-- lphi.ads Lagrange Phi functions, orthogonal polynomials
--         function prototype naming convention:
--           phi_dimensions_degree_optional-boundary-flags
--           phip_...       first derivative "p for prime"
--           phipp_...      second derivative,  etc
--
-- example  phip22(x, i, xg(), imin, imax,
--                 y, j, yg(), jmin, jmax)  is
--               ^_two dimensional
--              ^__second degree
--             ^___first derrivitive "prime"
--  xg() and yg() are x and y grid values, not necessarily
--  uniformly spaced. These may be artificial, yet the
--  indicies i and j for xg(i) and yg(j), xg(i-1), yg(j+1)
--  etc. must provide the intended grid coordinates.
--  All grid coordinates must be in increasing order.

package lphi is

   type xarray is array (integer range <>) of long_float;

  -- first order, one dimension
  function phi11 (x : long_float; i : integer; xg : xarray;
                  imin : integer; imax : integer) return Long_float;
  function phip11(x : long_float; i : integer; xg : xarray;
                  imin : integer; imax : integer) return Long_float;

  -- second order, one dimension
  function phi21  (x : long_float; i : integer; xg : xarray;
                   imin : integer; imax : integer) return Long_float;
  function phip21 (x : long_float; i : integer; xg : xarray;
                   imin : integer; imax : integer) return Long_float;
  function phipp21(x : long_float; i : integer; xg : xarray;
                   imin : integer; imax : integer) return Long_float;

end lphi;