schksy.c

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/* schksy.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__2 = 2;
static integer c__0 = 0;
static integer c_n1 = -1;
static integer c__1 = 1;
static integer c__8 = 8;

/* Subroutine */ int schksy_(logical *dotype, integer *nn, integer *nval, 
        integer *nnb, integer *nbval, integer *nns, integer *nsval, real *
        thresh, logical *tsterr, integer *nmax, real *a, real *afac, real *
        ainv, real *b, real *x, real *xact, real *work, real *rwork, integer *
        iwork, integer *nout)
{
    /* Initialized data */

    static integer iseedy[4] = { 1988,1989,1990,1991 };
    static char uplos[1*2] = "U" "L";

    /* Format strings */
    static char fmt_9999[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002, "
            "NB =\002,i4,\002, type \002,i2,\002, test \002,i2,\002, ratio "
            "=\002,g12.5)";
    static char fmt_9998[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002, "
            "NRHS=\002,i3,\002, type \002,i2,\002, test(\002,i2,\002) =\002,g"
            "12.5)";
    static char fmt_9997[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002"
            ",\002,10x,\002 type \002,i2,\002, test(\002,i2,\002) =\002,g12.5)"
            ;

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

    /* 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, n, i1, i2, nb, in, kl, ku, nt, lda, inb, ioff, mode, 
            imat, info;
    char path[3], dist[1];
    integer irhs, nrhs;
    char uplo[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 *);
    integer nimat;
    extern doublereal sget06_(real *, real *);
    real anorm;
    extern /* Subroutine */ int spot02_(char *, integer *, integer *, real *, 
            integer *, real *, integer *, real *, integer *, real *, real *);
    integer iuplo, izero, nerrs;
    extern /* Subroutine */ int spot03_(char *, integer *, real *, integer *, 
            real *, integer *, real *, integer *, real *, real *, real *), spot05_(char *, integer *, integer *, real *, integer *, 
            real *, integer *, real *, integer *, real *, integer *, real *, 
            real *, real *);
    integer lwork;
    logical zerot;
    extern /* Subroutine */ int ssyt01_(char *, integer *, real *, integer *, 
            real *, integer *, integer *, real *, integer *, real *, real *);
    char xtype[1];
    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;
    extern /* Subroutine */ int alasum_(char *, integer *, integer *, integer 
            *, integer *);
    real cndnum;
    logical trfcon;
    extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, 
            integer *, real *, integer *), slarhs_(char *, char *, 
            char *, char *, integer *, integer *, integer *, integer *, 
            integer *, real *, integer *, real *, integer *, real *, integer *
, integer *, integer *), xlaenv_(
            integer *, integer *), slatms_(integer *, integer *, char *, 
            integer *, char *, real *, integer *, real *, real *, integer *, 
            integer *, char *, real *, integer *, real *, integer *);
    extern doublereal slansy_(char *, char *, integer *, real *, integer *, 
            real *);
    real result[8];
    extern /* Subroutine */ int ssycon_(char *, integer *, real *, integer *, 
            integer *, real *, real *, real *, integer *, integer *), 
            serrsy_(char *, integer *), ssyrfs_(char *, integer *, 
            integer *, real *, integer *, real *, integer *, integer *, real *
, integer *, real *, integer *, real *, real *, real *, integer *, 
             integer *), ssytrf_(char *, integer *, real *, integer *, 
             integer *, real *, integer *, integer *), ssytri_(char *, 
             integer *, real *, integer *, integer *, real *, integer *), ssytrs_(char *, integer *, integer *, real *, integer *, 
            integer *, real *, integer *, integer *);

    /* Fortran I/O blocks */
    static cilist io___39 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___42 = { 0, 0, 0, fmt_9998, 0 };
    static cilist io___44 = { 0, 0, 0, fmt_9997, 0 };



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

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

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

/*  SCHKSY tests SSYTRF, -TRI, -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. */

