dtbt02.c

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/* dtbt02.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 integer c__1 = 1;
static doublereal c_b10 = -1.;

/* Subroutine */ int dtbt02_(char *uplo, char *trans, char *diag, integer *n, 
        integer *kd, integer *nrhs, doublereal *ab, integer *ldab, doublereal 
        *x, integer *ldx, doublereal *b, integer *ldb, doublereal *work, 
        doublereal *resid)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, b_dim1, b_offset, x_dim1, x_offset, i__1;
    doublereal d__1, d__2;

    /* Local variables */
    integer j;
    doublereal eps;
    extern logical lsame_(char *, char *);
    extern doublereal dasum_(integer *, doublereal *, integer *);
    doublereal anorm, bnorm;
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
            doublereal *, integer *), dtbmv_(char *, char *, char *, integer *
, integer *, doublereal *, integer *, doublereal *, integer *), daxpy_(integer *, doublereal *, 
            doublereal *, integer *, doublereal *, integer *);
    doublereal xnorm;
    extern doublereal dlamch_(char *), dlantb_(char *, char *, char *, 
             integer *, integer *, doublereal *, integer *, doublereal *);


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

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

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

/*  DTBT02 computes the residual for the computed solution to a */
/*  triangular system of linear equations  A*x = b  or  A' *x = b when */
/*  A is a triangular band matrix.  Here A' is the transpose of A and */
/*  x and b are N by NRHS matrices.  The test ratio is the maximum over */
/*  the number of right hand sides of */
/*     norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ), */
/*  where op(A) denotes A or A' and EPS is the machine epsilon. */

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

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

/*  TRANS   (input) CHARACTER*1 */
/*          Specifies the operation applied to A. */
/*          = 'N':  A *x = b  (No transpose) */
/*          = 'T':  A'*x = b  (Transpose) */
/*          = 'C':  A'*x = b  (Conjugate transpose = Transpose) */

/*  DIAG    (input) CHARACTER*1 */
/*          Specifies whether or not the matrix A is unit triangular. */
/*          = 'N':  Non-unit triangular */
/*          = 'U':  Unit triangular */

/*  N       (input) INTEGER */
/*          The order of the matrix A.  N >= 0. */

/*  KD      (input) INTEGER */
/*          The number of superdiagonals or subdiagonals of the */
/*          triangular band matrix A.  KD >= 0. */

/*  NRHS    (input) INTEGER */
/*          The number of right hand sides, i.e., the number of columns */
/*          of the matrices X and B.  NRHS >= 0. */

/*  AB      (input) DOUBLE PRECISION array, dimension (LDAB,N) */
/*          The upper or lower triangular band matrix A, stored in the */
/*          first kd+1 rows of the array. The j-th column of A is stored */
/*          in the j-th column of the array AB as follows: */
/*          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; */
/*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd). */

/*  LDAB    (input) INTEGER */
/*          The leading dimension of the array AB.  LDAB >= KD+1. */

/*  X       (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDB,NRHS) */
/*          The right hand side vectors for the system of linear */
/*          equations. */

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

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

/*  RESID   (output) DOUBLE PRECISION */
/*          The maximum over the number of right hand sides of */
/*          norm(op(A)*x - b) / ( norm(op(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 */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1;
    ab -= ab_offset;
    x_dim1 = *ldx;
    x_offset = 1 + x_dim1;
    x -= x_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    --work;

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

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

    if (lsame_(trans, "N")) {
        anorm = dlantb_("1", uplo, diag, n, kd, &ab[ab_offset], ldab, &work[1]
);
    } else {
        anorm = dlantb_("I", uplo, diag, n, kd, &ab[ab_offset], ldab, &work[1]
);
    }

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

    eps = dlamch_("Epsilon");
    if (anorm <= 0.) {
        *resid = 1. / eps;
        return 0;
    }

/*     Compute the maximum over the number of right hand sides of */
/*        norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). */

    *resid = 0.;
    i__1 = *nrhs;
    for (j = 1; j <= i__1; ++j) {
        dcopy_(n, &x[j * x_dim1 + 1], &c__1, &work[1], &c__1);
        dtbmv_(uplo, trans, diag, n, kd, &ab[ab_offset], ldab, &work[1], &
                c__1);
        daxpy_(n, &c_b10, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
        bnorm = dasum_(n, &work[1], &c__1);
        xnorm = dasum_(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);
        }
/* L10: */
    }

    return 0;

/*     End of DTBT02 */

} /* dtbt02_ */