# Maple code to compute 1-D Lagrange interpolation coefficients (orders 1-4)
# $Id$

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

#
# interpolating functions
#

fn_1d_order1 :=
proc(x)
+ c0 + c1*x
end proc;

fn_1d_order2 :=
proc(x)
+ c0 + c1*x + c2*x^2
end proc;

fn_1d_order3 :=
proc(x)
+ c0 + c1*x + c2*x^2 + c3*x^3
end proc;

fn_1d_order4 :=
proc(x)
+ c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4
end;

fn_1d_order5 :=
proc(x)
+ c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5
end;

fn_1d_order6 :=
proc(x)
+ c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 + c6*x^6
end;

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

#
# coefficients in interpolating functions
#

coeff_list_1d_order1 := [c0, c1];
coeff_list_1d_order2 := [c0, c1, c2];
coeff_list_1d_order3 := [c0, c1, c2, c3];
coeff_list_1d_order4 := [c0, c1, c2, c3, c4];
coeff_list_1d_order5 := [c0, c1, c2, c3, c4, c5];
coeff_list_1d_order6 := [c0, c1, c2, c3, c4, c5, c6];

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

#
# coordinates and interpolation points
#

coord_list_1d := [x];

# generate points in Fortran ordering
posn_list_1d_size2 := map(ListTools[Reverse], hypercube_points([ 0], [+1]));
posn_list_1d_size3 := map(ListTools[Reverse], hypercube_points([-1], [+1]));
posn_list_1d_size4 := map(ListTools[Reverse], hypercube_points([-1], [+2]));
posn_list_1d_size5 := map(ListTools[Reverse], hypercube_points([-2], [+2]));
posn_list_1d_size6 := map(ListTools[Reverse], hypercube_points([-2], [+3]));
posn_list_1d_size7 := map(ListTools[Reverse], hypercube_points([-3], [+3]));

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

#
# generic stuff for 1d, cube, size=2
#

data_var_list_1d_size2 := map(data_var_name, posn_list_1d_size2, "data_");

print_name_list_dcl(data_var_list_1d_size2, "fp",
		    "1d.coeffs/1d.cube.size2/data-var.dcl.c");
print_data_var_assign(posn_list_1d_size2, "data_",
		      "1d.coeffs/1d.cube.size2/data-var.assign.c");

print_interp_coeff_var_store(posn_list_1d_size2, "coeff_I_",
			     "1d.coeffs/1d.cube.size2/coeff-I.store.c");
print_interp_coeff_var_store(posn_list_1d_size2, "coeff_dx_",
			     "1d.coeffs/1d.cube.size2/coeff-dx.store.c");
print_interp_coeff_var_store(posn_list_1d_size2, "coeff_dxx_",
			     "1d.coeffs/1d.cube.size2/coeff-dxx.store.c");

print_name_list_dcl(map(coeff_name, posn_list_1d_size2, "coeff_I_"), "fp",
		    "1d.coeffs/1d.cube.size2/coeff-I.dcl.c");
print_name_list_dcl(map(coeff_name, posn_list_1d_size2, "coeff_dx_"), "fp",
		    "1d.coeffs/1d.cube.size2/coeff-dx.dcl.c");

print_interp_cmpt__lc_of_data(posn_list_1d_size2,
			      "result", "coeff_I_", "data_",
			      "1d.coeffs/1d.cube.size2/interp-I.compute.c");
print_interp_cmpt__lc_of_data(posn_list_1d_size2,
			      "result", "coeff_dx_", "data_",
			      "1d.coeffs/1d.cube.size2/interp-dx.compute.c");

