zgbmv.c

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/* zgbmv.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 zgbmv_(char *trans, integer *m, integer *n, integer *kl, 
        integer *ku, doublecomplex *alpha, doublecomplex *a, integer *lda, 
        doublecomplex *x, integer *incx, doublecomplex *beta, doublecomplex *
        y, integer *incy)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
    doublecomplex z__1, z__2, z__3;

    /* Builtin functions */
    void d_cnjg(doublecomplex *, doublecomplex *);

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

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

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

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

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

/*     y := alpha*conjg( 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*conjg( 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  - COMPLEX*16      . */
/*           On entry, ALPHA specifies the scalar alpha. */
/*           Unchanged on exit. */

/*  A      - COMPLEX*16       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      - COMPLEX*16       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   - COMPLEX*16      . */
/*           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      - COMPLEX*16       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_("ZGBMV ", &info);
        return 0;
    }

/*     Quick return if possible. */

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

    noconj = lsame_(trans, "T");

/*     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->r != 1. || beta->i != 0.) {
        if (*incy == 1) {
            if (beta->r == 0. && beta->i == 0.) {
                i__1 = leny;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    i__2 = i__;
                    y[i__2].r = 0., y[i__2].i = 0.;
/* L10: */
                }
            } else {
                i__1 = leny;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    i__2 = i__;
                    i__3 = i__;
                    z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, 
                            z__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
                            .r;
                    y[i__2].r = z__1.r, y[i__2].i = z__1.i;
/* L20: */
                }
            }
        } else {
            iy = ky;
            if (beta->r == 0. && beta->i == 0.) {
                i__1 = leny;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    i__2 = iy;
                    y[i__2].r = 0., y[i__2].i = 0.;
                    iy += *incy;
/* L30: */
                }
            } else {
                i__1 = leny;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    i__2 = iy;
                    i__3 = iy;
                    z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, 
                            z__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
                            .r;
                    y[i__2].r = z__1.r, y[i__2].i = z__1.i;
                    iy += *incy;
/* L40: */
                }
            }
        }
    }
    if (alpha->r == 0. && alpha->i == 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) {
                i__2 = jx;
                if (x[i__2].r != 0. || x[i__2].i != 0.) {
                    i__2 = jx;
                    z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, 
                            z__1.i = alpha->r * x[i__2].i + alpha->i * x[i__2]
                            .r;
                    temp.r = z__1.r, temp.i = z__1.i;
                    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__) {
                        i__2 = i__;
                        i__3 = i__;
                        i__5 = k + i__ + j * a_dim1;
                        z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, 
                                z__2.i = temp.r * a[i__5].i + temp.i * a[i__5]
                                .r;
                        z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + 
                                z__2.i;
                        y[i__2].r = z__1.r, y[i__2].i = z__1.i;
/* L50: */
                    }
                }
                jx += *incx;
/* L60: */
            }
        } else {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                i__4 = jx;
                if (x[i__4].r != 0. || x[i__4].i != 0.) {
                    i__4 = jx;
                    z__1.r = alpha->r * x[i__4].r - alpha->i * x[i__4].i, 
                            z__1.i = alpha->r * x[i__4].i + alpha->i * x[i__4]
                            .r;
                    temp.r = z__1.r, temp.i = z__1.i;
                    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__) {
                        i__4 = iy;
                        i__2 = iy;
                        i__5 = k + i__ + j * a_dim1;
                        z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, 
                                z__2.i = temp.r * a[i__5].i + temp.i * a[i__5]
                                .r;
                        z__1.r = y[i__2].r + z__2.r, z__1.i = y[i__2].i + 
                                z__2.i;
                        y[i__4].r = z__1.r, y[i__4].i = z__1.i;
                        iy += *incy;
/* L70: */
                    }
                }
                jx += *incx;
                if (j > *ku) {
                    ky += *incy;
                }
/* L80: */
            }
        }
    } else {

/*        Form  y := alpha*A'*x + y  or  y := alpha*conjg( A' )*x + y. */

        jy = ky;
        if (*incx == 1) {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                temp.r = 0., temp.i = 0.;
                k = kup1 - j;
                if (noconj) {
/* 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__) {
                        i__3 = k + i__ + j * a_dim1;
                        i__4 = i__;
                        z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4]
                                .i, z__2.i = a[i__3].r * x[i__4].i + a[i__3]
                                .i * x[i__4].r;
                        z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
                        temp.r = z__1.r, temp.i = z__1.i;
/* L90: */
                    }
                } else {
/* 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__) {
                        d_cnjg(&z__3, &a[k + i__ + j * a_dim1]);
                        i__2 = i__;
                        z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i, 
                                z__2.i = z__3.r * x[i__2].i + z__3.i * x[i__2]
                                .r;
                        z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
                        temp.r = z__1.r, temp.i = z__1.i;
/* L100: */
                    }
                }
                i__4 = jy;
                i__2 = jy;
                z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i = 
                        alpha->r * temp.i + alpha->i * temp.r;
                z__1.r = y[i__2].r + z__2.r, z__1.i = y[i__2].i + z__2.i;
                y[i__4].r = z__1.r, y[i__4].i = z__1.i;
                jy += *incy;
/* L110: */
            }
        } else {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                temp.r = 0., temp.i = 0.;
                ix = kx;
                k = kup1 - j;
                if (noconj) {
/* 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__) {
                        i__4 = k + i__ + j * a_dim1;
                        i__2 = ix;
                        z__2.r = a[i__4].r * x[i__2].r - a[i__4].i * x[i__2]
                                .i, z__2.i = a[i__4].r * x[i__2].i + a[i__4]
                                .i * x[i__2].r;
                        z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
                        temp.r = z__1.r, temp.i = z__1.i;
                        ix += *incx;
/* L120: */
                    }
                } else {
/* 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__) {
                        d_cnjg(&z__3, &a[k + i__ + j * a_dim1]);
                        i__3 = ix;
                        z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, 
                                z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3]
                                .r;
                        z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
                        temp.r = z__1.r, temp.i = z__1.i;
                        ix += *incx;
/* L130: */
                    }
                }
                i__2 = jy;
                i__3 = jy;
                z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i = 
                        alpha->r * temp.i + alpha->i * temp.r;
                z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;
                y[i__2].r = z__1.r, y[i__2].i = z__1.i;
                jy += *incy;
                if (j > *ku) {
                    kx += *incx;
                }
/* L140: */
            }
        }
    }

    return 0;

/*     End of ZGBMV . */

} /* zgbmv_ */