cebchvxx.c

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/* cebchvxx.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__6 = 6;
static integer c__2 = 2;
static integer c__3 = 3;
static integer c__1 = 1;
static integer c__4 = 4;
static integer c__5 = 5;
static integer c__7 = 7;
static integer c__8 = 8;

/* Subroutine */ int cebchvxx_(real *thresh, char *path)
{
    /* Format strings */
    static char fmt_8000[] = "(\002 C\002,a2,\002SVXX: N =\002,i2,\002, INFO"
            " = \002,i3,\002, ORCOND = \002,g12.5,\002, real RCOND = \002,g12"
            ".5)";
    static char fmt_9996[] = "(3x,i2,\002: Normwise guaranteed forward erro"
            "r\002,/5x,\002Guaranteed case: if norm ( abs( Xc - Xt )\002,\002"
            " / norm ( Xt ) .LE. ERRBND( *, nwise_i, bnd_i ), then\002,/5x"
            ",\002ERRBND( *, nwise_i, bnd_i ) .LE. MAX(SQRT(N), 10) * EPS\002)"
            ;
    static char fmt_9995[] = "(3x,i2,\002: Componentwise guaranteed forward "
            "error\002)";
    static char fmt_9994[] = "(3x,i2,\002: Backwards error\002)";
    static char fmt_9993[] = "(3x,i2,\002: Reciprocal condition number\002)";
    static char fmt_9992[] = "(3x,i2,\002: Reciprocal normwise condition num"
            "ber\002)";
    static char fmt_9991[] = "(3x,i2,\002: Raw normwise error estimate\002)";
    static char fmt_9990[] = "(3x,i2,\002: Reciprocal componentwise conditio"
            "n number\002)";
    static char fmt_9989[] = "(3x,i2,\002: Raw componentwise error estimat"
            "e\002)";
    static char fmt_9999[] = "(\002 C\002,a2,\002SVXX: N =\002,i2,\002, RHS "
            "= \002,i2,\002, NWISE GUAR. = \002,a,\002, CWISE GUAR. = \002,a"
            ",\002 test(\002,i1,\002) =\002,g12.5)";
    static char fmt_9998[] = "(\002 C\002,a2,\002SVXX: \002,i6,\002 out of"
            " \002,i6,\002 tests failed to pass the threshold\002)";
    static char fmt_9997[] = "(\002 C\002,a2,\002SVXX passed the tests of er"
            "ror bounds\002)";

    /* System generated locals */
    integer i__1, i__2, i__3, i__4, i__5, i__6;
    real r__1, r__2, r__3, r__4, r__5;
    complex q__1, q__2, q__3;

    /* Builtin functions */
    /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
    double sqrt(doublereal);
    integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
    double r_imag(complex *);
    void c_div(complex *, complex *, complex *);
    integer s_wsle(cilist *), e_wsle(void);

