SUBROUTINE STBSV ( 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(inout) :: a, x * .. * * Purpose * ======= * * STBSV 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 band matrix, with ( k + 1 ) * diagonals. * * 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. * * 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 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. * * * .. Local Scalars .. REAL TEMP INTEGER I, INFO, IX, J, JX, KPLUS1, KX, L LOGICAL NOUNIT, UPPER * .. Local Arrays .. REAL, array(N) :: xloc * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX, MIN INTRINSIC cshift * .. * .. 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( 'STBSV ', 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 by sequentially with one pass through A. * KPLUS1 = K + 1 IF( LSAME(TRANS, 'N') )THEN * * Form x := inv( A )*x. * IF( UPPER )THEN IF( NOUNIT ) then DO J = N, 2, -1 xloc(J) = xloc(J) / A(KPLUS1,J) l = max( 1, J - K ) xloc(l:j-1)=xloc(l:j-1)-xloc(j)*A(kplus1-j+l:k,j) ENDDO xloc(1) = xloc(1) / A(KPLUS1,1) else DO J = N, 2, -1 l = max( 1, J - K ) xloc(l:j-1)=xloc(l:j-1)-xloc(j)*A(kplus1-j+l:k,j) ENDDO endif ELSE IF( NOUNIT ) then DO J = 1, N-1 xloc(J) = xloc(J) / A(1,J) l = min( N, J + K ) xloc(j+1:l)=xloc(j+1:l)-xloc(j)*A(2:min(n-j+1,kplus1),j) ENDDO xloc(n) = xloc(n) / A(1,n) else DO J = 1, N-1 l = min( N, J + K ) xloc(j+1:l)=xloc(j+1:l)-xloc(j)*A(2:min(n-j+1,kplus1),j) ENDDO endif END IF ELSE * * Form x := inv( A')*x. * IF( UPPER )THEN do i = 1, k cts a(i:i,:) = cshift(a(i:i,:),2,(k+1-i)) a(i:i,:) = cshift(a(i:i,:),(k+1-i),2) enddo c IF( NOUNIT ) then DO J = 1, N-1 xloc(J) = xloc(J) / A(KPLUS1,J) l = min( N, J + K ) xloc(j+1:l) = xloc(j+1:l) & - xloc(j)*A(k:max(1,kplus1+j-n):-1,j) ENDDO xloc(n) = xloc(n) / A(KPLUS1,n) else DO J = 1, N-1 l = min( N, J + K ) xloc(j+1:l) = xloc(j+1:l) & - xloc(j)*A(k:max(1,kplus1+j-n):-1,j) ENDDO endif c do i = 1, k cts a(i:i,:) = cshift(a(i:i,:),2,-(k+1-i)) a(i:i,:) = cshift(a(i:i,:),-(k+1-i),2) enddo ELSE do i = 2, k+1 cts a(i:i,:) = cshift(a(i:i,:),2,1-i) a(i:i,:) = cshift(a(i:i,:),1-i,2) enddo c IF( NOUNIT ) then DO J = N, 2, -1 xloc(J) = xloc(J) / A(1,J) l = max( 1, J - K ) xloc(l:j-1)=xloc(l:j-1)-xloc(j)*A(min(kplus1,j):2:-1,j) ENDDO xloc(1) = xloc(1) / A(1,1) else DO J = N, 2, -1 l = max( 1, J - K ) xloc(l:j-1)=xloc(l:j-1)-xloc(j)*A(min(kplus1,j):2:-1,j) ENDDO endif c do i = 2, k+1 cts a(i:i,:) = cshift(a(i:i,:),2,i-1) a(i:i,:) = cshift(a(i:i,:),i-1,2) enddo END IF 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 STBSV . * END