cgbmv.c

/* cgbmv.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 cgbmv_(char *trans, integer *m, integer *n, integer *kl, 
	integer *ku, complex *alpha, complex *a, integer *lda, complex *x, 
	integer *incx, complex *beta, complex *y, integer *incy)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
    complex q__1, q__2, q__3;

    /* Builtin functions */
    void r_cnjg(complex *, complex *);

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

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

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

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

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

/*     Quick return if possible. */

    if (*m == 0 || *n == 0 || alpha->r == 0.f && alpha->i == 0.f && (beta->r 
	    == 1.f && beta->i == 0.f)) {
	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.f || beta->i != 0.f) {
	if (*incy == 1) {
	    if (beta->r == 0.f && beta->i == 0.f) {
		i__1 = leny;
		for (i__ = 1; i__ <= i__1; ++i__) {
		    i__2 = i__;
		    y[i__2].r = 0.f, y[i__2].i = 0.f;
/* L10: */
		}
	    } else {
		i__1 = leny;
		for (i__ = 1; i__ <= i__1; ++i__) {
		    i__2 = i__;
		    i__3 = i__;
		    q__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, 
			    q__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
			    .r;
		    y[i__2].r = q__1.r, y[i__2].i = q__1.i;
/* L20: */
		}
	    }
	} else {
	    iy = ky;
	    if (beta->r == 0.f && beta->i == 0.f) {
		i__1 = leny;
		for (i__ = 1; i__ <= i__1; ++i__) {
		    i__2 = iy;
		    y[i__2].r = 0.f, y[i__2].i = 0.f;
		    iy += *incy;
/* L30: */
		}
	    } else {
		i__1 = leny;
		for (i__ = 1; i__ <= i__1; ++i__) {
		    i__2 = iy;
		    i__3 = iy;
		    q__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, 
			    q__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
			    .r;
		    y[i__2].r = q__1.r, y[i__2].i = q__1.i;
		    iy += *incy;
/* L40: */
		}
	    }
	}
    }
    if (alpha->r == 0.f && alpha->i == 0.f) {
	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.f || x[i__2].i != 0.f) {
		    i__2 = jx;
		    q__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, 
			    q__1.i = alpha->r * x[i__2].i + alpha->i * x[i__2]
			    .r;
		    temp.r = q__1.r, temp.i = q__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;
			q__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, 
				q__2.i = temp.r * a[i__5].i + temp.i * a[i__5]
				.r;
			q__1.r = y[i__3].r + q__2.r, q__1.i = y[i__3].i + 
				q__2.i;
			y[i__2].r = q__1.r, y[i__2].i = q__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.f || x[i__4].i != 0.f) {
		    i__4 = jx;
		    q__1.r = alpha->r * x[i__4].r - alpha->i * x[i__4].i, 
			    q__1.i = alpha->r * x[i__4].i + alpha->i * x[i__4]
			    .r;
		    temp.r = q__1.r, temp.i = q__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;
			q__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, 
				q__2.i = temp.r * a[i__5].i + temp.i * a[i__5]
				.r;
			q__1.r = y[i__2].r + q__2.r, q__1.i = y[i__2].i + 
				q__2.i;
			y[i__4].r = q__1.r, y[i__4].i = q__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.f, temp.i = 0.f;
		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__;
			q__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4]
				.i, q__2.i = a[i__3].r * x[i__4].i + a[i__3]
				.i * x[i__4].r;
			q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
			temp.r = q__1.r, temp.i = q__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__) {
			r_cnjg(&q__3, &a[k + i__ + j * a_dim1]);
			i__2 = i__;
			q__2.r = q__3.r * x[i__2].r - q__3.i * x[i__2].i, 
				q__2.i = q__3.r * x[i__2].i + q__3.i * x[i__2]
				.r;
			q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
			temp.r = q__1.r, temp.i = q__1.i;
/* L100: */
		    }
		}
		i__4 = jy;
		i__2 = jy;
		q__2.r = alpha->r * temp.r - alpha->i * temp.i, q__2.i = 
			alpha->r * temp.i + alpha->i * temp.r;
		q__1.r = y[i__2].r + q__2.r, q__1.i = y[i__2].i + q__2.i;
		y[i__4].r = q__1.r, y[i__4].i = q__1.i;
		jy += *incy;
/* L110: */
	    }
	} else {
	    i__1 = *n;
	    for (j = 1; j <= i__1; ++j) {
		temp.r = 0.f, temp.i = 0.f;
		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;
			q__2.r = a[i__4].r * x[i__2].r - a[i__4].i * x[i__2]
				.i, q__2.i = a[i__4].r * x[i__2].i + a[i__4]
				.i * x[i__2].r;
			q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
			temp.r = q__1.r, temp.i = q__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__) {
			r_cnjg(&q__3, &a[k + i__ + j * a_dim1]);
			i__3 = ix;
			q__2.r = q__3.r * x[i__3].r - q__3.i * x[i__3].i, 
				q__2.i = q__3.r * x[i__3].i + q__3.i * x[i__3]
				.r;
			q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
			temp.r = q__1.r, temp.i = q__1.i;
			ix += *incx;
/* L130: */
		    }
		}
		i__2 = jy;
		i__3 = jy;
		q__2.r = alpha->r * temp.r - alpha->i * temp.i, q__2.i = 
			alpha->r * temp.i + alpha->i * temp.r;
		q__1.r = y[i__3].r + q__2.r, q__1.i = y[i__3].i + q__2.i;
		y[i__2].r = q__1.r, y[i__2].i = q__1.i;
		jy += *incy;
		if (j > *ku) {
		    kx += *incx;
		}
/* L140: */
	    }
	}
    }

    return 0;

/*     End of CGBMV . */

} /* cgbmv_ */