#include "f2c.h" #include "blaswrap.h" /* Subroutine */ int cher2_(char *uplo, integer *n, complex *alpha, complex * x, integer *incx, complex *y, integer *incy, complex *a, integer *lda) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6; real r__1; complex q__1, q__2, q__3, q__4; /* Builtin functions */ void r_cnjg(complex *, complex *); /* Local variables */ integer i__, j, ix, iy, jx, jy, kx, ky, info; complex temp1, temp2; extern logical lsame_(char *, char *); extern /* Subroutine */ int xerbla_(char *, integer *); /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CHER2 performs the hermitian rank 2 operation */ /* A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A, */ /* where alpha is a scalar, x and y are n element vectors and A is an n */ /* by n hermitian matrix. */ /* Arguments */ /* ========== */ /* 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 . */ /* On entry, ALPHA specifies the scalar alpha. */ /* Unchanged on exit. */ /* X - COMPLEX 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. */ /* Y - COMPLEX array of dimension at least */ /* ( 1 + ( n - 1 )*abs( INCY ) ). */ /* Before entry, the incremented array Y must contain the n */ /* element vector y. */ /* Unchanged on exit. */ /* INCY - INTEGER. */ /* On entry, INCY specifies the increment for the elements of */ /* Y. INCY must not be zero. */ /* Unchanged on exit. */ /* A - COMPLEX 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. On exit, the */ /* upper triangular part of the array A is overwritten by the */ /* upper triangular part of the updated matrix. */ /* 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. On exit, the */ /* lower triangular part of the array A is overwritten by the */ /* lower triangular part of the updated matrix. */ /* Note that the imaginary parts of the diagonal elements need */ /* not be set, they are assumed to be zero, and on exit they */ /* are set to zero. */ /* 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. */ /* 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 */ --x; --y; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; /* Function Body */ info = 0; if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { info = 1; } else if (*n < 0) { info = 2; } else if (*incx == 0) { info = 5; } else if (*incy == 0) { info = 7; } else if (*lda < max(1,*n)) { info = 9; } if (info != 0) { xerbla_("CHER2 ", &info); return 0; } /* Quick return if possible. */ if (*n == 0 || alpha->r == 0.f && alpha->i == 0.f) { return 0; } /* Set up the start points in X and Y if the increments are not both */ /* unity. */ if (*incx != 1 || *incy != 1) { if (*incx > 0) { kx = 1; } else { kx = 1 - (*n - 1) * *incx; } if (*incy > 0) { ky = 1; } else { ky = 1 - (*n - 1) * *incy; } jx = kx; jy = ky; } /* Start the operations. In this version the elements of A are */ /* accessed sequentially with one pass through the triangular part */ /* of A. */ if (lsame_(uplo, "U")) { /* Form A when A is stored in the upper triangle. */ if (*incx == 1 && *incy == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; i__3 = j; if (x[i__2].r != 0.f || x[i__2].i != 0.f || (y[i__3].r != 0.f || y[i__3].i != 0.f)) { r_cnjg(&q__2, &y[j]); q__1.r = alpha->r * q__2.r - alpha->i * q__2.i, q__1.i = alpha->r * q__2.i + alpha->i * q__2.r; temp1.r = q__1.r, temp1.i = q__1.i; i__2 = j; q__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, q__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] .r; r_cnjg(&q__1, &q__2); temp2.r = q__1.r, temp2.i = q__1.i; i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; i__4 = i__ + j * a_dim1; i__5 = i__; q__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, q__3.i = x[i__5].r * temp1.i + x[i__5].i * temp1.r; q__2.r = a[i__4].r + q__3.r, q__2.i = a[i__4].i + q__3.i; i__6 = i__; q__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, q__4.i = y[i__6].r * temp2.i + y[i__6].i * temp2.r; q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i; a[i__3].r = q__1.r, a[i__3].i = q__1.i; /* L10: */ } i__2 = j + j * a_dim1; i__3 = j + j * a_dim1; i__4 = j; q__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, q__2.i = x[i__4].r * temp1.i + x[i__4].i * temp1.r; i__5 = j; q__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, q__3.i = y[i__5].r * temp2.i + y[i__5].i * temp2.r; q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i; r__1 = a[i__3].r + q__1.r; a[i__2].r = r__1, a[i__2].i = 0.f; } else { i__2 = j + j * a_dim1; i__3 = j + j * a_dim1; r__1 = a[i__3].r; a[i__2].r = r__1, a[i__2].i = 0.f; } /* L20: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = jx; i__3 = jy; if (x[i__2].r != 0.f || x[i__2].i != 0.f || (y[i__3].r != 0.f || y[i__3].i != 