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SUBROUTINE DSYR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA )
* .. Scalar Arguments ..
DOUBLE PRECISION ALPHA
INTEGER INCX, INCY, LDA, N
CHARACTER*1 UPLO
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), X( * ), Y( * )
* ..
*
* Purpose
* =======
*
* DSYR2 performs the symmetric rank 2 operation
*
* A := alpha*x*y' + alpha*y*x' + A,
*
* where alpha is a scalar, x and y are n element vectors and A is an n
* by n symmetric matrix.
*
* Parameters
* ==========
*
* UPLO - CHARACTER*1.
* On entry, UPLO specifies whether the upper or lower
* triangular part of the array A is to be referenced as
* follows:
*
* UPLO = 'U' or 'u' Only the upper triangular part of A
* is to be referenced.
*
* UPLO = 'L' or 'l' Only the lower triangular part of A
* is to be referenced.
*
* 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 - DOUBLE PRECISION.
* 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.
*
* Y - DOUBLE PRECISION array of dimension at least
* ( 1 + ( n - 1 )*abs( INCY ) ).
* Before entry, the incremented array Y must contain the n
* element vector y.
* Unchanged on exit.
*
* INCY - INTEGER.
* On entry, INCY specifies the increment for the elements of
* Y. INCY must not be zero.
* Unchanged on exit.
*
* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
* Before entry with UPLO = 'U' or 'u', the leading n by n
* upper triangular part of the array A must contain the upper
* triangular part of the symmetric matrix and the strictly
* lower triangular part of A is not referenced. On exit, the
* upper triangular part of the array A is overwritten by the
* upper triangular part of the updated matrix.
* Before entry with UPLO = 'L' or 'l', the leading n by n
* lower triangular part of the array A must contain the lower
* triangular part of the symmetric matrix and the strictly
* upper triangular part of A is not referenced. On exit, the
* lower triangular part of the array A is overwritten by the
* lower triangular part of the updated matrix.
*
* LDA - INTEGER.
* On entry, LDA specifies the first dimension of A as declared
* in the calling (sub) program. LDA must be at least
* max( 1, n ).
* Unchanged on exit.
*
*
* Level 2 Blas routine.
*
* -- Written on 22-October-1986.
* Jack Dongarra, Argonne National Lab.
* Jeremy Du Croz, Nag Central Office.
* Sven Hammarling, Nag Central Office.
* Richard Hanson, Sandia National Labs.
*
*
* .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
* .. Local Scalars ..
DOUBLE PRECISION TEMP1, TEMP2
INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* .. External Subroutines ..
EXTERNAL XERBLA
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. 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
ELSE IF( INCY.EQ.0 )THEN
INFO = 7
ELSE IF( LDA.LT.MAX( 1, N ) )THEN
INFO = 9
END IF
IF( INFO.NE.0 )THEN
CALL XERBLA( 'DSYR2 ', INFO )
RETURN
END IF
*
* Quick return if possible.
*
IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) )
$ RETURN
*
* Set up the start points in X and Y if the increments are not both
* unity.
*
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
*
* Start the operations. In this version the elements of A are
* accessed sequentially with one pass through the triangular part
* of A.
*
IF( LSAME( UPLO, 'U' ) )THEN
*
* Form A when A is stored in the upper triangle.
*
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 )
DO 10, I = 1, J
A( I, J ) = A( I, J ) + X( I )*TEMP1 + Y( I )*TEMP2
10 CONTINUE
END IF
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, I = 1, J
A( I, J ) = A( I, J ) + X( IX )*TEMP1
$ + Y( IY )*TEMP2
IX = IX + INCX
IY = IY + INCY
30 CONTINUE
END IF
JX = JX + INCX
JY = JY + INCY
40 CONTINUE
END IF
ELSE
*
* Form A when A is stored in the lower triangle.
*
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 )
DO 50, I = J, N
A( I, J ) = A( I, J ) + X( I )*TEMP1 + Y( I )*TEMP2
50 CONTINUE
END IF
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, I = J, N
A( I, J ) = A( I, J ) + X( IX )*TEMP1
$ + Y( IY )*TEMP2
IX = IX + INCX
IY = IY + INCY
70 CONTINUE
END IF
JX = JX + INCX
JY = JY + INCY
80 CONTINUE
END IF
END IF
*
RETURN
*
* End of DSYR2 .
*
END
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