		    tmp = t[j1 + j1 * t_dim1];
		    if (tjj < smin) {
			tmp = smin;
			tjj = smin;
			*info = 1;
		    }

		    if (tjj < 1.) {
			if (xj > bignum * tjj) {
			    rec = 1. / xj;
			    dscal_(n, &rec, &x[1], &c__1);
			    *scale *= rec;
			    xmax *= rec;
			}
		    }
		    x[j1] /= tmp;
/* Computing MAX */
		    d__2 = xmax, d__3 = (d__1 = x[j1], abs(d__1));
		    xmax = max(d__2,d__3);

		} else {

/*                 2 by 2 diagonal block */

/*                 Scale if necessary to avoid overflow in forming the */
/*                 right-hand side elements by inner product. */

/* Computing MAX */
		    d__3 = (d__1 = x[j1], abs(d__1)), d__4 = (d__2 = x[j2], 
			    abs(d__2));
		    xj = max(d__3,d__4);
		    if (xmax > 1.) {
			rec = 1. / xmax;
/* Computing MAX */
			d__1 = work[j2], d__2 = work[j1];
			if (max(d__1,d__2) > (bignum - xj) * rec) {
			    dscal_(n, &rec, &x[1], &c__1);
			    *scale *= rec;
			    xmax *= rec;
			}
		    }

		    i__2 = j1 - 1;
		    d__[0] = x[j1] - ddot_(&i__2, &t[j1 * t_dim1 + 1], &c__1, 
			    &x[1], &c__1);
		    i__2 = j1 - 1;
		    d__[1] = x[j2] - ddot_(&i__2, &t[j2 * t_dim1 + 1], &c__1, 
			    &x[1], &c__1);

		    dlaln2_(&c_true, &c__2, &c__1, &smin, &c_b21, &t[j1 + j1 *
			     t_dim1], ldt, &c_b21, &c_b21, d__, &c__2, &c_b25, 
			     &c_b25, v, &c__2, &scaloc, &xnorm, &ierr);
		    if (ierr != 0) {
			*info = 2;
		    }

		    if (scaloc != 1.) {
			dscal_(n, &scaloc, &x[1], &c__1);
			*scale *= scaloc;
		    }
		    x[j1] = v[0];
		    x[j2] = v[1];
/* Computing MAX */
		    d__3 = (d__1 = x[j1], abs(d__1)), d__4 = (d__2 = x[j2], 
			    abs(d__2)), d__3 = max(d__3,d__4);
		    xmax = max(d__3,xmax);

		}
L40:
		;
	    }
	}

    } else {

/* Computing MAX */
	d__1 = eps * abs(*w);
	sminw = max(d__1,smin);
	if (notran) {

/*           Solve (T + iB)*(p+iq) = c+id */

	    jnext = *n;
	    for (j = *n; j >= 1; --j) {
		if (j > jnext) {
		    goto L70;
		}
		j1 = j;
		j2 = j;
		jnext = j - 1;
		if (j > 1) {
		    if (t[j + (j - 1) * t_dim1] != 0.) {
			j1 = j - 1;
			jnext = j - 2;
		    }
		}

		if (j1 == j2) {

/*                 1 by 1 diagonal block */

/*                 Scale if necessary to avoid overflow in division */

		    z__ = *w;
		    if (j1 == 1) {
			z__ = b[1];
		    }
		    xj = (d__1 = x[j1], abs(d__1)) + (d__2 = x[*n + j1], abs(
			    d__2));
		    tjj = (d__1 = t[j1 + j1 * t_dim1], abs(d__1)) + abs(z__);
		    tmp = t[j1 + j1 * t_dim1];
		    if (tjj < sminw) {
			tmp = sminw;
			tjj = sminw;
			*info = 1;
		    }

		    if (xj == 0.) {
			goto L70;
		    }

		    if (tjj < 1.) {
			if (xj > bignum * tjj) {
			    rec = 1. / xj;
			    dscal_(&n2, &rec, &x[1], &c__1);
			    *scale *= rec;
			    xmax *= rec;
			}
		    }
		    dladiv_(&x[j1], &x[*n + j1], &tmp, &z__, &sr, &si);
		    x[j1] = sr;
		    x[*n + j1] = si;
		    xj = (d__1 = x[j1], abs(d__1)) + (d__2 = x[*n + j1], abs(
			    d__2));

/*                 Scale x if necessary to avoid overflow when adding a */
/*                 multiple of column j1 of T. */

		    if (xj > 1.) {
			rec = 1. / xj;
			if (work[j1] > (bignum - xmax) * rec) {
			    dscal_(&n2, &rec, &x[1], &c__1);
			    *scale *= rec;
			}
		    }

		    if (j1 > 1) {
			i__1 = j1 - 1;
			d__1 = -x[j1];
			daxpy_(&i__1, &d__1, &t[j1 * t_dim1 + 1], &c__1, &x[1]
, &c__1);
			i__1 = j1 - 1;
			d__1 = -x[*n + j1];
			daxpy_(&i__1, &d__1, &t[j1 * t_dim1 + 1], &c__1, &x[*
				n + 1], &c__1);

			x[1] += b[j1] * x[*n + j1];
			x[*n + 1] -= b[j1] * x[j1];

			xmax = 0.;
			i__1 = j1 - 1;
			for (k = 1; k <= i__1; ++k) {
/* Computing MAX */
			    d__3 = xmax, d__4 = (d__1 = x[k], abs(d__1)) + (
				    d__2 = x[k + *n], abs(d__2));
			    xmax = max(d__3,d__4);
/* L50: */
			}
		    }

