Example #1
0
int
f2c_stbmv(char* uplo, char* trans, char* diag, integer* N, integer* K,
          real* A, integer* lda,
          real* X, integer* incX)
{
    stbmv_(uplo, trans, diag,
           N, K, A, lda, X, incX);
    return 0;
}
Example #2
0
/* Subroutine */ int stbt03_(char *uplo, char *trans, char *diag, integer *n,
                             integer *kd, integer *nrhs, real *ab, integer *ldab, real *scale,
                             real *cnorm, real *tscal, real *x, integer *ldx, real *b, integer *
                             ldb, real *work, real *resid)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, b_dim1, b_offset, x_dim1, x_offset, i__1;
    real r__1, r__2, r__3;

    /* Local variables */
    static integer j;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
    static real xscal;
    extern /* Subroutine */ int stbmv_(char *, char *, char *, integer *,
                                       integer *, real *, integer *, real *, integer *), scopy_(integer *, real *, integer *, real *, integer *);
    static real tnorm, xnorm;
    extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *,
                                       real *, integer *), slabad_(real *, real *);
    static integer ix;
    extern doublereal slamch_(char *);
    static real bignum;
    extern integer isamax_(integer *, real *, integer *);
    static real smlnum, eps, err;


#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
#define x_ref(a_1,a_2) x[(a_2)*x_dim1 + a_1]
#define ab_ref(a_1,a_2) ab[(a_2)*ab_dim1 + a_1]


    /*  -- LAPACK test routine (version 3.0) --
           Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
           Courant Institute, Argonne National Lab, and Rice University
           February 29, 1992


        Purpose
        =======

        STBT03 computes the residual for the solution to a scaled triangular
        system of equations  A*x = s*b  or  A'*x = s*b  when A is a
        triangular band matrix. Here A' is the transpose of A, s is a scalar,
        and x and b are N by NRHS matrices.  The test ratio is the maximum
        over the number of right hand sides of
           norm(s*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) REAL 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.

        SCALE   (input) REAL
                The scaling factor s used in solving the triangular system.

        CNORM   (input) REAL array, dimension (N)
                The 1-norms of the columns of A, not counting the diagonal.

        TSCAL   (input) REAL
                The scaling factor used in computing the 1-norms in CNORM.
                CNORM actually contains the column norms of TSCAL*A.

        X       (input) REAL 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) REAL 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) REAL array, dimension (N)

        RESID   (output) REAL
                The maximum over the number of right hand sides of
                norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).

        =====================================================================


           Quick exit if N = 0

           Parameter adjustments */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1 * 1;
    ab -= ab_offset;
    --cnorm;
    x_dim1 = *ldx;
    x_offset = 1 + x_dim1 * 1;
    x -= x_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    --work;

    /* Function Body */
    if (*n <= 0 || *nrhs <= 0) {
        *resid = 0.f;
        return 0;
    }
    eps = slamch_("Epsilon");
    smlnum = slamch_("Safe minimum");
    bignum = 1.f / smlnum;
    slabad_(&smlnum, &bignum);

    /*     Compute the norm of the triangular matrix A using the column
           norms already computed by SLATBS. */

    tnorm = 0.f;
    if (lsame_(diag, "N")) {
        if (lsame_(uplo, "U")) {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                /* Computing MAX */
                r__2 = tnorm, r__3 = *tscal * (r__1 = ab_ref(*kd + 1, j),
                                               dabs(r__1)) + cnorm[j];
                tnorm = dmax(r__2,r__3);
                /* L10: */
            }
        } else {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                /* Computing MAX */
                r__2 = tnorm, r__3 = *tscal * (r__1 = ab_ref(1, j), dabs(r__1)
                                              ) + cnorm[j];
                tnorm = dmax(r__2,r__3);
                /* L20: */
            }
        }
    } else {
        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {
            /* Computing MAX */
            r__1 = tnorm, r__2 = *tscal + cnorm[j];
            tnorm = dmax(r__1,r__2);
            /* L30: */
        }
    }