/*  NNB     (input) INTEGER */
/*          The number of values of NB contained in the vector NBVAL. */

/*  NBVAL   (input) INTEGER array, dimension (NBVAL) */
/*          The values of the blocksize NB. */

/*  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. */

/*  NMAX    (input) INTEGER */
/*          The maximum value permitted for N, used in dimensioning the */
/*          work arrays. */

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

/*  AFAC    (workspace) REAL array, dimension (NMAX*NMAX) */

/*  AINV    (workspace) REAL array, dimension (NMAX*NMAX) */

/*  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;
    --ainv;
    --afac;
    --a;
    --nsval;
    --nbval;
    --nval;
    --dotype;

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

/*     Initialize constants and the random number seed. */

    s_copy(path, "Single precision", (ftnlen)1, (ftnlen)16);
    s_copy(path + 1, "SY", (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) {
        serrsy_(path, nout);
    }
    infoc_1.infot = 0;
    xlaenv_(&c__2, &c__2);

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

    i__1 = *nn;
    for (in = 1; in <= i__1; ++in) {
        n = nval[in];
        lda = max(n,1);
        *(unsigned char *)xtype = 'N';
        nimat = 10;
        if (n <= 0) {
            nimat = 1;
        }

        izero = 0;
        i__2 = nimat;
        for (imat = 1; imat <= i__2; ++imat) {

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

            if (! dotype[imat]) {
                goto L170;
            }

/*           Skip types 3, 4, 5, or 6 if the matrix size is too small. */

            zerot = imat >= 3 && imat <= 6;
            if (zerot && n < imat - 2) {
                goto L170;
            }

/*           Do first for UPLO = 'U', then for UPLO = 'L' */

            for (iuplo = 1; iuplo <= 2; ++iuplo) {
                *(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1];

/*              Set up parameters with SLATB4 and generate a test matrix */
/*              with SLATMS. */

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

                s_copy(srnamc_1.srnamt, "SLATMS", (ftnlen)32, (ftnlen)6);
                slatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &
                        cndnum, &anorm, &kl, &ku, uplo, &a[1], &lda, &work[1], 
                         &info);

/*              Check error code from SLATMS. */

                if (info != 0) {
                    alaerh_(path, "SLATMS", &info, &c__0, uplo, &n, &n, &c_n1, 
                             &c_n1, &c_n1, &imat, &nfail, &nerrs, nout);
                    goto L160;
                }

/*              For types 3-6, zero one or more rows and columns of */
/*              the matrix to test that INFO is returned correctly. */

                if (zerot) {
                    if (imat == 3) {
                        izero = 1;
                    } else if (imat == 4) {
                        izero = n;
                    } else {
                        izero = n / 2 + 1;
                    }

                    if (imat < 6) {

/*                    Set row and column IZERO to zero. */

                        if (iuplo == 1) {
                            ioff = (izero - 1) * lda;
                            i__3 = izero - 1;
                            for (i__ = 1; i__ <= i__3; ++i__) {
                                a[ioff + i__] = 0.f;
/* L20: */
                            }
                            ioff += izero;
                            i__3 = n;
                            for (i__ = izero; i__ <= i__3; ++i__) {
                                a[ioff] = 0.f;
                                ioff += lda;
/* L30: */
                            }
                        } else {
                            ioff = izero;
                            i__3 = izero - 1;
                            for (i__ = 1; i__ <= i__3; ++i__) {
                                a[ioff] = 0.f;
                                ioff += lda;
/* L40: */
                            }
                            ioff -= izero;
                            i__3 = n;
                            for (i__ = izero; i__ <= i__3; ++i__) {
                                a[ioff + i__] = 0.f;
/* L50: */
                            }
                        }
                    } else {
                        ioff = 0;
                        if (iuplo == 1) {