    /* Local variables */
    extern /* Subroutine */ int csysvxx_(char *, char *, integer *, integer *, 
             complex *, integer *, complex *, integer *, integer *, char *, 
            real *, complex *, integer *, complex *, integer *, real *, real *
, real *, integer *, real *, real *, integer *, real *, complex *, 
             real *, integer *);
    real errbnd_c__[18], errbnd_n__[18];
    complex a[36]       /* was [6][6] */, b[36] /* was [6][6] */;
    real c__[6];
    integer i__, j, k;
    real m;
    integer n;
    real r__[6], s[6];
    complex x[36]       /* was [6][6] */;
    real cwise_bnd__;
    char c2[2];
    real nwise_bnd__, cwise_err__, nwise_err__, errthresh;
    complex ab[66]      /* was [11][6] */, af[36]       /* was [6][6] */;
    integer kl, ku;
    real condthresh;
    complex afb[96]     /* was [16][6] */;
    integer lda;
    real eps, cwise_rcond__, nwise_rcond__;
    integer n_aux_tests__, ldab;
    real diff[36]       /* was [6][6] */;
    char fact[1];
    real berr[6];
    integer info, ipiv[6], nrhs;
    real rinv[6];
    char uplo[1];
    complex work[90];
    real sumr;
    integer ldafb;
    real ccond;
    integer nfail;
    char cguar[3];
    real ncond;
    char equed[1];
    real rcond;
    complex acopy[36]   /* was [6][6] */;
    char nguar[3], trans[1];
    real rnorm, normt, sumri, rwork[18];
    logical printed_guide__;
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex 
            *, integer *, complex *, integer *), dlacpy_(char *, 
            integer *, integer *, complex *, integer *, complex *, integer *);
    complex abcopy[66]  /* was [11][6] */;
    extern logical lsamen_(integer *, char *, char *);
    real params[2], orcond, rinorm, tstrat[6], rpvgrw;
    extern /* Subroutine */ int clahilb_(integer *, integer *, complex *, 
            integer *, complex *, integer *, complex *, integer *, complex *, 
            integer *, char *);
    complex invhilb[36] /* was [6][6] */;
    real normdif;
    extern /* Subroutine */ int cgbsvxx_(char *, char *, integer *, integer *, 
             integer *, integer *, complex *, integer *, complex *, integer *, 
             integer *, char *, real *, real *, complex *, integer *, complex 
            *, integer *, real *, real *, real *, integer *, real *, real *, 
            integer *, real *, complex *, real *, integer *), cgesvxx_(char *, char *, integer *, integer *, complex *, 
             integer *, complex *, integer *, integer *, char *, real *, real 
            *, complex *, integer *, complex *, integer *, real *, real *, 
            real *, integer *, real *, real *, integer *, real *, complex *, 
            real *, integer *), chesvxx_(char *, char 
            *, integer *, integer *, complex *, integer *, complex *, integer 
            *, integer *, char *, real *, complex *, integer *, complex *, 
            integer *, real *, real *, real *, integer *, real *, real *, 
            integer *, real *, complex *, real *, integer *), cposvxx_(char *, char *, integer *, integer *, complex *, 
             integer *, complex *, integer *, char *, real *, complex *, 
            integer *, complex *, integer *, real *, real *, real *, integer *
, real *, real *, integer *, real *, complex *, real *, integer *);

    /* Fortran I/O blocks */
    static cilist io___42 = { 0, 6, 0, fmt_8000, 0 };
    static cilist io___66 = { 0, 6, 0, 0, 0 };
    static cilist io___67 = { 0, 6, 0, fmt_9996, 0 };
    static cilist io___68 = { 0, 6, 0, fmt_9995, 0 };
    static cilist io___69 = { 0, 6, 0, fmt_9994, 0 };
    static cilist io___70 = { 0, 6, 0, fmt_9993, 0 };
    static cilist io___71 = { 0, 6, 0, fmt_9992, 0 };
    static cilist io___72 = { 0, 6, 0, fmt_9991, 0 };
    static cilist io___73 = { 0, 6, 0, fmt_9990, 0 };
    static cilist io___74 = { 0, 6, 0, fmt_9989, 0 };
    static cilist io___75 = { 0, 6, 0, 0, 0 };
    static cilist io___76 = { 0, 6, 0, fmt_9999, 0 };
    static cilist io___77 = { 0, 6, 0, 0, 0 };
    static cilist io___78 = { 0, 6, 0, fmt_9998, 0 };
    static cilist io___79 = { 0, 6, 0, fmt_9997, 0 };


/*     .. Scalar Arguments .. */

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

/*  CEBCHVXX will run CGESVXX on a series of Hilbert matrices and then */
/*  compare the error bounds returned by CGESVXX to see if the returned */
/*  answer indeed falls within those bounds. */

/*  Eight test ratios will be computed.  The tests will pass if they are .LT. */
/*  THRESH.  There are two cases that are determined by 1 / (SQRT( N ) * EPS). */
/*  If that value is .LE. to the component wise reciprocal condition number, */
/*  it uses the guaranteed case, other wise it uses the unguaranteed case. */

/*  Test ratios: */
/*     Let Xc be X_computed and Xt be X_truth. */
/*     The norm used is the infinity norm. */
/*     Let A be the guaranteed case and B be the unguaranteed case. */

