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. * KX = 1 KY = 1 JX = 1 JY = 1 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