sla_gbamv.c

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/* sla_gbamv.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 sla_gbamv__(integer *trans, integer *m, integer *n, 
        integer *kl, integer *ku, real *alpha, real *ab, integer *ldab, real *
        x, integer *incx, real *beta, real *y, integer *incy)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4;
    real r__1;

    /* Builtin functions */
    double r_sign(real *, real *);

    /* Local variables */
    extern integer ilatrans_(char *);
    integer i__, j;
    logical symb_zero__;
    integer kd, iy, jx, kx, ky, info;
    real temp;
    integer lenx, leny;
    real safe1;
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int xerbla_(char *, integer *);


/*     -- LAPACK routine (version 3.2)                                 -- */
/*     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */
/*     -- Jason Riedy of Univ. of California Berkeley.                 -- */
/*     -- November 2008                                                -- */

/*     -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/*     -- Univ. of California Berkeley and NAG Ltd.                    -- */

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

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

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

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

/*  where alpha and beta are scalars, x and y are vectors and A is an */
/*  m by n matrix. */

/*  This function is primarily used in calculating error bounds. */
/*  To protect against underflow during evaluation, components in */
/*  the resulting vector are perturbed away from zero by (N+1) */
/*  times the underflow threshold.  To prevent unnecessarily large */
/*  errors for block-structure embedded in general matrices, */
/*  "symbolically" zero components are not perturbed.  A zero */
/*  entry is considered "symbolic" if all multiplications involved */
/*  in computing that entry have at least one zero multiplicand. */

/*  Parameters */
/*  ========== */

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

/*             BLAS_NO_TRANS      y := alpha*abs(A)*abs(x) + beta*abs(y) */
/*             BLAS_TRANS         y := alpha*abs(A')*abs(x) + beta*abs(y) */
/*             BLAS_CONJ_TRANS    y := alpha*abs(A')*abs(x) + beta*abs(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 */
/*           The number of subdiagonals within the band of A.  KL >= 0. */

/*  KU     - INTEGER */
/*           The number of superdiagonals within the band of A.  KU >= 0. */

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

/*  A      - REAL             array of DIMENSION ( LDA, n ) */
/*           Before entry, the leading m by n part of the array A must */
/*           contain the matrix of coefficients. */
/*           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 */
/*           max( 1, m ). */
/*           Unchanged on exit. */

/*  X      - REAL             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   - REAL */
/*           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      - REAL             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 with BETA non-zero, 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. */
/*     .. */
/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters. */

    /* Parameter adjustments */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1;
    ab -= ab_offset;
    --x;
    --y;

    /* Function Body */
    info = 0;
    if (! (*trans == ilatrans_("N") || *trans == ilatrans_("T") || *trans == ilatrans_("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 (*ldab < *kl + *ku + 1) {
        info = 6;
    } else if (*incx == 0) {
        info = 8;
    } else if (*incy == 0) {
        info = 11;
    }
    if (info != 0) {
        xerbla_("SLA_GBAMV ", &info);
        return 0;
    }

/*     Quick return if possible. */

    if (*m == 0 || *n == 0 || *alpha == 0.f && *beta == 1.f) {
        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 (*trans == ilatrans_("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;
    }

/*     Set SAFE1 essentially to be the underflow threshold times the */
/*     number of additions in each row. */

    safe1 = slamch_("Safe minimum");
    safe1 = (*n + 1) * safe1;

/*     Form  y := alpha*abs(A)*abs(x) + beta*abs(y). */

/*     The O(M*N) SYMB_ZERO tests could be replaced by O(N) queries to */
/*     the inexact flag.  Still doesn't help change the iteration order */
/*     to per-column. */

    kd = *ku + 1;
    iy = ky;
    if (*incx == 1) {
        i__1 = leny;
        for (i__ = 1; i__ <= i__1; ++i__) {
            if (*beta == 0.f) {
                symb_zero__ = TRUE_;
                y[iy] = 0.f;
            } else if (y[iy] == 0.f) {
                symb_zero__ = TRUE_;
            } else {
                symb_zero__ = FALSE_;
                y[iy] = *beta * (r__1 = y[iy], dabs(r__1));
            }
            if (*alpha != 0.f) {
/* Computing MAX */
                i__2 = i__ - *ku;
/* Computing MIN */
                i__4 = i__ + *kl;
                i__3 = min(i__4,lenx);
                for (j = max(i__2,1); j <= i__3; ++j) {
                    if (*trans == ilatrans_("N")) {
                        temp = (r__1 = ab[kd + i__ - j + j * ab_dim1], dabs(
                                r__1));
                    } else {
                        temp = (r__1 = ab[j + (kd + i__ - j) * ab_dim1], dabs(
                                r__1));
                    }
                    symb_zero__ = symb_zero__ && (x[j] == 0.f || temp == 0.f);
                    y[iy] += *alpha * (r__1 = x[j], dabs(r__1)) * temp;
                }
            }
            if (! symb_zero__) {
                y[iy] += r_sign(&safe1, &y[iy]);
            }
            iy += *incy;
        }
    } else {
        i__1 = leny;
        for (i__ = 1; i__ <= i__1; ++i__) {
            if (*beta == 0.f) {
                symb_zero__ = TRUE_;
                y[iy] = 0.f;
            } else if (y[iy] == 0.f) {
                symb_zero__ = TRUE_;
            } else {
                symb_zero__ = FALSE_;
                y[iy] = *beta * (r__1 = y[iy], dabs(r__1));
            }
            if (*alpha != 0.f) {
                jx = kx;
/* Computing MAX */
                i__3 = i__ - *ku;
/* Computing MIN */
                i__4 = i__ + *kl;
                i__2 = min(i__4,lenx);
                for (j = max(i__3,1); j <= i__2; ++j) {
                    if (*trans == ilatrans_("N")) {
                        temp = (r__1 = ab[kd + i__ - j + j * ab_dim1], dabs(
                                r__1));
                    } else {
                        temp = (r__1 = ab[j + (kd + i__ - j) * ab_dim1], dabs(
                                r__1));
                    }
                    symb_zero__ = symb_zero__ && (x[jx] == 0.f || temp == 0.f)
                            ;
                    y[iy] += *alpha * (r__1 = x[jx], dabs(r__1)) * temp;
                    jx += *incx;
                }
            }
            if (! symb_zero__) {
                y[iy] += r_sign(&safe1, &y[iy]);
            }
            iy += *incy;
        }
    }

    return 0;

/*     End of SLA_GBAMV */

} /* sla_gbamv__ */