		} else {

/*                 Meet 2 by 2 diagonal block */

		    d__[0] = x[j1];
		    d__[1] = x[j2];
		    d__[2] = x[*n + j1];
		    d__[3] = x[*n + j2];
		    d__1 = -(*w);
		    dlaln2_(&c_false, &c__2, &c__2, &sminw, &c_b21, &t[j1 + 
			    j1 * t_dim1], ldt, &c_b21, &c_b21, d__, &c__2, &
			    c_b25, &d__1, v, &c__2, &scaloc, &xnorm, &ierr);
		    if (ierr != 0) {
			*info = 2;
		    }

		    if (scaloc != 1.) {
			i__1 = *n << 1;
			dscal_(&i__1, &scaloc, &x[1], &c__1);
			*scale = scaloc * *scale;
		    }
		    x[j1] = v[0];
		    x[j2] = v[1];
		    x[*n + j1] = v[2];
		    x[*n + j2] = v[3];

/*                 Scale X(J1), .... to avoid overflow in */
/*                 updating right hand side. */

/* Computing MAX */
		    d__1 = abs(v[0]) + abs(v[2]), d__2 = abs(v[1]) + abs(v[3])
			    ;
		    xj = max(d__1,d__2);
		    if (xj > 1.) {
			rec = 1. / xj;
/* Computing MAX */
			d__1 = work[j1], d__2 = work[j2];
			if (max(d__1,d__2) > (bignum - xmax) * rec) {
			    dscal_(&n2, &rec, &x[1], &c__1);
			    *scale *= rec;
			}
		    }

/*                 Update the right-hand side. */

		    if (j1 > 1) {
			i__1 = j1 - 1;
			d__1 = -x[j1];
			daxpy_(&i__1, &d__1, &t[j1 * t_dim1 + 1], &c__1, &x[1]
, &c__1);
			i__1 = j1 - 1;
			d__1 = -x[j2];
			daxpy_(&i__1, &d__1, &t[j2 * t_dim1 + 1], &c__1, &x[1]
, &c__1);

			i__1 = j1 - 1;
			d__1 = -x[*n + j1];
			daxpy_(&i__1, &d__1, &t[j1 * t_dim1 + 1], &c__1, &x[*
				n + 1], &c__1);
			i__1 = j1 - 1;
			d__1 = -x[*n + j2];
			daxpy_(&i__1, &d__1, &t[j2 * t_dim1 + 1], &c__1, &x[*
				n + 1], &c__1);

			x[1] = x[1] + b[j1] * x[*n + j1] + b[j2] * x[*n + j2];
			x[*n + 1] = x[*n + 1] - b[j1] * x[j1] - b[j2] * x[j2];

			xmax = 0.;
			i__1 = j1 - 1;
			for (k = 1; k <= i__1; ++k) {
/* Computing MAX */
			    d__3 = (d__1 = x[k], abs(d__1)) + (d__2 = x[k + *
				    n], abs(d__2));
			    xmax = max(d__3,xmax);
/* L60: */
			}
		    }

		}
L70:
		;
	    }

	} else {

/*           Solve (T + iB)'*(p+iq) = c+id */

	    jnext = 1;
	    i__1 = *n;
	    for (j = 1; j <= i__1; ++j) {
		if (j < jnext) {
		    goto L80;
		}
		j1 = j;
		j2 = j;
		jnext = j + 1;
		if (j < *n) {
		    if (t[j + 1 + j * t_dim1] != 0.) {
			j2 = j + 1;
			jnext = j + 2;
		    }
		}

		if (j1 == j2) {

/*                 1 by 1 diagonal block */

/*                 Scale if necessary to avoid overflow in forming the */
/*                 right-hand side element by inner product. */

		    xj = (d__1 = x[j1], abs(d__1)) + (d__2 = x[j1 + *n], abs(
			    d__2));
		    if (xmax > 1.) {
			rec = 1. / xmax;
			if (work[j1] > (bignum - xj) * rec) {
			    dscal_(&n2, &rec, &x[1], &c__1);
			    *scale *= rec;
			    xmax *= rec;
			}
		    }

		    i__2 = j1 - 1;
		    x[j1] -= ddot_(&i__2, &t[j1 * t_dim1 + 1], &c__1, &x[1], &
			    c__1);
		    i__2 = j1 - 1;
		    x[*n + j1] -= ddot_(&i__2, &t[j1 * t_dim1 + 1], &c__1, &x[
			    *n + 1], &c__1);
		    if (j1 > 1) {
			x[j1] -= b[j1] * x[*n + 1];
			x[*n + j1] += b[j1] * x[1];
		    }
		    xj = (d__1 = x[j1], abs(d__1)) + (d__2 = x[j1 + *n], abs(
			    d__2));