/*       1. Normwise guaranteed forward error bound. */
/*       A: norm ( abs( Xc - Xt ) / norm ( Xt ) .LE. ERRBND( *, nwise_i, bnd_i ) and */
/*          ERRBND( *, nwise_i, bnd_i ) .LE. MAX(SQRT(N),10) * EPS. */
/*          If these conditions are met, the test ratio is set to be */
/*          ERRBND( *, nwise_i, bnd_i ) / MAX(SQRT(N), 10).  Otherwise it is 1/EPS. */
/*       B: For this case, CGESVXX should just return 1.  If it is less than */
/*          one, treat it the same as in 1A.  Otherwise it fails. (Set test */
/*          ratio to ERRBND( *, nwise_i, bnd_i ) * THRESH?) */

/*       2. Componentwise guaranteed forward error bound. */
/*       A: norm ( abs( Xc(j) - Xt(j) ) ) / norm (Xt(j)) .LE. ERRBND( *, cwise_i, bnd_i ) */
/*          for all j .AND. ERRBND( *, cwise_i, bnd_i ) .LE. MAX(SQRT(N), 10) * EPS. */
/*          If these conditions are met, the test ratio is set to be */
/*          ERRBND( *, cwise_i, bnd_i ) / MAX(SQRT(N), 10).  Otherwise it is 1/EPS. */
/*       B: Same as normwise test ratio. */

/*       3. Backwards error. */
/*       A: The test ratio is set to BERR/EPS. */
/*       B: Same test ratio. */

/*       4. Reciprocal condition number. */
/*       A: A condition number is computed with Xt and compared with the one */
/*          returned from CGESVXX.  Let RCONDc be the RCOND returned by CGESVXX */
/*          and RCONDt be the RCOND from the truth value.  Test ratio is set to */
/*          MAX(RCONDc/RCONDt, RCONDt/RCONDc). */
/*       B: Test ratio is set to 1 / (EPS * RCONDc). */

/*       5. Reciprocal normwise condition number. */
/*       A: The test ratio is set to */
/*          MAX(ERRBND( *, nwise_i, cond_i ) / NCOND, NCOND / ERRBND( *, nwise_i, cond_i )). */
/*       B: Test ratio is set to 1 / (EPS * ERRBND( *, nwise_i, cond_i )). */

/*       6. Reciprocal componentwise condition number. */
/*       A: Test ratio is set to */
/*          MAX(ERRBND( *, cwise_i, cond_i ) / CCOND, CCOND / ERRBND( *, cwise_i, cond_i )). */
/*       B: Test ratio is set to 1 / (EPS * ERRBND( *, cwise_i, cond_i )). */