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

#
# generic stuff for 1d, cube, size=3
#

data_var_list_1d_size3 := map(data_var_name, posn_list_1d_size3, "data_");

print_name_list_dcl(data_var_list_1d_size3, "fp",
		    "1d.coeffs/1d.cube.size3/data-var.dcl.c");
print_data_var_assign(posn_list_1d_size3, "data_",
		      "1d.coeffs/1d.cube.size3/data-var.assign.c");

print_interp_coeff_var_store(posn_list_1d_size3, "coeff_I_",
			     "1d.coeffs/1d.cube.size3/coeff-I.store.c");
print_interp_coeff_var_store(posn_list_1d_size3, "coeff_dx_",
			     "1d.coeffs/1d.cube.size3/coeff-dx.store.c");
print_interp_coeff_var_store(posn_list_1d_size3, "coeff_dxx_",
			     "1d.coeffs/1d.cube.size3/coeff-dxx.store.c");

print_name_list_dcl(map(coeff_name, posn_list_1d_size3, "coeff_I_"), "fp",
		    "1d.coeffs/1d.cube.size3/coeff-I.dcl.c");
print_name_list_dcl(map(coeff_name, posn_list_1d_size3, "coeff_dx_"), "fp",
		    "1d.coeffs/1d.cube.size3/coeff-dx.dcl.c");
print_name_list_dcl(map(coeff_name, posn_list_1d_size3, "coeff_dxx_"), "fp",
		    "1d.coeffs/1d.cube.size3/coeff-dxx.dcl.c");

print_interp_cmpt__lc_of_data(posn_list_1d_size3,
			      "result", "coeff_I_", "data_",
			      "1d.coeffs/1d.cube.size3/interp-I.compute.c");
print_interp_cmpt__lc_of_data(posn_list_1d_size3,
			      "result", "coeff_dx_", "data_",
			      "1d.coeffs/1d.cube.size3/interp-dx.compute.c");
print_interp_cmpt__lc_of_data(posn_list_1d_size3,
			      "result", "coeff_dxx_", "data_",
			      "1d.coeffs/1d.cube.size3/interp-dxx.compute.c");

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

#
# generic stuff for 1d, cube, size=4
#

data_var_list_1d_size4 := map(data_var_name, posn_list_1d_size4, "data_");

print_name_list_dcl(data_var_list_1d_size4, "fp",
		    "1d.coeffs/1d.cube.size4/data-var.dcl.c");
print_data_var_assign(posn_list_1d_size4, "data_",
		      "1d.coeffs/1d.cube.size4/data-var.assign.c");

print_interp_coeff_var_store(posn_list_1d_size4, "coeff_I_",
			     "1d.coeffs/1d.cube.size4/coeff-I.store.c");
print_interp_coeff_var_store(posn_list_1d_size4, "coeff_dx_",
			     "1d.coeffs/1d.cube.size4/coeff-dx.store.c");
print_interp_coeff_var_store(posn_list_1d_size4, "coeff_dxx_",
			     "1d.coeffs/1d.cube.size4/coeff-dxx.store.c");

print_name_list_dcl(map(coeff_name, posn_list_1d_size4, "coeff_I_"), "fp",
		    "1d.coeffs/1d.cube.size4/coeff-I.dcl.c");
print_name_list_dcl(map(coeff_name, posn_list_1d_size4, "coeff_dx_"), "fp",
		    "1d.coeffs/1d.cube.size4/coeff-dx.dcl.c");
print_name_list_dcl(map(coeff_name, posn_list_1d_size4, "coeff_dxx_"), "fp",
		    "1d.coeffs/1d.cube.size4/coeff-dxx.dcl.c");

print_interp_cmpt__lc_of_data(posn_list_1d_size4,
			      "result", "coeff_I_", "data_",
			      "1d.coeffs/1d.cube.size4/interp-I.compute.c");
print_interp_cmpt__lc_of_data(posn_list_1d_size4,
			      "result", "coeff_dx_", "data_",
			      "1d.coeffs/1d.cube.size4/interp-dx.compute.c");
print_interp_cmpt__lc_of_data(posn_list_1d_size4,
			      "result", "coeff_dxx_", "data_",
			      "1d.coeffs/1d.cube.size4/interp-dxx.compute.c");

