dsbmv.c

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/* dsbmv.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"

/* Subroutine */ int dsbmv_(char *uplo, integer *n, integer *k, doublereal *
        alpha, doublereal *a, integer *lda, doublereal *x, integer *incx, 
        doublereal *beta, doublereal *y, integer *incy)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3, i__4;

    /* Local variables */
    integer i__, j, l, ix, iy, jx, jy, kx, ky, info;
    doublereal temp1, temp2;
    extern logical lsame_(char *, char *);
    integer kplus1;
    extern /* Subroutine */ int xerbla_(char *, integer *);

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

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

/*  DSBMV  performs the matrix-vector  operation */

/*     y := alpha*A*x + beta*y, */

/*  where alpha and beta are scalars, x and y are n element vectors and */
/*  A is an n by n symmetric band matrix, with k super-diagonals. */

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

/*  UPLO   - CHARACTER*1. */
/*           On entry, UPLO specifies whether the upper or lower */
/*           triangular part of the band matrix A is being supplied as */
/*           follows: */

/*              UPLO = 'U' or 'u'   The upper triangular part of A is */
/*                                  being supplied. */

/*              UPLO = 'L' or 'l'   The lower triangular part of A is */
/*                                  being supplied. */

/*           Unchanged on exit. */

/*  N      - INTEGER. */
/*           On entry, N specifies the order of the matrix A. */
/*           N must be at least zero. */
/*           Unchanged on exit. */

/*  K      - INTEGER. */
/*           On entry, K specifies the number of super-diagonals of the */
/*           matrix A. K must satisfy  0 .le. K. */
/*           Unchanged on exit. */

/*  ALPHA  - DOUBLE PRECISION. */
/*           On entry, ALPHA specifies the scalar alpha. */
/*           Unchanged on exit. */

/*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ). */
/*           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) */
/*           by n part of the array A must contain the upper triangular */
/*           band part of the symmetric matrix, supplied column by */
/*           column, with the leading diagonal of the matrix in row */
/*           ( k + 1 ) of the array, the first super-diagonal starting at */
/*           position 2 in row k, and so on. The top left k by k triangle */
/*           of the array A is not referenced. */
/*           The following program segment will transfer the upper */
/*           triangular part of a symmetric band matrix from conventional */
/*           full matrix storage to band storage: */

/*                 DO 20, J = 1, N */
/*                    M = K + 1 - J */
/*                    DO 10, I = MAX( 1, J - K ), J */
/*                       A( M + I, J ) = matrix( I, J ) */
/*              10    CONTINUE */
/*              20 CONTINUE */

/*           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) */
/*           by n part of the array A must contain the lower triangular */
/*           band part of the symmetric matrix, supplied column by */
/*           column, with the leading diagonal of the matrix in row 1 of */
/*           the array, the first sub-diagonal starting at position 1 in */
/*           row 2, and so on. The bottom right k by k triangle of the */
/*           array A is not referenced. */
/*           The following program segment will transfer the lower */
/*           triangular part of a symmetric band matrix from conventional */
/*           full matrix storage to band storage: */

/*                 DO 20, J = 1, N */
/*                    M = 1 - J */
/*                    DO 10, I = J, MIN( N, J + K ) */
/*                       A( M + I, J ) = matrix( I, J ) */
/*              10    CONTINUE */
/*              20 CONTINUE */

/*           Unchanged on exit. */

/*  LDA    - INTEGER. */
/*           On entry, LDA specifies the first dimension of A as declared */
/*           in the calling (sub) program. LDA must be at least */
/*           ( k + 1 ). */
/*           Unchanged on exit. */

/*  X      - DOUBLE PRECISION array of DIMENSION at least */
/*           ( 1 + ( n - 1 )*abs( INCX ) ). */
/*           Before entry, the incremented array X must contain the */
/*           vector x. */
/*           Unchanged on exit. */

/*  INCX   - INTEGER. */
/*           On entry, INCX specifies the increment for the elements of */
/*           X. INCX must not be zero. */
/*           Unchanged on exit. */

/*  BETA   - DOUBLE PRECISION. */
/*           On entry, BETA specifies the scalar beta. */
/*           Unchanged on exit. */

/*  Y      - DOUBLE PRECISION array of DIMENSION at least */
/*           ( 1 + ( n - 1 )*abs( INCY ) ). */
/*           Before entry, the incremented array Y must contain the */
/*           vector y. On exit, Y is overwritten by the updated vector y. */

/*  INCY   - INTEGER. */
/*           On entry, INCY specifies the increment for the elements of */
/*           Y. INCY must not be zero. */
/*           Unchanged on exit. */


/*  Level 2 Blas routine. */

/*  -- Written on 22-October-1986. */
/*     Jack Dongarra, Argonne National Lab. */
/*     Jeremy Du Croz, Nag Central Office. */
/*     Sven Hammarling, Nag Central Office. */
/*     Richard Hanson, Sandia National Labs. */