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

    *resid = 0.f;
    i__1 = *nrhs;
    for (j = 1; j <= i__1; ++j) {
        scopy_(n, &x_ref(1, j), &c__1, &work[1], &c__1);
        ix = isamax_(n, &work[1], &c__1);
        /* Computing MAX */
        r__2 = 1.f, r__3 = (r__1 = x_ref(ix, j), dabs(r__1));
        xnorm = dmax(r__2,r__3);
        xscal = 1.f / xnorm / (real) (*kd + 1);
        sscal_(n, &xscal, &work[1], &c__1);
        stbmv_(uplo, trans, diag, n, kd, &ab[ab_offset], ldab, &work[1], &
               c__1);
        r__1 = -(*scale) * xscal;
        saxpy_(n, &r__1, &b_ref(1, j), &c__1, &work[1], &c__1);
        ix = isamax_(n, &work[1], &c__1);
        err = *tscal * (r__1 = work[ix], dabs(r__1));
        ix = isamax_(n, &x_ref(1, j), &c__1);
        xnorm = (r__1 = x_ref(ix, j), dabs(r__1));
        if (err * smlnum <= xnorm) {
            if (xnorm > 0.f) {
                err /= xnorm;
            }
        } else {
            if (err > 0.f) {
                err = 1.f / eps;
            }
        }
        if (err * smlnum <= tnorm) {
            if (tnorm > 0.f) {
                err /= tnorm;
            }
        } else {
            if (err > 0.f) {
                err = 1.f / eps;
            }
        }
        *resid = dmax(*resid,err);
        /* L40: */
    }

    return 0;

    /*     End of STBT03 */

} /* stbt03_ */
Example #3
0
void
stbmv(char uplo, char trans, char diag, int n, int k, float *a, int lda, float *x, int incx )
{
   stbmv_( &uplo, &trans, &diag, &n, &k, a, &lda, x, &incx );
}
Example #4
0
/* Subroutine */ int stbt02_(char *uplo, char *trans, char *diag, integer *n, 
	integer *kd, integer *nrhs, real *ab, integer *ldab, real *x, integer 
	*ldx, real *b, integer *ldb, real *work, real *resid)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, b_dim1, b_offset, x_dim1, x_offset, i__1;
    real r__1, r__2;

    /* Local variables */
    integer j;
    real eps;
    extern logical lsame_(char *, char *);
    real anorm, bnorm;
    extern doublereal sasum_(integer *, real *, integer *);
    extern /* Subroutine */ int stbmv_(char *, char *, char *, integer *, 
	    integer *, real *, integer *, real *, integer *), scopy_(integer *, real *, integer *, real *, integer *);
    real xnorm;
    extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *, 
	    real *, integer *);
    extern doublereal slamch_(char *), slantb_(char *, char *, char *, 
	     integer *, integer *, real *, integer *, real *);


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

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

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

/*  STBT02 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) REAL 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) REAL 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) REAL 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) REAL array, dimension (N) */

/*  RESID   (output) REAL */
/*          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.f;
	return 0;
    }

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

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

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

    eps = slamch_("Epsilon");
    if (anorm <= 0.f) {
	*resid = 1.f / 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.f;
    i__1 = *nrhs;
    for (j = 1; j <= i__1; ++j) {
	scopy_(n, &x[j * x_dim1 + 1], &c__1, &work[1], &c__1);
	stbmv_(uplo, trans, diag, n, kd, &ab[ab_offset], ldab, &work[1], &
		c__1);
	saxpy_(n, &c_b10, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
	bnorm = sasum_(n, &work[1], &c__1);
	xnorm = sasum_(n, &x[j * x_dim1 + 1], &c__1);
	if (xnorm <= 0.f) {
	    *resid = 1.f / eps;
	} else {
/* Computing MAX */
	    r__1 = *resid, r__2 = bnorm / anorm / xnorm / eps;
	    *resid = dmax(r__1,r__2);
	}
/* L10: */
    }

    return 0;

/*     End of STBT02 */

} /* stbt02_ */