dgbmv.c

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/* dgbmv.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 dgbmv_(char *trans, integer *m, integer *n, integer *kl, 
        integer *ku, 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, i__5, i__6;

    /* Local variables */
    integer i__, j, k, ix, iy, jx, jy, kx, ky, kup1, info;
    doublereal temp;
    integer lenx, leny;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int xerbla_(char *, integer *);

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

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

/*  DGBMV  performs one of the matrix-vector operations */

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

/*  where alpha and beta are scalars, x and y are vectors and A is an */
/*  m by n band matrix, with kl sub-diagonals and ku super-diagonals. */

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

/*  TRANS  - CHARACTER*1. */
/*           On entry, TRANS specifies the operation to be performed as */
/*           follows: */

/*              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y. */

/*              TRANS = 'T' or 't'   y := alpha*A'*x + beta*y. */

/*              TRANS = 'C' or 'c'   y := alpha*A'*x + beta*y. */

/*           Unchanged on exit. */

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

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

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

/*  KU     - INTEGER. */
/*           On entry, KU specifies the number of super-diagonals of the */
/*           matrix A. KU must satisfy  0 .le. KU. */
/*           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, the leading ( kl + ku + 1 ) by n part of the */
/*           array A must contain the matrix of coefficients, supplied */
/*           column by column, with the leading diagonal of the matrix in */
/*           row ( ku + 1 ) of the array, the first super-diagonal */
/*           starting at position 2 in row ku, the first sub-diagonal */
/*           starting at position 1 in row ( ku + 2 ), and so on. */
/*           Elements in the array A that do not correspond to elements */
/*           in the band matrix (such as the top left ku by ku triangle) */
/*           are not referenced. */
/*           The following program segment will transfer a band matrix */
/*           from conventional full matrix storage to band storage: */

/*                 DO 20, J = 1, N */
/*                    K = KU + 1 - J */
/*                    DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) */
/*                       A( K + 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 */
/*           ( kl + ku + 1 ). */
/*           Unchanged on exit. */

/*  X      - DOUBLE PRECISION array of DIMENSION at least */
/*           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' */
/*           and at least */
/*           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. */
/*           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. When BETA is */
/*           supplied as zero then Y need not be set on input. */
/*           Unchanged on exit. */

/*  Y      - DOUBLE PRECISION array of DIMENSION at least */
/*           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' */
/*           and at least */
/*           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. */
/*           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_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans, "C")
            ) {
        info = 1;
    } else if (*m < 0) {
        info = 2;
    } else if (*n < 0) {
        info = 3;
    } else if (*kl < 0) {
        info = 4;
    } else if (*ku < 0) {
        info = 5;
    } else if (*lda < *kl + *ku + 1) {
        info = 8;
    } else if (*incx == 0) {
        info = 10;
    } else if (*incy == 0) {
        info = 13;
    }
    if (info != 0) {
        xerbla_("DGBMV ", &info);
        return 0;
    }

/*     Quick return if possible. */

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

/*     Set  LENX  and  LENY, the lengths of the vectors x and y, and set */
/*     up the start points in  X  and  Y. */

    if (lsame_(trans, "N")) {
        lenx = *n;
        leny = *m;
    } else {
        lenx = *m;
        leny = *n;
    }
    if (*incx > 0) {
        kx = 1;
    } else {
        kx = 1 - (lenx - 1) * *incx;
    }
    if (*incy > 0) {
        ky = 1;
    } else {
        ky = 1 - (leny - 1) * *incy;
    }

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

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

    if (*beta != 1.) {
        if (*incy == 1) {
            if (*beta == 0.) {
                i__1 = leny;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    y[i__] = 0.;
/* L10: */
                }
            } else {
                i__1 = leny;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    y[i__] = *beta * y[i__];
/* L20: */
                }
            }
        } else {
            iy = ky;
            if (*beta == 0.) {
                i__1 = leny;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    y[iy] = 0.;
                    iy += *incy;
/* L30: */
                }
            } else {
                i__1 = leny;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    y[iy] = *beta * y[iy];
                    iy += *incy;
/* L40: */
                }
            }
        }
    }
    if (*alpha == 0.) {
        return 0;
    }
    kup1 = *ku + 1;
    if (lsame_(trans, "N")) {

/*        Form  y := alpha*A*x + y. */

        jx = kx;
        if (*incy == 1) {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                if (x[jx] != 0.) {
                    temp = *alpha * x[jx];
                    k = kup1 - j;
/* Computing MAX */
                    i__2 = 1, i__3 = j - *ku;
/* Computing MIN */
                    i__5 = *m, i__6 = j + *kl;
                    i__4 = min(i__5,i__6);
                    for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
                        y[i__] += temp * a[k + i__ + j * a_dim1];
/* L50: */
                    }
                }
                jx += *incx;
/* L60: */
            }
        } else {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                if (x[jx] != 0.) {
                    temp = *alpha * x[jx];
                    iy = ky;
                    k = kup1 - j;
/* Computing MAX */
                    i__4 = 1, i__2 = j - *ku;
/* Computing MIN */
                    i__5 = *m, i__6 = j + *kl;
                    i__3 = min(i__5,i__6);
                    for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
                        y[iy] += temp * a[k + i__ + j * a_dim1];
                        iy += *incy;
/* L70: */
                    }
                }
                jx += *incx;
                if (j > *ku) {
                    ky += *incy;
                }
/* L80: */
            }
        }
    } else {

/*        Form  y := alpha*A'*x + y. */

        jy = ky;
        if (*incx == 1) {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                temp = 0.;
                k = kup1 - j;
/* Computing MAX */
                i__3 = 1, i__4 = j - *ku;
/* Computing MIN */
                i__5 = *m, i__6 = j + *kl;
                i__2 = min(i__5,i__6);
                for (i__ = max(i__3,i__4); i__ <= i__2; ++i__) {
                    temp += a[k + i__ + j * a_dim1] * x[i__];
/* L90: */
                }
                y[jy] += *alpha * temp;
                jy += *incy;
/* L100: */
            }
        } else {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                temp = 0.;
                ix = kx;
                k = kup1 - j;
/* Computing MAX */
                i__2 = 1, i__3 = j - *ku;
/* Computing MIN */
                i__5 = *m, i__6 = j + *kl;
                i__4 = min(i__5,i__6);
                for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
                    temp += a[k + i__ + j * a_dim1] * x[ix];
                    ix += *incx;
/* L110: */
                }
                y[jy] += *alpha * temp;
                jy += *incy;
                if (j > *ku) {
                    kx += *incx;
                }
/* L120: */
            }
        }
    }

    return 0;

/*     End of DGBMV . */

} /* dgbmv_ */