		    z__ = *w;
		    if (j1 == 1) {
			z__ = b[1];
		    }

/*                 Scale if necessary to avoid overflow in */
/*                 complex division */

		    tjj = (d__1 = t[j1 + j1 * t_dim1], abs(d__1)) + abs(z__);
		    tmp = t[j1 + j1 * t_dim1];
		    if (tjj < sminw) {
			tmp = sminw;
			tjj = sminw;
			*info = 1;
		    }

		    if (tjj < 1.) {
			if (xj > bignum * tjj) {
			    rec = 1. / xj;
			    dscal_(&n2, &rec, &x[1], &c__1);
			    *scale *= rec;
			    xmax *= rec;
			}
		    }
		    d__1 = -z__;
		    dladiv_(&x[j1], &x[*n + j1], &tmp, &d__1, &sr, &si);
		    x[j1] = sr;
		    x[j1 + *n] = si;
/* Computing MAX */
		    d__3 = (d__1 = x[j1], abs(d__1)) + (d__2 = x[j1 + *n], 
			    abs(d__2));
		    xmax = max(d__3,xmax);

		} else {

/*                 2 by 2 diagonal block */

/*                 Scale if necessary to avoid overflow in forming the */
/*                 right-hand side element by inner product. */

/* Computing MAX */
		    d__5 = (d__1 = x[j1], abs(d__1)) + (d__2 = x[*n + j1], 
			    abs(d__2)), d__6 = (d__3 = x[j2], abs(d__3)) + (
			    d__4 = x[*n + j2], abs(d__4));
		    xj = max(d__5,d__6);
		    if (xmax > 1.) {
			rec = 1. / xmax;
/* Computing MAX */
			d__1 = work[j1], d__2 = work[j2];
			if (max(d__1,d__2) > (bignum - xj) / xmax) {
			    dscal_(&n2, &rec, &x[1], &c__1);
			    *scale *= rec;
			    xmax *= rec;
			}
		    }

		    i__2 = j1 - 1;
		    d__[0] = x[j1] - ddot_(&i__2, &t[j1 * t_dim1 + 1], &c__1, 
			    &x[1], &c__1);
		    i__2 = j1 - 1;
		    d__[1] = x[j2] - ddot_(&i__2, &t[j2 * t_dim1 + 1], &c__1, 
			    &x[1], &c__1);
		    i__2 = j1 - 1;
		    d__[2] = x[*n + j1] - ddot_(&i__2, &t[j1 * t_dim1 + 1], &
			    c__1, &x[*n + 1], &c__1);
		    i__2 = j1 - 1;
		    d__[3] = x[*n + j2] - ddot_(&i__2, &t[j2 * t_dim1 + 1], &
			    c__1, &x[*n + 1], &c__1);
		    d__[0] -= b[j1] * x[*n + 1];
		    d__[1] -= b[j2] * x[*n + 1];
		    d__[2] += b[j1] * x[1];
		    d__[3] += b[j2] * x[1];

		    dlaln2_(&c_true, &c__2, &c__2, &sminw, &c_b21, &t[j1 + j1 
			    * t_dim1], ldt, &c_b21, &c_b21, d__, &c__2, &
			    c_b25, w, v, &c__2, &scaloc, &xnorm, &ierr);
		    if (ierr != 0) {
			*info = 2;
		    }

		    if (scaloc != 1.) {
			dscal_(&n2, &scaloc, &x[1], &c__1);
			*scale = scaloc * *scale;
		    }
		    x[j1] = v[0];
		    x[j2] = v[1];
		    x[*n + j1] = v[2];
		    x[*n + j2] = v[3];
/* Computing MAX */
		    d__5 = (d__1 = x[j1], abs(d__1)) + (d__2 = x[*n + j1], 
			    abs(d__2)), d__6 = (d__3 = x[j2], abs(d__3)) + (
			    d__4 = x[*n + j2], abs(d__4)), d__5 = max(d__5,
			    d__6);
		    xmax = max(d__5,xmax);

		}

L80:
		;
	    }

	}

    }

    return 0;

/*     End of DLAQTR */

} /* dlaqtr_ */
コード例 #3
0
ファイル: dlaqtr.c プロジェクト: MichaelH13/sdkpub
/* Subroutine */ int dlaqtr_(logical *ltran, logical *lreal, integer *n, 
	doublereal *t, integer *ldt, doublereal *b, doublereal *w, doublereal 
	*scale, doublereal *x, doublereal *work, integer *info)
{
/*  -- LAPACK auxiliary routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       June 30, 1999   


    Purpose   
    =======   

    DLAQTR solves the real quasi-triangular system   

                 op(T)*p = scale*c,               if LREAL = .TRUE.   

    or the complex quasi-triangular systems   

               op(T + iB)*(p+iq) = scale*(c+id),  if LREAL = .FALSE.   

    in real arithmetic, where T is upper quasi-triangular.   
    If LREAL = .FALSE., then the first diagonal block of T must be   
    1 by 1, B is the specially structured matrix   

                   B = [ b(1) b(2) ... b(n) ]   
                       [       w            ]   
                       [           w        ]   
                       [              .     ]   
                       [                 w  ]   

    op(A) = A or A', A' denotes the conjugate transpose of   
    matrix A.   