/*     .. Parameters .. */
/*     NMAX is determined by the largest number in the inverse of the hilbert */
/*     matrix.  Precision is exhausted when the largest entry in it is greater */
/*     than 2 to the power of the number of bits in the fraction of the data */
/*     type used plus one, which is 24 for single precision. */
/*     NMAX should be 6 for single and 11 for double. */
/*     .. Local Scalars .. */
/*     .. Local Arrays .. */
/*     .. External Functions .. */
/*     .. External Subroutines .. */
/*     .. Intrinsic Functions .. */
/*     .. Statement Functions .. */
/*     .. */
/*     .. Statement Function Definitions .. */
/*     .. Parameters .. */
/*  Create the loop to test out the Hilbert matrices */
    *(unsigned char *)fact = 'E';
    *(unsigned char *)uplo = 'U';
    *(unsigned char *)trans = 'N';
    *(unsigned char *)equed = 'N';
    eps = slamch_("Epsilon");
    nfail = 0;
    n_aux_tests__ = 0;
    lda = 6;
    ldab = 11;
    ldafb = 16;
    s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2);
/*     Main loop to test the different Hilbert Matrices. */
    printed_guide__ = FALSE_;
    for (n = 1; n <= 6; ++n) {
        params[0] = -1.f;
        params[1] = -1.f;
        kl = n - 1;
        ku = n - 1;
        nrhs = n;
/* Computing MAX */
        r__1 = sqrt((real) n);
        m = dmax(r__1,10.f);
/*        Generate the Hilbert matrix, its inverse, and the */
/*        right hand side, all scaled by the LCM(1,..,2N-1). */
        clahilb_(&n, &n, a, &lda, invhilb, &lda, b, &lda, work, &info, path);
/*        Copy A into ACOPY. */
        clacpy_("ALL", &n, &n, a, &c__6, acopy, &c__6);
/*        Store A in band format for GB tests */
        i__1 = n;
        for (j = 1; j <= i__1; ++j) {
            i__2 = kl + ku + 1;
            for (i__ = 1; i__ <= i__2; ++i__) {
                i__3 = i__ + j * 11 - 12;
                ab[i__3].r = 0.f, ab[i__3].i = 0.f;
            }
        }
        i__1 = n;
        for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
            i__2 = 1, i__3 = j - ku;
/* Computing MIN */
            i__5 = n, i__6 = j + kl;
            i__4 = min(i__5,i__6);
            for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
                i__2 = ku + 1 + i__ - j + j * 11 - 12;
                i__3 = i__ + j * 6 - 7;
                ab[i__2].r = a[i__3].r, ab[i__2].i = a[i__3].i;
            }
        }
/*        Copy AB into ABCOPY. */
        i__1 = n;
        for (j = 1; j <= i__1; ++j) {
            i__4 = kl + ku + 1;
            for (i__ = 1; i__ <= i__4; ++i__) {
                i__2 = i__ + j * 11 - 12;
                abcopy[i__2].r = 0.f, abcopy[i__2].i = 0.f;
            }
        }
        i__1 = kl + ku + 1;
        dlacpy_("ALL", &i__1, &n, ab, &ldab, abcopy, &ldab);
/*        Call C**SVXX with default PARAMS and N_ERR_BND = 3. */
        if (lsamen_(&c__2, c2, "SY")) {
            csysvxx_(fact, uplo, &n, &nrhs, acopy, &lda, af, &lda, ipiv, 
                    equed, s, b, &lda, x, &lda, &orcond, &rpvgrw, berr, &c__3, 
                     errbnd_n__, errbnd_c__, &c__2, params, work, rwork, &
                    info);
        } else if (lsamen_(&c__2, c2, "PO")) {
            cposvxx_(fact, uplo, &n, &nrhs, acopy, &lda, af, &lda, equed, s, 
                    b, &lda, x, &lda, &orcond, &rpvgrw, berr, &c__3, 
                    errbnd_n__, errbnd_c__, &c__2, params, work, rwork, &info);
        } else if (lsamen_(&c__2, c2, "HE")) {
            chesvxx_(fact, uplo, &n, &nrhs, acopy, &lda, af, &lda, ipiv, 
                    equed, s, b, &lda, x, &lda, &orcond, &rpvgrw, berr, &c__3, 
                     errbnd_n__, errbnd_c__, &c__2, params, work, rwork, &
                    info);
        } else if (lsamen_(&c__2, c2, "GB")) {
            cgbsvxx_(fact, trans, &n, &kl, &ku, &nrhs, abcopy, &ldab, afb, &
                    ldafb, ipiv, equed, r__, c__, b, &lda, x, &lda, &orcond, &
