zchkpt.c

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/* zchkpt.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 doublereal c_b48 = 1.;
static doublereal c_b49 = 0.;
static integer c__7 = 7;

/* Subroutine */ int zchkpt_(logical *dotype, integer *nn, integer *nval, 
        integer *nns, integer *nsval, doublereal *thresh, logical *tsterr, 
        doublecomplex *a, doublereal *d__, doublecomplex *e, doublecomplex *b, 
         doublecomplex *x, doublecomplex *xact, doublecomplex *work, 
        doublereal *rwork, integer *nout)
{
    /* Initialized data */

    static integer iseedy[4] = { 0,0,0,1 };
    static char uplos[1*2] = "U" "L";

    /* Format strings */
    static char fmt_9999[] = "(\002 N =\002,i5,\002, type \002,i2,\002, te"
            "st \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, ratio "
            "= \002,g12.5)";

    /* System generated locals */
    integer i__1, i__2, i__3, i__4, i__5;
    doublereal d__1, d__2;

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

    /* Local variables */
    integer i__, j, k, n;
    doublecomplex z__[3];
    integer ia, in, kl, ku, ix, lda;
    doublereal cond;
    integer mode;
    doublereal dmax__;
    integer imat, info;
    char path[3], dist[1];
    integer irhs, nrhs;
    char uplo[1], type__[1];
    integer nrun;
    extern /* Subroutine */ int alahd_(integer *, char *), dscal_(
            integer *, doublereal *, doublereal *, integer *);
    integer nfail, iseed[4];
    extern doublereal dget06_(doublereal *, doublereal *);
    doublereal rcond;
    integer nimat;
    doublereal anorm;
    extern /* Subroutine */ int zget04_(integer *, integer *, doublecomplex *, 
             integer *, doublecomplex *, integer *, doublereal *, doublereal *
), dcopy_(integer *, doublereal *, integer *, doublereal *, 
            integer *);
    integer iuplo, izero, nerrs;
    logical zerot;
    extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *), zptt01_(integer *, doublereal *, 
            doublecomplex *, doublereal *, doublecomplex *, doublecomplex *, 
            doublereal *), zptt02_(char *, integer *, integer *, doublereal *, 
             doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
            integer *, doublereal *), zptt05_(integer *, integer *, 
            doublereal *, doublecomplex *, doublecomplex *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *, 
            doublereal *, doublereal *, doublereal *), 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 *);
    extern integer idamax_(integer *, doublereal *, integer *);
    doublereal rcondc;
    extern /* Subroutine */ int zdscal_(integer *, doublereal *, 
            doublecomplex *, integer *), alasum_(char *, integer *, integer *, 
             integer *, integer *), dlarnv_(integer *, integer *, 
            integer *, doublereal *);
    doublereal ainvnm;
    extern doublereal zlanht_(char *, integer *, doublereal *, doublecomplex *
);
    extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *);
    extern doublereal dzasum_(integer *, doublecomplex *, integer *);
    extern /* Subroutine */ int zlaptm_(char *, integer *, integer *, 
            doublereal *, doublereal *, doublecomplex *, doublecomplex *, 
            integer *, doublereal *, doublecomplex *, integer *), 
            zlatms_(integer *, integer *, char *, integer *, char *, 
            doublereal *, integer *, doublereal *, doublereal *, integer *, 
            integer *, char *, doublecomplex *, integer *, doublecomplex *, 
            integer *), zlarnv_(integer *, integer *, 
            integer *, doublecomplex *), zerrgt_(char *, integer *);
    doublereal result[7];
    extern /* Subroutine */ int zptcon_(integer *, doublereal *, 
            doublecomplex *, doublereal *, doublereal *, doublereal *, 
            integer *), zptrfs_(char *, integer *, integer *, doublereal *, 
            doublecomplex *, doublereal *, doublecomplex *, doublecomplex *, 
            integer *, doublecomplex *, integer *, doublereal *, doublereal *, 
             doublecomplex *, doublereal *, integer *), zpttrf_(
            integer *, doublereal *, doublecomplex *, integer *), zpttrs_(
            char *, integer *, integer *, doublereal *, doublecomplex *, 
            doublecomplex *, integer *, integer *);

    /* Fortran I/O blocks */
    static cilist io___30 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___38 = { 0, 0, 0, fmt_9998, 0 };
    static cilist io___40 = { 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 */
/*  ======= */

/*  ZCHKPT tests ZPTTRF, -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. */

/*  A       (workspace) COMPLEX*16 array, dimension (NMAX*2) */

/*  D       (workspace) DOUBLE PRECISION array, dimension (NMAX*2) */

/*  E       (workspace) COMPLEX*16 array, dimension (NMAX*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(3,NSMAX)) */

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

/*  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 */
    --rwork;
    --work;
    --xact;
    --x;
    --b;
    --e;
    --d__;
    --a;
    --nsval;
    --nval;
    --dotype;