    On input, X = [ c ].  On output, X = [ p ].   
                  [ d ]                  [ q ]   

    This subroutine is designed for the condition number estimation   
    in routine DTRSNA.   

    Arguments   
    =========   

    LTRAN   (input) LOGICAL   
            On entry, LTRAN specifies the option of conjugate transpose:   
               = .FALSE.,    op(T+i*B) = T+i*B,   
               = .TRUE.,     op(T+i*B) = (T+i*B)'.   

    LREAL   (input) LOGICAL   
            On entry, LREAL specifies the input matrix structure:   
               = .FALSE.,    the input is complex   
               = .TRUE.,     the input is real   

    N       (input) INTEGER   
            On entry, N specifies the order of T+i*B. N >= 0.   

    T       (input) DOUBLE PRECISION array, dimension (LDT,N)   
            On entry, T contains a matrix in Schur canonical form.   
            If LREAL = .FALSE., then the first diagonal block of T mu   
            be 1 by 1.   

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

    B       (input) DOUBLE PRECISION array, dimension (N)   
            On entry, B contains the elements to form the matrix   
            B as described above.   
            If LREAL = .TRUE., B is not referenced.   

    W       (input) DOUBLE PRECISION   
            On entry, W is the diagonal element of the matrix B.   
            If LREAL = .TRUE., W is not referenced.   

    SCALE   (output) DOUBLE PRECISION   
            On exit, SCALE is the scale factor.   

    X       (input/output) DOUBLE PRECISION array, dimension (2*N)   
            On entry, X contains the right hand side of the system.   
            On exit, X is overwritten by the solution.   

    WORK    (workspace) DOUBLE PRECISION array, dimension (N)   

    INFO    (output) INTEGER   
            On exit, INFO is set to   
               0: successful exit.   
                 1: the some diagonal 1 by 1 block has been perturbed by   
                    a small number SMIN to keep nonsingularity.   
                 2: the some diagonal 2 by 2 block has been perturbed by   
                    a small number in DLALN2 to keep nonsingularity.   
            NOTE: In the interests of speed, this routine does not   
                  check the inputs for errors.   

   =====================================================================   


       Do not test the input parameters for errors   

       Parameter adjustments */
    /* Table of constant values */
    static integer c__1 = 1;
    static logical c_false = FALSE_;
    static integer c__2 = 2;
    static doublereal c_b21 = 1.;
    static doublereal c_b25 = 0.;
    static logical c_true = TRUE_;
    
    /* System generated locals */
    integer t_dim1, t_offset, i__1, i__2;
    doublereal d__1, d__2, d__3, d__4, d__5, d__6;
    /* Local variables */
    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, 
	    integer *);
    static integer ierr;
    static doublereal smin, xmax, d__[4]	/* was [2][2] */;
    static integer i__, j, k;
    static doublereal v[4]	/* was [2][2] */, z__;
    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, 
	    integer *);
    extern doublereal dasum_(integer *, doublereal *, integer *);
    extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, 
	    integer *, doublereal *, integer *);
    static integer jnext, j1, j2;
    static doublereal sminw;
    static integer n1, n2;
    static doublereal xnorm;
    extern /* Subroutine */ int dlaln2_(logical *, integer *, integer *, 
	    doublereal *, doublereal *, doublereal *, integer *, doublereal *,
	     doublereal *, doublereal *, integer *, doublereal *, doublereal *
	    , doublereal *, integer *, doublereal *, doublereal *, integer *);
    extern doublereal dlamch_(char *), dlange_(char *, integer *, 
	    integer *, doublereal *, integer *, doublereal *);
    static doublereal si, xj;
    extern integer idamax_(integer *, doublereal *, integer *);
    static doublereal scaloc, sr;
    extern /* Subroutine */ int dladiv_(doublereal *, doublereal *, 
	    doublereal *, doublereal *, doublereal *, doublereal *);
    static doublereal bignum;
    static logical notran;
    static doublereal smlnum, rec, eps, tjj, tmp;
#define d___ref(a_1,a_2) d__[(a_2)*2 + a_1 - 3]
#define t_ref(a_1,a_2) t[(a_2)*t_dim1 + a_1]
#define v_ref(a_1,a_2) v[(a_2)*2 + a_1 - 3]


    t_dim1 = *ldt;
    t_offset = 1 + t_dim1 * 1;
    t -= t_offset;
    --b;
    --x;
    --work;

    /* Function Body */
    notran = ! (*ltran);
    *info = 0;

/*     Quick return if possible */

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

/*     Set constants to control overflow */

    eps = dlamch_("P");
    smlnum = dlamch_("S") / eps;
    bignum = 1. / smlnum;

    xnorm = dlange_("M", n, n, &t[t_offset], ldt, d__);
    if (! (*lreal)) {
/* Computing MAX */
	d__1 = xnorm, d__2 = abs(*w), d__1 = max(d__1,d__2), d__2 = dlange_(
		"M", n, &c__1, &b[1], n, d__);
	xnorm = max(d__1,d__2);
    }
/* Computing MAX */
    d__1 = smlnum, d__2 = eps * xnorm;
    smin = max(d__1,d__2);

