schkeq.c

Go to the documentation of this file.

/* schkeq.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 real c_b7 = 10.f;
static integer c_n1 = -1;
static integer c__5 = 5;
static integer c__13 = 13;
static integer c__1 = 1;

/* Subroutine */ int schkeq_(real *thresh, integer *nout)
{
    /* Format strings */
    static char fmt_9999[] = "(1x,\002All tests for \002,a3,\002 routines pa"
            "ssed the threshold\002)";
    static char fmt_9998[] = "(\002 SGEEQU failed test with value \002,e10"
            ".3,\002 exceeding\002,\002 threshold \002,e10.3)";
    static char fmt_9997[] = "(\002 SGBEQU failed test with value \002,e10"
            ".3,\002 exceeding\002,\002 threshold \002,e10.3)";
    static char fmt_9996[] = "(\002 SPOEQU failed test with value \002,e10"
            ".3,\002 exceeding\002,\002 threshold \002,e10.3)";
    static char fmt_9995[] = "(\002 SPPEQU failed test with value \002,e10"
            ".3,\002 exceeding\002,\002 threshold \002,e10.3)";
    static char fmt_9994[] = "(\002 SPBEQU failed test with value \002,e10"
            ".3,\002 exceeding\002,\002 threshold \002,e10.3)";

    /* System generated locals */
    integer i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8;
    real r__1, r__2, r__3;

    /* Builtin functions */
    /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
    double pow_ri(real *, integer *);
    integer pow_ii(integer *, integer *), s_wsle(cilist *), e_wsle(void), 
            s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);

    /* Local variables */
    real a[25]  /* was [5][5] */, c__[5];
    integer i__, j, m, n;
    real r__[5], ab[65] /* was [13][5] */, ap[15];
    integer kl;
    logical ok;
    integer ku;
    real eps, pow[11];
    integer info;
    char path[3];
    real norm, rpow[11], ccond, rcond, rcmin, rcmax, ratio;
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int sgbequ_(integer *, integer *, integer *, 
            integer *, real *, integer *, real *, real *, real *, real *, 
            real *, integer *), sgeequ_(integer *, integer *, real *, integer 
            *, real *, real *, real *, real *, real *, integer *), spbequ_(
            char *, integer *, integer *, real *, integer *, real *, real *, 
            real *, integer *);
    real reslts[5];
    extern /* Subroutine */ int spoequ_(integer *, real *, integer *, real *, 
            real *, real *, integer *), sppequ_(char *, integer *, real *, 
            real *, real *, real *, integer *);

    /* Fortran I/O blocks */
    static cilist io___25 = { 0, 0, 0, 0, 0 };
    static cilist io___26 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___27 = { 0, 0, 0, fmt_9998, 0 };
    static cilist io___28 = { 0, 0, 0, fmt_9997, 0 };
    static cilist io___29 = { 0, 0, 0, fmt_9996, 0 };
    static cilist io___30 = { 0, 0, 0, fmt_9995, 0 };
    static cilist io___31 = { 0, 0, 0, fmt_9994, 0 };



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

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

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

/*  SCHKEQ tests SGEEQU, SGBEQU, SPOEQU, SPPEQU and SPBEQU */

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

/*  THRESH  (input) REAL */
/*          Threshold for testing routines. Should be between 2 and 10. */

/*  NOUT    (input) INTEGER */
/*          The unit number for output. */

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

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

    s_copy(path, "Single precision", (ftnlen)1, (ftnlen)16);
    s_copy(path + 1, "EQ", (ftnlen)2, (ftnlen)2);

    eps = slamch_("P");
    for (i__ = 1; i__ <= 5; ++i__) {
        reslts[i__ - 1] = 0.f;
/* L10: */
    }
    for (i__ = 1; i__ <= 11; ++i__) {
        i__1 = i__ - 1;
        pow[i__ - 1] = pow_ri(&c_b7, &i__1);
        rpow[i__ - 1] = 1.f / pow[i__ - 1];
/* L20: */
    }

