421 lines
12 KiB
C
421 lines
12 KiB
C
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/* -- translated by f2c (version 19940927).
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You must link the resulting object file with the libraries:
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-lf2c -lm (in that order)
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*/
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#include "f2c.h"
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/* Subroutine */ int zhemv_(char *uplo, integer *n, doublecomplex *alpha,
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doublecomplex *a, integer *lda, doublecomplex *x, integer *incx,
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doublecomplex *beta, doublecomplex *y, integer *incy)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
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doublereal d__1;
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doublecomplex z__1, z__2, z__3, z__4;
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/* Builtin functions */
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void d_cnjg(doublecomplex *, doublecomplex *);
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/* Local variables */
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static integer info;
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static doublecomplex temp1, temp2;
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static integer i, j;
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extern logical lsame_(char *, char *);
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static integer ix, iy, jx, jy, kx, ky;
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extern /* Subroutine */ int xerbla_(char *, integer *);
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/* Purpose
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=======
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ZHEMV performs the matrix-vector operation
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y := alpha*A*x + beta*y,
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where alpha and beta are scalars, x and y are n element vectors and
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A is an n by n hermitian matrix.
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Parameters
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==========
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UPLO - CHARACTER*1.
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On entry, UPLO specifies whether the upper or lower
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triangular part of the array A is to be referenced as
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follows:
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UPLO = 'U' or 'u' Only the upper triangular part of A
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is to be referenced.
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UPLO = 'L' or 'l' Only the lower triangular part of A
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is to be referenced.
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Unchanged on exit.
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N - INTEGER.
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On entry, N specifies the order of the matrix A.
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N must be at least zero.
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Unchanged on exit.
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ALPHA - COMPLEX*16 .
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On entry, ALPHA specifies the scalar alpha.
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Unchanged on exit.
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A - COMPLEX*16 array of DIMENSION ( LDA, n ).
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Before entry with UPLO = 'U' or 'u', the leading n by n
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upper triangular part of the array A must contain the upper
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triangular part of the hermitian matrix and the strictly
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lower triangular part of A is not referenced.
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Before entry with UPLO = 'L' or 'l', the leading n by n
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lower triangular part of the array A must contain the lower
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triangular part of the hermitian matrix and the strictly
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upper triangular part of A is not referenced.
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Note that the imaginary parts of the diagonal elements need
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not be set and are assumed to be zero.
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Unchanged on exit.
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LDA - INTEGER.
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On entry, LDA specifies the first dimension of A as declared
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in the calling (sub) program. LDA must be at least
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max( 1, n ).
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Unchanged on exit.
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X - COMPLEX*16 array of dimension at least
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( 1 + ( n - 1 )*abs( INCX ) ).
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Before entry, the incremented array X must contain the n
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element vector x.
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Unchanged on exit.
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INCX - INTEGER.
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On entry, INCX specifies the increment for the elements of
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X. INCX must not be zero.
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Unchanged on exit.
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BETA - COMPLEX*16 .
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On entry, BETA specifies the scalar beta. When BETA is
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supplied as zero then Y need not be set on input.
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Unchanged on exit.
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Y - COMPLEX*16 array of dimension at least
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( 1 + ( n - 1 )*abs( INCY ) ).
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Before entry, the incremented array Y must contain the n
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element vector y. On exit, Y is overwritten by the updated
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vector y.
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INCY - INTEGER.
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On entry, INCY specifies the increment for the elements of
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Y. INCY must not be zero.
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Unchanged on exit.
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Level 2 Blas routine.
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-- Written on 22-October-1986.
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Jack Dongarra, Argonne National Lab.
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Jeremy Du Croz, Nag Central Office.
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Sven Hammarling, Nag Central Office.
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Richard Hanson, Sandia National Labs.
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Test the input parameters.
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Parameter adjustments
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Function Body */
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#define X(I) x[(I)-1]
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#define Y(I) y[(I)-1]
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#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
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info = 0;
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if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
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info = 1;
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} else if (*n < 0) {
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info = 2;
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} else if (*lda < max(1,*n)) {
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info = 5;
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} else if (*incx == 0) {
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info = 7;
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} else if (*incy == 0) {
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info = 10;
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}
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if (info != 0) {
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xerbla_("ZHEMV ", &info);
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return 0;
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}
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/* Quick return if possible. */
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if (*n == 0 || alpha->r == 0. && alpha->i == 0. && (beta->r == 1. &&
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beta->i == 0.)) {
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return 0;
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}
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/* Set up the start points in X and Y. */
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if (*incx > 0) {
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kx = 1;
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} else {
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kx = 1 - (*n - 1) * *incx;
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}
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if (*incy > 0) {
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ky = 1;
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} else {
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ky = 1 - (*n - 1) * *incy;
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}
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/* Start the operations. In this version the elements of A are
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accessed sequentially with one pass through the triangular part
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of A.