/*                       Set the first IZERO rows and columns to zero. */

                            i__3 = n;
                            for (j = 1; j <= i__3; ++j) {
                                i2 = min(j,izero);
                                i__4 = i2;
                                for (i__ = 1; i__ <= i__4; ++i__) {
                                    a[ioff + i__] = 0.f;
/* L60: */
                                }
                                ioff += lda;
/* L70: */
                            }
                        } else {

/*                       Set the last IZERO rows and columns to zero. */

                            i__3 = n;
                            for (j = 1; j <= i__3; ++j) {
                                i1 = max(j,izero);
                                i__4 = n;
                                for (i__ = i1; i__ <= i__4; ++i__) {
                                    a[ioff + i__] = 0.f;
/* L80: */
                                }
                                ioff += lda;
/* L90: */
                            }
                        }
                    }
                } else {
                    izero = 0;
                }

/*              Do for each value of NB in NBVAL */

                i__3 = *nnb;
                for (inb = 1; inb <= i__3; ++inb) {
                    nb = nbval[inb];
                    xlaenv_(&c__1, &nb);

/*                 Compute the L*D*L' or U*D*U' factorization of the */
/*                 matrix. */

                    slacpy_(uplo, &n, &n, &a[1], &lda, &afac[1], &lda);
                    lwork = max(2,nb) * lda;
                    s_copy(srnamc_1.srnamt, "SSYTRF", (ftnlen)32, (ftnlen)6);
                    ssytrf_(uplo, &n, &afac[1], &lda, &iwork[1], &ainv[1], &
                            lwork, &info);

/*                 Adjust the expected value of INFO to account for */
/*                 pivoting. */

                    k = izero;
                    if (k > 0) {
L100:
                        if (iwork[k] < 0) {
                            if (iwork[k] != -k) {
                                k = -iwork[k];
                                goto L100;
                            }
                        } else if (iwork[k] != k) {
                            k = iwork[k];
                            goto L100;
                        }
                    }

/*                 Check error code from SSYTRF. */

                    if (info != k) {
                        alaerh_(path, "SSYTRF", &info, &k, uplo, &n, &n, &
                                c_n1, &c_n1, &nb, &imat, &nfail, &nerrs, nout);
                    }
                    if (info != 0) {
                        trfcon = TRUE_;
                    } else {
                        trfcon = FALSE_;
                    }

/* +    TEST 1 */
/*                 Reconstruct matrix from factors and compute residual. */

                    ssyt01_(uplo, &n, &a[1], &lda, &afac[1], &lda, &iwork[1], 
                            &ainv[1], &lda, &rwork[1], result);
                    nt = 1;

/* +    TEST 2 */
/*                 Form the inverse and compute the residual. */

                    if (inb == 1 && ! trfcon) {
                        slacpy_(uplo, &n, &n, &afac[1], &lda, &ainv[1], &lda);
                        s_copy(srnamc_1.srnamt, "SSYTRI", (ftnlen)32, (ftnlen)
                                6);
                        ssytri_(uplo, &n, &ainv[1], &lda, &iwork[1], &work[1], 
                                 &info);

/*                 Check error code from SSYTRI. */

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

                        spot03_(uplo, &n, &a[1], &lda, &ainv[1], &lda, &work[
                                1], &lda, &rwork[1], &rcondc, &result[1]);
                        nt = 2;
                    }

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

                    i__4 = nt;
                    for (k = 1; k <= i__4; ++k) {
                        if (result[k - 1] >= *thresh) {
                            if (nfail == 0 && nerrs == 0) {
                                alahd_(nout, path);
                            }
                            io___39.ciunit = *nout;
                            s_wsfe(&io___39);
                            do_fio(&c__1, uplo, (ftnlen)1);
                            do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
                                    ;
                            do_fio(&c__1, (char *)&nb, (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;
                        }
/* L110: */
                    }
                    nrun += nt;

