zdrvsy.c

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/* zdrvsy.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__1 = 1;
static integer c__2 = 2;
static integer c__0 = 0;
static integer c_n1 = -1;
static doublecomplex c_b49 = {0.,0.};

/* Subroutine */ int zdrvsy_(logical *dotype, integer *nn, integer *nval, 
        integer *nrhs, 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";
    static char facts[1*2] = "F" "N";

    /* Format strings */
    static char fmt_9999[] = "(1x,a,\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[] = "(1x,a,\002, FACT='\002,a1,\002', UPLO='\002,"
            "a1,\002', N =\002,i5,\002, type \002,i2,\002, test \002,i2,\002,"
            " ratio =\002,g12.5)";

    /* System generated locals */
    address a__1[2];
    integer i__1, i__2, i__3, i__4, i__5, i__6[2];
    char ch__1[2];

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

    /* Local variables */
    integer i__, j, k, n, i1, i2, k1, nb, in, kl, ku, nt, lda;
    char fact[1];
    integer ioff, mode, imat, info;
    char path[3], dist[1], uplo[1], type__[1];
    integer nrun, ifact, nfail, iseed[4];
    extern doublereal dget06_(doublereal *, doublereal *);
    integer nbmin;
    doublereal rcond;
    integer nimat;
    doublereal anorm;
    extern /* Subroutine */ int zget04_(integer *, integer *, doublecomplex *, 
             integer *, doublecomplex *, integer *, doublereal *, doublereal *
);
    integer iuplo, izero, nerrs, lwork;
    extern /* Subroutine */ int zpot05_(char *, integer *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *, 
            doublereal *, doublereal *, doublereal *);
    logical zerot;
    char xtype[1];
    extern /* Subroutine */ int zsyt01_(char *, integer *, doublecomplex *, 
            integer *, doublecomplex *, integer *, integer *, doublecomplex *, 
             integer *, doublereal *, doublereal *), zsyt02_(char *, 
            integer *, integer *, doublecomplex *, integer *, doublecomplex *, 
             integer *, doublecomplex *, integer *, doublereal *, doublereal *
), zsysv_(char *, integer *, integer *, doublecomplex *, 
            integer *, integer *, doublecomplex *, integer *, doublecomplex *, 
             integer *, integer *), zlatb4_(char *, integer *, 
            integer *, integer *, char *, integer *, integer *, doublereal *, 
            integer *, doublereal *, char *), aladhd_(
            integer *, char *), alaerh_(char *, char *, integer *, 
            integer *, char *, integer *, integer *, integer *, integer *, 
            integer *, integer *, integer *, integer *, integer *);
    doublereal rcondc;
    extern /* Subroutine */ int alasvm_(char *, integer *, integer *, integer 
            *, integer *);
    doublereal cndnum, ainvnm;
    extern /* Subroutine */ int xlaenv_(integer *, integer *), 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 *), zlaset_(char *, integer *, integer *, 
            doublecomplex *, doublecomplex *, doublecomplex *, integer *), zlatms_(integer *, integer *, char *, integer *, char *, 
            doublereal *, integer *, doublereal *, doublereal *, integer *, 
            integer *, char *, doublecomplex *, integer *, doublecomplex *, 
            integer *);
    doublereal result[6];
    extern doublereal zlansy_(char *, char *, integer *, doublecomplex *, 
            integer *, doublereal *);
    extern /* Subroutine */ int zlatsy_(char *, integer *, doublecomplex *, 
            integer *, integer *), zerrvx_(char *, integer *),
             zsytrf_(char *, integer *, doublecomplex *, integer *, integer *, 
             doublecomplex *, integer *, integer *), zsytri_(char *, 
            integer *, doublecomplex *, integer *, integer *, doublecomplex *, 
             integer *), zsysvx_(char *, char *, integer *, integer *, 
             doublecomplex *, integer *, doublecomplex *, integer *, integer *
, doublecomplex *, integer *, doublecomplex *, integer *, 
            doublereal *, doublereal *, doublereal *, doublecomplex *, 
            integer *, doublereal *, integer *);

    /* Fortran I/O blocks */
    static cilist io___42 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___45 = { 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 */
/*  ======= */

/*  ZDRVSY tests the driver routines ZSYSV and -SVX. */

/*  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. */

/*  NRHS    (input) INTEGER */
/*          The number of right hand side vectors to be generated for */
/*          each linear system. */

