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SUBROUTINE ZSYR2( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA )
*
* -- PBLAS auxiliary routine (version 2.0) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* April 1, 1998
*
* .. Scalar Arguments ..
CHARACTER*1 UPLO
INTEGER INCX, INCY, LDA, N
COMPLEX*16 ALPHA
* ..
* .. Array Arguments ..
COMPLEX*16 A( LDA, * ), X( * ), Y( * )
* ..
*
* Purpose
* =======
*
* ZSYR2 performs the symmetric rank 2 operation
*
* A := alpha*x*y' + alpha*y*x' + A,
*
* where alpha is a complex scalar, x and y are n element vectors and A
* is an n by n SY matrix.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* On entry, UPLO specifies which part of the matrix A is to be
* referenced as follows:
*
* UPLO = 'L' or 'l' the lower trapezoid of A is referenced,
*
* UPLO = 'U' or 'u' the upper trapezoid of A is referenced,
*
* otherwise all of the matrix A is referenced.
*
* N (input) INTEGER
* On entry, N specifies the order of the matrix A. N must be at
* least zero.
*
* ALPHA (input) COMPLEX*16
* On entry, ALPHA specifies the scalar alpha.
*
* X (input) COMPLEX*16 array of dimension at least
* ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented
* array X must contain the vector x.
*
* INCX (input) INTEGER
* On entry, INCX specifies the increment for the elements of X.
* INCX must not be zero.
*
* Y (input) COMPLEX*16 array of dimension at least
* ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented
* array Y must contain the vector y.
*
* INCY (input) INTEGER
* On entry, INCY specifies the increment for the elements of Y.
* INCY must not be zero.
*
* A (input/output) COMPLEX*16 array
* On entry, A is an array of dimension (LDA,N). Before entry
* with UPLO = 'U' or 'u', the leading n by n part of the array
* A must contain the upper triangular part of the symmetric ma-
* trix and the strictly lower triangular part of A is not refe-
* renced. On exit, the upper triangular part of the array A is
* overwritten by the upper triangular part of the updated ma-
* trix. When UPLO = 'L' or 'l', the leading n by n part of the
* the array A must contain the lower triangular part of the
* symmetric matrix and the strictly upper trapezoidal 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 (input) INTEGER
* On entry, LDA specifies the leading dimension of the array A.
* LDA must be at least max( 1, N ).
*
* -- Written on April 1, 1998 by
* Antoine Petitet, University of Tennessee, Knoxville 37996, USA.
*
* =====================================================================
*
* .. Parameters ..
COMPLEX*16 ZERO
PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY
COMPLEX*16 TEMP1, TEMP2
* ..
* .. 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( 'ZSYR2', 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 ZSYR2
*
END
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