-- laphi.ads  Lagrange Phi functions, orthogonal polynomials
--         function prototype naming convention:
--           phi            basic Lagrange polynomial
--           phip           first derivative "p for prime"
--           phipp          second derivative,  etc
--
-- example  phip(x, i, n, xg()) is
--                     ^__ nth degree
--                  ^__ ith polynomial in set
--             ^___first derivative "prime"
--  xg() is x  grid values, not necessarily uniformly spaced.
--  xg(0) is minimum, left boundary.
--  xg(n) is maximum, right boundary.
--  All grid coordinates must be in increasing order.

with Real_Arrays; -- types real and real_vector and real_matrix
use Real_Arrays;

package laphi is
  -- phi
  function phi(x:real; j:integer; n:integer; xg:real_vector) return real;

  -- first derivative
  function phip(x:real; j:integer; n:integer; xg:real_vector) return real;

  -- second derivative
  function phipp(x:real; j:integer; n:integer; xg:real_vector) return real;

  -- third derivative
  function phippp(x:real; j:integer; n:integer; xg:real_vector) return real;

  -- fourth derivative
  function phipppp(x:real; j:integer; n:integer; xg:real_vector) return real;

end Laphi;