/*  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) */

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

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

/*  B       (workspace) COMPLEX*16 array, dimension (NMAX*NRHS) */

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

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

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

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

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

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

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. Local Arrays .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Scalars in Common .. */
/*     .. */
/*     .. Common blocks .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Data statements .. */
    /* Parameter adjustments */
    --iwork;
    --rwork;
    --work;
    --xact;
    --x;
    --b;
    --ainv;
    --afac;
    --a;
    --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, "SY", (ftnlen)2, (ftnlen)2);
    nrun = 0;
    nfail = 0;
    nerrs = 0;
    for (i__ = 1; i__ <= 4; ++i__) {
        iseed[i__ - 1] = iseedy[i__ - 1];
/* L10: */
    }
/* Computing MAX */
    i__1 = *nmax << 1, i__2 = *nmax * *nrhs;
    lwork = max(i__1,i__2);

/*     Test the error exits */

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

/*     Set the block size and minimum block size for testing. */

    nb = 1;
    nbmin = 2;
    xlaenv_(&c__1, &nb);
    xlaenv_(&c__2, &nbmin);

/*     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 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];

                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, uplo, &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 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__) {
                                    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 += lda;
/* 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 += lda;
/* 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 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 += lda;
/* L70: */
                                }
                            } else {

/*                          Set the last IZERO rows 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 += lda;
/* L90: */
                                }
                            }
                        }
                    } else {
                        izero = 0;
                    }
                } else {

/*                 IMAT = NTYPES:  Use a special block diagonal matrix to */
/*                 test alternate code for the 2-by-2 blocks. */

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

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

/*                 Do first for FACT = 'F', then for other values. */

                    *(unsigned char *)fact = *(unsigned char *)&facts[ifact - 
                            1];

/*                 Compute the condition number for comparison with */
/*                 the value returned by ZSYSVX. */

                    if (zerot) {
                        if (ifact == 1) {
                            goto L150;
                        }
                        rcondc = 0.;

                    } else if (ifact == 1) {

/*                    Compute the 1-norm of A. */

                        anorm = zlansy_("1", uplo, &n, &a[1], &lda, &rwork[1]);

/*                    Factor the matrix A. */

                        zlacpy_(uplo, &n, &n, &a[1], &lda, &afac[1], &lda);
                        zsytrf_(uplo, &n, &afac[1], &lda, &iwork[1], &work[1], 
                                 &lwork, &info);

/*                    Compute inv(A) and take its norm. */

                        zlacpy_(uplo, &n, &n, &afac[1], &lda, &ainv[1], &lda);
                        zsytri_(uplo, &n, &ainv[1], &lda, &iwork[1], &work[1], 
                                 &info);
                        ainvnm = zlansy_("1", uplo, &n, &ainv[1], &lda, &
                                rwork[1]);

/*                    Compute the 1-norm condition number of A. */

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

/*                 Form an exact solution and set the right hand side. */

                    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);
                    *(unsigned char *)xtype = 'C';

/*                 --- Test ZSYSV  --- */

                    if (ifact == 2) {
                        zlacpy_(uplo, &n, &n, &a[1], &lda, &afac[1], &lda);
                        zlacpy_("Full", &n, nrhs, &b[1], &lda, &x[1], &lda);

/*                    Factor the matrix and solve the system using ZSYSV. */

                        s_copy(srnamc_1.srnamt, "ZSYSV ", (ftnlen)32, (ftnlen)
                                6);
                        zsysv_(uplo, &n, nrhs, &afac[1], &lda, &iwork[1], &x[
                                1], &lda, &work[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 ZSYSV . */

                        if (info != k) {
                            alaerh_(path, "ZSYSV ", &info, &k, uplo, &n, &n, &
                                    c_n1, &c_n1, nrhs, &imat, &nfail, &nerrs, 
                                    nout);
                            goto L120;
                        } else if (info != 0) {
                            goto L120;
                        }

/*                    Reconstruct matrix from factors and compute */
/*                    residual. */

                        zsyt01_(uplo, &n, &a[1], &lda, &afac[1], &lda, &iwork[
                                1], &ainv[1], &lda, &rwork[1], result);

