zchksp.c

Go to the documentation of this file.

/* zchksp.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__0 = 0;
static integer c_n1 = -1;
static integer c__1 = 1;
static integer c__8 = 8;

/* Subroutine */ int zchksp_(logical *dotype, integer *nn, integer *nval, 
        integer *nns, integer *nsval, doublereal *thresh, logical *tsterr, 
        integer *nmax, doublecomplex *a, doublecomplex *afac, doublecomplex *
        ainv, doublecomplex *b, doublecomplex *x, doublecomplex *xact, 
        doublecomplex *work, doublereal *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, "
            "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)";

    /* System generated locals */
    integer i__1, i__2, i__3, i__4, i__5;

    /* 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, in, kl, ku, nt, lda, npp, 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];
    extern doublereal dget06_(doublereal *, doublereal *);
    extern logical lsame_(char *, char *);
    doublereal rcond;
    integer nimat;
    doublereal anorm;
    extern /* Subroutine */ int zget04_(integer *, integer *, doublecomplex *, 
             integer *, doublecomplex *, integer *, doublereal *, doublereal *
);
    integer iuplo, izero, nerrs;
    extern /* Subroutine */ int zspt01_(char *, integer *, doublecomplex *, 
            doublecomplex *, integer *, doublecomplex *, integer *, 
            doublereal *, doublereal *);
    logical zerot;
    extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *), zppt05_(char *, integer *, integer *, 
             doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
            integer *, doublecomplex *, integer *, doublereal *, doublereal *, 
             doublereal *), zspt02_(char *, integer *, integer *, 
            doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
            integer *, doublereal *, doublereal *), zspt03_(char *, 
            integer *, doublecomplex *, doublecomplex *, doublecomplex *, 
            integer *, doublereal *, doublereal *, doublereal *);
    char xtype[1];
    extern /* Subroutine */ int zlatb4_(char *, integer *, integer *, integer 
            *, char *, integer *, integer *, doublereal *, integer *, 
            doublereal *, char *), alaerh_(char *, 
            char *, integer *, integer *, char *, integer *, integer *, 
            integer *, integer *, integer *, integer *, integer *, integer *, 
            integer *);
    doublereal rcondc;
    char packit[1];
    extern /* Subroutine */ int alasum_(char *, integer *, integer *, integer 
            *, integer *);
    doublereal cndnum;
    logical trfcon;
    extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *), 
            zlarhs_(char *, char *, char *, char *, integer *, integer *, 
            integer *, integer *, integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *, integer *, 
             integer *);
    extern doublereal zlansp_(char *, char *, integer *, doublecomplex *, 
            doublereal *);
    extern /* Subroutine */ int zlatms_(integer *, integer *, char *, integer 
            *, char *, doublereal *, integer *, doublereal *, doublereal *, 
            integer *, integer *, char *, doublecomplex *, integer *, 
            doublecomplex *, integer *), zspcon_(char 
            *, integer *, doublecomplex *, integer *, doublereal *, 
            doublereal *, doublecomplex *, integer *), zlatsp_(char *, 
             integer *, doublecomplex *, integer *);
    doublereal result[8];
    extern /* Subroutine */ int zsprfs_(char *, integer *, integer *, 
            doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
            integer *, doublecomplex *, integer *, doublereal *, doublereal *, 
             doublecomplex *, doublereal *, integer *), zsptrf_(char *
, integer *, doublecomplex *, integer *, integer *), 
            zsptri_(char *, integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *), zerrsy_(char *, integer *), zsptrs_(char *, integer *, integer *, doublecomplex *, 
            integer *, doublecomplex *, integer *, integer *);

    /* Fortran I/O blocks */
    static cilist io___38 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___41 = { 0, 0, 0, fmt_9998, 0 };
    static cilist io___43 = { 0, 0, 0, fmt_9999, 0 };



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

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

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

/*  ZCHKSP tests ZSPTRF, -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. */

