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zspr

 NAME
      ZSPR - 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 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*16 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.