ZSPR    performs the symmetric rank 1 operation


    A := alpha*x*x**H + 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.

UPLO

          UPLO is 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

          N is INTEGER


           On entry, N specifies the order of the matrix A.


           N must be at least zero.


           Unchanged on exit.

ALPHA

          ALPHA is COMPLEX*16


           On entry, ALPHA specifies the scalar alpha.


           Unchanged on exit.

X

          X is 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

          INCX is INTEGER


           On entry, INCX specifies the increment for the elements of


           X. INCX must not be zero.


           Unchanged on exit.

AP

          AP is 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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016