/*     Test SGEEQU */

    for (n = 0; n <= 5; ++n) {
        for (m = 0; m <= 5; ++m) {

            for (j = 1; j <= 5; ++j) {
                for (i__ = 1; i__ <= 5; ++i__) {
                    if (i__ <= m && j <= n) {
                        i__1 = i__ + j;
                        a[i__ + j * 5 - 6] = pow[i__ + j] * pow_ii(&c_n1, &
                                i__1);
                    } else {
                        a[i__ + j * 5 - 6] = 0.f;
                    }
/* L30: */
                }
/* L40: */
            }

            sgeequ_(&m, &n, a, &c__5, r__, c__, &rcond, &ccond, &norm, &info);

            if (info != 0) {
                reslts[0] = 1.f;
            } else {
                if (n != 0 && m != 0) {
/* Computing MAX */
                    r__2 = reslts[0], r__3 = (r__1 = (rcond - rpow[m - 1]) / 
                            rpow[m - 1], dabs(r__1));
                    reslts[0] = dmax(r__2,r__3);
/* Computing MAX */
                    r__2 = reslts[0], r__3 = (r__1 = (ccond - rpow[n - 1]) / 
                            rpow[n - 1], dabs(r__1));
                    reslts[0] = dmax(r__2,r__3);
/* Computing MAX */
                    r__2 = reslts[0], r__3 = (r__1 = (norm - pow[n + m]) / 
                            pow[n + m], dabs(r__1));
                    reslts[0] = dmax(r__2,r__3);
                    i__1 = m;
                    for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
                        r__2 = reslts[0], r__3 = (r__1 = (r__[i__ - 1] - rpow[
                                i__ + n]) / rpow[i__ + n], dabs(r__1));
                        reslts[0] = dmax(r__2,r__3);
/* L50: */
                    }
                    i__1 = n;
                    for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
                        r__2 = reslts[0], r__3 = (r__1 = (c__[j - 1] - pow[n 
                                - j]) / pow[n - j], dabs(r__1));
                        reslts[0] = dmax(r__2,r__3);
/* L60: */
                    }
                }
            }

/* L70: */
        }
/* L80: */
    }

/*     Test with zero rows and columns */

    for (j = 1; j <= 5; ++j) {
        a[j * 5 - 2] = 0.f;
/* L90: */
    }
    sgeequ_(&c__5, &c__5, a, &c__5, r__, c__, &rcond, &ccond, &norm, &info);
    if (info != 4) {
        reslts[0] = 1.f;
    }

    for (j = 1; j <= 5; ++j) {
        a[j * 5 - 2] = 1.f;
/* L100: */
    }
    for (i__ = 1; i__ <= 5; ++i__) {
        a[i__ + 14] = 0.f;
/* L110: */
    }
    sgeequ_(&c__5, &c__5, a, &c__5, r__, c__, &rcond, &ccond, &norm, &info);
    if (info != 9) {
        reslts[0] = 1.f;
    }
    reslts[0] /= eps;

/*     Test SGBEQU */

    for (n = 0; n <= 5; ++n) {
        for (m = 0; m <= 5; ++m) {
/* Computing MAX */
            i__2 = m - 1;
            i__1 = max(i__2,0);
            for (kl = 0; kl <= i__1; ++kl) {
/* Computing MAX */
                i__3 = n - 1;
                i__2 = max(i__3,0);
                for (ku = 0; ku <= i__2; ++ku) {

                    for (j = 1; j <= 5; ++j) {
                        for (i__ = 1; i__ <= 13; ++i__) {
                            ab[i__ + j * 13 - 14] = 0.f;
/* L120: */
                        }
/* L130: */
                    }
                    i__3 = n;
                    for (j = 1; j <= i__3; ++j) {
                        i__4 = m;
                        for (i__ = 1; i__ <= i__4; ++i__) {
/* Computing MIN */
                            i__5 = m, i__6 = j + kl;
/* Computing MAX */
                            i__7 = 1, i__8 = j - ku;
                            if (i__ <= min(i__5,i__6) && i__ >= max(i__7,i__8)
                                     && j <= n) {
                                i__5 = i__ + j;
                                ab[ku + 1 + i__ - j + j * 13 - 14] = pow[i__ 
                                        + j] * pow_ii(&c_n1, &i__5);
                            }
/* L140: */
                        }
/* L150: */
                    }

                    sgbequ_(&m, &n, &kl, &ku, ab, &c__13, r__, c__, &rcond, &
                            ccond, &norm, &info);

                    if (info != 0) {
                        if (! (n + kl < m && info == n + kl + 1 || m + ku < n 
                                && info == (m << 1) + ku + 1)) {
                            reslts[1] = 1.f;
                        }
                    } else {
                        if (n != 0 && m != 0) {

                            rcmin = r__[0];
                            rcmax = r__[0];
                            i__3 = m;
                            for (i__ = 1; i__ <= i__3; ++i__) {
/* Computing MIN */
                                r__1 = rcmin, r__2 = r__[i__ - 1];
                                rcmin = dmin(r__1,r__2);
/* Computing MAX */
                                r__1 = rcmax, r__2 = r__[i__ - 1];
                                rcmax = dmax(r__1,r__2);
/* L160: */
                            }
                            ratio = rcmin / rcmax;
/* Computing MAX */
                            r__2 = reslts[1], r__3 = (r__1 = (rcond - ratio) /
                                     ratio, dabs(r__1));
                            reslts[1] = dmax(r__2,r__3);

