zhemv.c

SuperLU is a general purpose library for the direct solution of large, sparse, nonsymmetric systems

/*  -- translated by f2c (version 19940927).
   You must link the resulting object file with the libraries:
	-lf2c -lm   (in that order)
*/

#include "f2c.h"

/* Subroutine */ int zhemv_(char *uplo, integer *n, 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;
    doublereal d__1;
    doublecomplex z__1, z__2, z__3, z__4;

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

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


/*  Purpose   
    =======   

    ZHEMV  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 hermitian matrix.   

    Parameters   
    ==========   

    UPLO   - CHARACTER*1.   
             On entry, UPLO specifies whether the upper or lower   
             triangular part of the array A is to be referenced as   
             follows:   

                UPLO = 'U' or 'u'   Only the upper triangular part of A   
                                    is to be referenced.   

                UPLO = 'L' or 'l'   Only the lower triangular part of A   
                                    is to be referenced.   

             Unchanged on exit.   

    N      - INTEGER.   
             On entry, N specifies the order of the matrix A.   
             N must be at least zero.   
             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 with  UPLO = 'U' or 'u', the leading n by n   
             upper triangular part of the array A must contain the upper 
  
             triangular part of the hermitian matrix and the strictly   
             lower triangular part of A is not referenced.   
             Before entry with UPLO = 'L' or 'l', the leading n by n   
             lower triangular part of the array A must contain the lower 
  
             triangular part of the hermitian matrix and the strictly   
             upper triangular part of A is not referenced.   
             Note that the imaginary parts of the diagonal elements need 
  
             not be set and are assumed to be zero.   
             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, n ).   
             Unchanged on exit.   

    X      - COMPLEX*16       array of dimension at least   
             ( 1 + ( n - 1 )*abs( INCX ) ).   
             Before entry, the incremented array X must contain the n   
             element 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 + ( n - 1 )*abs( INCY ) ).   
             Before entry, the incremented array Y must contain the n   
             element 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.   



       Test the input parameters.   

    
   Parameter adjustments   
       Function Body */
#define X(I) x[(I)-1]
#define Y(I) y[(I)-1]

#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]

    info = 0;
    if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
	info = 1;
    } else if (*n < 0) {
	info = 2;
    } else if (*lda < max(1,*n)) {
	info = 5;
    } else if (*incx == 0) {
	info = 7;
    } else if (*incy == 0) {
	info = 10;
    }
    if (info != 0) {
	xerbla_("ZHEMV ", &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 A are   
       accessed sequentially with one pass through the triangular 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 = *n;
		for (i = 1; i <= *n; ++i) {
		    i__2 = i;
		    Y(i).r = 0., Y(i).i = 0.;
/* L10: */
		}
	    } else {
		i__1 = *n;
		for (i = 1; i <= *n; ++i) {
		    i__2 = i;
		    i__3 = i;
		    z__1.r = beta->r * Y(i).r - beta->i * Y(i).i, 
			    z__1.i = beta->r * Y(i).i + beta->i * Y(i)
			    .r;
		    Y(i).r = z__1.r, Y(i).i = z__1.i;
/* L20: */
		}
	    }
	} else {
	    iy = ky;
	    if (beta->r == 0. && beta->i == 0.) {
		i__1 = *n;
		for (i = 1; i <= *n; ++i) {
		    i__2 = iy;
		    Y(iy).r = 0., Y(iy).i = 0.;
		    iy += *incy;
/* L30: */
		}
	    } else {
		i__1 = *n;
		for (i = 1; i <= *n; ++i) {
		    i__2 = iy;
		    i__3 = iy;
		    z__1.r = beta->r * Y(iy).r - beta->i * Y(iy).i, 
			    z__1.i = beta->r * Y(iy).i + beta->i * Y(iy)
			    .r;
		    Y(iy).r = z__1.r, Y(iy).i = z__1.i;
		    iy += *incy;
/* L40: */
		}
	    }
	}
    }
    if (alpha->r == 0. && alpha->i == 0.) {
	return 0;
    }
    if (lsame_(uplo, "U")) {