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

#
# generic stuff for 1d, cube, size=5
#

data_var_list_1d_size5 := map(data_var_name, posn_list_1d_size5, "data_");

print_name_list_dcl(data_var_list_1d_size5, "fp",
		    "1d.coeffs/1d.cube.size5/data-var.dcl.c");
print_data_var_assign(posn_list_1d_size5, "data_",
		      "1d.coeffs/1d.cube.size5/data-var.assign.c");

print_interp_coeff_var_store(posn_list_1d_size5, "coeff_I_",
			     "1d.coeffs/1d.cube.size5/coeff-I.store.c");
print_interp_coeff_var_store(posn_list_1d_size5, "coeff_dx_",
			     "1d.coeffs/1d.cube.size5/coeff-dx.store.c");
print_interp_coeff_var_store(posn_list_1d_size5, "coeff_dxx_",
			     "1d.coeffs/1d.cube.size5/coeff-dxx.store.c");

print_name_list_dcl(map(coeff_name, posn_list_1d_size5, "coeff_I_"), "fp",
		    "1d.coeffs/1d.cube.size5/coeff-I.dcl.c");
print_name_list_dcl(map(coeff_name, posn_list_1d_size5, "coeff_dx_"), "fp",
		    "1d.coeffs/1d.cube.size5/coeff-dx.dcl.c");
print_name_list_dcl(map(coeff_name, posn_list_1d_size5, "coeff_dxx_"), "fp",
		    "1d.coeffs/1d.cube.size5/coeff-dxx.dcl.c");

print_interp_cmpt__lc_of_data(posn_list_1d_size5,
			      "result", "coeff_I_", "data_",
			      "1d.coeffs/1d.cube.size5/interp-I.compute.c");
print_interp_cmpt__lc_of_data(posn_list_1d_size5,
			      "result", "coeff_dx_", "data_",
			      "1d.coeffs/1d.cube.size5/interp-dx.compute.c");
print_interp_cmpt__lc_of_data(posn_list_1d_size5,
			      "result", "coeff_dxx_", "data_",
			      "1d.coeffs/1d.cube.size5/interp-dxx.compute.c");

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

#
# generic stuff for 1d, cube, size=6
#

data_var_list_1d_size6 := map(data_var_name, posn_list_1d_size6, "data_");

print_name_list_dcl(data_var_list_1d_size6, "fp",
		    "1d.coeffs/1d.cube.size6/data-var.dcl.c");
print_data_var_assign(posn_list_1d_size6, "data_",
		      "1d.coeffs/1d.cube.size6/data-var.assign.c");

print_interp_coeff_var_store(posn_list_1d_size6, "coeff_I_",
			     "1d.coeffs/1d.cube.size6/coeff-I.store.c");
print_interp_coeff_var_store(posn_list_1d_size6, "coeff_dx_",
			     "1d.coeffs/1d.cube.size6/coeff-dx.store.c");
print_interp_coeff_var_store(posn_list_1d_size6, "coeff_dxx_",
			     "1d.coeffs/1d.cube.size6/coeff-dxx.store.c");

print_name_list_dcl(map(coeff_name, posn_list_1d_size6, "coeff_I_"), "fp",
		    "1d.coeffs/1d.cube.size6/coeff-I.dcl.c");
print_name_list_dcl(map(coeff_name, posn_list_1d_size6, "coeff_dx_"), "fp",
		    "1d.coeffs/1d.cube.size6/coeff-dx.dcl.c");
print_name_list_dcl(map(coeff_name, posn_list_1d_size6, "coeff_dxx_"), "fp",
		    "1d.coeffs/1d.cube.size6/coeff-dxx.dcl.c");

print_interp_cmpt__lc_of_data(posn_list_1d_size6,
			      "result", "coeff_I_", "data_",
			      "1d.coeffs/1d.cube.size6/interp-I.compute.c");
print_interp_cmpt__lc_of_data(posn_list_1d_size6,
			      "result", "coeff_dx_", "data_",
			      "1d.coeffs/1d.cube.size6/interp-dx.compute.c");
print_interp_cmpt__lc_of_data(posn_list_1d_size6,
			      "result", "coeff_dxx_", "data_",
			      "1d.coeffs/1d.cube.size6/interp-dxx.compute.c");