                            rcmin = c__[0];
                            rcmax = c__[0];
                            i__3 = n;
                            for (j = 1; j <= i__3; ++j) {
/* Computing MIN */
                                r__1 = rcmin, r__2 = c__[j - 1];
                                rcmin = dmin(r__1,r__2);
/* Computing MAX */
                                r__1 = rcmax, r__2 = c__[j - 1];
                                rcmax = dmax(r__1,r__2);
/* L170: */
                            }
                            ratio = rcmin / rcmax;
/* Computing MAX */
                            r__2 = reslts[1], r__3 = (r__1 = (ccond - ratio) /
                                     ratio, dabs(r__1));
                            reslts[1] = dmax(r__2,r__3);

/* Computing MAX */
                            r__2 = reslts[1], r__3 = (r__1 = (norm - pow[n + 
                                    m]) / pow[n + m], dabs(r__1));
                            reslts[1] = dmax(r__2,r__3);
                            i__3 = m;
                            for (i__ = 1; i__ <= i__3; ++i__) {
                                rcmax = 0.f;
                                i__4 = n;
                                for (j = 1; j <= i__4; ++j) {
                                    if (i__ <= j + kl && i__ >= j - ku) {
                                        ratio = (r__1 = r__[i__ - 1] * pow[
                                                i__ + j] * c__[j - 1], dabs(
                                                r__1));
                                        rcmax = dmax(rcmax,ratio);
                                    }
/* L180: */
                                }
/* Computing MAX */
                                r__2 = reslts[1], r__3 = (r__1 = 1.f - rcmax, 
                                        dabs(r__1));
                                reslts[1] = dmax(r__2,r__3);
/* L190: */
                            }

                            i__3 = n;
                            for (j = 1; j <= i__3; ++j) {
                                rcmax = 0.f;
                                i__4 = m;
                                for (i__ = 1; i__ <= i__4; ++i__) {
                                    if (i__ <= j + kl && i__ >= j - ku) {
                                        ratio = (r__1 = r__[i__ - 1] * pow[
                                                i__ + j] * c__[j - 1], dabs(
                                                r__1));
                                        rcmax = dmax(rcmax,ratio);
                                    }
/* L200: */
                                }
/* Computing MAX */
                                r__2 = reslts[1], r__3 = (r__1 = 1.f - rcmax, 
                                        dabs(r__1));
                                reslts[1] = dmax(r__2,r__3);
/* L210: */
                            }
                        }
                    }

/* L220: */
                }
/* L230: */
            }
/* L240: */
        }
/* L250: */
    }
    reslts[1] /= eps;

/*     Test SPOEQU */

    for (n = 0; n <= 5; ++n) {

        for (i__ = 1; i__ <= 5; ++i__) {
            for (j = 1; j <= 5; ++j) {
                if (i__ <= n && j == i__) {
                    i__1 = i__ + j;
                    a[i__ + j * 5 - 6] = pow[i__ + j] * pow_ii(&c_n1, &i__1);
                } else {
                    a[i__ + j * 5 - 6] = 0.f;
                }
/* L260: */
            }
/* L270: */
        }

        spoequ_(&n, a, &c__5, r__, &rcond, &norm, &info);

        if (info != 0) {
            reslts[2] = 1.f;
        } else {
            if (n != 0) {
/* Computing MAX */
                r__2 = reslts[2], r__3 = (r__1 = (rcond - rpow[n - 1]) / rpow[
                        n - 1], dabs(r__1));
                reslts[2] = dmax(r__2,r__3);
/* Computing MAX */
                r__2 = reslts[2], r__3 = (r__1 = (norm - pow[n * 2]) / pow[n *
                         2], dabs(r__1));
                reslts[2] = dmax(r__2,r__3);
                i__1 = n;
                for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
                    r__2 = reslts[2], r__3 = (r__1 = (r__[i__ - 1] - rpow[i__]
                            ) / rpow[i__], dabs(r__1));
                    reslts[2] = dmax(r__2,r__3);
/* L280: */
                }
            }
        }
/* L290: */
    }
    a[18] = -1.f;
    spoequ_(&c__5, a, &c__5, r__, &rcond, &norm, &info);
    if (info != 4) {
        reslts[2] = 1.f;
    }
    reslts[2] /= eps;

