zsbmv.c

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/* zsbmv.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 zsbmv_(char *uplo, integer *n, integer *k, 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;
    doublecomplex z__1, z__2, z__3, z__4;

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


/*  -- LAPACK auxiliary routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*  ZSBMV  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  - COMPLEX*16 */
/*           On entry, ALPHA specifies the scalar alpha. */
/*           Unchanged on exit. */

/*  A      - COMPLEX*16 array, 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      - COMPLEX*16 array, 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   - COMPLEX*16 */
/*           On entry, BETA specifies the scalar beta. */
/*           Unchanged on exit. */

/*  Y      - COMPLEX*16 array, 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. */

/*  ===================================================================== */

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

/*     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_("ZSBMV ", &info);
        return 0;
    }

/*     Quick return if possible. */

    if (*n == 0 || alpha->r == 0. && alpha->i == 0. && (beta->r == 1. && 
            beta->i == 0.)) {
        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->r != 1. || beta->i != 0.) {
        if (*incy == 1) {
            if (beta->r == 0. && beta->i == 0.) {
                i__1 = *n;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    i__2 = i__;
                    y[i__2].r = 0., y[i__2].i = 0.;
/* L10: */
                }
            } else {
                i__1 = *n;
                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 = *n;
                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 = *n;
                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;
    }
    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) {
                i__2 = j;
                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;
                temp1.r = z__1.r, temp1.i = z__1.i;
                temp2.r = 0., temp2.i = 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__) {
                    i__2 = i__;
                    i__3 = i__;
                    i__5 = l + i__ + j * a_dim1;
                    z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, 
                            z__2.i = temp1.r * a[i__5].i + temp1.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;
                    i__2 = l + i__ + j * a_dim1;
                    i__3 = i__;
                    z__2.r = a[i__2].r * x[i__3].r - a[i__2].i * x[i__3].i, 
                            z__2.i = a[i__2].r * x[i__3].i + a[i__2].i * x[
                            i__3].r;
                    z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
                    temp2.r = z__1.r, temp2.i = z__1.i;
/* L50: */
                }
                i__4 = j;
                i__2 = j;
                i__3 = kplus1 + j * a_dim1;
                z__3.r = temp1.r * a[i__3].r - temp1.i * a[i__3].i, z__3.i = 
                        temp1.r * a[i__3].i + temp1.i * a[i__3].r;
                z__2.r = y[i__2].r + z__3.r, z__2.i = y[i__2].i + z__3.i;
                z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i = 
                        alpha->r * temp2.i + alpha->i * temp2.r;
                z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
                y[i__4].r = z__1.r, y[i__4].i = z__1.i;
/* L60: */
            }
        } else {
            jx = kx;
            jy = ky;
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                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;
                temp1.r = z__1.r, temp1.i = z__1.i;
                temp2.r = 0., temp2.i = 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__) {
                    i__4 = iy;
                    i__2 = iy;
                    i__5 = l + i__ + j * a_dim1;
                    z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, 
                            z__2.i = temp1.r * a[i__5].i + temp1.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;
                    i__4 = l + 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 = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
                    temp2.r = z__1.r, temp2.i = z__1.i;
                    ix += *incx;
                    iy += *incy;
/* L70: */
                }
                i__3 = jy;
                i__4 = jy;
                i__2 = kplus1 + j * a_dim1;
                z__3.r = temp1.r * a[i__2].r - temp1.i * a[i__2].i, z__3.i = 
                        temp1.r * a[i__2].i + temp1.i * a[i__2].r;
                z__2.r = y[i__4].r + z__3.r, z__2.i = y[i__4].i + z__3.i;
                z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i = 
                        alpha->r * temp2.i + alpha->i * temp2.r;
                z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
                y[i__3].r = z__1.r, y[i__3].i = z__1.i;
                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) {
                i__3 = j;
                z__1.r = alpha->r * x[i__3].r - alpha->i * x[i__3].i, z__1.i =
                         alpha->r * x[i__3].i + alpha->i * x[i__3].r;
                temp1.r = z__1.r, temp1.i = z__1.i;
                temp2.r = 0., temp2.i = 0.;
                i__3 = j;
                i__4 = j;
                i__2 = j * a_dim1 + 1;
                z__2.r = temp1.r * a[i__2].r - temp1.i * a[i__2].i, z__2.i = 
                        temp1.r * a[i__2].i + temp1.i * a[i__2].r;
                z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
                y[i__3].r = z__1.r, y[i__3].i = z__1.i;
                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__) {
                    i__4 = i__;
                    i__2 = i__;
                    i__5 = l + i__ + j * a_dim1;
                    z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, 
                            z__2.i = temp1.r * a[i__5].i + temp1.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;
                    i__4 = l + i__ + j * a_dim1;
                    i__2 = i__;
                    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 = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
                    temp2.r = z__1.r, temp2.i = z__1.i;
/* L90: */
                }
                i__3 = j;
                i__4 = j;
                z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i = 
                        alpha->r * temp2.i + alpha->i * temp2.r;
                z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
                y[i__3].r = z__1.r, y[i__3].i = z__1.i;
/* L100: */
            }
        } else {
            jx = kx;
            jy = ky;
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                i__3 = jx;
                z__1.r = alpha->r * x[i__3].r - alpha->i * x[i__3].i, z__1.i =
                         alpha->r * x[i__3].i + alpha->i * x[i__3].r;
                temp1.r = z__1.r, temp1.i = z__1.i;
                temp2.r = 0., temp2.i = 0.;
                i__3 = jy;
                i__4 = jy;
                i__2 = j * a_dim1 + 1;
                z__2.r = temp1.r * a[i__2].r - temp1.i * a[i__2].i, z__2.i = 
                        temp1.r * a[i__2].i + temp1.i * a[i__2].r;
                z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
                y[i__3].r = z__1.r, y[i__3].i = z__1.i;
                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;
                    i__4 = iy;
                    i__2 = iy;
                    i__5 = l + i__ + j * a_dim1;
                    z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, 
                            z__2.i = temp1.r * a[i__5].i + temp1.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;
                    i__4 = l + 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 = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
                    temp2.r = z__1.r, temp2.i = z__1.i;
/* L110: */
                }
                i__3 = jy;
                i__4 = jy;
                z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i = 
                        alpha->r * temp2.i + alpha->i * temp2.r;
                z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
                y[i__3].r = z__1.r, y[i__3].i = z__1.i;
                jx += *incx;
                jy += *incy;
/* L120: */
            }
        }
    }

    return 0;

/*     End of ZSBMV */

} /* zsbmv_ */