zpot06.c

Go to the documentation of this file.

/* zpot06.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"

/* Table of constant values */

static doublecomplex c_b1 = {1.,0.};
static doublecomplex c_b2 = {-1.,0.};
static integer c__1 = 1;

/* Subroutine */ int zpot06_(char *uplo, integer *n, integer *nrhs, 
        doublecomplex *a, integer *lda, doublecomplex *x, integer *ldx, 
        doublecomplex *b, integer *ldb, doublereal *rwork, doublereal *resid)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, x_dim1, x_offset, i__1, i__2;
    doublereal d__1, d__2;

    /* Builtin functions */
    double d_imag(doublecomplex *);

    /* Local variables */
    integer j;
    doublereal eps;
    integer ifail;
    doublereal anorm, bnorm;
    extern /* Subroutine */ int zhemm_(char *, char *, integer *, integer *, 
            doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
            integer *, doublecomplex *, doublecomplex *, integer *);
    doublereal xnorm;
    extern doublereal dlamch_(char *);
    extern integer izamax_(integer *, doublecomplex *, integer *);
    extern doublereal zlansy_(char *, char *, integer *, doublecomplex *, 
            integer *, doublereal *);


/*  -- LAPACK test routine (version 3.1.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     May 2007 */

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

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

/*  ZPOT06 computes the residual for a solution of a system of linear */
/*  equations  A*x = b : */
/*     RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ), */
/*  where EPS is the machine epsilon. */

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

/*  UPLO    (input) CHARACTER*1 */
/*          Specifies whether the upper or lower triangular part of the */
/*          symmetric matrix A is stored: */
/*          = 'U':  Upper triangular */
/*          = 'L':  Lower triangular */

/*  N       (input) INTEGER */
/*          The number of rows and columns of the matrix A.  N >= 0. */

/*  NRHS    (input) INTEGER */
/*          The number of columns of B, the matrix of right hand sides. */
/*          NRHS >= 0. */

/*  A       (input) COMPLEX*16 array, dimension (LDA,N) */
/*          The original M x N matrix A. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A.  LDA >= max(1,N). */

/*  X       (input) COMPLEX*16 array, dimension (LDX,NRHS) */
/*          The computed solution vectors for the system of linear */
/*          equations. */

/*  LDX     (input) INTEGER */
/*          The leading dimension of the array X.  If TRANS = 'N', */
/*          LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,N). */

/*  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS) */
/*          On entry, the right hand side vectors for the system of */
/*          linear equations. */
/*          On exit, B is overwritten with the difference B - A*X. */

/*  LDB     (input) INTEGER */
/*          The leading dimension of the array B.  IF TRANS = 'N', */
/*          LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N). */

/*  RWORK   (workspace) DOUBLE PRECISION array, dimension (N) */

/*  RESID   (output) DOUBLE PRECISION */
/*          The maximum over the number of right hand sides of */
/*          norm(B - A*X) / ( norm(A) * norm(X) * EPS ). */

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Statement Functions .. */
/*     .. */
/*     .. Statement Function definitions .. */
/*     .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Quick exit if N = 0 or NRHS = 0 */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    x_dim1 = *ldx;
    x_offset = 1 + x_dim1;
    x -= x_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    --rwork;

    /* Function Body */
    if (*n <= 0 || *nrhs == 0) {
        *resid = 0.;
        return 0;
    }

/*     Exit with RESID = 1/EPS if ANORM = 0. */

    eps = dlamch_("Epsilon");
    anorm = zlansy_("I", uplo, n, &a[a_offset], lda, &rwork[1]);
    if (anorm <= 0.) {
        *resid = 1. / eps;
        return 0;
    }

/*     Compute  B - A*X  and store in B. */
    ifail = 0;

    zhemm_("Left", uplo, n, nrhs, &c_b2, &a[a_offset], lda, &x[x_offset], ldx, 
             &c_b1, &b[b_offset], ldb);

/*     Compute the maximum over the number of right hand sides of */
/*        norm(B - A*X) / ( norm(A) * norm(X) * EPS ) . */

    *resid = 0.;
    i__1 = *nrhs;
    for (j = 1; j <= i__1; ++j) {
        i__2 = izamax_(n, &b[j * b_dim1 + 1], &c__1) + j * b_dim1;
        bnorm = (d__1 = b[i__2].r, abs(d__1)) + (d__2 = d_imag(&b[izamax_(n, &
                b[j * b_dim1 + 1], &c__1) + j * b_dim1]), abs(d__2));
        i__2 = izamax_(n, &x[j * x_dim1 + 1], &c__1) + j * x_dim1;
        xnorm = (d__1 = x[i__2].r, abs(d__1)) + (d__2 = d_imag(&x[izamax_(n, &
                x[j * x_dim1 + 1], &c__1) + j * x_dim1]), abs(d__2));
        if (xnorm <= 0.) {
            *resid = 1. / eps;
        } else {
/* Computing MAX */
            d__1 = *resid, d__2 = bnorm / anorm / xnorm / eps;
            *resid = max(d__1,d__2);
        }
/* L10: */
    }

    return 0;

/*     End of ZPOT06 */

} /* zpot06_ */