*DECK CHER2 SUBROUTINE CHER2 (UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA) C***BEGIN PROLOGUE CHER2 C***PURPOSE Perform Hermitian rank 2 update of a complex Hermitian C matrix. C***LIBRARY SLATEC (BLAS) C***CATEGORY D1B4 C***TYPE COMPLEX (SHER2-S, DHER2-D, CHER2-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 CHER2 performs the hermitian rank 2 operation C C A := alpha*x*conjg( y') + conjg( alpha)*y*conjg( x') + A, C C where alpha is a scalar, x and y are n element vectors and A is an n C by n hermitian matrix. C C Parameters C ========== C C UPLO - CHARACTER*1. C On entry, UPLO specifies whether the upper or lower C triangular part of the array A is to be referenced as C follows: C C UPLO = 'U' or 'u' Only the upper triangular part of A C is to be referenced. C C UPLO = 'L' or 'l' Only the lower triangular part of A C is to be referenced. 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 - COMPLEX . C On entry, ALPHA specifies the scalar alpha. C Unchanged on exit. C C X - COMPLEX 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 - COMPLEX 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 A - COMPLEX array of DIMENSION ( LDA, n ). C Before entry with UPLO = 'U' or 'u', the leading n by n C upper triangular part of the array A must contain the upper C triangular part of the hermitian matrix and the strictly C lower triangular part of A is not referenced. On exit, the C upper triangular part of the array A is overwritten by the C upper triangular part of the updated matrix. C Before entry with UPLO = 'L' or 'l', the leading n by n C lower triangular part of the array A must contain the lower C triangular part of the hermitian matrix and the strictly C upper triangular part of A is not referenced. On exit, the C lower triangular part of the array A is overwritten by the C lower triangular part of the updated matrix. C Note that the imaginary parts of the diagonal elements need C not be set, they are assumed to be zero, and on exit they C are set to zero. C C LDA - INTEGER. C On entry, LDA specifies the first dimension of A as declared C in the calling (sub) program. LDA must be at least C max( 1, n ). C Unchanged on exit. 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 CHER2 C .. Scalar Arguments .. COMPLEX ALPHA INTEGER INCX, INCY, LDA, N CHARACTER*1 UPLO C .. Array Arguments .. COMPLEX A( LDA, * ), X( * ), Y( * ) C .. Parameters .. COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) C .. Local Scalars .. COMPLEX TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY C .. External Functions .. LOGICAL LSAME EXTERNAL LSAME C .. External Subroutines .. EXTERNAL XERBLA C .. Intrinsic Functions .. INTRINSIC CONJG, MAX, REAL C***FIRST EXECUTABLE STATEMENT CHER2 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 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CHER2 ', 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 A are C accessed sequentially with one pass through the triangular part C of A. C IF( LSAME( UPLO, 'U' ) )THEN C C Form A when A is stored in the upper triangle. 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*CONJG( Y( J ) ) TEMP2 = CONJG( ALPHA*X( J ) ) DO 10, I = 1, J - 1 A( I, J ) = A( I, J ) + X( I )*TEMP1 + Y( I )*TEMP2 10 CONTINUE A( J, J ) = REAL( A( J, J ) ) + $ REAL( X( J )*TEMP1 + Y( J )*TEMP2 ) ELSE A( J, J ) = REAL( A( J, J ) ) END IF 20 CONTINUE ELSE DO 40, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*CONJG( Y( JY ) ) TEMP2 = CONJG( ALPHA*X( JX ) ) IX = KX IY = KY DO 30, I = 1, J - 1 A( I, J ) = A( I, J ) + X( IX )*TEMP1 $ + Y( IY )*TEMP2 IX = IX + INCX IY = IY + INCY 30 CONTINUE A( J, J ) = REAL( A( J, J ) ) + $ REAL( X( JX )*TEMP1 + Y( JY )*TEMP2 ) ELSE A( J, J ) = REAL( A( J, J ) ) END IF JX = JX + INCX JY = JY + INCY 40 CONTINUE END IF ELSE C C Form A when A is stored in the lower triangle. 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*CONJG( Y( J ) ) TEMP2 = CONJG( ALPHA*X( J ) ) A( J, J ) = REAL( A( J, J ) ) + $ REAL( X( J )*TEMP1 + Y( J )*TEMP2 ) DO 50, I = J + 1, N A( I, J ) = A( I, J ) + X( I )*TEMP1 + Y( I )*TEMP2 50 CONTINUE ELSE A( J, J ) = REAL( A( J, J ) ) END IF 60 CONTINUE ELSE DO 80, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*CONJG( Y( JY ) ) TEMP2 = CONJG( ALPHA*X( JX ) ) A( J, J ) = REAL( A( J, J ) ) + $ REAL( X( JX )*TEMP1 + Y( JY )*TEMP2 ) IX = JX IY = JY DO 70, I = J + 1, N IX = IX + INCX IY = IY + INCY A( I, J ) = A( I, J ) + X( IX )*TEMP1 $ + Y( IY )*TEMP2 70 CONTINUE ELSE A( J, J ) = REAL( A( J, J ) ) END IF JX = JX + INCX JY = JY + INCY 80 CONTINUE END IF END IF C RETURN C C End of CHER2 . C END