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

#
# generic stuff for 1d, cube, size=7
#

data_var_list_1d_size7 := map(data_var_name, posn_list_1d_size7, "data_");

print_name_list_dcl(data_var_list_1d_size7, "fp",
		    "1d.coeffs/1d.cube.size7/data-var.dcl.c");
print_data_var_assign(posn_list_1d_size7, "data_",
		      "1d.coeffs/1d.cube.size7/data-var.assign.c");

print_interp_coeff_var_store(posn_list_1d_size7, "coeff_I_",
			     "1d.coeffs/1d.cube.size7/coeff-I.store.c");
print_interp_coeff_var_store(posn_list_1d_size7, "coeff_dx_",
			     "1d.coeffs/1d.cube.size7/coeff-dx.store.c");
print_interp_coeff_var_store(posn_list_1d_size7, "coeff_dxx_",
			     "1d.coeffs/1d.cube.size7/coeff-dxx.store.c");

print_name_list_dcl(map(coeff_name, posn_list_1d_size7, "coeff_I_"), "fp",
		    "1d.coeffs/1d.cube.size7/coeff-I.dcl.c");
print_name_list_dcl(map(coeff_name, posn_list_1d_size7, "coeff_dx_"), "fp",
		    "1d.coeffs/1d.cube.size7/coeff-dx.dcl.c");
print_name_list_dcl(map(coeff_name, posn_list_1d_size7, "coeff_dxx_"), "fp",
		    "1d.coeffs/1d.cube.size7/coeff-dxx.dcl.c");

print_interp_cmpt__lc_of_data(posn_list_1d_size7,
			      "result", "coeff_I_", "data_",
			      "1d.coeffs/1d.cube.size7/interp-I.compute.c");
print_interp_cmpt__lc_of_data(posn_list_1d_size7,
			      "result", "coeff_dx_", "data_",
			      "1d.coeffs/1d.cube.size7/interp-dx.compute.c");
print_interp_cmpt__lc_of_data(posn_list_1d_size7,
			      "result", "coeff_dxx_", "data_",
			      "1d.coeffs/1d.cube.size7/interp-dxx.compute.c");

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

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

# interpolating polynomial
interp_1d_cube_order1_smooth0
	:= polynomial_interpolant(fn_1d_order1, coeff_list_1d_order1,
				  coord_list_1d, posn_list_1d_size2);

# I
coeff_as_lc_of_data(%, posn_list_1d_size2);
print_coeff__lc_of_data(%, "coeff_I_", "fp",
			"1d.coeffs/1d.cube.order1.smooth0/coeff-I.compute.c");

# d/dx
simplify( diff(interp_1d_cube_order1_smooth0,x) );
coeff_as_lc_of_data(%, posn_list_1d_size2);
print_coeff__lc_of_data(%, "coeff_dx_", "fp",
			"1d.coeffs/1d.cube.order1.smooth0/coeff-dx.compute.c");

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

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

# interpolating polynomial
interp_1d_cube_order2_smooth0
	:= polynomial_interpolant(fn_1d_order2, coeff_list_1d_order2,
				  coord_list_1d, posn_list_1d_size3);

# I
coeff_as_lc_of_data(%, posn_list_1d_size3);
print_coeff__lc_of_data(%, "coeff_I_", "fp",
			"1d.coeffs/1d.cube.order2.smooth0/coeff-I.compute.c");

# d/dx
simplify( diff(interp_1d_cube_order2_smooth0,x) );
coeff_as_lc_of_data(%, posn_list_1d_size3);
print_coeff__lc_of_data(%, "coeff_dx_", "fp",
			"1d.coeffs/1d.cube.order2.smooth0/coeff-dx.compute.c");

# d^2/dx^2
simplify( diff(interp_1d_cube_order2_smooth0,x,x) );
coeff_as_lc_of_data(%, posn_list_1d_size3);
print_coeff__lc_of_data(%, "coeff_dxx_", "fp",
			"1d.coeffs/1d.cube.order2.smooth0/coeff-dxx.compute.c");

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

#
# 1d, cube, order=3, smoothing=0 (size=4)
#

# interpolating polynomial
interp_1d_cube_order3_smooth0
	:= polynomial_interpolant(fn_1d_order3, coeff_list_1d_order3,
				  coord_list_1d, posn_list_1d_size4);

# I
coeff_as_lc_of_data(%, posn_list_1d_size4);
print_coeff__lc_of_data(%, "coeff_I_", "fp",
			"1d.coeffs/1d.cube.order3.smooth0/coeff-I.compute.c");

