schkgt.c

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/* schkgt.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"

/* Common Block Declarations */

struct {
    integer infot, nunit;
    logical ok, lerr;
} infoc_;

#define infoc_1 infoc_

struct {
    char srnamt[32];
} srnamc_;

#define srnamc_1 srnamc_

/* Table of constant values */

static integer c__3 = 3;
static integer c__0 = 0;
static integer c_n1 = -1;
static integer c__1 = 1;
static integer c__2 = 2;
static integer c__7 = 7;
static real c_b63 = 1.f;
static real c_b64 = 0.f;

/* Subroutine */ int schkgt_(logical *dotype, integer *nn, integer *nval, 
        integer *nns, integer *nsval, real *thresh, logical *tsterr, real *a, 
        real *af, real *b, real *x, real *xact, real *work, real *rwork, 
        integer *iwork, integer *nout)
{
    /* Initialized data */

    static integer iseedy[4] = { 0,0,0,1 };
    static char transs[1*3] = "N" "T" "C";

    /* Format strings */
    static char fmt_9999[] = "(12x,\002N =\002,i5,\002,\002,10x,\002 type"
            " \002,i2,\002, test(\002,i2,\002) = \002,g12.5)";
    static char fmt_9997[] = "(\002 NORM ='\002,a1,\002', N =\002,i5,\002"
            ",\002,10x,\002 type \002,i2,\002, test(\002,i2,\002) = \002,g12."
            "5)";
    static char fmt_9998[] = "(\002 TRANS='\002,a1,\002', N =\002,i5,\002, N"
            "RHS=\002,i3,\002, type \002,i2,\002, test(\002,i2,\002) = \002,g"
            "12.5)";

    /* System generated locals */
    integer i__1, i__2, i__3, i__4;
    real r__1, r__2;

    /* Builtin functions */
    /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
    integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);

    /* Local variables */
    integer i__, j, k, m, n;
    real z__[3];
    integer in, kl, ku, ix, lda;
    real cond;
    integer mode, koff, imat, info;
    char path[3], dist[1];
    integer irhs, nrhs;
    char norm[1], type__[1];
    integer nrun;
    extern /* Subroutine */ int alahd_(integer *, char *);
    integer nfail, iseed[4];
    real rcond;
    extern /* Subroutine */ int sget04_(integer *, integer *, real *, integer 
            *, real *, integer *, real *, real *), sscal_(integer *, real *, 
            real *, integer *);
    integer nimat;
    extern doublereal sget06_(real *, real *);
    real anorm;
    integer itran;
    extern /* Subroutine */ int sgtt01_(integer *, real *, real *, real *, 
            real *, real *, real *, real *, integer *, real *, integer *, 
            real *, real *), sgtt02_(char *, integer *, integer *, real *, 
            real *, real *, real *, integer *, real *, integer *, real *, 
            real *), sgtt05_(char *, integer *, integer *, real *, 
            real *, real *, real *, integer *, real *, integer *, real *, 
            integer *, real *, real *, real *);
    char trans[1];
    integer izero, nerrs;
    extern doublereal sasum_(integer *, real *, integer *);
    extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 
            integer *);
    logical zerot;
    extern /* Subroutine */ int slatb4_(char *, integer *, integer *, integer 
            *, char *, integer *, integer *, real *, integer *, real *, char *
), alaerh_(char *, char *, integer *, 
            integer *, char *, integer *, integer *, integer *, integer *, 
            integer *, integer *, integer *, integer *, integer *);
    real rcondc, rcondi, rcondo;
    extern /* Subroutine */ int alasum_(char *, integer *, integer *, integer 
            *, integer *), serrge_(char *, integer *);
    real ainvnm;
    extern doublereal slangt_(char *, integer *, real *, real *, real *);
    extern /* Subroutine */ int slagtm_(char *, integer *, integer *, real *, 
            real *, real *, real *, real *, integer *, real *, real *, 
            integer *);
    logical trfcon;
    extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, 
            integer *, real *, integer *), sgtcon_(char *, integer *, 
            real *, real *, real *, real *, integer *, real *, real *, real *, 
             integer *, integer *), slatms_(integer *, integer *, 
            char *, integer *, char *, real *, integer *, real *, real *, 
            integer *, integer *, char *, real *, integer *, real *, integer *
), slarnv_(integer *, integer *, integer *
, real *), sgtrfs_(char *, integer *, integer *, real *, real *, 
            real *, real *, real *, real *, real *, integer *, real *, 
            integer *, real *, integer *, real *, real *, real *, integer *, 
            integer *), sgttrf_(integer *, real *, real *, real *, 
            real *, integer *, integer *);
    real result[7];
    extern /* Subroutine */ int sgttrs_(char *, integer *, integer *, real *, 
            real *, real *, real *, integer *, real *, integer *, integer *);

