SUBROUTINE STBMV ( UPLO, TRANS, DIAG, N, K, 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, K, LDA, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. REAL, array(:,:) :: a REAL, array(:) :: x intent(in) :: a intent(inout) :: x * .. * * Purpose * ======= * * STBMV 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 band matrix, with ( k + 1 ) diagonals. * * 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. * * K - INTEGER. * On entry with UPLO = 'U' or 'u', K specifies the number of * super-diagonals of the matrix A. * On entry with UPLO = 'L' or 'l', K specifies the number of * sub-diagonals of the matrix A. * K must satisfy 0 .le. K. * Unchanged on exit. * * A - REAL array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) * by n part of the array A must contain the upper triangular * band part of the matrix of coefficients, supplied column by * column, with the leading diagonal of the matrix in row * ( k + 1 ) of the array, the first super-diagonal starting at * position 2 in row k, and so on. The top left k by k triangle * of the array A is not referenced. * The following program segment will transfer an upper * triangular band matrix from conventional full matrix storage * to band storage: * * DO 20, J = 1, N * M = K + 1 - J * DO 10, I = MAX( 1, J - K ), J * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) * by n part of the array A must contain the lower triangular * band part of the matrix of coefficients, supplied column by * column, with the leading diagonal of the matrix in row 1 of * the array, the first sub-diagonal starting at position 1 in * row 2, and so on. The bottom right k by k triangle of the * array A is not referenced. * The following program segment will transfer a lower * triangular band matrix from conventional full matrix storage * to band storage: * * DO 20, J = 1, N * M = 1 - J * DO 10, I = J, MIN( N, J + K ) * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Note that when DIAG = 'U' or 'u' the elements of the array A * corresponding to the diagonal elements of the matrix are not * referenced, 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 * ( k + 1 ). * Unchanged on exit. * * X - REAL 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 .. * .. Local Arrays .. REAL, array(n) :: xloc, y * .. Local Scalars .. INTEGER i, INFO, KX LOGICAL NOUNIT, UPPER * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. * .. 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( K.LT.0 )THEN INFO = 5 ELSE IF( LDA.LT.( K + 1 ) )THEN INFO = 7 ELSE IF( INCX.EQ.0 )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'STBMV ', 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) endif * * 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 := A*x. * IF( UPPER )THEN if (nounit) then y = a(k+1,1:n) * xloc else y = xloc endif do i = k, 1, -1 y(1:n-k-1+i) = y(1:n-k-1+i) + a(i,k+2-i:n)*xloc(k+2-i:n) enddo ELSE if (nounit) then y = a(1,1:n) * xloc else y = xloc endif do i = 2, k+1 y(i:n) = y(i:n) + a(i,1:n+1-i)*xloc(1:n+1-i) enddo END IF ELSE * * Form x := A'*x. * IF( UPPER )THEN if (nounit) then y = a(k+1,1:n) * xloc else y = xloc endif do i = k, 1, -1 y(k+2-i:n) = y(k+2-i:n) + a(i,k+2-i:n)*xloc(1:n-(k+1)+i) enddo ELSE if (nounit) then y = a(1,1:n) * xloc else y = xloc endif do i = 2, k+1 y(1:n+1-i) = y(1:n+1-i) + a(i,1:n+1-i)*xloc(i:n) enddo END IF END IF * if( incx.eq.1 )then x(1:n) = y else x(kx : kx+incx*(n-1) : incx) = y end if * RETURN * * End of STBMV . * END