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

    s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17);
    s_copy(path + 1, "PT", (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) {
        zerrgt_(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];
        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 (n > 0 && ! dotype[imat]) {
                goto L110;
            }

/*           Set up parameters with ZLATB4. */

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

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

/*              Type 1-6:  generate a Hermitian tridiagonal matrix of */
/*              known condition number in lower triangular band storage. */

                s_copy(srnamc_1.srnamt, "ZLATMS", (ftnlen)32, (ftnlen)6);
                zlatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &cond, 
                        &anorm, &kl, &ku, "B", &a[1], &c__2, &work[1], &info);

/*              Check the error code from ZLATMS. */

                if (info != 0) {
                    alaerh_(path, "ZLATMS", &info, &c__0, " ", &n, &n, &kl, &
                            ku, &c_n1, &imat, &nfail, &nerrs, nout);
                    goto L110;
                }
                izero = 0;

/*              Copy the matrix to D and E. */

                ia = 1;
                i__3 = n - 1;
                for (i__ = 1; i__ <= i__3; ++i__) {
                    i__4 = ia;
                    d__[i__] = a[i__4].r;
                    i__4 = i__;
                    i__5 = ia + 1;
                    e[i__4].r = a[i__5].r, e[i__4].i = a[i__5].i;
                    ia += 2;
/* L20: */
                }
                if (n > 0) {
                    i__3 = ia;
                    d__[n] = a[i__3].r;
                }
            } else {

/*              Type 7-12:  generate a diagonally dominant matrix with */
/*              unknown condition number in the vectors D and E. */

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

/*                 Let E be complex, D real, with values from [-1,1]. */

                    dlarnv_(&c__2, iseed, &n, &d__[1]);
                    i__3 = n - 1;
                    zlarnv_(&c__2, iseed, &i__3, &e[1]);

/*                 Make the tridiagonal matrix diagonally dominant. */

                    if (n == 1) {
                        d__[1] = abs(d__[1]);
                    } else {
                        d__[1] = abs(d__[1]) + z_abs(&e[1]);
                        d__[n] = (d__1 = d__[n], abs(d__1)) + z_abs(&e[n - 1])
                                ;
                        i__3 = n - 1;
                        for (i__ = 2; i__ <= i__3; ++i__) {
                            d__[i__] = (d__1 = d__[i__], abs(d__1)) + z_abs(&
                                    e[i__]) + z_abs(&e[i__ - 1]);
/* L30: */
                        }
                    }

/*                 Scale D and E so the maximum element is ANORM. */

                    ix = idamax_(&n, &d__[1], &c__1);
                    dmax__ = d__[ix];
                    d__1 = anorm / dmax__;
                    dscal_(&n, &d__1, &d__[1], &c__1);
                    i__3 = n - 1;
                    d__1 = anorm / dmax__;
                    zdscal_(&i__3, &d__1, &e[1], &c__1);

                } else if (izero > 0) {

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

                    if (izero == 1) {
                        d__[1] = z__[1].r;
                        if (n > 1) {
                            e[1].r = z__[2].r, e[1].i = z__[2].i;
                        }
                    } else if (izero == n) {
                        i__3 = n - 1;
                        e[i__3].r = z__[0].r, e[i__3].i = z__[0].i;
                        i__3 = n;
                        d__[i__3] = z__[1].r;
                    } else {
                        i__3 = izero - 1;
                        e[i__3].r = z__[0].r, e[i__3].i = z__[0].i;
                        i__3 = izero;
                        d__[i__3] = z__[1].r;
                        i__3 = izero;
                        e[i__3].r = z__[2].r, e[i__3].i = z__[2].i;
                    }
                }

/*              For types 8-10, set one row and column of the matrix to */
/*              zero. */

                izero = 0;
                if (imat == 8) {
                    izero = 1;
                    z__[1].r = d__[1], z__[1].i = 0.;
                    d__[1] = 0.;
                    if (n > 1) {
                        z__[2].r = e[1].r, z__[2].i = e[1].i;
                        e[1].r = 0., e[1].i = 0.;
                    }
                } else if (imat == 9) {
                    izero = n;
                    if (n > 1) {
                        i__3 = n - 1;
                        z__[0].r = e[i__3].r, z__[0].i = e[i__3].i;
                        i__3 = n - 1;
                        e[i__3].r = 0., e[i__3].i = 0.;
                    }
                    i__3 = n;
                    z__[1].r = d__[i__3], z__[1].i = 0.;
                    d__[n] = 0.;
                } else if (imat == 10) {
                    izero = (n + 1) / 2;
                    if (izero > 1) {
                        i__3 = izero - 1;
                        z__[0].r = e[i__3].r, z__[0].i = e[i__3].i;
                        i__3 = izero;
                        z__[2].r = e[i__3].r, z__[2].i = e[i__3].i;
                        i__3 = izero - 1;
                        e[i__3].r = 0., e[i__3].i = 0.;
                        i__3 = izero;
                        e[i__3].r = 0., e[i__3].i = 0.;
                    }
                    i__3 = izero;
                    z__[1].r = d__[i__3], z__[1].i = 0.;
                    d__[izero] = 0.;
                }
            }

            dcopy_(&n, &d__[1], &c__1, &d__[n + 1], &c__1);
            if (n > 1) {
                i__3 = n - 1;
                zcopy_(&i__3, &e[1], &c__1, &e[n + 1], &c__1);
            }

