ZSPR (3lapack)

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

SYNOPSIS

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

      CHARACTER    UPLO

      INTEGER      INCX, N

      COMPLEX*16   ALPHA

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

PURPOSE

  ZSPR    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*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.