*
************************************************************************
*
SUBROUTINE ESSPR ( UPLO, N, ALPHA, X, INCX, AP )
* .. Scalar Arguments ..
REAL ALPHA
INTEGER INCX, N
CHARACTER*1 UPLO
* .. Array Arguments ..
DOUBLE PRECISION X( * )
REAL AP( * )
* ..
*
* Purpose
* =======
*
* ESSPR performs the symmetric rank 1 operation
*
* A := alpha*x*x' + A,
*
* where alpha is a real scalar, x is an n element vector and A is an
* n by n symmetric matrix. Additional precision arithmetic is used in
* the computation.
*
* Parameters
* ==========
*
* 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 - REAL .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* X - DOUBLE PRECISION array of 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 - REAL array of 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. At least REAL arithmetic is
* used in the computation of A.
*
*
* Level 2 Blas routine.
*
* -- Written on 20-July-1986.
* Sven Hammarling, Nag Central Office.
* Richard Hanson, Sandia National Labs.
*
*
* .. Parameters ..
REAL ZERO
PARAMETER ( ZERO = 0.0E+0 )
* .. Local Scalars ..
DOUBLE PRECISION TEMP
INTEGER I, INFO, IX, J, JX, K, KK, KX
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* .. External Subroutines ..
EXTERNAL XERBLA
* .. Intrinsic Functions ..
INTRINSIC DBLE
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
IF ( .NOT.LSAME( UPLO, 'U' ).AND.
$ .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = 1
ELSE IF ( N.LT.0 ) THEN
INFO = 2
ELSE IF ( INCX.EQ.0 ) THEN
INFO = 5
END IF
IF( INFO.NE.0 )THEN
CALL XERBLA( 'ESSPR ', INFO )
RETURN
END IF
*
* Quick return if possible.
*
IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) )
$ RETURN
*
* Set the start point in X if the increment is not unity.
*
IF( INCX.LE.0 )THEN
KX = 1 - ( N - 1 )*INCX
ELSE IF( INCX.NE.1 )THEN
KX = 1
END IF
*
* Start the operations. In this version the elements of the array AP
* are accessed sequentially with one pass through AP.
*
K = 1
IF( LSAME( UPLO, 'U' ) )THEN
*
* Form A when upper triangle is stored in AP.
*
IF( INCX.EQ.1 )THEN
DO 20, J = 1, N
IF( X( J ).NE.DBLE( ZERO ) )THEN
TEMP = ALPHA*X( J )
DO 10, I = 1, J - 1
AP( K ) = AP( K ) + X( I )*TEMP
K = K + 1
10 CONTINUE
AP( K ) = AP( K ) + DBLE( X( J )*TEMP )
K = K + 1
ELSE
K = K + J
END IF
20 CONTINUE
ELSE
JX = KX
DO 40, J = 1, N
IF( X( JX ).NE.DBLE( ZERO ) )THEN
TEMP = ALPHA*X( JX )
IX = KX
KK = K
DO 30, K = KK, KK + J - 2
AP( K ) = AP( K ) + X( IX )*TEMP
IX = IX + INCX
30 CONTINUE
AP( K ) = AP( K ) + DBLE( X( JX )*TEMP )
K = K + 1
ELSE
K = K + J
END IF
JX = JX + INCX
40 CONTINUE
END IF
ELSE
*
* Form A when lower triangle is stored in AP.
*
IF( INCX.EQ.1 )THEN
DO 60, J = 1, N
IF( X( J ).NE.DBLE( ZERO ) )THEN
TEMP = ALPHA*X( J )
AP( K ) = AP( K ) + DBLE( TEMP*X( J ) )
K = K + 1
DO 50, I = J + 1, N
AP( K ) = AP( K ) + X( I )*TEMP
K = K + 1
50 CONTINUE
ELSE
K = K + N - J + 1
END IF
60 CONTINUE
ELSE
JX = KX
DO 80, J = 1, N
IF( X( JX ).NE.DBLE( ZERO ) )THEN
TEMP = ALPHA*X( JX )
AP( K ) = AP( K ) + DBLE( TEMP*X( JX ) )
IX = JX
KK = K + 1
DO 70, K = KK, KK + N - J
IX = IX + INCX
AP( K ) = AP( K ) + X( IX )*TEMP
70 CONTINUE
ELSE
K = K + N - J + 1
END IF
JX = JX + INCX
80 CONTINUE
END IF
END IF
*
RETURN
*
* End of ESSPR .
*
END