                    rpvgrw, berr, &c__3, errbnd_n__, errbnd_c__, &c__2, 
                    params, work, rwork, &info);
        } else {
            cgesvxx_(fact, trans, &n, &nrhs, acopy, &lda, af, &lda, ipiv, 
                    equed, r__, c__, b, &lda, x, &lda, &orcond, &rpvgrw, berr, 
                     &c__3, errbnd_n__, errbnd_c__, &c__2, params, work, 
                    rwork, &info);
        }
        ++n_aux_tests__;
        if (orcond < eps) {
/*        Either factorization failed or the matrix is flagged, and 1 <= */
/*        INFO <= N+1. We don't decide based on rcond anymore. */
/*            IF (INFO .EQ. 0 .OR. INFO .GT. N+1) THEN */
/*               NFAIL = NFAIL + 1 */
/*               WRITE (*, FMT=8000) N, INFO, ORCOND, RCOND */
/*            END IF */
        } else {
/*        Either everything succeeded (INFO == 0) or some solution failed */
/*        to converge (INFO > N+1). */
            if (info > 0 && info <= n + 1) {
                ++nfail;
                s_wsfe(&io___42);
                do_fio(&c__1, c2, (ftnlen)2);
                do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
                do_fio(&c__1, (char *)&info, (ftnlen)sizeof(integer));
                do_fio(&c__1, (char *)&orcond, (ftnlen)sizeof(real));
                do_fio(&c__1, (char *)&rcond, (ftnlen)sizeof(real));
                e_wsfe();
            }
        }
/*        Calculating the difference between C**SVXX's X and the true X. */
        i__1 = n;
        for (i__ = 1; i__ <= i__1; ++i__) {
            i__4 = nrhs;
            for (j = 1; j <= i__4; ++j) {
                i__2 = i__ + j * 6 - 7;
                i__3 = i__ + j * 6 - 7;
                i__5 = i__ + j * 6 - 7;
                q__1.r = x[i__3].r - invhilb[i__5].r, q__1.i = x[i__3].i - 
                        invhilb[i__5].i;
                diff[i__2] = q__1.r;
            }
        }
/*        Calculating the RCOND */
        rnorm = 0.f;
        rinorm = 0.f;
        if (lsamen_(&c__2, c2, "PO") || lsamen_(&c__2, 
                c2, "SY") || lsamen_(&c__2, c2, "HE")) {
            i__1 = n;
            for (i__ = 1; i__ <= i__1; ++i__) {
                sumr = 0.f;
                sumri = 0.f;
                i__4 = n;
                for (j = 1; j <= i__4; ++j) {
                    i__2 = i__ + j * 6 - 7;
                    sumr += s[i__ - 1] * ((r__1 = a[i__2].r, dabs(r__1)) + (
                            r__2 = r_imag(&a[i__ + j * 6 - 7]), dabs(r__2))) *
                             s[j - 1];
                    i__2 = i__ + j * 6 - 7;
                    sumri += ((r__1 = invhilb[i__2].r, dabs(r__1)) + (r__2 = 
                            r_imag(&invhilb[i__ + j * 6 - 7]), dabs(r__2))) / 
                            (s[j - 1] * s[i__ - 1]);
                }
                rnorm = dmax(rnorm,sumr);
                rinorm = dmax(rinorm,sumri);
            }
        } else if (lsamen_(&c__2, c2, "GE") || lsamen_(&
                c__2, c2, "GB")) {
            i__1 = n;
            for (i__ = 1; i__ <= i__1; ++i__) {
                sumr = 0.f;
                sumri = 0.f;
                i__4 = n;
                for (j = 1; j <= i__4; ++j) {
                    i__2 = i__ + j * 6 - 7;
                    sumr += r__[i__ - 1] * ((r__1 = a[i__2].r, dabs(r__1)) + (
                            r__2 = r_imag(&a[i__ + j * 6 - 7]), dabs(r__2))) *
                             c__[j - 1];
                    i__2 = i__ + j * 6 - 7;
                    sumri += ((r__1 = invhilb[i__2].r, dabs(r__1)) + (r__2 = 
                            r_imag(&invhilb[i__ + j * 6 - 7]), dabs(r__2))) / 
                            (r__[j - 1] * c__[i__ - 1]);
                }
                rnorm = dmax(rnorm,sumr);
                rinorm = dmax(rinorm,sumri);
            }
        }
        rnorm /= (r__1 = a[0].r, dabs(r__1)) + (r__2 = r_imag(a), dabs(r__2));
        rcond = 1.f / (rnorm * rinorm);
/*        Calculating the R for normwise rcond. */
        i__1 = n;
