dtbsv.f

Go to the documentation of this file.

      SUBROUTINE dtbsv ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX )
*     .. Scalar Arguments ..
      INTEGER            INCX, K, LDA, N
      CHARACTER*1        DIAG, TRANS, UPLO
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), X( * )
*     ..
*
*  Purpose
*  =======
*
*  DTBSV  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      - DOUBLE PRECISION 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      - 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 Scalars ..
      DOUBLE PRECISION   TEMP
      INTEGER            I, INFO, IX, J, JX, KPLUS1, KX, L
      LOGICAL            NOUNIT
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     .. External Subroutines ..
      EXTERNAL           xerbla
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      IF     ( .NOT.lsame( uplo , 'U' ).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( 'DTBSV ', info )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( n.EQ.0 )
     $   RETURN
*
      nounit = lsame( diag, 'N' )
*
*     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 by sequentially with one pass through A.
*
      IF( lsame( trans, 'N' ) )THEN
*
*        Form  x := inv( A )*x.
*
         IF( lsame( uplo, 'U' ) )THEN
            kplus1 = k + 1
            IF( incx.EQ.1 )THEN
               DO 20, j = n, 1, -1
                  IF( x( j ).NE.zero )THEN
                     l = kplus1 - j
                     IF( nounit )
     $                  x( j ) = x( j )/a( kplus1, j )
                     temp = x( j )
                     DO 10, i = j - 1, max( 1, j - k ), -1
                        x( i ) = x( i ) - temp*a( l + i, j )
   10                CONTINUE
                  END IF
   20          CONTINUE
            ELSE
               kx = kx + ( n - 1 )*incx
               jx = kx
               DO 40, j = n, 1, -1
                  kx = kx - incx
                  IF( x( jx ).NE.zero )THEN
                     ix = kx
                     l  = kplus1 - j
                     IF( nounit )
     $                  x( jx ) = x( jx )/a( kplus1, j )
                     temp = x( jx )
                     DO 30, i = j - 1, max( 1, j - k ), -1
                        x( ix ) = x( ix ) - temp*a( l + i, j )
                        ix      = ix      - incx
   30                CONTINUE
                  END IF
                  jx = jx - incx
   40          CONTINUE
            END IF
         ELSE
            IF( incx.EQ.1 )THEN
               DO 60, j = 1, n
                  IF( x( j ).NE.zero )THEN
                     l = 1 - j
                     IF( nounit )
     $                  x( j ) = x( j )/a( 1, j )
                     temp = x( j )
                     DO 50, i = j + 1, min( n, j + k )
                        x( i ) = x( i ) - temp*a( l + i, j )
   50                CONTINUE
                  END IF
   60          CONTINUE
            ELSE
               jx = kx
               DO 80, j = 1, n
                  kx = kx + incx
                  IF( x( jx ).NE.zero )THEN
                     ix = kx
                     l  = 1  - j
                     IF( nounit )
     $                  x( jx ) = x( jx )/a( 1, j )
                     temp = x( jx )
                     DO 70, i = j + 1, min( n, j + k )
                        x( ix ) = x( ix ) - temp*a( l + i, j )
                        ix      = ix      + incx
   70                CONTINUE
                  END IF
                  jx = jx + incx
   80          CONTINUE
            END IF
         END IF
      ELSE
*
*        Form  x := inv( A')*x.
*
         IF( lsame( uplo, 'U' ) )THEN
            kplus1 = k + 1
            IF( incx.EQ.1 )THEN
               DO 100, j = 1, n
                  temp = x( j )
                  l    = kplus1 - j
                  DO 90, i = max( 1, j - k ), j - 1
                     temp = temp - a( l + i, j )*x( i )
   90             CONTINUE
                  IF( nounit )
     $               temp = temp/a( kplus1, j )
                  x( j ) = temp
  100          CONTINUE
            ELSE
               jx = kx
               DO 120, j = 1, n
                  temp = x( jx )
                  ix   = kx
                  l    = kplus1  - j
                  DO 110, i = max( 1, j - k ), j - 1
                     temp = temp - a( l + i, j )*x( ix )
                     ix   = ix   + incx
  110             CONTINUE
                  IF( nounit )
     $               temp = temp/a( kplus1, j )
                  x( jx ) = temp
                  jx      = jx   + incx
                  IF( j.GT.k )
     $               kx = kx + incx
  120          CONTINUE
            END IF
         ELSE
            IF( incx.EQ.1 )THEN
               DO 140, j = n, 1, -1
                  temp = x( j )
                  l    = 1      - j
                  DO 130, i = min( n, j + k ), j + 1, -1
                     temp = temp - a( l + i, j )*x( i )
  130             CONTINUE
                  IF( nounit )
     $               temp = temp/a( 1, j )
                  x( j ) = temp
  140          CONTINUE
            ELSE
               kx = kx + ( n - 1 )*incx
               jx = kx
               DO 160, j = n, 1, -1
                  temp = x( jx )
                  ix   = kx
                  l    = 1       - j
                  DO 150, i = min( n, j + k ), j + 1, -1
                     temp = temp - a( l + i, j )*x( ix )
                     ix   = ix   - incx
  150             CONTINUE
                  IF( nounit )
     $               temp = temp/a( 1, j )
                  x( jx ) = temp
                  jx      = jx   - incx
                  IF( ( n - j ).GE.k )
     $               kx = kx - incx
  160          CONTINUE
            END IF
         END IF
      END IF
*
      RETURN
*
*     End of DTBSV .
*
      END