/*  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) DOUBLE PRECISION */
/*          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) COMPLEX*16 array, dimension */
/*                      (NMAX*(NMAX+1)/2) */

/*  AFAC    (workspace) COMPLEX*16 array, dimension */
/*                      (NMAX*(NMAX+1)/2) */

/*  AINV    (workspace) COMPLEX*16 array, dimension */
/*                      (NMAX*(NMAX+1)/2) */

/*  B       (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */
/*          where NSMAX is the largest entry in NSVAL. */

/*  X       (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */

/*  XACT    (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */

/*  WORK    (workspace) COMPLEX*16 array, dimension */
/*                      (NMAX*max(2,NSMAX)) */

/*  RWORK   (workspace) DOUBLE PRECISION array, */
/*                                 dimension (NMAX+2*NSMAX) */

/*  IWORK   (workspace) INTEGER array, dimension (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;
    --nval;
    --dotype;

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

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

    s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17);
    s_copy(path + 1, "SP", (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) {
        zerrsy_(path, nout);
    }
    infoc_1.infot = 0;

/*     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 = 11;
        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 L160;
            }

/*           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 L160;
            }

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

            for (iuplo = 1; iuplo <= 2; ++iuplo) {
                *(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1];
                if (lsame_(uplo, "U")) {
                    *(unsigned char *)packit = 'C';
                } else {
                    *(unsigned char *)packit = 'R';
                }

                if (imat != 11) {

/*                 Set up parameters with ZLATB4 and generate a test */
/*                 matrix with ZLATMS. */

                    zlatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &
                            mode, &cndnum, dist);

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

/*                 Check error code from ZLATMS. */

                    if (info != 0) {
                        alaerh_(path, "ZLATMS", &info, &c__0, uplo, &n, &n, &
                                c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, 
                                nout);
                        goto L150;
                    }

/*                 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) * izero / 2;
                                i__3 = izero - 1;
                                for (i__ = 1; i__ <= i__3; ++i__) {
                                    i__4 = ioff + i__;
                                    a[i__4].r = 0., a[i__4].i = 0.;
/* L20: */
                                }
                                ioff += izero;
                                i__3 = n;
                                for (i__ = izero; i__ <= i__3; ++i__) {
                                    i__4 = ioff;
                                    a[i__4].r = 0., a[i__4].i = 0.;
                                    ioff += i__;
/* L30: */
                                }
                            } else {
                                ioff = izero;
                                i__3 = izero - 1;
                                for (i__ = 1; i__ <= i__3; ++i__) {
                                    i__4 = ioff;
                                    a[i__4].r = 0., a[i__4].i = 0.;
                                    ioff = ioff + n - i__;
/* L40: */
                                }
                                ioff -= izero;
                                i__3 = n;
                                for (i__ = izero; i__ <= i__3; ++i__) {
                                    i__4 = ioff + i__;
                                    a[i__4].r = 0., a[i__4].i = 0.;
/* L50: */
                                }
                            }
                        } else {
                            if (iuplo == 1) {

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

                                ioff = 0;
                                i__3 = n;
                                for (j = 1; j <= i__3; ++j) {
                                    i2 = min(j,izero);
                                    i__4 = i2;
                                    for (i__ = 1; i__ <= i__4; ++i__) {
                                        i__5 = ioff + i__;
                                        a[i__5].r = 0., a[i__5].i = 0.;
/* L60: */
                                    }
                                    ioff += j;
/* L70: */
                                }
                            } else {

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

                                ioff = 0;
                                i__3 = n;
                                for (j = 1; j <= i__3; ++j) {
                                    i1 = max(j,izero);
                                    i__4 = n;
                                    for (i__ = i1; i__ <= i__4; ++i__) {
                                        i__5 = ioff + i__;
                                        a[i__5].r = 0., a[i__5].i = 0.;
/* L80: */
                                    }
                                    ioff = ioff + n - j;
/* L90: */
                                }
                            }
                        }
                    } else {
                        izero = 0;
                    }
                } else {

