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SUBROUTINE <a name="ZHPR.1"></a><a href="zhpr.f.html#ZHPR.1">ZHPR</a>(UPLO,N,ALPHA,X,INCX,AP)
<span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> DOUBLE PRECISION ALPHA
INTEGER INCX,N
CHARACTER UPLO
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> DOUBLE COMPLEX AP(*),X(*)
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="ZHPR.14"></a><a href="zhpr.f.html#ZHPR.1">ZHPR</a> performs the hermitian rank 1 operation
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A := alpha*x*conjg( x' ) + A,
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> where alpha is a real scalar, x is an n element vector and A is an
</span><span class="comment">*</span><span class="comment"> n by n hermitian matrix, supplied in packed form.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> ==========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> UPLO - CHARACTER*1.
</span><span class="comment">*</span><span class="comment"> On entry, UPLO specifies whether the upper or lower
</span><span class="comment">*</span><span class="comment"> triangular part of the matrix A is supplied in the packed
</span><span class="comment">*</span><span class="comment"> array AP as follows:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> UPLO = 'U' or 'u' The upper triangular part of A is
</span><span class="comment">*</span><span class="comment"> supplied in AP.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> UPLO = 'L' or 'l' The lower triangular part of A is
</span><span class="comment">*</span><span class="comment"> supplied in AP.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N - INTEGER.
</span><span class="comment">*</span><span class="comment"> On entry, N specifies the order of the matrix A.
</span><span class="comment">*</span><span class="comment"> N must be at least zero.
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ALPHA - DOUBLE PRECISION.
</span><span class="comment">*</span><span class="comment"> On entry, ALPHA specifies the scalar alpha.
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> X - COMPLEX*16 array of dimension at least
</span><span class="comment">*</span><span class="comment"> ( 1 + ( n - 1 )*abs( INCX ) ).
</span><span class="comment">*</span><span class="comment"> Before entry, the incremented array X must contain the n
</span><span class="comment">*</span><span class="comment"> element vector x.
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INCX - INTEGER.
</span><span class="comment">*</span><span class="comment"> On entry, INCX specifies the increment for the elements of
</span><span class="comment">*</span><span class="comment"> X. INCX must not be zero.
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> AP - COMPLEX*16 array of DIMENSION at least
</span><span class="comment">*</span><span class="comment"> ( ( n*( n + 1 ) )/2 ).
</span><span class="comment">*</span><span class="comment"> Before entry with UPLO = 'U' or 'u', the array AP must
</span><span class="comment">*</span><span class="comment"> contain the upper triangular part of the hermitian matrix
</span><span class="comment">*</span><span class="comment"> packed sequentially, column by column, so that AP( 1 )
</span><span class="comment">*</span><span class="comment"> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
</span><span class="comment">*</span><span class="comment"> and a( 2, 2 ) respectively, and so on. On exit, the array
</span><span class="comment">*</span><span class="comment"> AP is overwritten by the upper triangular part of the
</span><span class="comment">*</span><span class="comment"> updated matrix.
</span><span class="comment">*</span><span class="comment"> Before entry with UPLO = 'L' or 'l', the array AP must
</span><span class="comment">*</span><span class="comment"> contain the lower triangular part of the hermitian matrix
</span><span class="comment">*</span><span class="comment"> packed sequentially, column by column, so that AP( 1 )
</span><span class="comment">*</span><span class="comment"> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
</span><span class="comment">*</span><span class="comment"> and a( 3, 1 ) respectively, and so on. On exit, the array
</span><span class="comment">*</span><span class="comment"> AP is overwritten by the lower triangular part of the
</span><span class="comment">*</span><span class="comment"> updated matrix.
</span><span class="comment">*</span><span class="comment"> Note that the imaginary parts of the diagonal elements need
</span><span class="comment">*</span><span class="comment"> not be set, they are assumed to be zero, and on exit they
</span><span class="comment">*</span><span class="comment"> are set to zero.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Level 2 Blas routine.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- Written on 22-October-1986.
</span><span class="comment">*</span><span class="comment"> Jack Dongarra, Argonne National Lab.
</span><span class="comment">*</span><span class="comment"> Jeremy Du Croz, Nag Central Office.
</span><span class="comment">*</span><span class="comment"> Sven Hammarling, Nag Central Office.
</span><span class="comment">*</span><span class="comment"> Richard Hanson, Sandia National Labs.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> DOUBLE COMPLEX TEMP
INTEGER I,INFO,IX,J,JX,K,KK,KX
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.96"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
EXTERNAL <a name="LSAME.97"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL <a name="XERBLA.100"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
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