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First form y := beta*y. */
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if (beta->r != 1. || beta->i != 0.) {
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if (*incy == 1) {
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if (beta->r == 0. && beta->i == 0.) {
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i__1 = *n;
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for (i = 1; i <= *n; ++i) {
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i__2 = i;
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Y(i).r = 0., Y(i).i = 0.;
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/* L10: */
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}
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} else {
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i__1 = *n;
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for (i = 1; i <= *n; ++i) {
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i__2 = i;
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i__3 = i;
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z__1.r = beta->r * Y(i).r - beta->i * Y(i).i,
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z__1.i = beta->r * Y(i).i + beta->i * Y(i)
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.r;
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Y(i).r = z__1.r, Y(i).i = z__1.i;
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/* L20: */
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}
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}
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} else {
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iy = ky;
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if (beta->r == 0. && beta->i == 0.) {
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i__1 = *n;
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for (i = 1; i <= *n; ++i) {
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i__2 = iy;
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Y(iy).r = 0., Y(iy).i = 0.;
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iy += *incy;
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/* L30: */
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}
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} else {
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i__1 = *n;
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for (i = 1; i <= *n; ++i) {
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i__2 = iy;
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i__3 = iy;
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z__1.r = beta->r * Y(iy).r - beta->i * Y(iy).i,
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z__1.i = beta->r * Y(iy).i + beta->i * Y(iy)
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.r;
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Y(iy).r = z__1.r, Y(iy).i = z__1.i;
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iy += *incy;
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/* L40: */
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}
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}
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}
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}
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if (alpha->r == 0. && alpha->i == 0.) {
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return 0;
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}
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if (lsame_(uplo, "U")) {
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/* Form y when A is stored in upper triangle. */
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if (*incx == 1 && *incy == 1) {
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i__1 = *n;
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for (j = 1; j <= *n; ++j) {
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i__2 = j;
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z__1.r = alpha->r * X(j).r - alpha->i * X(j).i, z__1.i =
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alpha->r * X(j).i + alpha->i * X(j).r;
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temp1.r = z__1.r, temp1.i = z__1.i;
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temp2.r = 0., temp2.i = 0.;
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i__2 = j - 1;
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for (i = 1; i <= j-1; ++i) {
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i__3 = i;
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i__4 = i;
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i__5 = i + j * a_dim1;
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z__2.r = temp1.r * A(i,j).r - temp1.i * A(i,j).i,
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z__2.i = temp1.r * A(i,j).i + temp1.i * A(i,j)
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.r;
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z__1.r = Y(i).r + z__2.r, z__1.i = Y(i).i + z__2.i;
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Y(i).r = z__1.r, Y(i).i = z__1.i;
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d_cnjg(&z__3, &A(i,j));
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i__3 = i;
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z__2.r = z__3.r * X(i).r - z__3.i * X(i).i, z__2.i =
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z__3.r * X(i).i + z__3.i * X(i).r;
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z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
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temp2.r = z__1.r, temp2.i = z__1.i;
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/* L50: */
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}
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i__2 = j;
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i__3 = j;
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i__4 = j + j * a_dim1;
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d__1 = A(j,j).r;
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z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i;
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z__2.r = Y(j).r + z__3.r, z__2.i = Y(j).i + z__3.i;
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z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i =
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alpha->r * temp2.i + alpha->i * temp2.r;
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z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
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Y(j).r = z__1.r, Y(j).i = z__1.i;
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/* L60: */
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}
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} else {
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jx = kx;
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jy = ky;
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i__1 = *n;
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for (j = 1; j <= *n; ++j) {
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i__2 = jx;
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z__1.r = alpha->r * X(jx).r - alpha->i * X(jx).i, z__1.i =
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alpha->r * X(jx).i + alpha->i * X(jx).r;
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temp1.r = z__1.r, temp1.i = z__1.i;
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temp2.r = 0., temp2.i = 0.;
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ix = kx;
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iy = ky;
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i__2 = j - 1;
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for (i = 1; i <= j-1; ++i) {
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i__3 = iy;
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i__4 = iy;
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i__5 = i + j * a_dim1;
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z__2.r = temp1.r * A(i,j).r - temp1.i * A(i,j).i,
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z__2.i = temp1.r * A(i,j).i + temp1.i * A(i,j)
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.r;
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z__1.r = Y(iy).r + z__2.r, z__1.i = Y(iy).i + z__2.i;
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Y(iy).r = z__1.r, Y(iy).i = z__1.i;
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d_cnjg(&z__3, &A(i,j));
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i__3 = ix;
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z__2.r = z__3.r * X(ix).r - z__3.i * X(ix).i, z__2.i =
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z__3.r * X(ix).i + z__3.i * X(ix).r;
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z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
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temp2.r = z__1.r, temp2.i = z__1.i;
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ix += *incx;