/*                 Skip the other tests if this is not the first block */
/*                 size. */

                    if (inb > 1) {
                        goto L150;
                    }

/*                 Do only the condition estimate if INFO is not 0. */

                    if (trfcon) {
                        rcondc = 0.f;
                        goto L140;
                    }

                    i__4 = *nns;
                    for (irhs = 1; irhs <= i__4; ++irhs) {
                        nrhs = nsval[irhs];

/* +    TEST 3 */
/*                 Solve and compute residual for  A * X = B. */

                        s_copy(srnamc_1.srnamt, "SLARHS", (ftnlen)32, (ftnlen)
                                6);
                        slarhs_(path, xtype, uplo, " ", &n, &n, &kl, &ku, &
                                nrhs, &a[1], &lda, &xact[1], &lda, &b[1], &
                                lda, iseed, &info);
                        slacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &lda);

                        s_copy(srnamc_1.srnamt, "SSYTRS", (ftnlen)32, (ftnlen)
                                6);
                        ssytrs_(uplo, &n, &nrhs, &afac[1], &lda, &iwork[1], &
                                x[1], &lda, &info);

/*                 Check error code from SSYTRS. */

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

                        slacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1], &
                                lda);
                        spot02_(uplo, &n, &nrhs, &a[1], &lda, &x[1], &lda, &
                                work[1], &lda, &rwork[1], &result[2]);

/* +    TEST 4 */
/*                 Check solution from generated exact solution. */

                        sget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &
                                rcondc, &result[3]);

/* +    TESTS 5, 6, and 7 */
/*                 Use iterative refinement to improve the solution. */

                        s_copy(srnamc_1.srnamt, "SSYRFS", (ftnlen)32, (ftnlen)
                                6);
                        ssyrfs_(uplo, &n, &nrhs, &a[1], &lda, &afac[1], &lda, 
                                &iwork[1], &b[1], &lda, &x[1], &lda, &rwork[1]
, &rwork[nrhs + 1], &work[1], &iwork[n + 1], &
                                info);

/*                 Check error code from SSYRFS. */

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

                        sget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &
                                rcondc, &result[4]);
                        spot05_(uplo, &n, &nrhs, &a[1], &lda, &b[1], &lda, &x[
                                1], &lda, &xact[1], &lda, &rwork[1], &rwork[
                                nrhs + 1], &result[5]);

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

                        for (k = 3; k <= 7; ++k) {
                            if (result[k - 1] >= *thresh) {
                                if (nfail == 0 && nerrs == 0) {
                                    alahd_(nout, path);
                                }
                                io___42.ciunit = *nout;
                                s_wsfe(&io___42);
                                do_fio(&c__1, uplo, (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;
                            }
/* L120: */
                        }
                        nrun += 5;
/* L130: */
                    }

/* +    TEST 8 */
/*                 Get an estimate of RCOND = 1/CNDNUM. */

L140:
                    anorm = slansy_("1", uplo, &n, &a[1], &lda, &rwork[1]);
                    s_copy(srnamc_1.srnamt, "SSYCON", (ftnlen)32, (ftnlen)6);
                    ssycon_(uplo, &n, &afac[1], &lda, &iwork[1], &anorm, &
                            rcond, &work[1], &iwork[n + 1], &info);

/*                 Check error code from SSYCON. */

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

                    result[7] = sget06_(&rcond, &rcondc);

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

                    if (result[7] >= *thresh) {
                        if (nfail == 0 && nerrs == 0) {
                            alahd_(nout, path);
                        }
                        io___44.ciunit = *nout;
                        s_wsfe(&io___44);
                        do_fio(&c__1, uplo, (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__8, (ftnlen)sizeof(integer));
                        do_fio(&c__1, (char *)&result[7], (ftnlen)sizeof(real)
                                );
                        e_wsfe();
                        ++nfail;
                    }
                    ++nrun;
L150:
                    ;
                }

L160:
                ;
            }
L170:
            ;
        }
/* L180: */
    }

/*     Print a summary of the results. */

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

    return 0;

/*     End of SCHKSY */

} /* schksy_ */