        for (i__ = 1; i__ <= i__1; ++i__) {
            rinv[i__ - 1] = 0.f;
        }
        i__1 = n;
        for (j = 1; j <= i__1; ++j) {
            i__4 = n;
            for (i__ = 1; i__ <= i__4; ++i__) {
                i__2 = i__ + j * 6 - 7;
                rinv[i__ - 1] += (r__1 = a[i__2].r, dabs(r__1)) + (r__2 = 
                        r_imag(&a[i__ + j * 6 - 7]), dabs(r__2));
            }
        }
/*        Calculating the Normwise rcond. */
        rinorm = 0.f;
        i__1 = n;
        for (i__ = 1; i__ <= i__1; ++i__) {
            sumri = 0.f;
            i__4 = n;
            for (j = 1; j <= i__4; ++j) {
                i__2 = i__ + j * 6 - 7;
                i__3 = j - 1;
                q__2.r = rinv[i__3] * invhilb[i__2].r, q__2.i = rinv[i__3] * 
                        invhilb[i__2].i;
                q__1.r = q__2.r, q__1.i = q__2.i;
                sumri += (r__1 = q__1.r, dabs(r__1)) + (r__2 = r_imag(&q__1), 
                        dabs(r__2));
            }
            rinorm = dmax(rinorm,sumri);
        }
/*        invhilb is the inverse *unscaled* Hilbert matrix, so scale its norm */
/*        by 1/A(1,1) to make the scaling match A (the scaled Hilbert matrix) */
        ncond = ((r__1 = a[0].r, dabs(r__1)) + (r__2 = r_imag(a), dabs(r__2)))
                 / rinorm;
        condthresh = m * eps;
        errthresh = m * eps;
        i__1 = nrhs;
        for (k = 1; k <= i__1; ++k) {
            normt = 0.f;
            normdif = 0.f;
            cwise_err__ = 0.f;
            i__4 = n;
            for (i__ = 1; i__ <= i__4; ++i__) {
/* Computing MAX */
                i__2 = i__ + k * 6 - 7;
                r__3 = (r__1 = invhilb[i__2].r, dabs(r__1)) + (r__2 = r_imag(&
                        invhilb[i__ + k * 6 - 7]), dabs(r__2));
                normt = dmax(r__3,normt);
                i__2 = i__ + k * 6 - 7;
                i__3 = i__ + k * 6 - 7;
                q__2.r = x[i__2].r - invhilb[i__3].r, q__2.i = x[i__2].i - 
                        invhilb[i__3].i;
                q__1.r = q__2.r, q__1.i = q__2.i;
/* Computing MAX */
                r__3 = (r__1 = q__1.r, dabs(r__1)) + (r__2 = r_imag(&q__1), 
                        dabs(r__2));
                normdif = dmax(r__3,normdif);
                i__2 = i__ + k * 6 - 7;
                if (invhilb[i__2].r != 0.f || invhilb[i__2].i != 0.f) {
                    i__2 = i__ + k * 6 - 7;
                    i__3 = i__ + k * 6 - 7;
                    q__2.r = x[i__2].r - invhilb[i__3].r, q__2.i = x[i__2].i 
                            - invhilb[i__3].i;
                    q__1.r = q__2.r, q__1.i = q__2.i;
/* Computing MAX */
                    i__5 = i__ + k * 6 - 7;
                    r__5 = ((r__1 = q__1.r, dabs(r__1)) + (r__2 = r_imag(&
                            q__1), dabs(r__2))) / ((r__3 = invhilb[i__5].r, 
                            dabs(r__3)) + (r__4 = r_imag(&invhilb[i__ + k * 6 
                            - 7]), dabs(r__4)));
                    cwise_err__ = dmax(r__5,cwise_err__);
                } else /* if(complicated condition) */ {
                    i__2 = i__ + k * 6 - 7;
                    if (x[i__2].r != 0.f || x[i__2].i != 0.f) {
                        cwise_err__ = slamch_("OVERFLOW");
                    }
                }
            }
            if (normt != 0.f) {
                nwise_err__ = normdif / normt;
            } else if (normdif != 0.f) {
                nwise_err__ = slamch_("OVERFLOW");
            } else {
                nwise_err__ = 0.f;
            }
            i__4 = n;
            for (i__ = 1; i__ <= i__4; ++i__) {
                rinv[i__ - 1] = 0.f;
            }
            i__4 = n;
            for (j = 1; j <= i__4; ++j) {
                i__2 = n;
                for (i__ = 1; i__ <= i__2; ++i__) {
                    i__3 = i__ + j * 6 - 7;
                    i__5 = j + k * 6 - 7;
                    q__2.r = a[i__3].r * invhilb[i__5].r - a[i__3].i * 