# d/dx
simplify( diff(interp_1d_cube_order3_smooth0,x) );
coeff_as_lc_of_data(%, posn_list_1d_size4);
print_coeff__lc_of_data(%, "coeff_dx_", "fp",
			"1d.coeffs/1d.cube.order3.smooth0/coeff-dx.compute.c");

# d^2/dx^2
simplify( diff(interp_1d_cube_order3_smooth0,x,x) );
coeff_as_lc_of_data(%, posn_list_1d_size4);
print_coeff__lc_of_data(%, "coeff_dxx_", "fp",
			"1d.coeffs/1d.cube.order3.smooth0/coeff-dxx.compute.c");

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

#
# 1d, cube, order=4, smoothing=0 (size=5)
#

# interpolating polynomial
interp_1d_cube_order4_smooth0
	:= polynomial_interpolant(fn_1d_order4, coeff_list_1d_order4,
				  coord_list_1d, posn_list_1d_size5);

# I
coeff_as_lc_of_data(%, posn_list_1d_size5);
print_coeff__lc_of_data(%, "coeff_I_", "fp",
			"1d.coeffs/1d.cube.order4.smooth0/coeff-I.compute.c");

# d/dx
simplify( diff(interp_1d_cube_order4_smooth0,x) );
coeff_as_lc_of_data(%, posn_list_1d_size5);
print_coeff__lc_of_data(%, "coeff_dx_", "fp",
			"1d.coeffs/1d.cube.order4.smooth0/coeff-dx.compute.c");

# d^2/dx^2
simplify( diff(interp_1d_cube_order4_smooth0,x,x) );
coeff_as_lc_of_data(%, posn_list_1d_size5);
print_coeff__lc_of_data(%, "coeff_dxx_", "fp",
			"1d.coeffs/1d.cube.order4.smooth0/coeff-dxx.compute.c");

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

#
# 1d, cube, order=5, smoothing=0 (size=6)
#

# interpolating polynomial
interp_1d_cube_order5_smooth0
	:= polynomial_interpolant(fn_1d_order5, coeff_list_1d_order5,
				  coord_list_1d, posn_list_1d_size6);

# I
coeff_as_lc_of_data(%, posn_list_1d_size6);
print_coeff__lc_of_data(%, "coeff_I_", "fp",
			"1d.coeffs/1d.cube.order5.smooth0/coeff-I.compute.c");

# d/dx
simplify( diff(interp_1d_cube_order5_smooth0,x) );
coeff_as_lc_of_data(%, posn_list_1d_size6);
print_coeff__lc_of_data(%, "coeff_dx_", "fp",
			"1d.coeffs/1d.cube.order5.smooth0/coeff-dx.compute.c");

# d^2/dx^2
simplify( diff(interp_1d_cube_order5_smooth0,x,x) );
coeff_as_lc_of_data(%, posn_list_1d_size6);
print_coeff__lc_of_data(%, "coeff_dxx_", "fp",
			"1d.coeffs/1d.cube.order5.smooth0/coeff-dxx.compute.c");

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

#
# 1d, cube, order=6, smoothing=0 (size=7)
#

# interpolating polynomial
interp_1d_cube_order6_smooth0
	:= polynomial_interpolant(fn_1d_order6, coeff_list_1d_order6,
				  coord_list_1d, posn_list_1d_size7);

# I
coeff_as_lc_of_data(%, posn_list_1d_size7);
print_coeff__lc_of_data(%, "coeff_I_", "fp",
			"1d.coeffs/1d.cube.order6.smooth0/coeff-I.compute.c");

# d/dx
simplify( diff(interp_1d_cube_order6_smooth0,x) );
coeff_as_lc_of_data(%, posn_list_1d_size7);
print_coeff__lc_of_data(%, "coeff_dx_", "fp",
			"1d.coeffs/1d.cube.order6.smooth0/coeff-dx.compute.c");

# d^2/dx^2
simplify( diff(interp_1d_cube_order6_smooth0,x,x) );
coeff_as_lc_of_data(%, posn_list_1d_size7);
print_coeff__lc_of_data(%, "coeff_dxx_", "fp",
			"1d.coeffs/1d.cube.order6.smooth0/coeff-dxx.compute.c");

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