    /* Fortran I/O blocks */
    static cilist io___29 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___39 = { 0, 0, 0, fmt_9997, 0 };
    static cilist io___44 = { 0, 0, 0, fmt_9998, 0 };



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

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

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

/*  SCHKGT tests SGTTRF, -TRS, -RFS, and -CON */

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

/*  DOTYPE  (input) LOGICAL array, dimension (NTYPES) */
/*          The matrix types to be used for testing.  Matrices of type j */
/*          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = */
/*          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. */

/*  NN      (input) INTEGER */
/*          The number of values of N contained in the vector NVAL. */

/*  NVAL    (input) INTEGER array, dimension (NN) */
/*          The values of the matrix dimension N. */

/*  NNS     (input) INTEGER */
/*          The number of values of NRHS contained in the vector NSVAL. */

/*  NSVAL   (input) INTEGER array, dimension (NNS) */
/*          The values of the number of right hand sides NRHS. */

/*  THRESH  (input) REAL */
/*          The threshold value for the test ratios.  A result is */
/*          included in the output file if RESULT >= THRESH.  To have */
/*          every test ratio printed, use THRESH = 0. */

/*  TSTERR  (input) LOGICAL */
/*          Flag that indicates whether error exits are to be tested. */

/*  A       (workspace) REAL array, dimension (NMAX*4) */

/*  AF      (workspace) REAL array, dimension (NMAX*4) */

/*  B       (workspace) REAL array, dimension (NMAX*NSMAX) */
/*          where NSMAX is the largest entry in NSVAL. */

/*  X       (workspace) REAL array, dimension (NMAX*NSMAX) */

/*  XACT    (workspace) REAL array, dimension (NMAX*NSMAX) */

/*  WORK    (workspace) REAL array, dimension */
/*                      (NMAX*max(3,NSMAX)) */

/*  RWORK   (workspace) REAL array, dimension */
/*                      (max(NMAX,2*NSMAX)) */

/*  IWORK   (workspace) INTEGER array, dimension (2*NMAX) */

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

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. Local Arrays .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Scalars in Common .. */
/*     .. */
/*     .. Common blocks .. */
/*     .. */
/*     .. Data statements .. */
    /* Parameter adjustments */
    --iwork;
    --rwork;
    --work;
    --xact;
    --x;
    --b;
    --af;
    --a;
    --nsval;
    --nval;
    --dotype;

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

    s_copy(path, "Single precision", (ftnlen)1, (ftnlen)16);
    s_copy(path + 1, "GT", (ftnlen)2, (ftnlen)2);
    nrun = 0;
    nfail = 0;
    nerrs = 0;
    for (i__ = 1; i__ <= 4; ++i__) {
        iseed[i__ - 1] = iseedy[i__ - 1];
/* L10: */
    }

/*     Test the error exits */

    if (*tsterr) {
        serrge_(path, nout);
    }
    infoc_1.infot = 0;

    i__1 = *nn;
    for (in = 1; in <= i__1; ++in) {

/*        Do for each value of N in NVAL. */

        n = nval[in];
/* Computing MAX */
        i__2 = n - 1;
        m = max(i__2,0);
        lda = max(1,n);
        nimat = 12;
        if (n <= 0) {
            nimat = 1;
        }

        i__2 = nimat;
        for (imat = 1; imat <= i__2; ++imat) {

/*           Do the tests only if DOTYPE( IMAT ) is true. */

            if (! dotype[imat]) {
                goto L100;
            }

/*           Set up parameters with SLATB4. */

            slatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode, &
                    cond, dist);

            zerot = imat >= 8 && imat <= 10;
            if (imat <= 6) {

/*              Types 1-6:  generate matrices of known condition number. */

/* Computing MAX */
                i__3 = 2 - ku, i__4 = 3 - max(1,n);
                koff = max(i__3,i__4);
                s_copy(srnamc_1.srnamt, "SLATMS", (ftnlen)32, (ftnlen)6);
                slatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &cond, 
                        &anorm, &kl, &ku, "Z", &af[koff], &c__3, &work[1], &
                        info);

