#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int zhpmv_(char *uplo, integer *n, doublecomplex *alpha, doublecomplex *ap, doublecomplex *x, integer *incx, doublecomplex * beta, doublecomplex *y, integer *incy) { /* System generated locals */ integer 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 i__, j, k, kk, ix, iy, jx, jy, kx, ky, info; static doublecomplex temp1, temp2; extern logical lsame_(char *, char *); extern /* Subroutine */ int xerbla_(char *, integer *); /* Purpose ======= ZHPMV 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, supplied in packed form. Arguments ========== UPLO - CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows: UPLO = 'U' or 'u' The upper triangular part of A is supplied in AP. UPLO = 'L' or 'l' The lower triangular part of A is supplied in AP. 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. AP - COMPLEX*16 array of DIMENSION at least ( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the hermitian matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the hermitian matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero. 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 */ --y; --x; --ap; /* Function Body */ info = 0; if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { info = 1; } else if (*n < 0) { info = 2; } else if (*incx == 0) { info = 6; } else if (*incy == 0) { info = 9; } if (info != 0) { xerbla_("ZHPMV ", &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 AP are accessed sequentially with one pass through AP. 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; } kk = 1; if (lsame_(uplo, "U")) { /* Form y when AP contains the upper triangle. */ 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.; k = kk; i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__; i__4 = i__; i__5 = k; z__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i, z__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5] .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; d_cnjg(&z__3, &ap[k]); i__3 = i__; 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 = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; temp2.r = z__1.r, temp2.i = z__1.i; ++k; /* L50: */ } i__2 = j; i__3 = j; i__4 = kk + j - 1; d__1 = ap[i__4].r; z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i; z__2.r = y[i__3].r + z__3.r, z__2.i = y[i__3].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__2].r = z__1.r, y[i__2].i = z__1.i; kk += j; /* L60: */ } } else { jx = kx; jy = ky; i__1 = *n; for (j = 1; j <= i__1; ++j) { 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; temp1.r = z__1.r, temp1.i = z__1.i; temp2.r = 0., temp2.i = 0.; ix = kx; iy = ky; i__2 = kk + j - 2; for (k = kk; k <= i__2; ++k) { i__3 = iy; i__4 = iy; i__5 = k; z__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i, z__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5] .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; d_cnjg(&z__3, &ap[k]); 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 = 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 = kk + j - 1; d__1 = ap[i__4].r; z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i; z__2.r = y[i__3].r + z__3.r, z__2.i = y[i__3].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__2].r = z__1.r, y[i__2].i = z__1.i; jx += *incx; jy += *incy; kk += j; /* L80: */ } } } else { /* Form y when AP contains the lower triangle. */ 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.; i__2 = j; i__3 = j; i__4 = kk; d__1 = ap[i__4].r; z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i; 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; k = kk + 1; i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = i__; i__4 = i__; i__5 = k; z__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i, z__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5] .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; d_cnjg(&z__3, &ap[k]); i__3 = i__; 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 = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; temp2.r = z__1.r, temp2.i = z__1.i; ++k; /* 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[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; kk += *n - j + 1; /* L100: */ } } else { jx = kx; jy = ky; i__1 = *n; for (j = 1; j <= i__1; ++j) { 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; temp1.r = z__1.r, temp1.i = z__1.i; temp2.r = 0., temp2.i = 0.; i__2 = jy; i__3 = jy; i__4 = kk; d__1 = ap[i__4].r; z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i; 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; ix = jx; iy = jy; i__2 = kk + *n - j; for (k = kk + 1; k <= i__2; ++k) { ix += *incx; iy += *incy; i__3 = iy; i__4 = iy; i__5 = k; z__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i, z__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5] .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; d_cnjg(&z__3, &ap[k]); 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 = 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[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; jx += *incx; jy += *incy; kk += *n - j + 1; /* L120: */ } } } return 0; /* End of ZHPMV . */ } /* zhpmv_ */