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iy += *incy;
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/* L70: */
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}
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i__2 = jy;
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i__3 = jy;
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i__4 = j + j * a_dim1;
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d__1 = A(j,j).r;
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z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i;
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z__2.r = Y(jy).r + z__3.r, z__2.i = Y(jy).i + z__3.i;
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z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i =
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alpha->r * temp2.i + alpha->i * temp2.r;
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z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
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Y(jy).r = z__1.r, Y(jy).i = z__1.i;
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jx += *incx;
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jy += *incy;
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/* L80: */
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}
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}
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} else {
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/* Form y when A is stored in lower triangle. */
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if (*incx == 1 && *incy == 1) {
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i__1 = *n;
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for (j = 1; j <= *n; ++j) {
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i__2 = j;
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z__1.r = alpha->r * X(j).r - alpha->i * X(j).i, z__1.i =
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alpha->r * X(j).i + alpha->i * X(j).r;
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temp1.r = z__1.r, temp1.i = z__1.i;
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temp2.r = 0., temp2.i = 0.;
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i__2 = j;
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i__3 = j;
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i__4 = j + j * a_dim1;
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d__1 = A(j,j).r;
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z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i;
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z__1.r = Y(j).r + z__2.r, z__1.i = Y(j).i + z__2.i;
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Y(j).r = z__1.r, Y(j).i = z__1.i;
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i__2 = *n;
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for (i = j + 1; i <= *n; ++i) {
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i__3 = i;
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i__4 = i;
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i__5 = i + j * a_dim1;
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z__2.r = temp1.r * A(i,j).r - temp1.i * A(i,j).i,
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z__2.i = temp1.r * A(i,j).i + temp1.i * A(i,j)
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.r;
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z__1.r = Y(i).r + z__2.r, z__1.i = Y(i).i + z__2.i;
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Y(i).r = z__1.r, Y(i).i = z__1.i;
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d_cnjg(&z__3, &A(i,j));
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i__3 = i;
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z__2.r = z__3.r * X(i).r - z__3.i * X(i).i, z__2.i =
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z__3.r * X(i).i + z__3.i * X(i).r;
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z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
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temp2.r = z__1.r, temp2.i = z__1.i;
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/* L90: */
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}
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i__2 = j;
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i__3 = j;
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z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i =
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alpha->r * temp2.i + alpha->i * temp2.r;
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z__1.r = Y(j).r + z__2.r, z__1.i = Y(j).i + z__2.i;
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Y(j).r = z__1.r, Y(j).i = z__1.i;
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/* L100: */
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}
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} else {
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jx = kx;
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jy = ky;
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i__1 = *n;
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for (j = 1; j <= *n; ++j) {
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i__2 = jx;
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z__1.r = alpha->r * X(jx).r - alpha->i * X(jx).i, z__1.i =
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alpha->r * X(jx).i + alpha->i * X(jx).r;
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temp1.r = z__1.r, temp1.i = z__1.i;
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temp2.r = 0., temp2.i = 0.;
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i__2 = jy;
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i__3 = jy;
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i__4 = j + j * a_dim1;
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d__1 = A(j,j).r;
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z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i;
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z__1.r = Y(jy).r + z__2.r, z__1.i = Y(jy).i + z__2.i;
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Y(jy).r = z__1.r, Y(jy).i = z__1.i;
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ix = jx;
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iy = jy;
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i__2 = *n;
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for (i = j + 1; i <= *n; ++i) {
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ix += *incx;
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iy += *incy;
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i__3 = iy;
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i__4 = iy;
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i__5 = i + j * a_dim1;
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z__2.r = temp1.r * A(i,j).r - temp1.i * A(i,j).i,
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z__2.i = temp1.r * A(i,j).i + temp1.i * A(i,j)
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.r;
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z__1.r = Y(iy).r + z__2.r, z__1.i = Y(iy).i + z__2.i;
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Y(iy).r = z__1.r, Y(iy).i = z__1.i;
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d_cnjg(&z__3, &A(i,j));
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i__3 = ix;
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z__2.r = z__3.r * X(ix).r - z__3.i * X(ix).i, z__2.i =
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z__3.r * X(ix).i + z__3.i * X(ix).r;
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z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
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temp2.r = z__1.r, temp2.i = z__1.i;
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/* L110: */
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}
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i__2 = jy;
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i__3 = jy;
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z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i =
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alpha->r * temp2.i + alpha->i * temp2.r;
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z__1.r = Y(jy).r + z__2.r, z__1.i = Y(jy).i + z__2.i;
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Y(jy).r = z__1.r, Y(jy).i = z__1.i;
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jx += *incx;
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jy += *incy;
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/* L120: */
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}
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}
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}
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return 0;
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/* End of ZHEMV . */
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} /* zhemv_ */
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