/*        Form  y  when A is stored in upper triangle. */

	if (*incx == 1 && *incy == 1) {
	    i__1 = *n;
	    for (j = 1; j <= *n; ++j) {
		i__2 = j;
		z__1.r = alpha->r * X(j).r - alpha->i * X(j).i, z__1.i =
			 alpha->r * X(j).i + alpha->i * X(j).r;
		temp1.r = z__1.r, temp1.i = z__1.i;
		temp2.r = 0., temp2.i = 0.;
		i__2 = j - 1;
		for (i = 1; i <= j-1; ++i) {
		    i__3 = i;
		    i__4 = i;
		    i__5 = i + j * a_dim1;
		    z__2.r = temp1.r * A(i,j).r - temp1.i * A(i,j).i, 
			    z__2.i = temp1.r * A(i,j).i + temp1.i * A(i,j)
			    .r;
		    z__1.r = Y(i).r + z__2.r, z__1.i = Y(i).i + z__2.i;
		    Y(i).r = z__1.r, Y(i).i = z__1.i;
		    d_cnjg(&z__3, &A(i,j));
		    i__3 = i;
		    z__2.r = z__3.r * X(i).r - z__3.i * X(i).i, z__2.i =
			     z__3.r * X(i).i + z__3.i * X(i).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__2 = j;
		i__3 = j;
		i__4 = j + j * a_dim1;
		d__1 = A(j,j).r;
		z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i;
		z__2.r = Y(j).r + z__3.r, z__2.i = Y(j).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(j).r = z__1.r, Y(j).i = z__1.i;
/* L60: */
	    }
	} else {
	    jx = kx;
	    jy = ky;
	    i__1 = *n;
	    for (j = 1; j <= *n; ++j) {
		i__2 = jx;
		z__1.r = alpha->r * X(jx).r - alpha->i * X(jx).i, z__1.i =
			 alpha->r * X(jx).i + alpha->i * X(jx).r;
		temp1.r = z__1.r, temp1.i = z__1.i;
		temp2.r = 0., temp2.i = 0.;
		ix = kx;
		iy = ky;
		i__2 = j - 1;
		for (i = 1; i <= j-1; ++i) {
		    i__3 = iy;
		    i__4 = iy;
		    i__5 = i + j * a_dim1;
		    z__2.r = temp1.r * A(i,j).r - temp1.i * A(i,j).i, 
			    z__2.i = temp1.r * A(i,j).i + temp1.i * A(i,j)
			    .r;
		    z__1.r = Y(iy).r + z__2.r, z__1.i = Y(iy).i + z__2.i;
		    Y(iy).r = z__1.r, Y(iy).i = z__1.i;
		    d_cnjg(&z__3, &A(i,j));
		    i__3 = ix;
		    z__2.r = z__3.r * X(ix).r - z__3.i * X(ix).i, z__2.i =
			     z__3.r * X(ix).i + z__3.i * X(ix).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__2 = jy;
		i__3 = jy;
		i__4 = j + j * a_dim1;
		d__1 = A(j,j).r;
		z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i;
		z__2.r = Y(jy).r + z__3.r, z__2.i = Y(jy).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(jy).r = z__1.r, Y(jy).i = z__1.i;
		jx += *incx;
		jy += *incy;
/* L80: */
	    }
	}
    } else {

/*        Form  y  when A is stored in lower triangle. */

	if (*incx == 1 && *incy == 1) {
	    i__1 = *n;
	    for (j = 1; j <= *n; ++j) {
		i__2 = j;
		z__1.r = alpha->r * X(j).r - alpha->i * X(j).i, z__1.i =
			 alpha->r * X(j).i + alpha->i * X(j).r;
		temp1.r = z__1.r, temp1.i = z__1.i;
		temp2.r = 0., temp2.i = 0.;
		i__2 = j;
		i__3 = j;
		i__4 = j + j * a_dim1;
		d__1 = A(j,j).r;
		z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i;
		z__1.r = Y(j).r + z__2.r, z__1.i = Y(j).i + z__2.i;
		Y(j).r = z__1.r, Y(j).i = z__1.i;
		i__2 = *n;
		for (i = j + 1; i <= *n; ++i) {
		    i__3 = i;
		    i__4 = i;
		    i__5 = i + j * a_dim1;
		    z__2.r = temp1.r * A(i,j).r - temp1.i * A(i,j).i, 
			    z__2.i = temp1.r * A(i,j).i + temp1.i * A(i,j)
			    .r;
		    z__1.r = Y(i).r + z__2.r, z__1.i = Y(i).i + z__2.i;
		    Y(i).r = z__1.r, Y(i).i = z__1.i;
		    d_cnjg(&z__3, &A(i,j));
		    i__3 = i;
		    z__2.r = z__3.r * X(i).r - z__3.i * X(i).i, z__2.i =
			     z__3.r * X(i).i + z__3.i * X(i).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__2 = j;
		i__3 = 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(j).r + z__2.r, z__1.i = Y(j).i + z__2.i;
		Y(j).r = z__1.r, Y(j).i = z__1.i;
/* L100: */
	    }
	} else {
	    jx = kx;
	    jy = ky;
	    i__1 = *n;
	    for (j = 1; j <= *n; ++j) {
		i__2 = jx;
		z__1.r = alpha->r * X(jx).r - alpha->i * X(jx).i, z__1.i =
			 alpha->r * X(jx).i + alpha->i * X(jx).r;
		temp1.r = z__1.r, temp1.i = z__1.i;
		temp2.r = 0., temp2.i = 0.;
		i__2 = jy;
		i__3 = jy;
		i__4 = j + j * a_dim1;
		d__1 = A(j,j).r;
		z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i;
		z__1.r = Y(jy).r + z__2.r, z__1.i = Y(jy).i + z__2.i;
		Y(jy).r = z__1.r, Y(jy).i = z__1.i;
		ix = jx;
		iy = jy;
		i__2 = *n;
		for (i = j + 1; i <= *n; ++i) {
		    ix += *incx;
		    iy += *incy;
		    i__3 = iy;
		    i__4 = iy;
		    i__5 = i + j * a_dim1;
		    z__2.r = temp1.r * A(i,j).r - temp1.i * A(i,j).i, 
			    z__2.i = temp1.r * A(i,j).i + temp1.i * A(i,j)
			    .r;
		    z__1.r = Y(iy).r + z__2.r, z__1.i = Y(iy).i + z__2.i;
		    Y(iy).r = z__1.r, Y(iy).i = z__1.i;
		    d_cnjg(&z__3, &A(i,j));
		    i__3 = ix;
		    z__2.r = z__3.r * X(ix).r - z__3.i * X(ix).i, z__2.i =
			     z__3.r * X(ix).i + z__3.i * X(ix).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__2 = jy;
		i__3 = 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(jy).r + z__2.r, z__1.i = Y(jy).i + z__2.i;
		Y(jy).r = z__1.r, Y(jy).i = z__1.i;
		jx += *incx;
		jy += *incy;
/* L120: */
	    }
	}
    }

    return 0;

/*     End of ZHEMV . */

} /* zhemv_ */