/*     Test SPPEQU */

    for (n = 0; n <= 5; ++n) {

/*        Upper triangular packed storage */

        i__1 = n * (n + 1) / 2;
        for (i__ = 1; i__ <= i__1; ++i__) {
            ap[i__ - 1] = 0.f;
/* L300: */
        }
        i__1 = n;
        for (i__ = 1; i__ <= i__1; ++i__) {
            ap[i__ * (i__ + 1) / 2 - 1] = pow[i__ * 2];
/* L310: */
        }

        sppequ_("U", &n, ap, r__, &rcond, &norm, &info);

        if (info != 0) {
            reslts[3] = 1.f;
        } else {
            if (n != 0) {
/* Computing MAX */
                r__2 = reslts[3], r__3 = (r__1 = (rcond - rpow[n - 1]) / rpow[
                        n - 1], dabs(r__1));
                reslts[3] = dmax(r__2,r__3);
/* Computing MAX */
                r__2 = reslts[3], r__3 = (r__1 = (norm - pow[n * 2]) / pow[n *
                         2], dabs(r__1));
                reslts[3] = dmax(r__2,r__3);
                i__1 = n;
                for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
                    r__2 = reslts[3], r__3 = (r__1 = (r__[i__ - 1] - rpow[i__]
                            ) / rpow[i__], dabs(r__1));
                    reslts[3] = dmax(r__2,r__3);
/* L320: */
                }
            }
        }

/*        Lower triangular packed storage */

        i__1 = n * (n + 1) / 2;
        for (i__ = 1; i__ <= i__1; ++i__) {
            ap[i__ - 1] = 0.f;
/* L330: */
        }
        j = 1;
        i__1 = n;
        for (i__ = 1; i__ <= i__1; ++i__) {
            ap[j - 1] = pow[i__ * 2];
            j += n - i__ + 1;
/* L340: */
        }

        sppequ_("L", &n, ap, r__, &rcond, &norm, &info);

        if (info != 0) {
            reslts[3] = 1.f;
        } else {
            if (n != 0) {
/* Computing MAX */
                r__2 = reslts[3], r__3 = (r__1 = (rcond - rpow[n - 1]) / rpow[
                        n - 1], dabs(r__1));
                reslts[3] = dmax(r__2,r__3);
/* Computing MAX */
                r__2 = reslts[3], r__3 = (r__1 = (norm - pow[n * 2]) / pow[n *
                         2], dabs(r__1));
                reslts[3] = dmax(r__2,r__3);
                i__1 = n;
                for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
                    r__2 = reslts[3], r__3 = (r__1 = (r__[i__ - 1] - rpow[i__]
                            ) / rpow[i__], dabs(r__1));
                    reslts[3] = dmax(r__2,r__3);
/* L350: */
                }
            }
        }

/* L360: */
    }
    i__ = 13;
    ap[i__ - 1] = -1.f;
    sppequ_("L", &c__5, ap, r__, &rcond, &norm, &info);
    if (info != 4) {
        reslts[3] = 1.f;
    }
    reslts[3] /= eps;

/*     Test SPBEQU */

    for (n = 0; n <= 5; ++n) {
/* Computing MAX */
        i__2 = n - 1;
        i__1 = max(i__2,0);
        for (kl = 0; kl <= i__1; ++kl) {

/*           Test upper triangular storage */

            for (j = 1; j <= 5; ++j) {
                for (i__ = 1; i__ <= 13; ++i__) {
                    ab[i__ + j * 13 - 14] = 0.f;
/* L370: */
                }
/* L380: */
            }
            i__2 = n;
            for (j = 1; j <= i__2; ++j) {
                ab[kl + 1 + j * 13 - 14] = pow[j * 2];
/* L390: */
            }

            spbequ_("U", &n, &kl, ab, &c__13, r__, &rcond, &norm, &info);

            if (info != 0) {
                reslts[4] = 1.f;
            } else {
                if (n != 0) {
/* Computing MAX */
                    r__2 = reslts[4], r__3 = (r__1 = (rcond - rpow[n - 1]) / 
                            rpow[n - 1], dabs(r__1));
                    reslts[4] = dmax(r__2,r__3);
/* Computing MAX */
                    r__2 = reslts[4], r__3 = (r__1 = (norm - pow[n * 2]) / 
                            pow[n * 2], dabs(r__1));
                    reslts[4] = dmax(r__2,r__3);
                    i__2 = n;
                    for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
                        r__2 = reslts[4], r__3 = (r__1 = (r__[i__ - 1] - rpow[
                                i__]) / rpow[i__], dabs(r__1));
                        reslts[4] = dmax(r__2,r__3);
/* L400: */
                    }
                }
            }
            if (n != 0) {
/* Computing MAX */
                i__2 = n - 1;
                ab[kl + 1 + max(i__2,1) * 13 - 14] = -1.f;
                spbequ_("U", &n, &kl, ab, &c__13, r__, &rcond, &norm, &info);
/* Computing MAX */
                i__2 = n - 1;
                if (info != max(i__2,1)) {
                    reslts[4] = 1.f;
                }
            }

