SUBROUTINE DATRMV( UPLO, TRANS, DIAG, N, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY ) * * -- 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 DIAG, TRANS, UPLO INTEGER INCX, INCY, LDA, N DOUBLE PRECISION ALPHA, BETA * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * DATRMV performs one of the matrix-vector operations * * y := abs( alpha )*abs( A )*abs( x )+ abs( beta*y ), * * or * * y := abs( alpha )*abs( A' )*abs( x ) + abs( beta*y ), * * where alpha and beta are real scalars, y is a real vector, x is a * vector and A is an n by n unit or non-unit, upper or lower triangular * matrix. * * Arguments * ========= * * UPLO (input) CHARACTER*1 * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * TRANS (input) CHARACTER*1 * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n': * y := abs( alpha )*abs( A )*abs( x )+ abs( beta*y ) * * TRANS = 'T' or 't': * y := abs( alpha )*abs( A' )*abs( x ) + abs( beta*y ) * * TRANS = 'C' or 'c': * y := abs( alpha )*abs( A' )*abs( x ) + abs( beta*y ) * * DIAG (input) CHARACTER*1 * On entry, DIAG specifies whether or not A is unit triangular * as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit triangular. * * N (input) INTEGER * On entry, N specifies the order of the matrix A. N must be at * least zero. * * ALPHA (input) DOUBLE PRECISION * On entry, ALPHA specifies the real scalar alpha. * * A (input) DOUBLE PRECISION 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 matrix A and * the strictly lower triangular part of A is not referenced. * When UPLO = 'L' or 'l', the leading n by n part of the array * A must contain the lower triangular part of the matrix A and * the strictly upper trapezoidal part of A is not referenced. * Note that when DIAG = 'U' or 'u', the diagonal elements of A * are not referenced either, but are assumed to be unity. * * LDA (input) INTEGER * On entry, LDA specifies the leading dimension of the array A. * LDA must be at least max( 1, N ). * * X (input) DOUBLE PRECISION 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. * * BETA (input) DOUBLE PRECISION * On entry, BETA specifies the real scalar beta. When BETA is * supplied as zero then Y need not be set on input. * * Y (input/output) DOUBLE PRECISION array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). Before entry with BETA non- * zero, the incremented array Y must contain the vector y. On * exit, the incremented array Y is overwritten by the updated * vector y. * * INCY (input) INTEGER * On entry, INCY specifies the increment for the elements of Y. * INCY must not be zero. * * -- Written on April 1, 1998 by * Antoine Petitet, University of Tennessee, Knoxville 37996, USA. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY LOGICAL NOUNIT DOUBLE PRECISION ABSX, TALPHA, TEMP * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 7 ELSE IF( INCX.EQ.0 )THEN INFO = 9 ELSE IF( INCY.EQ.0 ) THEN INFO = 12 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DATRMV', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR. $ ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * NOUNIT = LSAME( DIAG , 'N' ) * * Set up the start points in X and Y. * 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 * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * * First form y := abs( beta*y ). * IF( INCY.EQ.1 ) THEN IF( BETA.EQ.ZERO ) THEN DO 10, I = 1, N Y( I ) = ZERO 10 CONTINUE ELSE IF( BETA.EQ.ONE ) THEN DO 20, I = 1, N Y( I ) = ABS( Y( I ) ) 20 CONTINUE ELSE DO 30, I = 1, N Y( I ) = ABS( BETA * Y( I ) ) 30 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO ) THEN DO 40, I = 1, N Y( IY ) = ZERO IY = IY + INCY 40 CONTINUE ELSE IF( BETA.EQ.ONE ) THEN DO 50, I = 1, N Y( IY ) = ABS( Y( IY ) ) IY = IY + INCY 50 CONTINUE ELSE DO 60, I = 1, N Y( IY ) = ABS( BETA * Y( IY ) ) IY = IY + INCY 60 CONTINUE END IF END IF * IF( ALPHA.EQ.ZERO ) $ RETURN * TALPHA = ABS( ALPHA ) * IF( LSAME( TRANS, 'N' ) )THEN * * Form y := abs( alpha ) * abs( A ) * abs( x ) + y. * IF( LSAME( UPLO, 'U' ) )THEN JX = KX IF( INCY.EQ.1 ) THEN DO 80, J = 1, N ABSX = ABS( X( JX ) ) IF( ABSX.NE.ZERO ) THEN TEMP = TALPHA * ABSX DO 70, I = 1, J - 1 Y( I ) = Y( I ) + TEMP * ABS( A( I, J ) ) 70 CONTINUE * IF( NOUNIT ) THEN Y( J ) = Y( J ) + TEMP * ABS( A( J, J ) ) ELSE Y( J ) = Y( J ) + TEMP END IF END IF JX = JX + INCX 80 CONTINUE * ELSE * DO 100, J = 1, N ABSX = ABS( X( JX ) ) IF( ABSX.NE.ZERO ) THEN TEMP = TALPHA * ABSX IY = KY DO 90, I = 1, J - 1 Y( IY ) = Y( IY ) + TEMP * ABS( A( I, J ) ) IY = IY + INCY 90 CONTINUE * IF( NOUNIT ) THEN Y( IY ) = Y( IY ) + TEMP * ABS( A( J, J ) ) ELSE Y( IY ) = Y( IY ) + TEMP END IF END IF JX = JX + INCX 100 CONTINUE * END IF * ELSE * JX = KX IF( INCY.EQ.1 ) THEN DO 120, J = 1, N ABSX = ABS( X( JX ) ) IF( ABSX.NE.ZERO ) THEN * TEMP = TALPHA * ABSX * IF( NOUNIT ) THEN Y( J ) = Y( J ) + TEMP * ABS( A( J, J ) ) ELSE Y( J ) = Y( J ) + TEMP END IF * DO 110, I = J + 1, N Y( I ) = Y( I ) + TEMP * ABS( A( I, J ) ) 110 CONTINUE END IF JX = JX + INCX 120 CONTINUE * ELSE * DO 140, J = 1, N ABSX = ABS( X( JX ) ) IF( ABSX.NE.ZERO ) THEN TEMP = TALPHA * ABSX IY = KY + ( J - 1 ) * INCY * IF( NOUNIT ) THEN Y( IY ) = Y( IY ) + TEMP * ABS( A( J, J ) ) ELSE Y( IY ) = Y( IY ) + TEMP END IF * DO 130, I = J + 1, N IY = IY + INCY Y( IY ) = Y( IY ) + TEMP * ABS( A( I, J ) ) 130 CONTINUE END IF JX = JX + INCX 140 CONTINUE * END IF * END IF * ELSE * * Form y := abs( alpha ) * abs( A' ) * abs( x ) + y. * IF( LSAME( UPLO, 'U' ) )THEN JY = KY IF( INCX.EQ.1 ) THEN DO 160, J = 1, N * TEMP = ZERO * DO 150, I = 1, J - 1 TEMP = TEMP + ABS( A( I, J ) * X( I ) ) 150 CONTINUE * IF( NOUNIT ) THEN TEMP = TEMP + ABS( A( J, J ) * X( J ) ) ELSE TEMP = TEMP + ABS( X( J ) ) END IF * Y( JY ) = Y( JY ) + TALPHA * TEMP JY = JY + INCY * 160 CONTINUE * ELSE * DO 180, J = 1, N TEMP = ZERO IX = KX DO 170, I = 1, J - 1 TEMP = TEMP + ABS( A( I, J ) * X( IX ) ) IX = IX + INCX 170 CONTINUE * IF( NOUNIT ) THEN TEMP = TEMP + ABS( A( J, J ) * X( IX ) ) ELSE TEMP = TEMP + ABS( X( IX ) ) END IF * Y( JY ) = Y( JY ) + TALPHA * TEMP JY = JY + INCY * 180 CONTINUE * END IF * ELSE * JY = KY IF( INCX.EQ.1 ) THEN * DO 200, J = 1, N * IF( NOUNIT ) THEN TEMP = ABS( A( J, J ) * X( J ) ) ELSE TEMP = ABS( X( J ) ) END IF * DO 190, I = J + 1, N TEMP = TEMP + ABS( A( I, J ) * X( I ) ) 190 CONTINUE * Y( JY ) = Y( JY ) + TALPHA * TEMP JY = JY + INCY * 200 CONTINUE * ELSE * DO 220, J = 1, N * IX = KX + ( J - 1 ) * INCX * IF( NOUNIT ) THEN TEMP = ABS( A( J, J ) * X( IX ) ) ELSE TEMP = ABS( X( IX ) ) END IF * DO 210, I = J + 1, N IX = IX + INCX TEMP = TEMP + ABS( A( I, J ) * X( IX ) ) 210 CONTINUE Y( JY ) = Y( JY ) + TALPHA * TEMP JY = JY + INCY 220 CONTINUE END IF END IF * END IF * RETURN * * End of DATRMV * END