0.f)) { r_cnjg(&q__2, &y[jy]); q__1.r = alpha->r * q__2.r - alpha->i * q__2.i, q__1.i = alpha->r * q__2.i + alpha->i * q__2.r; temp1.r = q__1.r, temp1.i = q__1.i; i__2 = jx; q__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, q__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] .r; r_cnjg(&q__1, &q__2); temp2.r = q__1.r, temp2.i = q__1.i; ix = kx; iy = ky; i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; i__4 = i__ + j * a_dim1; i__5 = ix; q__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, q__3.i = x[i__5].r * temp1.i + x[i__5].i * temp1.r; q__2.r = a[i__4].r + q__3.r, q__2.i = a[i__4].i + q__3.i; i__6 = iy; q__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, q__4.i = y[i__6].r * temp2.i + y[i__6].i * temp2.r; q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i; a[i__3].r = q__1.r, a[i__3].i = q__1.i; ix += *incx; iy += *incy; /* L30: */ } i__2 = j + j * a_dim1; i__3 = j + j * a_dim1; i__4 = jx; q__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, q__2.i = x[i__4].r * temp1.i + x[i__4].i * temp1.r; i__5 = jy; q__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, q__3.i = y[i__5].r * temp2.i + y[i__5].i * temp2.r; q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i; r__1 = a[i__3].r + q__1.r; a[i__2].r = r__1, a[i__2].i = 0.f; } else { i__2 = j + j * a_dim1; i__3 = j + j * a_dim1; r__1 = a[i__3].r; a[i__2].r = r__1, a[i__2].i = 0.f; } jx += *incx; jy += *incy; /* L40: */ } } } else { /* Form A when A is stored in the lower triangle. */ if (*incx == 1 && *incy == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; i__3 = j; if (x[i__2].r != 0.f || x[i__2].i != 0.f || (y[i__3].r != 0.f || y[i__3].i != 0.f)) { r_cnjg(&q__2, &y[j]); q__1.r = alpha->r * q__2.r - alpha->i * q__2.i, q__1.i = alpha->r * q__2.i + alpha->i * q__2.r; temp1.r = q__1.r, temp1.i = q__1.i; i__2 = j; q__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, q__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] .r; r_cnjg(&q__1, &q__2); temp2.r = q__1.r, temp2.i = q__1.i; i__2 = j + j * a_dim1; i__3 = j + j * a_dim1; i__4 = j; q__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, q__2.i = x[i__4].r * temp1.i + x[i__4].i * temp1.r; i__5 = j; q__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, q__3.i = y[i__5].r * temp2.i + y[i__5].i * temp2.r; q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i; r__1 = a[i__3].r + q__1.r; a[i__2].r = r__1, a[i__2].i = 0.f; i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; i__4 = i__ + j * a_dim1; i__5 = i__; q__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, q__3.i = x[i__5].r * temp1.i + x[i__5].i * temp1.r; q__2.r = a[i__4].r + q__3.r, q__2.i = a[i__4].i + q__3.i; i__6 = i__; q__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, q__4.i = y[i__6].r * temp2.i + y[i__6].i * temp2.r; q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i; a[i__3].r = q__1.r, a[i__3].i = q__1.i; /* L50: */ } } else { i__2 = j + j * a_dim1; i__3 = j + j * a_dim1; r__1 = a[i__3].r; a[i__2].r = r__1, a[i__2].i = 0.f; } /* L60: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = jx; i__3 = jy; if (x[i__2].r != 0.f || x[i__2].i != 0.f || (y[i__3].r != 0.f || y[i__3].i != 0.f)) { r_cnjg(&q__2, &y[jy]); q__1.r = alpha->r * q__2.r - alpha->i * q__2.i, q__1.i = alpha->r * q__2.i + alpha->i * q__2.r; temp1.r = q__1.r, temp1.i = q__1.i; i__2 = jx; q__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, q__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] .r; r_cnjg(&q__1, &q__2); temp2.r = q__1.r, temp2.i = q__1.i; i__2 = j + j * a_dim1; i__3 = j + j * a_dim1; i__4 = jx; q__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, q__2.i = x[i__4].r * temp1.i + x[i__4].i * temp1.r; i__5 = jy; q__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, q__3.i = y[i__5].r * temp2.i + y[i__5].i * temp2.r; q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i; r__1 = a[i__3].r + q__1.r; a[i__2].r = r__1, a[i__2].i = 0.f; ix = jx; iy = jy; i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { ix += *incx; iy += *incy; i__3 = i__ + j * a_dim1; i__4 = i__ + j * a_dim1; i__5 = ix; q__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, q__3.i = x[i__5].r * temp1.i + x[i__5].i * temp1.r; q__2.r = a[i__4].r + q__3.r, q__2.i = a[i__4].i + q__3.i; i__6 = iy; q__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, q__4.i = y[i__6].r * temp2.i + y[i__6].i * temp2.r; q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i; a[i__3].r = q__1.r, a[i__3].i = q__1.i; /* L70: */ } } else { i__2 = j + j * a_dim1; i__3 = j + j * a_dim1; r__1 = a[i__3].r; a[i__2].r = r__1, a[i__2].i = 0.f; } jx += *incx; jy += *incy; /* L80: */ } } } return 0; /* End of CHER2 . */ } /* cher2_ */