# 3d.maple -- compute Lagrange interpolation coefficients in 3-D
# $Header$

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

#
# 3d, cube, order=1, smoothing=0 (size=2)
#

# interpolating polynomial
interp_3d_cube_order1_smooth0
	:= Lagrange_polynomial_interpolant(fn_3d_order1, coeff_list_3d_order1,
					   coord_list_3d, posn_list_3d_size2);

# I
coeff_as_lc_of_data(%, posn_list_3d_size2);
print_coeff__lc_of_data(%, "coeff_I_", "fp",
			"3d.coeffs/3d.cube.order1.smooth0/coeff-I.compute.c");

# d/dx
simplify( diff(interp_3d_cube_order1_smooth0,x) );
coeff_as_lc_of_data(%, posn_list_3d_size2);
print_coeff__lc_of_data(%, "coeff_dx_", "fp",
			"3d.coeffs/3d.cube.order1.smooth0/coeff-dx.compute.c");

# d/dy
simplify( diff(interp_3d_cube_order1_smooth0,y) );
coeff_as_lc_of_data(%, posn_list_3d_size2);
print_coeff__lc_of_data(%, "coeff_dy_", "fp",
			"3d.coeffs/3d.cube.order1.smooth0/coeff-dy.compute.c");

# d/dz
simplify( diff(interp_3d_cube_order1_smooth0,z) );
coeff_as_lc_of_data(%, posn_list_3d_size2);
print_coeff__lc_of_data(%, "coeff_dz_", "fp",
			"3d.coeffs/3d.cube.order1.smooth0/coeff-dz.compute.c");

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

#
# 3d, cube, order=2, smoothing=0 (size=3)
#

# interpolating polynomial
interp_3d_cube_order2_smooth0
	:= Lagrange_polynomial_interpolant(fn_3d_order2, coeff_list_3d_order2,
					   coord_list_3d, posn_list_3d_size3);

# I
coeff_as_lc_of_data(%, posn_list_3d_size3);
print_coeff__lc_of_data(%, "coeff_I_", "fp",
			"3d.coeffs/3d.cube.order2.smooth0/coeff-I.compute.c");

# d/dx
simplify( diff(interp_3d_cube_order2_smooth0,x) );
coeff_as_lc_of_data(%, posn_list_3d_size3);
print_coeff__lc_of_data(%, "coeff_dx_", "fp",
			"3d.coeffs/3d.cube.order2.smooth0/coeff-dx.compute.c");

# d/dy
simplify( diff(interp_3d_cube_order2_smooth0,y) );
coeff_as_lc_of_data(%, posn_list_3d_size3);
print_coeff__lc_of_data(%, "coeff_dy_", "fp",
			"3d.coeffs/3d.cube.order2.smooth0/coeff-dy.compute.c");

# d/dz
simplify( diff(interp_3d_cube_order2_smooth0,z) );
coeff_as_lc_of_data(%, posn_list_3d_size3);
print_coeff__lc_of_data(%, "coeff_dz_", "fp",
			"3d.coeffs/3d.cube.order2.smooth0/coeff-dz.compute.c");

# d^2/dx^2
simplify( diff(interp_3d_cube_order2_smooth0,x,x) );
coeff_as_lc_of_data(%, posn_list_3d_size3);
print_coeff__lc_of_data(%, "coeff_dxx_", "fp",
			"3d.coeffs/3d.cube.order2.smooth0/coeff-dxx.compute.c");

# d^2/dxdy
simplify( diff(interp_3d_cube_order2_smooth0,x,y) );
coeff_as_lc_of_data(%, posn_list_3d_size3);
print_coeff__lc_of_data(%, "coeff_dxy_", "fp",
			"3d.coeffs/3d.cube.order2.smooth0/coeff-dxy.compute.c");

# d^2/dxdz
simplify( diff(interp_3d_cube_order2_smooth0,x,z) );
coeff_as_lc_of_data(%, posn_list_3d_size3);
print_coeff__lc_of_data(%, "coeff_dxz_", "fp",
			"3d.coeffs/3d.cube.order2.smooth0/coeff-dxz.compute.c");

