* ************************************************************************ * SUBROUTINE ECHPMV( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY ) * .. Scalar Arguments .. COMPLEX ALPHA, BETA INTEGER INCX, INCY, N CHARACTER*1 UPLO * .. Array Arguments .. COMPLEX*16 Y( * ) COMPLEX AP( * ), X( * ) * .. * * Purpose * ======= * * ECHPMV performs the matrix-vector operation * * y := alpha*A*x + beta*y, * * where alpha and beta are scalars, x and y are n element vectors and * A is an n by n hermitian matrix. Additional precision arithmetic is * used in the computation. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the matrix A is supplied in the packed * array AP as follows: * * UPLO = 'U' or 'u' The upper triangular part of A is * supplied in AP. * * UPLO = 'L' or 'l' The lower triangular part of A is * supplied in AP. * * 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 - COMPLEX . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * AP - COMPLEX array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular part of the hermitian matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) * and a( 2, 2 ) respectively, and so on. * Before entry with UPLO = 'L' or 'l', the array AP must * contain the lower triangular part of the hermitian matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) * and a( 3, 1 ) respectively, and so on. * Note that the imaginary parts of the diagonal elements need * not be set and are assumed to be zero. * Unchanged on exit. * * X - COMPLEX 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. * * BETA - COMPLEX . * On entry, BETA specifies the scalar beta. When BETA is * supplied as zero then Y need not be set on input. * Unchanged on exit. * * Y - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. On exit, Y is overwritten by the updated * vector y. At least double precision arithmetic is used in * the computation of y. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 20-July-1986. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX ONE PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCMPLX, CONJG, REAL * .. * .. 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 = 6 ELSE IF ( INCY.EQ.0 ) THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ECHPMV', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) \$ RETURN * * Start the operations. In this version the elements of the array AP * are accessed sequentially with one pass through AP. * * First form y := beta*y and set up the start points in X and Y if * the increments are not both unity. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN IF( BETA.NE.ONE )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 END IF ELSE 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 IF( BETA.NE.ONE )THEN 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 K = 1 IF( LSAME( UPLO, 'U' ) )THEN * * Form y when AP contains the upper triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N TEMP1 = DCMPLX( ALPHA )*X( J ) TEMP2 = ZERO DO 50, I = 1, J - 1 Y( I ) = Y( I ) + TEMP1*AP( K ) TEMP2 = TEMP2 + CONJG( AP( K ) )*DCMPLX( X( I ) ) K = K + 1 50 CONTINUE Y( J ) = Y( J ) + TEMP1*REAL( AP( K ) ) + ALPHA*TEMP2 K = K + 1 60 CONTINUE ELSE IX = KX - INCX DO 80, J = 1, N TEMP1 = DCMPLX( ALPHA )*X( IX + INCX ) TEMP2 = ZERO IX = KX IY = KY KK = K DO 70, K = KK, KK + J - 2 Y( IY ) = Y( IY ) + TEMP1*AP( K ) TEMP2 = TEMP2 + CONJG( AP( K ) )*DCMPLX( X( IX ) ) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y( IY ) = Y( IY ) + TEMP1*REAL( AP( K ) ) + ALPHA*TEMP2 K = K + 1 80 CONTINUE END IF ELSE * * Form y when AP contains the lower triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 100, J = 1, N TEMP1 = DCMPLX( ALPHA )*X( J ) TEMP2 = ZERO Y( J ) = Y( J ) + TEMP1*REAL( AP( K ) ) K = K + 1 DO 90, I = J + 1, N Y( I ) = Y( I ) + TEMP1*AP( K ) TEMP2 = TEMP2 + CONJG( AP( K ) )*DCMPLX( X( I ) ) K = K + 1 90 CONTINUE Y( J ) = Y( J ) + ALPHA*TEMP2 100 CONTINUE ELSE JX = KX JY = KY DO 120, J = 1, N TEMP1 = DCMPLX( ALPHA )*X( JX ) TEMP2 = ZERO Y( JY ) = Y( JY ) + TEMP1*REAL( AP( K ) ) IX = JX IY = JY KK = K + 1 DO 110, K = KK, KK + N - ( J + 1 ) IX = IX + INCX IY = IY + INCY Y( IY ) = Y( IY ) + TEMP1*AP( K ) TEMP2 = TEMP2 + CONJG( AP( K ) )*DCMPLX( X( IX ) ) 110 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 120 CONTINUE END IF END IF * RETURN * * End of ECHPMV. * END