-- nuderiv4d.ads  non uniform derivatives of arbitrady gemoetry
--                compute cx:real_vector based on a set of 70 points
--                in four dimensions  x,y,z,t
--                compute derivative based on dF(x,y,z,t)/dx =
--                sum i in 1..70  cx(i)*F(x(i),y(i),z(i),t(i))
--
-- example  nu4dx(order, npoint, point, x, y, z, t, c);
--                                                  ^_ returned coefficients
--                                      __________ given points in 4 space
--                                 ^__ ith point where derivative computed
--                        ^__ number of points
--                  ^__ max order 1,2,3,4
--              ^___first derivative with respect to x

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

package nuderiv4d is
  procedure nu4dx(order:Integer; npoint:Integer; point:Integer;
                  x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                  c:out Real_vector);
  procedure nu4dy(order:Integer; npoint:Integer; point:Integer;
                  x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                  c:out Real_vector);
  procedure nu4dz(order:Integer; npoint:Integer; point:Integer;
                  x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                  c:out Real_vector);
  procedure nu4dt(order:Integer; npoint:Integer; point:Integer;
                  x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                  c:out Real_vector);
  procedure nu4dxx(order:Integer; npoint:Integer; point:Integer;
                   x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                   c:out Real_vector);
  procedure nu4dxy(order:Integer; npoint:Integer; point:Integer;
                   x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                   c:out Real_vector);
  procedure nu4dxz(order:Integer; npoint:Integer; point:Integer;
                   x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                   c:out Real_vector);
  procedure nu4dxt(order:Integer; npoint:Integer; point:Integer;
                   x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                   c:out Real_vector);
  procedure nu4dyy(order:Integer; npoint:Integer; point:Integer;
                   x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                   c:out Real_vector);
  procedure nu4dyz(order:Integer; npoint:Integer; point:Integer;
                   x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                   c:out Real_vector);
  procedure nu4dyt(order:Integer; npoint:Integer; point:Integer;
                   x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                   c:out Real_vector);
  procedure nu4dzz(order:Integer; npoint:Integer; point:Integer;
                   x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                   c:out Real_vector);
  procedure nu4dzt(order:Integer; npoint:Integer; point:Integer;
                   x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                   c:out Real_vector);
  procedure nu4dtt(order:Integer; npoint:Integer; point:Integer;
                   x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                   c:out Real_vector);
  procedure nu4dxxx(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dxxy(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dxxz(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dxxt(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dxyy(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dxyz(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dxyt(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dxzz(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dxzt(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dxtt(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dyyy(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dyyz(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dyyt(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dyzz(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dyzt(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dytt(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dzzz(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dzzt(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dztt(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dttt(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dxxxx(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dxxxy(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dxxxz(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dxxxt(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dxxyy(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dxxyz(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dxxyt(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dxxzz(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dxxzt(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dxxtt(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dyyyy(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dzzzz(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);
  procedure nu4dtttt(order:Integer; npoint:Integer; point:Integer;
                    x:Real_Vector; y:Real_Vector; z:Real_Vector; t:Real_Vector;
                    c:out Real_vector);

end nuderiv4d;