# d^2/dy^2
simplify( diff(interp_3d_cube_order2_smooth0,y,y) );
coeff_as_lc_of_data(%, posn_list_3d_size3);
print_coeff__lc_of_data(%, "coeff_dyy_", "fp",
			"3d.coeffs/3d.cube.order2.smooth0/coeff-dyy.compute.c");

# d^2/dydz
simplify( diff(interp_3d_cube_order2_smooth0,y,z) );
coeff_as_lc_of_data(%, posn_list_3d_size3);
print_coeff__lc_of_data(%, "coeff_dyz_", "fp",
			"3d.coeffs/3d.cube.order2.smooth0/coeff-dyz.compute.c");

# d^2/dz^2
simplify( diff(interp_3d_cube_order2_smooth0,z,z) );
coeff_as_lc_of_data(%, posn_list_3d_size3);
print_coeff__lc_of_data(%, "coeff_dzz_", "fp",
			"3d.coeffs/3d.cube.order2.smooth0/coeff-dzz.compute.c");

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

#
# 3d, cube, order=3, smoothing=0 (size=4)
#

# interpolating polynomial
interp_3d_cube_order3_smooth0
	:= Lagrange_polynomial_interpolant(fn_3d_order3, coeff_list_3d_order3,
					   coord_list_3d, posn_list_3d_size4);

# I
coeff_as_lc_of_data(%, posn_list_3d_size4);
print_coeff__lc_of_data(%, "coeff_I_", "fp",
			"3d.coeffs/3d.cube.order3.smooth0/coeff-I.compute.c");

# d/dx
simplify( diff(interp_3d_cube_order3_smooth0,x) );
coeff_as_lc_of_data(%, posn_list_3d_size4);
print_coeff__lc_of_data(%, "coeff_dx_", "fp",
			"3d.coeffs/3d.cube.order3.smooth0/coeff-dx.compute.c");

# d/dy
simplify( diff(interp_3d_cube_order3_smooth0,y) );
coeff_as_lc_of_data(%, posn_list_3d_size4);
print_coeff__lc_of_data(%, "coeff_dy_", "fp",
			"3d.coeffs/3d.cube.order3.smooth0/coeff-dy.compute.c");

# d/dz
simplify( diff(interp_3d_cube_order3_smooth0,z) );
coeff_as_lc_of_data(%, posn_list_3d_size4);
print_coeff__lc_of_data(%, "coeff_dz_", "fp",
			"3d.coeffs/3d.cube.order3.smooth0/coeff-dz.compute.c");

# d^2/dx^2
simplify( diff(interp_3d_cube_order3_smooth0,x,x) );
coeff_as_lc_of_data(%, posn_list_3d_size4);
print_coeff__lc_of_data(%, "coeff_dxx_", "fp",
			"3d.coeffs/3d.cube.order3.smooth0/coeff-dxx.compute.c");

# d^2/dxdy
simplify( diff(interp_3d_cube_order3_smooth0,x,y) );
coeff_as_lc_of_data(%, posn_list_3d_size4);
print_coeff__lc_of_data(%, "coeff_dxy_", "fp",
			"3d.coeffs/3d.cube.order3.smooth0/coeff-dxy.compute.c");

# d^2/dxdz
simplify( diff(interp_3d_cube_order3_smooth0,x,z) );
coeff_as_lc_of_data(%, posn_list_3d_size4);
print_coeff__lc_of_data(%, "coeff_dxz_", "fp",
			"3d.coeffs/3d.cube.order3.smooth0/coeff-dxz.compute.c");

# d^2/dy^2
simplify( diff(interp_3d_cube_order3_smooth0,y,y) );
coeff_as_lc_of_data(%, posn_list_3d_size4);
print_coeff__lc_of_data(%, "coeff_dyy_", "fp",
			"3d.coeffs/3d.cube.order3.smooth0/coeff-dyy.compute.c");

