SUBROUTINE DTRMV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX ) **************************************************************************** * * * DATA PARALLEL BLAS based on MPL * * * * Version 1.0 1/9-92 , * * For MasPar MP-1 computers * * * * para//ab, University of Bergen, NORWAY * * * * These programs must be called using F90 style array syntax. * * Note that the F77 style calling sequence has been retained * * in this version for compatibility reasons, be aware that * * parameters related to the array dimensions and shape therefore may * * be redundant and without any influence. * * The calling sequence may be changed in a future version. * * Please report any BUGs, ideas for improvement or other * * comments to * * adm@parallab.uib.no * * * * Future versions may then reflect your suggestions. * * The most current version of this software is available * * from netlib@nac.no , send the message `send index from maspar' * * * * REVISIONS: * * * **************************************************************************** implicit none * .. Scalar Arguments .. INTEGER INCX, LDA, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. double precision, array(:,:) :: a double precision, array(:) :: x intent(in) :: a intent(inout) :: x * .. * * Purpose * ======= * * DTRMV performs one of the matrix-vector operations * * x := A*x, or x := A'*x, * * where x is an n element vector and A is an n by n unit, or non-unit, * upper or lower triangular matrix. * * Parameters * ========== * * UPLO - 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. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' x := A*x. * * TRANS = 'T' or 't' x := A'*x. * * TRANS = 'C' or 'c' x := A'*x. * * Unchanged on exit. * * DIAG - 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. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * A - double precision array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array A must contain the upper * triangular matrix and the strictly lower triangular part of * A is not referenced. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array A must contain the lower * triangular matrix and the strictly upper triangular 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. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, n ). * Unchanged on exit. * * X - double precision array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. On exit, X is overwritten with the * tranformed vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. double precision ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. Local Arrays .. double precision, array(n) :: xloc double precision, array(n,n) :: xb integer, array(n,n) :: irow, icol * .. Local Scalars .. INTEGER INFO, KX, i, j LOGICAL NOUNIT, UPPER * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX INTRINSIC spread INTRINSIC sum * .. * .. Executable Statements .. * * Test the input parameters. * NOUNIT = LSAME( DIAG, 'N' ) UPPER = LSAME( UPLO, 'U' ) * INFO = 0 IF ( .NOT.UPPER .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 = 6 ELSE IF( INCX.EQ.0 )THEN INFO = 8 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DTRMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) RETURN * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * xb = zero if( incx.eq.1 )then xloc(1:n) = x(1:n) else xloc(1:n) = x(kx : kx+incx*(n-1) : incx) end if * forall ( i=1:n,j=1:n ) icol(i,j) = j forall ( i=1:n ) irow(i,:) = i cts do i = 1 , n cts icol(:,i) = i cts irow(i,:) = i cts enddo * IF( LSAME( TRANS, 'N' ) )THEN * * Form x := A*x. * if (nounit) then IF( UPPER )THEN where (irow .le. icol) xb = a * spread(xloc,1,n) ELSE where (irow .ge. icol) xb = a * spread(xloc,1,n) END IF xloc = sum( xb, 2 ) else IF( UPPER )THEN where (irow .lt. icol) xb = a * spread(xloc,1,n) ELSE where (irow .gt. icol) xb = a * spread(xloc,1,n) END IF xloc = xloc + sum( xb, 2 ) endif ELSE * * Form x := A'*x. * if (nounit) then IF( UPPER )THEN where (irow .le. icol) xb = a * spread(xloc,2,n) ELSE where (irow .ge. icol) xb = a * spread(xloc,2,n) END IF xloc = sum( xb, 1 ) else IF( UPPER )THEN where (irow .lt. icol) xb = a * spread(xloc,2,n) ELSE where (irow .gt. icol) xb = a * spread(xloc,2,n) END IF xloc = xloc + sum( xb, 1 ) endif END IF * if( incx.eq.1 )then x(1:n) = xloc else x(kx : kx+incx*(n-1) : incx) = xloc end if * RETURN * * End of DTRMV . * END