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NAME ZHPR - perform the hermitian rank 1 operation A := alpha*x*conjg( x' ) + A, SYNOPSIS SUBROUTINE ZHPR ( UPLO, N, ALPHA, X, INCX, AP ) DOUBLE PRECISION ALPHA INTEGER INCX, N CHARACTER*1 UPLO COMPLEX*16 AP( * ), X( * ) PURPOSE ZHPR performs the hermitian rank 1 operation where alpha is a real scalar, x is an n element vector and A is an n by n hermitian matrix, supplied in packed form. PARAMETERS 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 - DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. 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 ele- ments of X. INCX must not be zero. 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 triangu- lar 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. On exit, the array AP is overwritten by the upper triangular part of the updated matrix. 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 ) respec- tively, and so on. On exit, the array AP is overwrit- ten by the lower triangular part of the updated matrix. Note that the imaginary parts of the diago- nal elements need not be set, they are assumed to be zero, and on exit they are set to zero. 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.