/* -- translated by f2c (version 19940927). You must link the resulting object file with the libraries: -lf2c -lm (in that order) */ #include #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; static integer ix, iy, jx, jy, kx, ky; extern int input_error(char *, int *); /* 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 ( strncmp(uplo, "U", 1)!=0 && strncmp(uplo, "L", 1)!=0 ) { 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) { input_error("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 (strncmp(uplo, "U", 1)==0) { /* 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_ */