/*                 Use a special block diagonal matrix to test alternate */
/*                 code for the 2 x 2 blocks. */

                    zlatsp_(uplo, &n, &a[1], iseed);
                }

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

                npp = n * (n + 1) / 2;
                zcopy_(&npp, &a[1], &c__1, &afac[1], &c__1);
                s_copy(srnamc_1.srnamt, "ZSPTRF", (ftnlen)32, (ftnlen)6);
                zsptrf_(uplo, &n, &afac[1], &iwork[1], &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 ZSPTRF. */

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

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

                zspt01_(uplo, &n, &a[1], &afac[1], &iwork[1], &ainv[1], &lda, 
                        &rwork[1], result);
                nt = 1;

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

                if (! trfcon) {
                    zcopy_(&npp, &afac[1], &c__1, &ainv[1], &c__1);
                    s_copy(srnamc_1.srnamt, "ZSPTRI", (ftnlen)32, (ftnlen)6);
                    zsptri_(uplo, &n, &ainv[1], &iwork[1], &work[1], &info);

/*              Check error code from ZSPTRI. */

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

                    zspt03_(uplo, &n, &a[1], &ainv[1], &work[1], &lda, &rwork[
                            1], &rcondc, &result[1]);
                    nt = 2;
                }

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

                i__3 = nt;
                for (k = 1; k <= i__3; ++k) {
                    if (result[k - 1] >= *thresh) {
                        if (nfail == 0 && nerrs == 0) {
                            alahd_(nout, path);
                        }
                        io___38.ciunit = *nout;
                        s_wsfe(&io___38);
                        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 *)&k, (ftnlen)sizeof(integer));
                        do_fio(&c__1, (char *)&result[k - 1], (ftnlen)sizeof(
                                doublereal));
                        e_wsfe();
                        ++nfail;
                    }
/* L110: */
                }
                nrun += nt;

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

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

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

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

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

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

/*              Check error code from ZSPTRS. */

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

                    zlacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1], &lda);
                    zspt02_(uplo, &n, &nrhs, &a[1], &x[1], &lda, &work[1], &
                            lda, &rwork[1], &result[2]);

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

                    zget04_(&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, "ZSPRFS", (ftnlen)32, (ftnlen)6);
                    zsprfs_(uplo, &n, &nrhs, &a[1], &afac[1], &iwork[1], &b[1]
, &lda, &x[1], &lda, &rwork[1], &rwork[nrhs + 1], 
                            &work[1], &rwork[(nrhs << 1) + 1], &info);

/*              Check error code from ZSPRFS. */

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

                    zget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &rcondc, &
                            result[4]);
                    zppt05_(uplo, &n, &nrhs, &a[1], &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___41.ciunit = *nout;
                            s_wsfe(&io___41);
                            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(doublereal));
                            e_wsfe();
                            ++nfail;
                        }
/* L120: */
                    }
                    nrun += 5;
/* L130: */
                }

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

L140:
                anorm = zlansp_("1", uplo, &n, &a[1], &rwork[1]);
                s_copy(srnamc_1.srnamt, "ZSPCON", (ftnlen)32, (ftnlen)6);
                zspcon_(uplo, &n, &afac[1], &iwork[1], &anorm, &rcond, &work[
                        1], &info);

/*              Check error code from ZSPCON. */

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

                result[7] = dget06_(&rcond, &rcondc);

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

                if (result[7] >= *thresh) {
                    if (nfail == 0 && nerrs == 0) {
                        alahd_(nout, path);
                    }
                    io___43.ciunit = *nout;
                    s_wsfe(&io___43);
                    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(
                            doublereal));
                    e_wsfe();
                    ++nfail;
                }
                ++nrun;
L150:
                ;
            }
L160:
            ;
        }
/* L170: */
    }

/*     Print a summary of the results. */

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

    return 0;

/*     End of ZCHKSP */

} /* zchksp_ */