/*              Check the error code from SLATMS. */

                if (info != 0) {
                    alaerh_(path, "SLATMS", &info, &c__0, " ", &n, &n, &kl, &
                            ku, &c_n1, &imat, &nfail, &nerrs, nout);
                    goto L100;
                }
                izero = 0;

                if (n > 1) {
                    i__3 = n - 1;
                    scopy_(&i__3, &af[4], &c__3, &a[1], &c__1);
                    i__3 = n - 1;
                    scopy_(&i__3, &af[3], &c__3, &a[n + m + 1], &c__1);
                }
                scopy_(&n, &af[2], &c__3, &a[m + 1], &c__1);
            } else {

/*              Types 7-12:  generate tridiagonal matrices with */
/*              unknown condition numbers. */

                if (! zerot || ! dotype[7]) {

/*                 Generate a matrix with elements from [-1,1]. */

                    i__3 = n + (m << 1);
                    slarnv_(&c__2, iseed, &i__3, &a[1]);
                    if (anorm != 1.f) {
                        i__3 = n + (m << 1);
                        sscal_(&i__3, &anorm, &a[1], &c__1);
                    }
                } else if (izero > 0) {

/*                 Reuse the last matrix by copying back the zeroed out */
/*                 elements. */

                    if (izero == 1) {
                        a[n] = z__[1];
                        if (n > 1) {
                            a[1] = z__[2];
                        }
                    } else if (izero == n) {
                        a[n * 3 - 2] = z__[0];
                        a[(n << 1) - 1] = z__[1];
                    } else {
                        a[(n << 1) - 2 + izero] = z__[0];
                        a[n - 1 + izero] = z__[1];
                        a[izero] = z__[2];
                    }
                }

/*              If IMAT > 7, set one column of the matrix to 0. */

                if (! zerot) {
                    izero = 0;
                } else if (imat == 8) {
                    izero = 1;
                    z__[1] = a[n];
                    a[n] = 0.f;
                    if (n > 1) {
                        z__[2] = a[1];
                        a[1] = 0.f;
                    }
                } else if (imat == 9) {
                    izero = n;
                    z__[0] = a[n * 3 - 2];
                    z__[1] = a[(n << 1) - 1];
                    a[n * 3 - 2] = 0.f;
                    a[(n << 1) - 1] = 0.f;
                } else {
                    izero = (n + 1) / 2;
                    i__3 = n - 1;
                    for (i__ = izero; i__ <= i__3; ++i__) {
                        a[(n << 1) - 2 + i__] = 0.f;
                        a[n - 1 + i__] = 0.f;
                        a[i__] = 0.f;
/* L20: */
                    }
                    a[n * 3 - 2] = 0.f;
                    a[(n << 1) - 1] = 0.f;
                }
            }

/* +    TEST 1 */
/*           Factor A as L*U and compute the ratio */
/*              norm(L*U - A) / (n * norm(A) * EPS ) */

            i__3 = n + (m << 1);
            scopy_(&i__3, &a[1], &c__1, &af[1], &c__1);
            s_copy(srnamc_1.srnamt, "SGTTRF", (ftnlen)32, (ftnlen)6);
            sgttrf_(&n, &af[1], &af[m + 1], &af[n + m + 1], &af[n + (m << 1) 
                    + 1], &iwork[1], &info);

/*           Check error code from SGTTRF. */

            if (info != izero) {
                alaerh_(path, "SGTTRF", &info, &izero, " ", &n, &n, &c__1, &
                        c__1, &c_n1, &imat, &nfail, &nerrs, nout);
            }
            trfcon = info != 0;

            sgtt01_(&n, &a[1], &a[m + 1], &a[n + m + 1], &af[1], &af[m + 1], &
                    af[n + m + 1], &af[n + (m << 1) + 1], &iwork[1], &work[1], 
                     &lda, &rwork[1], result);

