dget31.c

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/* dget31.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 integer c__2 = 2;

/* 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_ */