*DECK DSPR2
SUBROUTINE DSPR2 (UPLO, N, ALPHA, X, INCX, Y, INCY, AP)
C***BEGIN PROLOGUE DSPR2
C***PURPOSE Perform the symmetric rank 2 operation.
C***LIBRARY SLATEC (BLAS)
C***CATEGORY D1B4
C***TYPE DOUBLE PRECISION (SSPR2-S, DSPR2-D, CSPR2-C)
C***KEYWORDS LEVEL 2 BLAS, LINEAR ALGEBRA
C***AUTHOR Dongarra, J. J., (ANL)
C Du Croz, J., (NAG)
C Hammarling, S., (NAG)
C Hanson, R. J., (SNLA)
C***DESCRIPTION
C
C DSPR2 performs the symmetric rank 2 operation
C
C A := alpha*x*y' + alpha*y*x' + A,
C
C where alpha is a scalar, x and y are n element vectors and A is an
C n by n symmetric matrix, supplied in packed form.
C
C Parameters
C ==========
C
C UPLO - CHARACTER*1.
C On entry, UPLO specifies whether the upper or lower
C triangular part of the matrix A is supplied in the packed
C array AP as follows:
C
C UPLO = 'U' or 'u' The upper triangular part of A is
C supplied in AP.
C
C UPLO = 'L' or 'l' The lower triangular part of A is
C supplied in AP.
C
C Unchanged on exit.
C
C N - INTEGER.
C On entry, N specifies the order of the matrix A.
C N must be at least zero.
C Unchanged on exit.
C
C ALPHA - DOUBLE PRECISION.
C On entry, ALPHA specifies the scalar alpha.
C Unchanged on exit.
C
C X - DOUBLE PRECISION array of dimension at least
C ( 1 + ( n - 1)*abs( INCX)).
C Before entry, the incremented array X must contain the n
C element vector x.
C Unchanged on exit.
C
C INCX - INTEGER.
C On entry, INCX specifies the increment for the elements of
C X. INCX must not be zero.
C Unchanged on exit.
C
C Y - DOUBLE PRECISION array of dimension at least
C ( 1 + ( n - 1 )*abs( INCY ) ).
C Before entry, the incremented array Y must contain the n
C element vector y.
C Unchanged on exit.
C
C INCY - INTEGER.
C On entry, INCY specifies the increment for the elements of
C Y. INCY must not be zero.
C Unchanged on exit.
C
C AP - DOUBLE PRECISION array of DIMENSION at least
C ( ( n*( n + 1 ) )/2 ).
C Before entry with UPLO = 'U' or 'u', the array AP must
C contain the upper triangular part of the symmetric matrix
C packed sequentially, column by column, so that AP( 1 )
C contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
C and a( 2, 2 ) respectively, and so on. On exit, the array
C AP is overwritten by the upper triangular part of the
C updated matrix.
C Before entry with UPLO = 'L' or 'l', the array AP must
C contain the lower triangular part of the symmetric matrix
C packed sequentially, column by column, so that AP( 1 )
C contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
C and a( 3, 1 ) respectively, and so on. On exit, the array
C AP is overwritten by the lower triangular part of the
C updated matrix.
C
C***REFERENCES Dongarra, J. J., Du Croz, J., Hammarling, S., and
C Hanson, R. J. An extended set of Fortran basic linear
C algebra subprograms. ACM TOMS, Vol. 14, No. 1,
C pp. 1-17, March 1988.
C***ROUTINES CALLED LSAME, XERBLA
C***REVISION HISTORY (YYMMDD)
C 861022 DATE WRITTEN
C 910605 Modified to meet SLATEC prologue standards. Only comment
C lines were modified. (BKS)
C***END PROLOGUE DSPR2
C .. Scalar Arguments ..
DOUBLE PRECISION ALPHA
INTEGER INCX, INCY, N
CHARACTER*1 UPLO
C .. Array Arguments ..
DOUBLE PRECISION AP( * ), X( * ), Y( * )
C .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
C .. Local Scalars ..
DOUBLE PRECISION TEMP1, TEMP2
INTEGER I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY
C .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
C .. External Subroutines ..
EXTERNAL XERBLA
C***FIRST EXECUTABLE STATEMENT DSPR2
C
C Test the input parameters.
C
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
ELSE IF( INCY.EQ.0 )THEN
INFO = 7
END IF
IF( INFO.NE.0 )THEN
CALL XERBLA( 'DSPR2 ', INFO )
RETURN
END IF
C
C Quick return if possible.
C
IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) )
$ RETURN
C
C Set up the start points in X and Y if the increments are not both
C unity.
C
IF( ( INCX.NE.1 ).OR.( INCY.NE.1 ) )THEN
IF( INCX.GT.0 )THEN
KX = 1
ELSE
KX = 1 - ( N - 1 )*INCX
END IF
IF( INCY.GT.0 )THEN
KY = 1
ELSE
KY = 1 - ( N - 1 )*INCY
END IF
JX = KX
JY = KY
END IF
C
C Start the operations. In this version the elements of the array AP
C are accessed sequentially with one pass through AP.
C
KK = 1
IF( LSAME( UPLO, 'U' ) )THEN
C
C Form A when upper triangle is stored in AP.
C
IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
DO 20, J = 1, N
IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN
TEMP1 = ALPHA*Y( J )
TEMP2 = ALPHA*X( J )
K = KK
DO 10, I = 1, J
AP( K ) = AP( K ) + X( I )*TEMP1 + Y( I )*TEMP2
K = K + 1
10 CONTINUE
END IF
KK = KK + J
20 CONTINUE
ELSE
DO 40, J = 1, N
IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN
TEMP1 = ALPHA*Y( JY )
TEMP2 = ALPHA*X( JX )
IX = KX
IY = KY
DO 30, K = KK, KK + J - 1
AP( K ) = AP( K ) + X( IX )*TEMP1 + Y( IY )*TEMP2
IX = IX + INCX
IY = IY + INCY
30 CONTINUE
END IF
JX = JX + INCX
JY = JY + INCY
KK = KK + J
40 CONTINUE
END IF
ELSE
C
C Form A when lower triangle is stored in AP.
C
IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
DO 60, J = 1, N
IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN
TEMP1 = ALPHA*Y( J )
TEMP2 = ALPHA*X( J )
K = KK
DO 50, I = J, N
AP( K ) = AP( K ) + X( I )*TEMP1 + Y( I )*TEMP2
K = K + 1
50 CONTINUE
END IF
KK = KK + N - J + 1
60 CONTINUE
ELSE
DO 80, J = 1, N
IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN
TEMP1 = ALPHA*Y( JY )
TEMP2 = ALPHA*X( JX )
IX = JX
IY = JY
DO 70, K = KK, KK + N - J
AP( K ) = AP( K ) + X( IX )*TEMP1 + Y( IY )*TEMP2
IX = IX + INCX
IY = IY + INCY
70 CONTINUE
END IF
JX = JX + INCX
JY = JY + INCY
KK = KK + N - J + 1
80 CONTINUE
END IF
END IF
C
RETURN
C
C End of DSPR2 .
C
END