diff options
Diffstat (limited to 'src/GeneralizedPolynomial-Uniform/1d.maple')
| -rw-r--r-- | src/GeneralizedPolynomial-Uniform/1d.maple | 446 |
1 files changed, 0 insertions, 446 deletions
diff --git a/src/GeneralizedPolynomial-Uniform/1d.maple b/src/GeneralizedPolynomial-Uniform/1d.maple deleted file mode 100644 index 6743108..0000000 --- a/src/GeneralizedPolynomial-Uniform/1d.maple +++ /dev/null @@ -1,446 +0,0 @@ -# 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, "factor", "coeff_dx_", - "1d.coeffs/1d.cube.size2/coeff-dx.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, "factor", "coeff_dx_", - "1d.coeffs/1d.cube.size3/coeff-dx.store.c"); -print_interp_coeff_var_store(posn_list_1d_size3, "factor", "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, "factor", "coeff_dx_", - "1d.coeffs/1d.cube.size4/coeff-dx.store.c"); -print_interp_coeff_var_store(posn_list_1d_size4, "factor", "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, "factor", "coeff_dx_", - "1d.coeffs/1d.cube.size5/coeff-dx.store.c"); -print_interp_coeff_var_store(posn_list_1d_size5, "factor", "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, "factor", "coeff_dx_", - "1d.coeffs/1d.cube.size6/coeff-dx.store.c"); -print_interp_coeff_var_store(posn_list_1d_size6, "factor", "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, "factor", "coeff_dx_", - "1d.coeffs/1d.cube.size7/coeff-dx.store.c"); -print_interp_coeff_var_store(posn_list_1d_size7, "factor", "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"); - -################################################################################ |