                            invhilb[i__5].i, q__2.i = a[i__3].r * invhilb[
                            i__5].i + a[i__3].i * invhilb[i__5].r;
                    q__1.r = q__2.r, q__1.i = q__2.i;
                    rinv[i__ - 1] += (r__1 = q__1.r, dabs(r__1)) + (r__2 = 
                            r_imag(&q__1), dabs(r__2));
                }
            }
            rinorm = 0.f;
            i__4 = n;
            for (i__ = 1; i__ <= i__4; ++i__) {
                sumri = 0.f;
                i__2 = n;
                for (j = 1; j <= i__2; ++j) {
                    i__3 = i__ + j * 6 - 7;
                    i__5 = j - 1;
                    q__3.r = rinv[i__5] * invhilb[i__3].r, q__3.i = rinv[i__5]
                             * invhilb[i__3].i;
                    c_div(&q__2, &q__3, &invhilb[i__ + k * 6 - 7]);
                    q__1.r = q__2.r, q__1.i = q__2.i;
                    sumri += (r__1 = q__1.r, dabs(r__1)) + (r__2 = r_imag(&
                            q__1), dabs(r__2));
                }
                rinorm = dmax(rinorm,sumri);
            }
/*        invhilb is the inverse *unscaled* Hilbert matrix, so scale its norm */
/*        by 1/A(1,1) to make the scaling match A (the scaled Hilbert matrix) */
            ccond = ((r__1 = a[0].r, dabs(r__1)) + (r__2 = r_imag(a), dabs(
                    r__2))) / rinorm;
/*        Forward error bound tests */
            nwise_bnd__ = errbnd_n__[k + nrhs - 1];
            cwise_bnd__ = errbnd_c__[k + nrhs - 1];
            nwise_rcond__ = errbnd_n__[k + (nrhs << 1) - 1];
            cwise_rcond__ = errbnd_c__[k + (nrhs << 1) - 1];
/*            write (*,*) 'nwise : ', n, k, ncond, nwise_rcond, */
/*     $           condthresh, ncond.ge.condthresh */
/*            write (*,*) 'nwise2: ', k, nwise_bnd, nwise_err, errthresh */
            if (ncond >= condthresh) {
                s_copy(nguar, "YES", (ftnlen)3, (ftnlen)3);
                if (nwise_bnd__ > errthresh) {
                    tstrat[0] = 1 / (eps * 2.f);
                } else {
                    if (nwise_bnd__ != 0.f) {
                        tstrat[0] = nwise_err__ / nwise_bnd__;
                    } else if (nwise_err__ != 0.f) {
                        tstrat[0] = 1 / (eps * 16.f);
                    } else {
                        tstrat[0] = 0.f;
                    }
                    if (tstrat[0] > 1.f) {
                        tstrat[0] = 1 / (eps * 4.f);
                    }
                }
            } else {
                s_copy(nguar, "NO", (ftnlen)3, (ftnlen)2);
                if (nwise_bnd__ < 1.f) {
                    tstrat[0] = 1 / (eps * 8.f);
                } else {
                    tstrat[0] = 1.f;
                }
            }
/*            write (*,*) 'cwise : ', n, k, ccond, cwise_rcond, */
/*     $           condthresh, ccond.ge.condthresh */
/*            write (*,*) 'cwise2: ', k, cwise_bnd, cwise_err, errthresh */
            if (ccond >= condthresh) {
                s_copy(cguar, "YES", (ftnlen)3, (ftnlen)3);
                if (cwise_bnd__ > errthresh) {
                    tstrat[1] = 1 / (eps * 2.f);
                } else {
                    if (cwise_bnd__ != 0.f) {
                        tstrat[1] = cwise_err__ / cwise_bnd__;
                    } else if (cwise_err__ != 0.f) {
                        tstrat[1] = 1 / (eps * 16.f);
                    } else {
                        tstrat[1] = 0.f;
                    }
                    if (tstrat[1] > 1.f) {
                        tstrat[1] = 1 / (eps * 4.f);
                    }
                }
            } else {
                s_copy(cguar, "NO", (ftnlen)3, (ftnlen)2);
                if (cwise_bnd__ < 1.f) {
                    tstrat[1] = 1 / (eps * 8.f);
                } else {
                    tstrat[1] = 1.f;
                }
            }
/*     Backwards error test */
            tstrat[2] = berr[k - 1] / eps;
/*     Condition number tests */
