SUBROUTINE DTPMV ( UPLO, TRANS, DIAG, N, AP, 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, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. double precision, array(:) :: ap, x intent(inout) :: ap, x * .. * * Purpose * ======= * * DTPMV 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, supplied in packed form. * * 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. * * AP - DOUBLE PRECISION array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular 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 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 when DIAG = 'U' or 'u', the diagonal elements of * A are not referenced, but are assumed to be unity. * 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 ) c c later adjust ncutoff for most efficiency c integer ncutoff parameter ( ncutoff = 8 ) * .. Local Scalars .. double precision t INTEGER INFO, KX, na, i, j LOGICAL NOUNIT, UPPER * .. Local Arrays double precision, array(n, n) :: fulla double precision, array(n) :: xloc double precision, array(n*(n+1)/2) :: xs logical, array(n*(n+1)/2) :: segpvar * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA EXTERNAL dfillo EXTERNAL dpacku EXTERNAL DTRMV EXTERNAL degad * .. Intrinsic Functions .. INTRINSIC spread * .. * .. 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( INCX.EQ.0 )THEN INFO = 7 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DTPMV ', 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 (n .le. ncutoff) then call dfillo ( fulla, uplo, n, n*n, ap ) call dtrmv ( uplo, trans, diag, n, fulla, n, x, incx ) else c c n is > cutoff c na = n * (n+1) / 2 if( incx.eq.1 )then xloc(1:n) = x(1:n) else xloc(1:n) = x(kx : kx+incx*(n-1) : incx) endif c if (lsame(trans, 'N')) then if (upper) then i = 1 if (nounit) xloc(1) = ap(1) * xloc(1) i = i + 1 do j = 2, n if (nounit) then t = xloc(j) xloc(j) = zero xloc(1:j) = xloc(1:j) + ap(i:i+j) * t else xloc(1:j-1)=xloc(1:j-1)+ap(i:i+j-1)*xloc(j) endif i = i + j enddo else i = n * (n + 1) / 2 if (nounit) xloc(n) = ap(i) * xloc(n) i = i - 2 do j = n-1, 1, -1 if (nounit) then t = xloc(j) xloc(j) = zero xloc(j:n) = xloc(j:n) + ap(i:i+(n-j)) * t else xloc(j+1:n)=xloc(j+1:n)+ap(i+1:i+(n-j))*xloc(j) endif i = i - (n - j + 2) enddo endif else c c code for a' * x c if (upper) then if (nounit) then call dpacku(xs, uplo, n, na, spread(xloc,2,n)) xs = xs * ap segpvar(1:na) = .false. clater forall (j=1:n) segpvar(j * (j+1) / 2) = .true. do j = 1, n segpvar(j * (j+1) / 2) = .true. enddo clater xs = degaddscan(xs, na, segpvar, 'R' ) call degad ( xs, xs, na, segpvar, 'R' ) clater forall (j = 1:n) xloc(j) = xs( j * (j+1) / 2 ) do j = 1, n xloc(j) = xs( j * (j+1) / 2 ) enddo else call dpacku(xs, uplo, n, na, spread(xloc,2,n)) segpvar(1:na) = .false. clater forall (j=1:n) segpvar(j * (j+1) / 2) = .true. do j = 1, n segpvar(j * (j+1) / 2) = .true. enddo where (.not. segpvar) xs = xs * ap clater xs = degaddscan(xs, na, segpvar, 'R') call degad ( xs, xs, na, segpvar, 'R' ) clater forall (j = 1:n) xloc(j) = xs( j * (j+1) / 2 ) do j = 1, n xloc(j) = xs( j * (j+1) / 2 ) enddo endif else if (nounit) then call dpacku(xs, uplo, n, na, spread(xloc,2,n)) xs = xs * ap segpvar(1:na) = .false. clater forall (j=1:n) segpvar(j * (j+1) / 2) = .true. do j = 1, n segpvar((na+1) - j * (j+1) / 2) = .true. enddo clater xs = degaddscan(xs, na, segpvar, 'L') call degad ( xs, xs, na, segpvar, 'L' ) clater forall (j = 1:n) xloc(n+1-j) = xs( (na+1) - j * (j+1) / 2 ) do j = 1, n xloc(n+1-j) = xs( (na+1) - j * (j+1) / 2 ) enddo else call dpacku(xs, uplo, n, na, spread(xloc,2,n)) segpvar(1:na) = .false. clater forall (j=1:n) segpvar((na+1) - j * (j+1) / 2) = .true. do j = 1, n segpvar((na+1) - j * (j+1) / 2) = .true. enddo where (.not. segpvar ) xs = xs * ap clater xs = degaddscan(xs, na, segpvar, 'L') call degad ( xs, xs, na, segpvar, 'L' ) clater forall (j = 1:n) xloc(n+1-j) = xs( (na+1) - j * (j+1) / 2 ) do j = 1, n xloc(n+1-j) = xs( (na+1) - j * (j+1) / 2 ) enddo endif endif endif c if( incx.eq.1 )then x(1:n) = xloc else x(kx : kx+incx*(n-1) : incx) = xloc endif endif * RETURN * * End of DTPMV . * END