CXML
        	    
LAPACK version 3.0
zspr(3)

PURPOSE
  ZSPR - perform the symmetric rank 1 operation	 A := alpha*x*conjg( x' ) +
  A,

SYNTAX
  SUBROUTINE ZSPR( UPLO, N, ALPHA, X, INCX, AP )

      CHARACTER	   UPLO

      INTEGER	   INCX, N

      COMPLEX*16   ALPHA

      COMPLEX*16   AP( * ), X( * )

DESCRIPTION
  ZSPR performs the symmetric rank 1 operation A := alpha*x*conjg( x' ) + A,
  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*16
	 On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

  X	 - COMPLEX*16 array, 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.

  AP	 - COMPLEX*16 array, 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 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 ) respectively, and so on. On exit, the array AP
	 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.