-- test_laphi.adb  family of Lagrange functions and derivatives
--             L_n,j(x) = product i=1,n i/=j (x-x_i)/(x_j-x_i)
--             for points x_1, x_2, ... , x_n
--  generate L_n,j(x) for n=2,6  j=1,n and derivatives to 4th
--  should be same results as produced by test_laphi.c

with Ada.Text_IO;
use  Ada.Text_IO;
with Real_Arrays;
use Real_Arrays;
with Laphi;
use Laphi;

procedure test_laphi is
  NN : Integer := 6;
  h, hf : real;
  xg : Real_Vector(1..NN);
  x, y, yp, ypp, yppp, ypppp : real;
  xmin : Real := 0.0; -- xg(0)
  xmax : Real := 1.0; -- xg(n)
  Package Real_IO is new Float_IO(Real);
  use Real_IO;
begin
  Put_Line("test_laphi.adb running on 0<x<1 for N="&Integer'image(NN));
  Put_Line(" L_order,point  order is highest power of x, point 1..n ");
  Put_Line("    L_n,j(x) = product i=1,n i/=j (x-x_i)/(x_j-x_i)  ");
  Put_Line("    for points x_1, x_2, ... , x_n ");
  Put_Line("    generate L_n,j(x) for n:=2,6  j:=1,n and derivatives to 4th ");

  for n in 2..NN loop -- points go 1 to n
    h := (xmax-xmin)/Real(n-1);
    for j in 1..n loop
      xg(j) := xmin+Real(j-1)*h;
      Put("xg("&Integer'Image(j)&")=");
      Put(xg(j),2,4,0);
      New_Line;
    end loop;
    hf := h/4.0;
    for j in 1..n loop
      for k in 1..4*(n-1)+1 loop
        x := xmin+Real(k-1)*hf;

        -- evaluate function, n,j,x,xg,denom
        y := phi(x, j, n, xg);

        -- evaluate first derivative of function, n,j,x,xg,denom
        yp := phip(x, j, n, xg);

        -- evaluate second derivative of function, n,j,x,xg,denom
        ypp := phipp(x, j, n, xg);

        -- evaluate third derivative of function, n,j,x,xg,denom
        yppp := phippp(x, j, n, xg);

        -- evaluate fourth derivative of function, n,j,x,xg,denom
        ypppp := phipppp(x, j, n, xg);

        Put("L_"&Integer'Image(n)&","&Integer'Image(J)&"(");
        Put(x,2,3,0); Put(")=");
        Put(y,3,3,0); Put(", yp=");
        Put(yp,3,2,0); Put(", ypp=");
        Put(ypp,4,2,0); Put(", yppp=");
        Put(yppp,5,1,0); Put(", ypppp=");
        Put(ypppp,5,1,0);
        New_Line;
      end loop; -- on k,x
      New_Line;
    end loop; -- on j
    New_Line;
  end loop; -- on n

  Put_Line("end test_laphi.adb ");
end test_laphi;