SUBROUTINE DTRSV ( 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 * ======= * * DTRSV solves one of the systems of equations * * A*x = b, or A'*x = b, * * where b and x are n element vectors and A is an n by n unit, or * non-unit, upper or lower triangular matrix. * * No test for singularity or near-singularity is included in this * routine. Such tests must be performed before calling this routine. * * 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 equations to be solved as * follows: * * TRANS = 'N' or 'n' A*x = b. * * TRANS = 'T' or 't' A'*x = b. * * TRANS = 'C' or 'c' A'*x = b. * * 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 right-hand side vector b. On exit, X is overwritten * with the solution 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 * .. Local Scalars .. INTEGER INFO, J, KX LOGICAL NOUNIT, UPPER * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. 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( 'DTRSV ', 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 * if( incx .eq. 1 )then xloc(1:n) = x(1:n) else xloc(1:n) = x(kx : kx+incx*(n-1) : incx) end if * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * if( lsame( trans, 'N' ) )then * * Form x := inv( A )*x. * if( upper )then do j = n, 2, -1 if ( nounit ) xloc( j ) = xloc( j )/a( j, j ) xloc(1:j-1) = xloc(1:j-1) - xloc(j)*a(1:j-1,j) enddo if ( nounit ) xloc( 1 ) = xloc( 1 )/a( 1, 1 ) else do j = 1, n-1 if ( nounit ) xloc( j ) = xloc( j )/a( j, j ) xloc(j+1:n) = xloc(j+1:n) - xloc(j)*a(j+1:n,j) enddo if ( nounit ) xloc( n ) = xloc( n )/a( n, n ) end if else * * Form x := inv( A' )*x. * if( upper )then do j = 1, n-1 if ( nounit ) xloc( j ) = xloc( j )/a( j, j ) xloc(j+1:n) = xloc(j+1:n) - xloc(j)*a(j,j+1:n) enddo if ( nounit ) xloc( n ) = xloc( n )/a( n, n ) else do j = n, 2, -1 if ( nounit ) xloc( j ) = xloc( j )/a( j, j ) xloc(1:j-1) = xloc(1:j-1) - xloc(j)*a(j,1:j-1) enddo if ( nounit ) xloc( 1 ) = xloc( 1 )/a( 1, 1 ) end if end if * if( incx .eq. 1 )then x(1:n) = xloc(1:n) else x(kx : kx+incx*(n-1) : incx) = xloc(1:n) end if * RETURN * * End of DTRSV . * END