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SUBROUTINE <a name="ZSPR.1"></a><a href="zspr.f.html#ZSPR.1">ZSPR</a>( UPLO, N, ALPHA, X, INCX, AP )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> CHARACTER UPLO
INTEGER INCX, N
COMPLEX*16 ALPHA
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> COMPLEX*16 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="ZSPR.19"></a><a href="zspr.f.html#ZSPR.1">ZSPR</a> performs the symmetric 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 complex scalar, x is an n element vector and A is an
</span><span class="comment">*</span><span class="comment"> n by n symmetric 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 (input) 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 (input) 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 (input) COMPLEX*16
</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 (input) COMPLEX*16 array, 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 (input) 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 (input/output) COMPLEX*16 array, 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 symmetric 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 symmetric 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">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> COMPLEX*16 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> INTEGER I, INFO, IX, J, JX, K, KK, KX
COMPLEX*16 TEMP
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.93"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
EXTERNAL <a name="LSAME.94"></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.97"></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"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
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