/*                    Compute residual of the computed solution. */

                        zlacpy_("Full", &n, nrhs, &b[1], &lda, &work[1], &lda);
                        zsyt02_(uplo, &n, nrhs, &a[1], &lda, &x[1], &lda, &
                                work[1], &lda, &rwork[1], &result[1]);

/*                    Check solution from generated exact solution. */

                        zget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda, &
                                rcondc, &result[2]);
                        nt = 3;

/*                    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) {
                                    aladhd_(nout, path);
                                }
                                io___42.ciunit = *nout;
                                s_wsfe(&io___42);
                                do_fio(&c__1, "ZSYSV ", (ftnlen)6);
                                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;
L120:
                        ;
                    }

/*                 --- Test ZSYSVX --- */

                    if (ifact == 2) {
                        zlaset_(uplo, &n, &n, &c_b49, &c_b49, &afac[1], &lda);
                    }
                    zlaset_("Full", &n, nrhs, &c_b49, &c_b49, &x[1], &lda);

/*                 Solve the system and compute the condition number and */
/*                 error bounds using ZSYSVX. */

                    s_copy(srnamc_1.srnamt, "ZSYSVX", (ftnlen)32, (ftnlen)6);
                    zsysvx_(fact, uplo, &n, nrhs, &a[1], &lda, &afac[1], &lda, 
                             &iwork[1], &b[1], &lda, &x[1], &lda, &rcond, &
                            rwork[1], &rwork[*nrhs + 1], &work[1], &lwork, &
                            rwork[(*nrhs << 1) + 1], &info);

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

                    k = izero;
                    if (k > 0) {
L130:
                        if (iwork[k] < 0) {
                            if (iwork[k] != -k) {
                                k = -iwork[k];
                                goto L130;
                            }
                        } else if (iwork[k] != k) {
                            k = iwork[k];
                            goto L130;
                        }
                    }

/*                 Check the error code from ZSYSVX. */

                    if (info != k) {
/* Writing concatenation */
                        i__6[0] = 1, a__1[0] = fact;
                        i__6[1] = 1, a__1[1] = uplo;
                        s_cat(ch__1, a__1, i__6, &c__2, (ftnlen)2);
                        alaerh_(path, "ZSYSVX", &info, &k, ch__1, &n, &n, &
                                c_n1, &c_n1, nrhs, &imat, &nfail, &nerrs, 
                                nout);
                        goto L150;
                    }

                    if (info == 0) {
                        if (ifact >= 2) {

/*                       Reconstruct matrix from factors and compute */
/*                       residual. */

                            zsyt01_(uplo, &n, &a[1], &lda, &afac[1], &lda, &
                                    iwork[1], &ainv[1], &lda, &rwork[(*nrhs <<
                                     1) + 1], result);
                            k1 = 1;
                        } else {
                            k1 = 2;
                        }

/*                    Compute residual of the computed solution. */

                        zlacpy_("Full", &n, nrhs, &b[1], &lda, &work[1], &lda);
                        zsyt02_(uplo, &n, nrhs, &a[1], &lda, &x[1], &lda, &
                                work[1], &lda, &rwork[(*nrhs << 1) + 1], &
                                result[1]);

/*                    Check solution from generated exact solution. */

                        zget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda, &
                                rcondc, &result[2]);

/*                    Check the error bounds from iterative refinement. */

                        zpot05_(uplo, &n, nrhs, &a[1], &lda, &b[1], &lda, &x[
                                1], &lda, &xact[1], &lda, &rwork[1], &rwork[*
                                nrhs + 1], &result[3]);
                    } else {
                        k1 = 6;
                    }

/*                 Compare RCOND from ZSYSVX with the computed value */
/*                 in RCONDC. */

                    result[5] = dget06_(&rcond, &rcondc);

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

                    for (k = k1; k <= 6; ++k) {
                        if (result[k - 1] >= *thresh) {
                            if (nfail == 0 && nerrs == 0) {
                                aladhd_(nout, path);
                            }
                            io___45.ciunit = *nout;
                            s_wsfe(&io___45);
                            do_fio(&c__1, "ZSYSVX", (ftnlen)6);
                            do_fio(&c__1, fact, (ftnlen)1);
                            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;
                        }
/* L140: */
                    }
                    nrun = nrun + 7 - k1;

L150:
                    ;
                }

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

/*     Print a summary of the results. */

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

    return 0;

/*     End of ZDRVSY */

} /* zdrvsy_ */