/*           Print the test ratio if it is .GE. THRESH. */

            if (result[0] >= *thresh) {
                if (nfail == 0 && nerrs == 0) {
                    alahd_(nout, path);
                }
                io___29.ciunit = *nout;
                s_wsfe(&io___29);
                do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
                do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(integer));
                do_fio(&c__1, (char *)&c__1, (ftnlen)sizeof(integer));
                do_fio(&c__1, (char *)&result[0], (ftnlen)sizeof(real));
                e_wsfe();
                ++nfail;
            }
            ++nrun;

            for (itran = 1; itran <= 2; ++itran) {
                *(unsigned char *)trans = *(unsigned char *)&transs[itran - 1]
                        ;
                if (itran == 1) {
                    *(unsigned char *)norm = 'O';
                } else {
                    *(unsigned char *)norm = 'I';
                }
                anorm = slangt_(norm, &n, &a[1], &a[m + 1], &a[n + m + 1]);

                if (! trfcon) {

/*                 Use SGTTRS to solve for one column at a time of inv(A) */
/*                 or inv(A^T), computing the maximum column sum as we */
/*                 go. */

                    ainvnm = 0.f;
                    i__3 = n;
                    for (i__ = 1; i__ <= i__3; ++i__) {
                        i__4 = n;
                        for (j = 1; j <= i__4; ++j) {
                            x[j] = 0.f;
/* L30: */
                        }
                        x[i__] = 1.f;
                        sgttrs_(trans, &n, &c__1, &af[1], &af[m + 1], &af[n + 
                                m + 1], &af[n + (m << 1) + 1], &iwork[1], &x[
                                1], &lda, &info);
/* Computing MAX */
                        r__1 = ainvnm, r__2 = sasum_(&n, &x[1], &c__1);
                        ainvnm = dmax(r__1,r__2);
/* L40: */
                    }

/*                 Compute RCONDC = 1 / (norm(A) * norm(inv(A)) */

                    if (anorm <= 0.f || ainvnm <= 0.f) {
                        rcondc = 1.f;
                    } else {
                        rcondc = 1.f / anorm / ainvnm;
                    }
                    if (itran == 1) {
                        rcondo = rcondc;
                    } else {
                        rcondi = rcondc;
                    }
                } else {
                    rcondc = 0.f;
                }

/* +    TEST 7 */
/*              Estimate the reciprocal of the condition number of the */
/*              matrix. */

                s_copy(srnamc_1.srnamt, "SGTCON", (ftnlen)32, (ftnlen)6);
                sgtcon_(norm, &n, &af[1], &af[m + 1], &af[n + m + 1], &af[n + 
                        (m << 1) + 1], &iwork[1], &anorm, &rcond, &work[1], &
                        iwork[n + 1], &info);

/*              Check error code from SGTCON. */

                if (info != 0) {
                    alaerh_(path, "SGTCON", &info, &c__0, norm, &n, &n, &c_n1, 
                             &c_n1, &c_n1, &imat, &nfail, &nerrs, nout);
                }

                result[6] = sget06_(&rcond, &rcondc);

/*              Print the test ratio if it is .GE. THRESH. */

                if (result[6] >= *thresh) {
                    if (nfail == 0 && nerrs == 0) {
                        alahd_(nout, path);
                    }
                    io___39.ciunit = *nout;
                    s_wsfe(&io___39);
                    do_fio(&c__1, norm, (ftnlen)1);
                    do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
                    do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(integer));
                    do_fio(&c__1, (char *)&c__7, (ftnlen)sizeof(integer));
                    do_fio(&c__1, (char *)&result[6], (ftnlen)sizeof(real));
                    e_wsfe();
                    ++nfail;
                }
                ++nrun;
/* L50: */
            }

/*           Skip the remaining tests if the matrix is singular. */

            if (trfcon) {
                goto L100;
            }

            i__3 = *nns;
            for (irhs = 1; irhs <= i__3; ++irhs) {
                nrhs = nsval[irhs];

