# 2d.maple -- compute Hermite interpolation coefficients in 2-D
# $Header$

################################################################################

#
# 2d, cube, polynomial order=3, derivatives via 3-point order=2 formula
# ==> overall order=2, 4-point molecule
#

# interpolating polynomial
interp_2d_cube_order2
  := Hermite_polynomial_interpolant(fn_2d_order3,
				    coeff_set_2d_order3,
				    [x,y],
				    {
				      {x}   = deriv_2d_dx_3point,
				      {y}   = deriv_2d_dy_3point,
				      {x,y} = deriv_2d_dxy_3point
				    },
				    {op(posn_list_2d_size2)},
				    {op(posn_list_2d_size2)});

# I
coeff_as_lc_of_data(%, posn_list_2d_size4);
print_coeff__lc_of_data(%, "coeff_I_", "fp",
			"2d.coeffs/2d.cube.order2/coeff-I.compute.c");

# d/dx
simplify( diff(interp_2d_cube_order2,x) );
coeff_as_lc_of_data(%, posn_list_2d_size4);
print_coeff__lc_of_data(%, "coeff_dx_", "fp",
			"2d.coeffs/2d.cube.order2/coeff-dx.compute.c");

# d/dy
simplify( diff(interp_2d_cube_order2,y) );
coeff_as_lc_of_data(%, posn_list_2d_size4);
print_coeff__lc_of_data(%, "coeff_dy_", "fp",
			"2d.coeffs/2d.cube.order2/coeff-dy.compute.c");

# d^2/dx^2
simplify( diff(interp_2d_cube_order2,x,x) );
coeff_as_lc_of_data(%, posn_list_2d_size4);
print_coeff__lc_of_data(%, "coeff_dxx_", "fp",
			"2d.coeffs/2d.cube.order2/coeff-dxx.compute.c");

# d^2/dxdy
simplify( diff(interp_2d_cube_order2,x,y) );
coeff_as_lc_of_data(%, posn_list_2d_size4);
print_coeff__lc_of_data(%, "coeff_dxy_", "fp",
			"2d.coeffs/2d.cube.order2/coeff-dxy.compute.c");

# d^2/dy^2
simplify( diff(interp_2d_cube_order2,y,y) );
coeff_as_lc_of_data(%, posn_list_2d_size4);
print_coeff__lc_of_data(%, "coeff_dyy_", "fp",
			"2d.coeffs/2d.cube.order2/coeff-dyy.compute.c");

################################################################################

#
# 2d, cube, polynomial order=3, derivatives via 5-point order=4 formula
# ==> overall order=3, 6-point molecule
#

# interpolating polynomial
interp_2d_cube_order3
  := Hermite_polynomial_interpolant(fn_2d_order3,
				    coeff_set_2d_order3,
				    [x,y],
				    {
				      {x}   = deriv_2d_dx_5point,
				      {y}   = deriv_2d_dy_5point,
				      {x,y} = deriv_2d_dxy_5point
				    },
				    {op(posn_list_2d_size2)},
				    {op(posn_list_2d_size2)});

# I
coeff_as_lc_of_data(%, posn_list_2d_size6);
print_coeff__lc_of_data(%, "coeff_I_", "fp",
			"2d.coeffs/2d.cube.order3/coeff-I.compute.c");

# d/dx
simplify( diff(interp_2d_cube_order3,x) );
coeff_as_lc_of_data(%, posn_list_2d_size6);
print_coeff__lc_of_data(%, "coeff_dx_", "fp",
			"2d.coeffs/2d.cube.order3/coeff-dx.compute.c");

# d/dy
simplify( diff(interp_2d_cube_order3,y) );
coeff_as_lc_of_data(%, posn_list_2d_size6);
print_coeff__lc_of_data(%, "coeff_dy_", "fp",
			"2d.coeffs/2d.cube.order3/coeff-dy.compute.c");

# d^2/dx^2
simplify( diff(interp_2d_cube_order3,x,x) );
coeff_as_lc_of_data(%, posn_list_2d_size6);
print_coeff__lc_of_data(%, "coeff_dxx_", "fp",
			"2d.coeffs/2d.cube.order3/coeff-dxx.compute.c");

# d^2/dxdy
simplify( diff(interp_2d_cube_order3,x,y) );
coeff_as_lc_of_data(%, posn_list_2d_size6);
print_coeff__lc_of_data(%, "coeff_dxy_", "fp",
			"2d.coeffs/2d.cube.order3/coeff-dxy.compute.c");

# d^2/dy^2
simplify( diff(interp_2d_cube_order3,y,y) );
coeff_as_lc_of_data(%, posn_list_2d_size6);
print_coeff__lc_of_data(%, "coeff_dyy_", "fp",
			"2d.coeffs/2d.cube.order3/coeff-dyy.compute.c");

################################################################################