            tstrat[3] = rcond / orcond;
            if (rcond >= condthresh && tstrat[3] < 1.f) {
                tstrat[3] = 1.f / tstrat[3];
            }
            tstrat[4] = ncond / nwise_rcond__;
            if (ncond >= condthresh && tstrat[4] < 1.f) {
                tstrat[4] = 1.f / tstrat[4];
            }
            tstrat[5] = ccond / nwise_rcond__;
            if (ccond >= condthresh && tstrat[5] < 1.f) {
                tstrat[5] = 1.f / tstrat[5];
            }
            for (i__ = 1; i__ <= 6; ++i__) {
                if (tstrat[i__ - 1] > *thresh) {
                    if (! printed_guide__) {
                        s_wsle(&io___66);
                        e_wsle();
                        s_wsfe(&io___67);
                        do_fio(&c__1, (char *)&c__1, (ftnlen)sizeof(integer));
                        e_wsfe();
                        s_wsfe(&io___68);
                        do_fio(&c__1, (char *)&c__2, (ftnlen)sizeof(integer));
                        e_wsfe();
                        s_wsfe(&io___69);
                        do_fio(&c__1, (char *)&c__3, (ftnlen)sizeof(integer));
                        e_wsfe();
                        s_wsfe(&io___70);
                        do_fio(&c__1, (char *)&c__4, (ftnlen)sizeof(integer));
                        e_wsfe();
                        s_wsfe(&io___71);
                        do_fio(&c__1, (char *)&c__5, (ftnlen)sizeof(integer));
                        e_wsfe();
                        s_wsfe(&io___72);
                        do_fio(&c__1, (char *)&c__6, (ftnlen)sizeof(integer));
                        e_wsfe();
                        s_wsfe(&io___73);
                        do_fio(&c__1, (char *)&c__7, (ftnlen)sizeof(integer));
                        e_wsfe();
                        s_wsfe(&io___74);
                        do_fio(&c__1, (char *)&c__8, (ftnlen)sizeof(integer));
                        e_wsfe();
                        s_wsle(&io___75);
                        e_wsle();
                        printed_guide__ = TRUE_;
                    }
                    s_wsfe(&io___76);
                    do_fio(&c__1, c2, (ftnlen)2);
                    do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
                    do_fio(&c__1, (char *)&k, (ftnlen)sizeof(integer));
                    do_fio(&c__1, nguar, (ftnlen)3);
                    do_fio(&c__1, cguar, (ftnlen)3);
                    do_fio(&c__1, (char *)&i__, (ftnlen)sizeof(integer));
                    do_fio(&c__1, (char *)&tstrat[i__ - 1], (ftnlen)sizeof(
                            real));
                    e_wsfe();
                    ++nfail;
                }
            }
        }
/* $$$         WRITE(*,*) */
/* $$$         WRITE(*,*) 'Normwise Error Bounds' */
/* $$$         WRITE(*,*) 'Guaranteed error bound: ',ERRBND(NRHS,nwise_i,bnd_i) */
/* $$$         WRITE(*,*) 'Reciprocal condition number: ',ERRBND(NRHS,nwise_i,cond_i) */
/* $$$         WRITE(*,*) 'Raw error estimate: ',ERRBND(NRHS,nwise_i,rawbnd_i) */
/* $$$         WRITE(*,*) */
/* $$$         WRITE(*,*) 'Componentwise Error Bounds' */
/* $$$         WRITE(*,*) 'Guaranteed error bound: ',ERRBND(NRHS,cwise_i,bnd_i) */
/* $$$         WRITE(*,*) 'Reciprocal condition number: ',ERRBND(NRHS,cwise_i,cond_i) */
/* $$$         WRITE(*,*) 'Raw error estimate: ',ERRBND(NRHS,cwise_i,rawbnd_i) */
/* $$$         print *, 'Info: ', info */
/* $$$         WRITE(*,*) */
/*         WRITE(*,*) 'TSTRAT: ',TSTRAT */
    }
    s_wsle(&io___77);
    e_wsle();
    if (nfail > 0) {
        s_wsfe(&io___78);
        do_fio(&c__1, c2, (ftnlen)2);
        do_fio(&c__1, (char *)&nfail, (ftnlen)sizeof(integer));
        i__1 = n * 6 + n_aux_tests__;
        do_fio(&c__1, (char *)&i__1, (ftnlen)sizeof(integer));
        e_wsfe();
    } else {
        s_wsfe(&io___79);
        do_fio(&c__1, c2, (ftnlen)2);
        e_wsfe();
    }
/*     Test ratios. */
    return 0;
} /* cebchvxx_ */