function [ phii, phiix ] = phi ( il, x, xleft, xrite )

%% PHI evaluates a linear basis function and its derivative.
%
%  Discussion:
%
%    The functions are evaluated at a point X in an interval.  In any
%    interval, there are just two basis functions.  The first
%    basis function is a line which is 1 at the left endpoint
%    and 0 at the right.  The second basis function is 0 at
%    the left endpoint and 1 at the right.
%
%  Modified:
%
%    05 November 2006
%
%  Parameters:
%
%    Input, integer IL, the local index of the basis function.
%
%    Input, real X, the evaluation point.
%
%    Input, real XLEFT, XRITE, the endpoints of the interval.
%
%    Output, real PHII, PHIIX, the value of the basis function
%    and its derivative.
%
  if ( xleft <= x & x <= xrite )

    if ( il == 1 )
      phii = ( xrite - x ) / ( xrite - xleft );
      phiix = -1.0 / ( xrite - xleft );
    else
      phii = ( x - xleft ) / ( xrite - xleft );
      phiix = 1.0 / ( xrite - xleft );
    end
%
%  If X is outside of the interval, then the basis function
%  is always zero.
%
  else
    phii = 0.0;
    phiix = 0.0;
  end