r8vec_expand_linear2 Subroutine

subroutine r8vec_expand_linear2 ( n, x, before, fat, after, xfat )

  !*****************************************************************************80
  !
  !! R8VEC_EXPAND_LINEAR2 linearly interpolates new data into an R8VEC.
  !
  !  Discussion:
  !
  !    This routine starts with a vector of data.
  !
  !    The intent is to "fatten" the data, that is, to insert more points
  !    between successive values of the original data.
  !
  !    There will also be extra points placed BEFORE the first original
  !    value and AFTER that last original value.
  !
  !    The "fattened" data is equally spaced between the original points.
  !
  !    The BEFORE data uses the spacing of the first original interval,
  !    and the AFTER data uses the spacing of the last original interval.
  !
  !  Example:
  !
  !    N = 3
  !    BEFORE = 3
  !    FAT = 2
  !    AFTER = 1
  !
  !    X(1:N)        = (/                   0.0,           6.0,             7.0       /)
  !    XFAT(1:2*3+1) = (/ -6.0, -4.0, -2.0, 0.0, 2.0, 4.0, 6.0, 6.33, 6.66, 7.0, 7.66 /)
  !                       3 "BEFORE's"      Old  2 "FATS"  Old    2 "FATS"  Old  1 "AFTER"
  !
  !  Licensing:
  !
  !    This code is distributed under the GNU LGPL license. 
  !
  !  Modified:
  !
  !    03 December 2007
  !
  !  Author:
  !
  !    John Burkardt
  !
  !  Parameters:
  !
  !    Input, integer ( kind = 4 ) N, the number of input data values.
  !    N must be at least 2.
  !
  !    Input, real ( kind = 8 ) X(N), the original data.
  !
  !    Input, integer ( kind = 4 ) BEFORE, the number of "before" values.
  !
  !    Input, integer ( kind = 4 ) FAT, the number of data values to interpolate
  !    between each pair of original data values.
  !
  !    Input, integer ( kind = 4 ) AFTER, the number of "after" values.
  !
  !    Output, real ( kind = 8 ) XFAT(BEFORE+(N-1)*(FAT+1)+1+AFTER), the "fattened" data.
  !
  implicit none

  integer ( kind = 4 ) after
  integer ( kind = 4 ) before
  integer ( kind = 4 ) fat
  integer ( kind = 4 ) n

  integer ( kind = 4 ) i
  integer ( kind = 4 ) j
  integer ( kind = 4 ) k
  real    ( kind = 8 ) x(n)
  real    ( kind = 8 ) xfat(before+(n-1)*(fat+1)+1+after)

  k = 0
  !
  !  Points BEFORE.
  !
  do j = 1 - before + fat, fat
     k = k + 1
     xfat(k) = ( real ( fat - j + 1, kind = 8 ) * ( x(1) - ( x(2) - x(1) ) ) &
          + real (       j,     kind = 8 ) *   x(1)          ) &
          / real ( fat     + 1, kind = 8 )
  end do
  !
  !  Original points and FAT points.
  !
  do i = 1, n - 1

     k = k + 1
     xfat(k) = x(i)

     do j = 1, fat
        k = k + 1
        xfat(k) = ( real ( fat - j + 1, kind = 8 ) * x(i)     &
             + real (       j,     kind = 8 ) * x(i+1) ) &
             / real ( fat     + 1, kind = 8 )
     end do

  end do

  k = k + 1
  xfat(k) = x(n)
  !
  !  Points AFTER.
  !
  do j = 1, after
     k = k + 1
     xfat(k) = ( real ( fat - j + 1, kind = 8 ) * x(n)     &
          + real (       j,     kind = 8 ) * ( x(n) + ( x(n) - x(n-1) ) ) ) &
          / real ( fat     + 1, kind = 8 )
  end do

  return
end subroutine r8vec_expand_linear2