/*     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) {
	i__2 = j - 1;
	work[j] = dasum_(&i__2, &t_ref(1, j), &c__1);
/* L10: */
    }

    if (! (*lreal)) {
	i__1 = *n;
	for (i__ = 2; i__ <= i__1; ++i__) {
	    work[i__] += (d__1 = b[i__], abs(d__1));
/* L20: */
	}
    }

    n2 = *n << 1;
    n1 = *n;
    if (! (*lreal)) {
	n1 = n2;
    }
    k = idamax_(&n1, &x[1], &c__1);
    xmax = (d__1 = x[k], abs(d__1));
    *scale = 1.;

    if (xmax > bignum) {
	*scale = bignum / xmax;
	dscal_(&n1, scale, &x[1], &c__1);
	xmax = bignum;
    }

    if (*lreal) {

	if (notran) {

/*           Solve T*p = scale*c */

	    jnext = *n;
	    for (j = *n; j >= 1; --j) {
		if (j > jnext) {
		    goto L30;
		}
		j1 = j;
		j2 = j;
		jnext = j - 1;
		if (j > 1) {
		    if (t_ref(j, j - 1) != 0.) {
			j1 = j - 1;
			jnext = j - 2;
		    }
		}

		if (j1 == j2) {

/*                 Meet 1 by 1 diagonal block   

                   Scale to avoid overflow when computing   
                       x(j) = b(j)/T(j,j) */

		    xj = (d__1 = x[j1], abs(d__1));
		    tjj = (d__1 = t_ref(j1, j1), abs(d__1));
		    tmp = t_ref(j1, j1);
		    if (tjj < smin) {
			tmp = smin;
			tjj = smin;
			*info = 1;
		    }

		    if (xj == 0.) {
			goto L30;
		    }

		    if (tjj < 1.) {
			if (xj > bignum * tjj) {
			    rec = 1. / xj;
			    dscal_(n, &rec, &x[1], &c__1);
			    *scale *= rec;
			    xmax *= rec;
			}
		    }
		    x[j1] /= tmp;
		    xj = (d__1 = x[j1], abs(d__1));

/*                 Scale x if necessary to avoid overflow when adding a   
                   multiple of column j1 of T. */

		    if (xj > 1.) {
			rec = 1. / xj;
			if (work[j1] > (bignum - xmax) * rec) {
			    dscal_(n, &rec, &x[1], &c__1);
			    *scale *= rec;
			}
		    }
		    if (j1 > 1) {
			i__1 = j1 - 1;
			d__1 = -x[j1];
			daxpy_(&i__1, &d__1, &t_ref(1, j1), &c__1, &x[1], &
				c__1);
			i__1 = j1 - 1;
			k = idamax_(&i__1, &x[1], &c__1);
			xmax = (d__1 = x[k], abs(d__1));
		    }

		} else {

/*                 Meet 2 by 2 diagonal block   

                   Call 2 by 2 linear system solve, to take   
                   care of possible overflow by scaling factor. */

		    d___ref(1, 1) = x[j1];
		    d___ref(2, 1) = x[j2];
		    dlaln2_(&c_false, &c__2, &c__1, &smin, &c_b21, &t_ref(j1, 
			    j1), ldt, &c_b21, &c_b21, d__, &c__2, &c_b25, &
			    c_b25, v, &c__2, &scaloc, &xnorm, &ierr);
		    if (ierr != 0) {
			*info = 2;
		    }

		    if (scaloc != 1.) {
			dscal_(n, &scaloc, &x[1], &c__1);
			*scale *= scaloc;
		    }
		    x[j1] = v_ref(1, 1);
		    x[j2] = v_ref(2, 1);

/*                 Scale V(1,1) (= X(J1)) and/or V(2,1) (=X(J2))   
                   to avoid overflow in updating right-hand side.   

   Computing MAX */
		    d__3 = (d__1 = v_ref(1, 1), abs(d__1)), d__4 = (d__2 = 
			    v_ref(2, 1), abs(d__2));
		    xj = max(d__3,d__4);
		    if (xj > 1.) {
			rec = 1. / xj;
/* Computing MAX */
			d__1 = work[j1], d__2 = work[j2];
			if (max(d__1,d__2) > (bignum - xmax) * rec) {
			    dscal_(n, &rec, &x[1], &c__1);
			    *scale *= rec;
			}
		    }

/*                 Update right-hand side */

		    if (j1 > 1) {
			i__1 = j1 - 1;
			d__1 = -x[j1];
			daxpy_(&i__1, &d__1, &t_ref(1, j1), &c__1, &x[1], &
				c__1);
			i__1 = j1 - 1;
			d__1 = -x[j2];
			daxpy_(&i__1, &d__1, &t_ref(1, j2), &c__1, &x[1], &
				c__1);
			i__1 = j1 - 1;
			k = idamax_(&i__1, &x[1], &c__1);
			xmax = (d__1 = x[k], abs(d__1));
		    }

