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NAME CSPR - perform the symmetric rank 1 operation A := alpha*x*conjg( x' ) + A, SYNOPSIS SUBROUTINE CSPR( UPLO, N, ALPHA, X, INCX, AP ) CHARACTER UPLO INTEGER INCX, N COMPLEX ALPHA COMPLEX AP( * ), X( * ) PURPOSE CSPR performs the symmetric rank 1 operation where alpha is a complex scalar, x is an n element vector and A is an n by n symmetric 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 On entry, ALPHA specifies the scalar alpha. Unchanged on exit. X - COMPLEX array, dimension at least ( 1 + ( N - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the N- element vec- tor 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. AP - COMPLEX array, 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 symmetric 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 symmetric 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.