zpbt02.c

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/* zpbt02.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 integer c__1 = 1;

/* Subroutine */ int zpbt02_(char *uplo, integer *n, integer *kd, 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;
    doublereal d__1, d__2;
    doublecomplex z__1;

    /* Local variables */
    integer j;
    doublereal eps, anorm, bnorm;
    extern /* Subroutine */ int zhbmv_(char *, integer *, integer *, 
            doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
            integer *, doublecomplex *, doublecomplex *, integer *);
    doublereal xnorm;
    extern doublereal dlamch_(char *), zlanhb_(char *, char *, 
            integer *, integer *, doublecomplex *, integer *, doublereal *), dzasum_(integer *, doublecomplex *, integer *);


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

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

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

/*  ZPBT02 computes the residual for a solution of a Hermitian banded */
/*  system of equations  A*x = b: */
/*     RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS) */
/*  where EPS is the machine precision. */

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

/*  UPLO    (input) CHARACTER*1 */
/*          Specifies whether the upper or lower triangular part of the */
/*          Hermitian 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. */

/*  KD      (input) INTEGER */
/*          The number of super-diagonals of the matrix A if UPLO = 'U', */
/*          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0. */

/*  A       (input) COMPLEX*16 array, dimension (LDA,N) */
/*          The original Hermitian band matrix A.  If UPLO = 'U', the */
/*          upper triangular part of A is stored as a band matrix; if */
/*          UPLO = 'L', the lower triangular part of A is stored.  The */
/*          columns of the appropriate triangle are stored in the columns */
/*          of A and the diagonals of the triangle are stored in the rows */
/*          of A.  See ZPBTRF for further details. */

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

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

/*     Compute  B - A*X */

    i__1 = *nrhs;
    for (j = 1; j <= i__1; ++j) {
        z__1.r = -1., z__1.i = -0.;
        zhbmv_(uplo, n, kd, &z__1, &a[a_offset], lda, &x[j * x_dim1 + 1], &
                c__1, &c_b1, &b[j * b_dim1 + 1], &c__1);
/* L10: */
    }

/*     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) {
        bnorm = dzasum_(n, &b[j * b_dim1 + 1], &c__1);
        xnorm = dzasum_(n, &x[j * x_dim1 + 1], &c__1);
        if (xnorm <= 0.) {
            *resid = 1. / eps;
        } else {
/* Computing MAX */
            d__1 = *resid, d__2 = bnorm / anorm / xnorm / eps;
            *resid = max(d__1,d__2);
        }
/* L20: */
    }

    return 0;

/*     End of ZPBT02 */

} /* zpbt02_ */