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double *l1pp_apply ( int n, double h, double u[] )

/******************************************************************************/
/*
  Purpose:

    L1PP_APPLY applies the 1D PP Laplacian to a vector.

  Discussion:

    The N grid points are assumed to be evenly spaced by H.

    For N = 5, the discrete Laplacian with periodic boundary conditions
    on [0,6] has the matrix form L:

       2 -1  0  0 -1
      -1  2 -1  0  0
       0 -1  2 -1  0
       0  0 -1  2 -1
      -1  0  0 -1  2

  Licensing:

    This code is distributed under the GNU LGPL license.

  Modified:

    30 October 2013

  Author:

    John Burkardt

  Parameters:

    Input, int N, the number of points.
    N must be at least 3.

    Input, double H, the spacing between points.

    Input, double U[N], the value at each point.

    Output, double L1PP_APPLY[N], the Laplacian evaluated at each point.
*/
{
  int i;
  double *lu;

  if ( n < 3 )
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "L1PP_APPLY - Fatal error!\n" );
    fprintf ( stderr, "  N < 3.\n" );
    exit ( 1 );
  }

  lu = ( double * ) malloc ( n * sizeof ( double ) );

  i = 0;
  lu[i] = ( - u[n-1] + 2.0 * u[i] - u[i+1] ) / h / h;
  for ( i = 1; i < n - 1; i++ )
  {
    lu[i] = ( - u[i-1] + 2.0 * u[i] - u[i+1] ) / h / h;
  }
  i = n - 1;
  lu[i] = ( - u[i-1] + 2.0 * u[i] - u[0] ) / h / h;

  return lu;
}
/******************************************************************************/