/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */

/*     Test the input parameters. */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --x;
    --y;

    /* Function Body */
    info = 0;
    if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
        info = 1;
    } else if (*n < 0) {
        info = 2;
    } else if (*k < 0) {
        info = 3;
    } else if (*lda < *k + 1) {
        info = 6;
    } else if (*incx == 0) {
        info = 8;
    } else if (*incy == 0) {
        info = 11;
    }
    if (info != 0) {
        xerbla_("DSBMV ", &info);
        return 0;
    }

/*     Quick return if possible. */

    if (*n == 0 || *alpha == 0. && *beta == 1.) {
        return 0;
    }

/*     Set up the start points in  X  and  Y. */

    if (*incx > 0) {
        kx = 1;
    } else {
        kx = 1 - (*n - 1) * *incx;
    }
    if (*incy > 0) {
        ky = 1;
    } else {
        ky = 1 - (*n - 1) * *incy;
    }

/*     Start the operations. In this version the elements of the array A */
/*     are accessed sequentially with one pass through A. */

/*     First form  y := beta*y. */

    if (*beta != 1.) {
        if (*incy == 1) {
            if (*beta == 0.) {
                i__1 = *n;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    y[i__] = 0.;
/* L10: */
                }
            } else {
                i__1 = *n;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    y[i__] = *beta * y[i__];
/* L20: */
                }
            }
        } else {
            iy = ky;
            if (*beta == 0.) {
                i__1 = *n;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    y[iy] = 0.;
                    iy += *incy;
/* L30: */
                }
            } else {
                i__1 = *n;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    y[iy] = *beta * y[iy];
                    iy += *incy;
/* L40: */
                }
            }
        }
    }
    if (*alpha == 0.) {
        return 0;
    }
    if (lsame_(uplo, "U")) {

/*        Form  y  when upper triangle of A is stored. */

        kplus1 = *k + 1;
        if (*incx == 1 && *incy == 1) {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                temp1 = *alpha * x[j];
                temp2 = 0.;
                l = kplus1 - j;
/* Computing MAX */
                i__2 = 1, i__3 = j - *k;
                i__4 = j - 1;
                for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
                    y[i__] += temp1 * a[l + i__ + j * a_dim1];
                    temp2 += a[l + i__ + j * a_dim1] * x[i__];
/* L50: */
                }
                y[j] = y[j] + temp1 * a[kplus1 + j * a_dim1] + *alpha * temp2;
/* L60: */
            }
        } else {
            jx = kx;
            jy = ky;
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                temp1 = *alpha * x[jx];
                temp2 = 0.;
                ix = kx;
                iy = ky;
                l = kplus1 - j;
/* Computing MAX */
                i__4 = 1, i__2 = j - *k;
                i__3 = j - 1;
                for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
                    y[iy] += temp1 * a[l + i__ + j * a_dim1];
                    temp2 += a[l + i__ + j * a_dim1] * x[ix];
                    ix += *incx;
                    iy += *incy;
/* L70: */
                }
                y[jy] = y[jy] + temp1 * a[kplus1 + j * a_dim1] + *alpha * 
                        temp2;
                jx += *incx;
                jy += *incy;
                if (j > *k) {
                    kx += *incx;
                    ky += *incy;
                }
/* L80: */
            }
        }
    } else {

/*        Form  y  when lower triangle of A is stored. */

        if (*incx == 1 && *incy == 1) {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                temp1 = *alpha * x[j];
                temp2 = 0.;
                y[j] += temp1 * a[j * a_dim1 + 1];
                l = 1 - j;
/* Computing MIN */
                i__4 = *n, i__2 = j + *k;
                i__3 = min(i__4,i__2);
                for (i__ = j + 1; i__ <= i__3; ++i__) {
                    y[i__] += temp1 * a[l + i__ + j * a_dim1];
                    temp2 += a[l + i__ + j * a_dim1] * x[i__];
/* L90: */
                }
                y[j] += *alpha * temp2;
/* L100: */
            }
        } else {
            jx = kx;
            jy = ky;
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                temp1 = *alpha * x[jx];
                temp2 = 0.;
                y[jy] += temp1 * a[j * a_dim1 + 1];
                l = 1 - j;
                ix = jx;
                iy = jy;
/* Computing MIN */
                i__4 = *n, i__2 = j + *k;
                i__3 = min(i__4,i__2);
                for (i__ = j + 1; i__ <= i__3; ++i__) {
                    ix += *incx;
                    iy += *incy;
                    y[iy] += temp1 * a[l + i__ + j * a_dim1];
                    temp2 += a[l + i__ + j * a_dim1] * x[ix];
/* L110: */
                }
                y[jy] += *alpha * temp2;
                jx += *incx;
                jy += *incy;
/* L120: */
            }
        }
    }

    return 0;

/*     End of DSBMV . */

} /* dsbmv_ */