# d^2/dydz
simplify( diff(interp_3d_cube_order3_smooth0,y,z) );
coeff_as_lc_of_data(%, posn_list_3d_size4);
print_coeff__lc_of_data(%, "coeff_dyz_", "fp",
			"3d.coeffs/3d.cube.order3.smooth0/coeff-dyz.compute.c");

# d^2/dz^2
simplify( diff(interp_3d_cube_order3_smooth0,z,z) );
coeff_as_lc_of_data(%, posn_list_3d_size4);
print_coeff__lc_of_data(%, "coeff_dzz_", "fp",
			"3d.coeffs/3d.cube.order3.smooth0/coeff-dzz.compute.c");

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

#
# 3d, cube, order=4, smoothing=0 (size=5)
#

# interpolating polynomial
interp_3d_cube_order4_smooth0
	:= Lagrange_polynomial_interpolant(fn_3d_order4, coeff_list_3d_order4,
					   coord_list_3d, posn_list_3d_size5);

# I
coeff_as_lc_of_data(%, posn_list_3d_size5);
print_coeff__lc_of_data(%, "coeff_I_", "fp",
			"3d.coeffs/3d.cube.order4.smooth0/coeff-I.compute.c");

# d/dx
simplify( diff(interp_3d_cube_order4_smooth0,x) );
coeff_as_lc_of_data(%, posn_list_3d_size5);
print_coeff__lc_of_data(%, "coeff_dx_", "fp",
			"3d.coeffs/3d.cube.order4.smooth0/coeff-dx.compute.c");

# d/dy
simplify( diff(interp_3d_cube_order4_smooth0,y) );
coeff_as_lc_of_data(%, posn_list_3d_size5);
print_coeff__lc_of_data(%, "coeff_dy_", "fp",
			"3d.coeffs/3d.cube.order4.smooth0/coeff-dy.compute.c");

# d/dz
simplify( diff(interp_3d_cube_order4_smooth0,z) );
coeff_as_lc_of_data(%, posn_list_3d_size5);
print_coeff__lc_of_data(%, "coeff_dz_", "fp",
			"3d.coeffs/3d.cube.order4.smooth0/coeff-dz.compute.c");

# d^2/dx^2
simplify( diff(interp_3d_cube_order4_smooth0,x,x) );
coeff_as_lc_of_data(%, posn_list_3d_size5);
print_coeff__lc_of_data(%, "coeff_dxx_", "fp",
			"3d.coeffs/3d.cube.order4.smooth0/coeff-dxx.compute.c");

# d^2/dxdy
simplify( diff(interp_3d_cube_order4_smooth0,x,y) );
coeff_as_lc_of_data(%, posn_list_3d_size5);
print_coeff__lc_of_data(%, "coeff_dxy_", "fp",
			"3d.coeffs/3d.cube.order4.smooth0/coeff-dxy.compute.c");

# d^2/dxdz
simplify( diff(interp_3d_cube_order4_smooth0,x,z) );
coeff_as_lc_of_data(%, posn_list_3d_size5);
print_coeff__lc_of_data(%, "coeff_dxz_", "fp",
			"3d.coeffs/3d.cube.order4.smooth0/coeff-dxz.compute.c");

# d^2/dy^2
simplify( diff(interp_3d_cube_order4_smooth0,y,y) );
coeff_as_lc_of_data(%, posn_list_3d_size5);
print_coeff__lc_of_data(%, "coeff_dyy_", "fp",
			"3d.coeffs/3d.cube.order4.smooth0/coeff-dyy.compute.c");

# d^2/dydz
simplify( diff(interp_3d_cube_order4_smooth0,y,z) );
coeff_as_lc_of_data(%, posn_list_3d_size5);
print_coeff__lc_of_data(%, "coeff_dyz_", "fp",
			"3d.coeffs/3d.cube.order4.smooth0/coeff-dyz.compute.c");

# d^2/dz^2
simplify( diff(interp_3d_cube_order4_smooth0,z,z) );
coeff_as_lc_of_data(%, posn_list_3d_size5);
print_coeff__lc_of_data(%, "coeff_dzz_", "fp",
			"3d.coeffs/3d.cube.order4.smooth0/coeff-dzz.compute.c");

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