		}

L30:
		;
	    }

	} else {

/*           Solve T'*p = scale*c */

	    jnext = 1;
	    i__1 = *n;
	    for (j = 1; j <= i__1; ++j) {
		if (j < jnext) {
		    goto L40;
		}
		j1 = j;
		j2 = j;
		jnext = j + 1;
		if (j < *n) {
		    if (t_ref(j + 1, j) != 0.) {
			j2 = j + 1;
			jnext = j + 2;
		    }
		}

		if (j1 == j2) {

/*                 1 by 1 diagonal block   

                   Scale if necessary to avoid overflow in forming the   
                   right-hand side element by inner product. */

		    xj = (d__1 = x[j1], abs(d__1));
		    if (xmax > 1.) {
			rec = 1. / xmax;
			if (work[j1] > (bignum - xj) * rec) {
			    dscal_(n, &rec, &x[1], &c__1);
			    *scale *= rec;
			    xmax *= rec;
			}
		    }

		    i__2 = j1 - 1;
		    x[j1] -= ddot_(&i__2, &t_ref(1, j1), &c__1, &x[1], &c__1);

		    xj = (d__1 = x[j1], abs(d__1));
		    tjj = (d__1 = t_ref(j1, j1), abs(d__1));
		    tmp = t_ref(j1, j1);
		    if (tjj < smin) {
			tmp = smin;
			tjj = smin;
			*info = 1;
		    }

		    if (tjj < 1.) {
			if (xj > bignum * tjj) {
			    rec = 1. / xj;
			    dscal_(n, &rec, &x[1], &c__1);
			    *scale *= rec;
			    xmax *= rec;
			}
		    }
		    x[j1] /= tmp;
/* Computing MAX */
		    d__2 = xmax, d__3 = (d__1 = x[j1], abs(d__1));
		    xmax = max(d__2,d__3);

		} else {

/*                 2 by 2 diagonal block   

                   Scale if necessary to avoid overflow in forming the   
                   right-hand side elements by inner product.   

   Computing MAX */
		    d__3 = (d__1 = x[j1], abs(d__1)), d__4 = (d__2 = x[j2], 
			    abs(d__2));
		    xj = max(d__3,d__4);
		    if (xmax > 1.) {
			rec = 1. / xmax;
/* Computing MAX */
			d__1 = work[j2], d__2 = work[j1];
			if (max(d__1,d__2) > (bignum - xj) * rec) {
			    dscal_(n, &rec, &x[1], &c__1);
			    *scale *= rec;
			    xmax *= rec;
			}
		    }

		    i__2 = j1 - 1;
		    d___ref(1, 1) = x[j1] - ddot_(&i__2, &t_ref(1, j1), &c__1,
			     &x[1], &c__1);
		    i__2 = j1 - 1;
		    d___ref(2, 1) = x[j2] - ddot_(&i__2, &t_ref(1, j2), &c__1,
			     &x[1], &c__1);

		    dlaln2_(&c_true, &c__2, &c__1, &smin, &c_b21, &t_ref(j1, 
			    j1), ldt, &c_b21, &c_b21, d__, &c__2, &c_b25, &
			    c_b25, v, &c__2, &scaloc, &xnorm, &ierr);
		    if (ierr != 0) {
			*info = 2;
		    }

		    if (scaloc != 1.) {
			dscal_(n, &scaloc, &x[1], &c__1);
			*scale *= scaloc;
		    }
		    x[j1] = v_ref(1, 1);
		    x[j2] = v_ref(2, 1);
/* Computing MAX */
		    d__3 = (d__1 = x[j1], abs(d__1)), d__4 = (d__2 = x[j2], 
			    abs(d__2)), d__3 = max(d__3,d__4);
		    xmax = max(d__3,xmax);

		}
L40:
		;
	    }
	}

    } else {

/* Computing MAX */
	d__1 = eps * abs(*w);
	sminw = max(d__1,smin);
	if (notran) {

/*           Solve (T + iB)*(p+iq) = c+id */

	    jnext = *n;
	    for (j = *n; j >= 1; --j) {
		if (j > jnext) {
		    goto L70;
		}
		j1 = j;
		j2 = j;
		jnext = j - 1;
		if (j > 1) {
		    if (t_ref(j, j - 1) != 0.) {
			j1 = j - 1;
			jnext = j - 2;
		    }
		}

		if (j1 == j2) {

/*                 1 by 1 diagonal block   

                   Scale if necessary to avoid overflow in division */

		    z__ = *w;
		    if (j1 == 1) {
			z__ = b[1];
		    }
		    xj = (d__1 = x[j1], abs(d__1)) + (d__2 = x[*n + j1], abs(
			    d__2));
		    tjj = (d__1 = t_ref(j1, j1), abs(d__1)) + abs(z__);
		    tmp = t_ref(j1, j1);
		    if (tjj < sminw) {
			tmp = sminw;
			tjj = sminw;
			*info = 1;
		    }

		    if (xj == 0.) {
			goto L70;
		    }

		    if (tjj < 1.) {
			if (xj > bignum * tjj) {
			    rec = 1. / xj;
			    dscal_(&n2, &rec, &x[1], &c__1);
			    *scale *= rec;
			    xmax *= rec;
			}
		    }
		    dladiv_(&x[j1], &x[*n + j1], &tmp, &z__, &sr, &si);
		    x[j1] = sr;
		    x[*n + j1] = si;
		    xj = (d__1 = x[j1], abs(d__1)) + (d__2 = x[*n + j1], abs(
			    d__2));

