*DECK CHEMV SUBROUTINE CHEMV (UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) C***BEGIN PROLOGUE CHEMV C***PURPOSE Multiply a complex vector by a complex Hermitian matrix. C***LIBRARY SLATEC (BLAS) C***CATEGORY D1B4 C***TYPE COMPLEX (SHEMV-S, DHEMV-D, CHEMV-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 CHEMV performs the matrix-vector operation C C y := alpha*A*x + beta*y, C C where alpha and beta are scalars, x and y are n element vectors and C A is an n 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 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. 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. C Note that the imaginary parts of the diagonal elements need C not be set and are assumed to be zero. C Unchanged on exit. 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 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 BETA - COMPLEX . C On entry, BETA specifies the scalar beta. When BETA is C supplied as zero then Y need not be set on input. 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. On exit, Y is overwritten by the updated C vector y. 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***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 CHEMV C .. Scalar Arguments .. COMPLEX ALPHA, BETA INTEGER INCX, INCY, LDA, N CHARACTER*1 UPLO C .. Array Arguments .. COMPLEX A( LDA, * ), X( * ), Y( * ) C .. Parameters .. COMPLEX ONE PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) 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 CHEMV 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( LDA.LT.MAX( 1, N ) )THEN INFO = 5 ELSE IF( INCX.EQ.0 )THEN INFO = 7 ELSE IF( INCY.EQ.0 )THEN INFO = 10 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CHEMV ', INFO ) RETURN END IF C C Quick return if possible. C IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN C C Set up the start points in X and Y. C 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 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 C First form y := beta*y. C IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, N Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, N Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, N Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, N Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN IF( LSAME( UPLO, 'U' ) )THEN C C Form y when A is stored in upper triangle. C IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO DO 50, I = 1, J - 1 Y( I ) = Y( I ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + CONJG( A( I, J ) )*X( I ) 50 CONTINUE Y( J ) = Y( J ) + TEMP1*REAL( A( J, J ) ) + ALPHA*TEMP2 60 CONTINUE ELSE JX = KX JY = KY DO 80, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO IX = KX IY = KY DO 70, I = 1, J - 1 Y( IY ) = Y( IY ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + CONJG( A( I, J ) )*X( IX ) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y( JY ) = Y( JY ) + TEMP1*REAL( A( J, J ) ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 80 CONTINUE END IF ELSE C C Form y when A is stored in lower triangle. C IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 100, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO Y( J ) = Y( J ) + TEMP1*REAL( A( J, J ) ) DO 90, I = J + 1, N Y( I ) = Y( I ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + CONJG( A( I, J ) )*X( I ) 90 CONTINUE Y( J ) = Y( J ) + ALPHA*TEMP2 100 CONTINUE ELSE JX = KX JY = KY DO 120, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO Y( JY ) = Y( JY ) + TEMP1*REAL( A( J, J ) ) IX = JX IY = JY DO 110, I = J + 1, N IX = IX + INCX IY = IY + INCY Y( IY ) = Y( IY ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + CONJG( A( I, J ) )*X( IX ) 110 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 120 CONTINUE END IF END IF C RETURN C C End of CHEMV . C END