/*           Test lower triangular storage */

            for (j = 1; j <= 5; ++j) {
                for (i__ = 1; i__ <= 13; ++i__) {
                    ab[i__ + j * 13 - 14] = 0.f;
/* L410: */
                }
/* L420: */
            }
            i__2 = n;
            for (j = 1; j <= i__2; ++j) {
                ab[j * 13 - 13] = pow[j * 2];
/* L430: */
            }

            spbequ_("L", &n, &kl, ab, &c__13, r__, &rcond, &norm, &info);

            if (info != 0) {
                reslts[4] = 1.f;
            } else {
                if (n != 0) {
/* Computing MAX */
                    r__2 = reslts[4], r__3 = (r__1 = (rcond - rpow[n - 1]) / 
                            rpow[n - 1], dabs(r__1));
                    reslts[4] = dmax(r__2,r__3);
/* Computing MAX */
                    r__2 = reslts[4], r__3 = (r__1 = (norm - pow[n * 2]) / 
                            pow[n * 2], dabs(r__1));
                    reslts[4] = dmax(r__2,r__3);
                    i__2 = n;
                    for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
                        r__2 = reslts[4], r__3 = (r__1 = (r__[i__ - 1] - rpow[
                                i__]) / rpow[i__], dabs(r__1));
                        reslts[4] = dmax(r__2,r__3);
/* L440: */
                    }
                }
            }
            if (n != 0) {
/* Computing MAX */
                i__2 = n - 1;
                ab[max(i__2,1) * 13 - 13] = -1.f;
                spbequ_("L", &n, &kl, ab, &c__13, r__, &rcond, &norm, &info);
/* Computing MAX */
                i__2 = n - 1;
                if (info != max(i__2,1)) {
                    reslts[4] = 1.f;
                }
            }
/* L450: */
        }
/* L460: */
    }
    reslts[4] /= eps;
    ok = reslts[0] <= *thresh && reslts[1] <= *thresh && reslts[2] <= *thresh 
            && reslts[3] <= *thresh && reslts[4] <= *thresh;
    io___25.ciunit = *nout;
    s_wsle(&io___25);
    e_wsle();
    if (ok) {
        io___26.ciunit = *nout;
        s_wsfe(&io___26);
        do_fio(&c__1, path, (ftnlen)3);
        e_wsfe();
    } else {
        if (reslts[0] > *thresh) {
            io___27.ciunit = *nout;
            s_wsfe(&io___27);
            do_fio(&c__1, (char *)&reslts[0], (ftnlen)sizeof(real));
            do_fio(&c__1, (char *)&(*thresh), (ftnlen)sizeof(real));
            e_wsfe();
        }
        if (reslts[1] > *thresh) {
            io___28.ciunit = *nout;
            s_wsfe(&io___28);
            do_fio(&c__1, (char *)&reslts[1], (ftnlen)sizeof(real));
            do_fio(&c__1, (char *)&(*thresh), (ftnlen)sizeof(real));
            e_wsfe();
        }
        if (reslts[2] > *thresh) {
            io___29.ciunit = *nout;
            s_wsfe(&io___29);
            do_fio(&c__1, (char *)&reslts[2], (ftnlen)sizeof(real));
            do_fio(&c__1, (char *)&(*thresh), (ftnlen)sizeof(real));
            e_wsfe();
        }
        if (reslts[3] > *thresh) {
            io___30.ciunit = *nout;
            s_wsfe(&io___30);
            do_fio(&c__1, (char *)&reslts[3], (ftnlen)sizeof(real));
            do_fio(&c__1, (char *)&(*thresh), (ftnlen)sizeof(real));
            e_wsfe();
        }
        if (reslts[4] > *thresh) {
            io___31.ciunit = *nout;
            s_wsfe(&io___31);
            do_fio(&c__1, (char *)&reslts[4], (ftnlen)sizeof(real));
            do_fio(&c__1, (char *)&(*thresh), (ftnlen)sizeof(real));
            e_wsfe();
        }
    }
    return 0;

/*     End of SCHKEQ */

} /* schkeq_ */