diff options
Diffstat (limited to 'src/GeneralizedPolynomial-Uniform/2d.maple')
| -rw-r--r-- | src/GeneralizedPolynomial-Uniform/2d.maple | 465 |
1 files changed, 0 insertions, 465 deletions
diff --git a/src/GeneralizedPolynomial-Uniform/2d.maple b/src/GeneralizedPolynomial-Uniform/2d.maple deleted file mode 100644 index bfd149f..0000000 --- a/src/GeneralizedPolynomial-Uniform/2d.maple +++ /dev/null @@ -1,465 +0,0 @@ -# Maple code to compute 2-D Lagrange interpolation coefficients (orders 1-4) -# $Id$ - -################################################################################ - -# -# interpolating functions -# - -fn_2d_order1 := -proc(x,y) -+ c01*y -+ c00 + c10*x -end proc; - -fn_2d_order2 := -proc(x,y) -+ c02*y^2 -+ c01*y + c11*x*y -+ c00 + c10*x + c20*x^2 -end proc; - -fn_2d_order3 := -proc(x,y) -+ c03*y^3 -+ c02*y^2 + c12*x*y^2 -+ c01*y + c11*x*y + c21*x^2*y -+ c00 + c10*x + c20*x^2 + c30*x^3 -end proc; - -fn_2d_order4 := -proc(x,y) -+ c04*y^4 -+ c03*y^3 + c13*x*y^3 -+ c02*y^2 + c12*x*y^2 + c22*x^2*y^2 -+ c01*y + c11*x*y + c21*x^2*y + c31*x^3*y -+ c00 + c10*x + c20*x^2 + c30*x^3 + c40*x^4 -end; - -######################################## - -# -# coefficients in interpolating functions -# - -coeff_list_2d_order1 := [ - c01, - c00, c10 - ]; -coeff_list_2d_order2 := [ - c02, - c01, c11, - c00, c10, c20 - ]; -coeff_list_2d_order3 := [ - c03, - c02, c12, - c01, c11, c21, - c00, c10, c20, c30 - ]; -coeff_list_2d_order4 := [ - c04, - c03, c13, - c02, c12, c22, - c01, c11, c21, c31, - c00, c10, c20, c30, c40 - ]; - -######################################## - -# -# coordinates and interpolation points -# - -coord_list_2d := [x,y]; - -# generate points in Fortran ordering -posn_list_2d_size2 := map(ListTools[Reverse], - hypercube_points([ 0, 0], [+1,+1])); -posn_list_2d_size3 := map(ListTools[Reverse], - hypercube_points([-1,-1], [+1,+1])); -posn_list_2d_size4 := map(ListTools[Reverse], - hypercube_points([-1,-1], [+2,+2])); -posn_list_2d_size5 := map(ListTools[Reverse], - hypercube_points([-2,-2], [+2,+2])); - -################################################################################ - -# -# generic stuff for 2d, cube, size=2 -# - -data_var_list_2d_size2 := map(data_var_name, posn_list_2d_size2, "data_"); - -print_name_list_dcl(data_var_list_2d_size2, "fp", - "2d.coeffs/2d.cube.size2/data-var.dcl.c"); -print_data_var_assign(posn_list_2d_size2, "data_", - "2d.coeffs/2d.cube.size2/data-var.assign.c"); - -print_interp_coeff_var_store(posn_list_2d_size2, "", "coeff_I_", - "2d.coeffs/2d.cube.size2/coeff-I.store.c"); -print_interp_coeff_var_store(posn_list_2d_size2, "factor", "coeff_dx_", - "2d.coeffs/2d.cube.size2/coeff-dx.store.c"); -print_interp_coeff_var_store(posn_list_2d_size2, "factor", "coeff_dy_", - "2d.coeffs/2d.cube.size2/coeff-dy.store.c"); - -print_name_list_dcl(map(coeff_name, posn_list_2d_size2, "coeff_I_"), "fp", - "2d.coeffs/2d.cube.size2/coeff-I.dcl.c"); -print_name_list_dcl(map(coeff_name, posn_list_2d_size2, "coeff_dx_"), "fp", - "2d.coeffs/2d.cube.size2/coeff-dx.dcl.c"); -print_name_list_dcl(map(coeff_name, posn_list_2d_size2, "coeff_dy_"), "fp", - "2d.coeffs/2d.cube.size2/coeff-dy.dcl.c"); - -print_interp_cmpt__lc_of_data(posn_list_2d_size2, - "result", "coeff_I_", "data_", - "2d.coeffs/2d.cube.size2/interp-I.compute.c"); -print_interp_cmpt__lc_of_data(posn_list_2d_size2, - "result", "coeff_dx_", "data_", - "2d.coeffs/2d.cube.size2/interp-dx.compute.c"); -print_interp_cmpt__lc_of_data(posn_list_2d_size2, - "result", "coeff_dy_", "data_", - "2d.coeffs/2d.cube.size2/interp-dy.compute.c"); - -######################################## - -# -# generic