DSPR2(1) BLAS routine DSPR2(1)[top]NAMEDSPR2 - performs the symmetric rank 2 operation A := alpha*x*y' + alpha*y*x' + A,SYNOPSISSUBROUTINE DSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) DOUBLE PRECISION ALPHA INTEGER INCX,INCY,N CHARACTER UPLO DOUBLE PRECISION AP(*),X(*),Y(*)PURPOSEDSPR2 performs the symmetric rank 2 operation where alpha is a scalar, x and y are n element vectors and A is an n by n symmetric matrix, supplied in packed form.ARGUMENTSUPLO - 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 fol‐ lows: 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 - DOUBLE PRECISION 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 - DOUBLE PRECISION 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. AP - DOUBLE PRECISION 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 sym‐ metric 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 sequen‐ tially, 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 overwritten by the lower triangular part of the updated matrix.FURTHER DETAILSLevel 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.--BLAS routineNovember 2008 DSPR2(1)

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