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

            zpttrf_(&n, &d__[n + 1], &e[n + 1], &info);

/*           Check error code from ZPTTRF. */

            if (info != izero) {
                alaerh_(path, "ZPTTRF", &info, &izero, " ", &n, &n, &c_n1, &
                        c_n1, &c_n1, &imat, &nfail, &nerrs, nout);
                goto L110;
            }

            if (info > 0) {
                rcondc = 0.;
                goto L100;
            }

            zptt01_(&n, &d__[1], &e[1], &d__[n + 1], &e[n + 1], &work[1], 
                    result);

/*           Print the test ratio if greater than or equal to THRESH. */

            if (result[0] >= *thresh) {
                if (nfail == 0 && nerrs == 0) {
                    alahd_(nout, path);
                }
                io___30.ciunit = *nout;
                s_wsfe(&io___30);
                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(doublereal));
                e_wsfe();
                ++nfail;
            }
            ++nrun;

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

/*           Compute norm(A). */

            anorm = zlanht_("1", &n, &d__[1], &e[1]);

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

            ainvnm = 0.;
            i__3 = n;
            for (i__ = 1; i__ <= i__3; ++i__) {
                i__4 = n;
                for (j = 1; j <= i__4; ++j) {
                    i__5 = j;
                    x[i__5].r = 0., x[i__5].i = 0.;
/* L40: */
                }
                i__4 = i__;
                x[i__4].r = 1., x[i__4].i = 0.;
                zpttrs_("Lower", &n, &c__1, &d__[n + 1], &e[n + 1], &x[1], &
                        lda, &info);
/* Computing MAX */
                d__1 = ainvnm, d__2 = dzasum_(&n, &x[1], &c__1);
                ainvnm = max(d__1,d__2);
/* L50: */
            }
/* Computing MAX */
            d__1 = 1., d__2 = anorm * ainvnm;
            rcondc = 1. / max(d__1,d__2);

            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) {
                    zlarnv_(&c__2, iseed, &n, &xact[ix]);
                    ix += lda;
/* L60: */
                }

                for (iuplo = 1; iuplo <= 2; ++iuplo) {

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

                    *(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 
                            1];

/*              Set the right hand side. */

                    zlaptm_(uplo, &n, &nrhs, &c_b48, &d__[1], &e[1], &xact[1], 
                             &lda, &c_b49, &b[1], &lda);

/* +    TEST 2 */
/*              Solve A*x = b and compute the residual. */

                    zlacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &lda);
                    zpttrs_(uplo, &n, &nrhs, &d__[n + 1], &e[n + 1], &x[1], &
                            lda, &info);

/*              Check error code from ZPTTRS. */

                    if (info != 0) {
                        alaerh_(path, "ZPTTRS", &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);
                    zptt02_(uplo, &n, &nrhs, &d__[1], &e[1], &x[1], &lda, &
                            work[1], &lda, &result[1]);

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

                    zget04_(&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, "ZPTRFS", (ftnlen)32, (ftnlen)6);
                    zptrfs_(uplo, &n, &nrhs, &d__[1], &e[1], &d__[n + 1], &e[
                            n + 1], &b[1], &lda, &x[1], &lda, &rwork[1], &
                            rwork[nrhs + 1], &work[1], &rwork[(nrhs << 1) + 1]
, &info);

/*              Check error code from ZPTRFS. */

                    if (info != 0) {
                        alaerh_(path, "ZPTRFS", &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[3]);
                    zptt05_(&n, &nrhs, &d__[1], &e[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___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 *)&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;
                        }
/* L70: */
                    }
                    nrun += 5;

/* L80: */
                }
/* L90: */
            }

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

L100:
            s_copy(srnamc_1.srnamt, "ZPTCON", (ftnlen)32, (ftnlen)6);
            zptcon_(&n, &d__[n + 1], &e[n + 1], &anorm, &rcond, &rwork[1], &
                    info);

/*           Check error code from ZPTCON. */

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

            result[6] = dget06_(&rcond, &rcondc);

/*           Print the test ratio if greater than or equal to THRESH. */

            if (result[6] >= *thresh) {
                if (nfail == 0 && nerrs == 0) {
                    alahd_(nout, path);
                }
                io___40.ciunit = *nout;
                s_wsfe(&io___40);
                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(doublereal));
                e_wsfe();
                ++nfail;
            }
            ++nrun;
L110:
            ;
        }
/* L120: */
    }

/*     Print a summary of the results. */

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

    return 0;

/*     End of ZCHKPT */

} /* zchkpt_ */