/*                 Scale x if necessary to avoid overflow when adding a   
                   multiple of column j1 of T. */

		    if (xj > 1.) {
			rec = 1. / xj;
			if (work[j1] > (bignum - xmax) * rec) {
			    dscal_(&n2, &rec, &x[1], &c__1);
			    *scale *= rec;
			}
		    }

		    if (j1 > 1) {
			i__1 = j1 - 1;
			d__1 = -x[j1];
			daxpy_(&i__1, &d__1, &t_ref(1, j1), &c__1, &x[1], &
				c__1);
			i__1 = j1 - 1;
			d__1 = -x[*n + j1];
			daxpy_(&i__1, &d__1, &t_ref(1, j1), &c__1, &x[*n + 1],
				 &c__1);

			x[1] += b[j1] * x[*n + j1];
			x[*n + 1] -= b[j1] * x[j1];

			xmax = 0.;
			i__1 = j1 - 1;
			for (k = 1; k <= i__1; ++k) {
/* Computing MAX */
			    d__3 = xmax, d__4 = (d__1 = x[k], abs(d__1)) + (
				    d__2 = x[k + *n], abs(d__2));
			    xmax = max(d__3,d__4);
/* L50: */
			}
		    }

		} else {

/*                 Meet 2 by 2 diagonal block */

		    d___ref(1, 1) = x[j1];
		    d___ref(2, 1) = x[j2];
		    d___ref(1, 2) = x[*n + j1];
		    d___ref(2, 2) = x[*n + j2];
		    d__1 = -(*w);
		    dlaln2_(&c_false, &c__2, &c__2, &sminw, &c_b21, &t_ref(j1,
			     j1), ldt, &c_b21, &c_b21, d__, &c__2, &c_b25, &
			    d__1, v, &c__2, &scaloc, &xnorm, &ierr);
		    if (ierr != 0) {
			*info = 2;
		    }

		    if (scaloc != 1.) {
			i__1 = *n << 1;
			dscal_(&i__1, &scaloc, &x[1], &c__1);
			*scale = scaloc * *scale;
		    }
		    x[j1] = v_ref(1, 1);
		    x[j2] = v_ref(2, 1);
		    x[*n + j1] = v_ref(1, 2);
		    x[*n + j2] = v_ref(2, 2);

/*                 Scale X(J1), .... to avoid overflow in   
                   updating right hand side.   

   Computing MAX */
		    d__5 = (d__1 = v_ref(1, 1), abs(d__1)) + (d__2 = v_ref(1, 
			    2), abs(d__2)), d__6 = (d__3 = v_ref(2, 1), abs(
			    d__3)) + (d__4 = v_ref(2, 2), abs(d__4));
		    xj = max(d__5,d__6);
		    if (xj > 1.) {
			rec = 1. / xj;
/* Computing MAX */
			d__1 = work[j1], d__2 = work[j2];
			if (max(d__1,d__2) > (bignum - xmax) * rec) {
			    dscal_(&n2, &rec, &x[1], &c__1);
			    *scale *= rec;
			}
		    }

/*                 Update the right-hand side. */

		    if (j1 > 1) {
			i__1 = j1 - 1;
			d__1 = -x[j1];
			daxpy_(&i__1, &d__1, &t_ref(1, j1), &c__1, &x[1], &
				c__1);
			i__1 = j1 - 1;
			d__1 = -x[j2];
			daxpy_(&i__1, &d__1, &t_ref(1, j2), &c__1, &x[1], &
				c__1);

			i__1 = j1 - 1;
			d__1 = -x[*n + j1];
			daxpy_(&i__1, &d__1, &t_ref(1, j1), &c__1, &x[*n + 1],
				 &c__1);
			i__1 = j1 - 1;
			d__1 = -x[*n + j2];
			daxpy_(&i__1, &d__1, &t_ref(1, j2), &c__1, &x[*n + 1],
				 &c__1);

			x[1] = x[1] + b[j1] * x[*n + j1] + b[j2] * x[*n + j2];
			x[*n + 1] = x[*n + 1] - b[j1] * x[j1] - b[j2] * x[j2];

			xmax = 0.;
			i__1 = j1 - 1;
			for (k = 1; k <= i__1; ++k) {
/* Computing MAX */
			    d__3 = (d__1 = x[k], abs(d__1)) + (d__2 = x[k + *
				    n], abs(d__2));
			    xmax = max(d__3,xmax);
/* L60: */
			}
		    }