/*              Generate NRHS random solution vectors. */

                ix = 1;
                i__4 = nrhs;
                for (j = 1; j <= i__4; ++j) {
                    slarnv_(&c__2, iseed, &n, &xact[ix]);
                    ix += lda;
/* L60: */
                }

                for (itran = 1; itran <= 3; ++itran) {
                    *(unsigned char *)trans = *(unsigned char *)&transs[itran 
                            - 1];
                    if (itran == 1) {
                        rcondc = rcondo;
                    } else {
                        rcondc = rcondi;
                    }

/*                 Set the right hand side. */

                    slagtm_(trans, &n, &nrhs, &c_b63, &a[1], &a[m + 1], &a[n 
                            + m + 1], &xact[1], &lda, &c_b64, &b[1], &lda);

/* +    TEST 2 */
/*                 Solve op(A) * X = B and compute the residual. */

                    slacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &lda);
                    s_copy(srnamc_1.srnamt, "SGTTRS", (ftnlen)32, (ftnlen)6);
                    sgttrs_(trans, &n, &nrhs, &af[1], &af[m + 1], &af[n + m + 
                            1], &af[n + (m << 1) + 1], &iwork[1], &x[1], &lda, 
                             &info);

/*                 Check error code from SGTTRS. */

                    if (info != 0) {
                        alaerh_(path, "SGTTRS", &info, &c__0, trans, &n, &n, &
                                c_n1, &c_n1, &nrhs, &imat, &nfail, &nerrs, 
                                nout);
                    }

                    slacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1], &lda);
                    sgtt02_(trans, &n, &nrhs, &a[1], &a[m + 1], &a[n + m + 1], 
                             &x[1], &lda, &work[1], &lda, &rwork[1], &result[
                            1]);

/* +    TEST 3 */
/*                 Check solution from generated exact solution. */

                    sget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &rcondc, &
                            result[2]);

/* +    TESTS 4, 5, and 6 */
/*                 Use iterative refinement to improve the solution. */

                    s_copy(srnamc_1.srnamt, "SGTRFS", (ftnlen)32, (ftnlen)6);
                    sgtrfs_(trans, &n, &nrhs, &a[1], &a[m + 1], &a[n + m + 1], 
                             &af[1], &af[m + 1], &af[n + m + 1], &af[n + (m <<
                             1) + 1], &iwork[1], &b[1], &lda, &x[1], &lda, &
                            rwork[1], &rwork[nrhs + 1], &work[1], &iwork[n + 
                            1], &info);

/*                 Check error code from SGTRFS. */

                    if (info != 0) {
                        alaerh_(path, "SGTRFS", &info, &c__0, trans, &n, &n, &
                                c_n1, &c_n1, &nrhs, &imat, &nfail, &nerrs, 
                                nout);
                    }

                    sget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &rcondc, &
                            result[3]);
                    sgtt05_(trans, &n, &nrhs, &a[1], &a[m + 1], &a[n + m + 1], 
                             &b[1], &lda, &x[1], &lda, &xact[1], &lda, &rwork[
                            1], &rwork[nrhs + 1], &result[4]);

/*                 Print information about the tests that did not pass */
/*                 the threshold. */

                    for (k = 2; k <= 6; ++k) {
                        if (result[k - 1] >= *thresh) {
                            if (nfail == 0 && nerrs == 0) {
                                alahd_(nout, path);
                            }
                            io___44.ciunit = *nout;
                            s_wsfe(&io___44);
                            do_fio(&c__1, trans, (ftnlen)1);
                            do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
                                    ;
                            do_fio(&c__1, (char *)&nrhs, (ftnlen)sizeof(
                                    integer));
                            do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(
                                    integer));
                            do_fio(&c__1, (char *)&k, (ftnlen)sizeof(integer))
                                    ;
                            do_fio(&c__1, (char *)&result[k - 1], (ftnlen)
                                    sizeof(real));
                            e_wsfe();
                            ++nfail;
                        }
/* L70: */
                    }
                    nrun += 5;
/* L80: */
                }
/* L90: */
            }

L100:
            ;
        }
/* L110: */
    }

/*     Print a summary of the results. */

    alasum_(path, nout, &nfail, &nrun, &nerrs);

    return 0;

/*     End of SCHKGT */

} /* schkgt_ */