		}
L70:
		;
	    }

	} else {

/*           Solve (T + iB)'*(p+iq) = c+id */

	    jnext = 1;
	    i__1 = *n;
	    for (j = 1; j <= i__1; ++j) {
		if (j < jnext) {
		    goto L80;
		}
		j1 = j;
		j2 = j;
		jnext = j + 1;
		if (j < *n) {
		    if (t_ref(j + 1, j) != 0.) {
			j2 = j + 1;
			jnext = j + 2;
		    }
		}

		if (j1 == j2) {

/*                 1 by 1 diagonal block   

                   Scale if necessary to avoid overflow in forming the   
                   right-hand side element by inner product. */

		    xj = (d__1 = x[j1], abs(d__1)) + (d__2 = x[j1 + *n], abs(
			    d__2));
		    if (xmax > 1.) {
			rec = 1. / xmax;
			if (work[j1] > (bignum - xj) * rec) {
			    dscal_(&n2, &rec, &x[1], &c__1);
			    *scale *= rec;
			    xmax *= rec;
			}
		    }

		    i__2 = j1 - 1;
		    x[j1] -= ddot_(&i__2, &t_ref(1, j1), &c__1, &x[1], &c__1);
		    i__2 = j1 - 1;
		    x[*n + j1] -= ddot_(&i__2, &t_ref(1, j1), &c__1, &x[*n + 
			    1], &c__1);
		    if (j1 > 1) {
			x[j1] -= b[j1] * x[*n + 1];
			x[*n + j1] += b[j1] * x[1];
		    }
		    xj = (d__1 = x[j1], abs(d__1)) + (d__2 = x[j1 + *n], abs(
			    d__2));

		    z__ = *w;
		    if (j1 == 1) {
			z__ = b[1];
		    }

/*                 Scale if necessary to avoid overflow in   
                   complex division */

		    tjj = (d__1 = t_ref(j1, j1), abs(d__1)) + abs(z__);
		    tmp = t_ref(j1, j1);
		    if (tjj < sminw) {
			tmp = sminw;
			tjj = sminw;
			*info = 1;
		    }

		    if (tjj < 1.) {
			if (xj > bignum * tjj) {
			    rec = 1. / xj;
			    dscal_(&n2, &rec, &x[1], &c__1);
			    *scale *= rec;
			    xmax *= rec;
			}
		    }
		    d__1 = -z__;
		    dladiv_(&x[j1], &x[*n + j1], &tmp, &d__1, &sr, &si);
		    x[j1] = sr;
		    x[j1 + *n] = si;
/* Computing MAX */
		    d__3 = (d__1 = x[j1], abs(d__1)) + (d__2 = x[j1 + *n], 
			    abs(d__2));
		    xmax = max(d__3,xmax);

		} else {

/*                 2 by 2 diagonal block   

                   Scale if necessary to avoid overflow in forming the   
                   right-hand side element by inner product.   

   Computing MAX */
		    d__5 = (d__1 = x[j1], abs(d__1)) + (d__2 = x[*n + j1], 
			    abs(d__2)), d__6 = (d__3 = x[j2], abs(d__3)) + (
			    d__4 = x[*n + j2], abs(d__4));
		    xj = max(d__5,d__6);
		    if (xmax > 1.) {
			rec = 1. / xmax;
/* Computing MAX */
			d__1 = work[j1], d__2 = work[j2];
			if (max(d__1,d__2) > (bignum - xj) / xmax) {
			    dscal_(&n2, &rec, &x[1], &c__1);
			    *scale *= rec;
			    xmax *= rec;
			}
		    }

		    i__2 = j1 - 1;
		    d___ref(1, 1) = x[j1] - ddot_(&i__2, &t_ref(1, j1), &c__1,
			     &x[1], &c__1);
		    i__2 = j1 - 1;
		    d___ref(2, 1) = x[j2] - ddot_(&i__2, &t_ref(1, j2), &c__1,
			     &x[1], &c__1);
		    i__2 = j1 - 1;
		    d___ref(1, 2) = x[*n + j1] - ddot_(&i__2, &t_ref(1, j1), &
			    c__1, &x[*n + 1], &c__1);
		    i__2 = j1 - 1;
		    d___ref(2, 2) = x[*n + j2] - ddot_(&i__2, &t_ref(1, j2), &
			    c__1, &x[*n + 1], &c__1);
		    d___ref(1, 1) = d___ref(1, 1) - b[j1] * x[*n + 1];
		    d___ref(2, 1) = d___ref(2, 1) - b[j2] * x[*n + 1];
		    d___ref(1, 2) = d___ref(1, 2) + b[j1] * x[1];
		    d___ref(2, 2) = d___ref(2, 2) + b[j2] * x[1];

		    dlaln2_(&c_true, &c__2, &c__2, &sminw, &c_b21, &t_ref(j1, 
			    j1), ldt, &c_b21, &c_b21, d__, &c__2, &c_b25, w, 
			    v, &c__2, &scaloc, &xnorm, &ierr);
		    if (ierr != 0) {
			*info = 2;
		    }

		    if (scaloc != 1.) {
			dscal_(&n2, &scaloc, &x[1], &c__1);
			*scale = scaloc * *scale;
		    }
		    x[j1] = v_ref(1, 1);
		    x[j2] = v_ref(2, 1);
		    x[*n + j1] = v_ref(1, 2);
		    x[*n + j2] = v_ref(2, 2);
/* Computing MAX */
		    d__5 = (d__1 = x[j1], abs(d__1)) + (d__2 = x[*n + j1], 
			    abs(d__2)), d__6 = (d__3 = x[j2], abs(d__3)) + (
			    d__4 = x[*n + j2], abs(d__4)), d__5 = max(d__5,
			    d__6);
		    xmax = max(d__5,xmax);

		}

L80:
		;
	    }

	}

    }

    return 0;

/*     End of DLAQTR */

} /* dlaqtr_ */