stuff for 2d, cube, size=3 -# - -data_var_list_2d_size3 := map(data_var_name, posn_list_2d_size3, "data_"); - -print_name_list_dcl(data_var_list_2d_size3, "fp", - "2d.coeffs/2d.cube.size3/data-var.dcl.c"); -print_data_var_assign(posn_list_2d_size3, "data_", - "2d.coeffs/2d.cube.size3/data-var.assign.c"); - -print_interp_coeff_var_store(posn_list_2d_size3, "", "coeff_I_", - "2d.coeffs/2d.cube.size3/coeff-I.store.c"); -print_interp_coeff_var_store(posn_list_2d_size3, "factor", "coeff_dx_", - "2d.coeffs/2d.cube.size3/coeff-dx.store.c"); -print_interp_coeff_var_store(posn_list_2d_size3, "factor", "coeff_dy_", - "2d.coeffs/2d.cube.size3/coeff-dy.store.c"); -print_interp_coeff_var_store(posn_list_2d_size3, "factor", "coeff_dxx_", - "2d.coeffs/2d.cube.size3/coeff-dxx.store.c"); -print_interp_coeff_var_store(posn_list_2d_size3, "factor", "coeff_dxy_", - "2d.coeffs/2d.cube.size3/coeff-dxy.store.c"); -print_interp_coeff_var_store(posn_list_2d_size3, "factor", "coeff_dyy_", - "2d.coeffs/2d.cube.size3/coeff-dyy.store.c"); - -print_name_list_dcl(map(coeff_name, posn_list_2d_size3, "coeff_I_"), "fp", - "2d.coeffs/2d.cube.size3/coeff-I.dcl.c"); -print_name_list_dcl(map(coeff_name, posn_list_2d_size3, "coeff_dx_"), "fp", - "2d.coeffs/2d.cube.size3/coeff-dx.dcl.c"); -print_name_list_dcl(map(coeff_name, posn_list_2d_size3, "coeff_dy_"), "fp", - "2d.coeffs/2d.cube.size3/coeff-dy.dcl.c"); -print_name_list_dcl(map(coeff_name, posn_list_2d_size3, "coeff_dxx_"), "fp", - "2d.coeffs/2d.cube.size3/coeff-dxx.dcl.c"); -print_name_list_dcl(map(coeff_name, posn_list_2d_size3, "coeff_dxy_"), "fp", - "2d.coeffs/2d.cube.size3/coeff-dxy.dcl.c"); -print_name_list_dcl(map(coeff_name, posn_list_2d_size3, "coeff_dyy_"), "fp", - "2d.coeffs/2d.cube.size3/coeff-dyy.dcl.c"); - -print_interp_cmpt__lc_of_data(posn_list_2d_size3, - "result", "coeff_I_", "data_", - "2d.coeffs/2d.cube.size3/interp-I.compute.c"); -print_interp_cmpt__lc_of_data(posn_list_2d_size3, - "result", "coeff_dx_", "data_", - "2d.coeffs/2d.cube.size3/interp-dx.compute.c"); -print_interp_cmpt__lc_of_data(posn_list_2d_size3, - "result", "coeff_dy_", "data_", - "2d.coeffs/2d.cube.size3/interp-dy.compute.c"); -print_interp_cmpt__lc_of_data(posn_list_2d_size3, - "result", "coeff_dxx_", "data_", - "2d.coeffs/2d.cube.size3/interp-dxx.compute.c"); -print_interp_cmpt__lc_of_data(posn_list_2d_size3, - "result", "coeff_dxy_", "data_", - "2d.coeffs/2d.cube.size3/interp-dxy.compute.c"); -print_interp_cmpt__lc_of_data(posn_list_2d_size3, - "result", "coeff_dyy_", "data_", - "2d.coeffs/2d.cube.size3/interp-dyy.compute.c"); - -######################################## - -# -# generic stuff for 2d, cube, size=4 -# - -data_var_list_2d_size4 := map(data_var_name, posn_list_2d_size4, "data_"); - -print_name_list_dcl(data_var_list_2d_size4, "fp", - "2d.coeffs/2d.cube.size4/data-var.dcl.c"); -print_data_var_assign(posn_list_2d_size4, "data_", - "2d.coeffs/2d.cube.size4/data-var.assign.c"); - -print_interp_coeff_var_store(posn_list_2d_size4, "", "coeff_I_", - "2d.coeffs/2d.cube.size4/coeff-I.store.c"); -print_interp_coeff_var_store(posn_list_2d_size4, "factor", "coeff_dx_", - "2d.coeffs/2d.cube.size4/coeff-dx.store.c"); -print_interp_coeff_var_store(posn_list_2d_size4, "factor", "coeff_dy_", - "2d.coeffs/2d.cube.size4/coeff-dy.store.c"); -print_interp_coeff_var_store(posn_list_2d_size4, "factor", "coeff_dxx_", - "2d.coeffs/2d.cube.size4/coeff-dxx.store.c"); -print_interp_coeff_var_store(posn_list_2d_size4, "factor", "coeff_dxy_", - "2d.coeffs/2d.cube.size4/coeff-dxy.store.c"); -print_interp_coeff_var_store(posn_list_2d_size4, "factor", "coeff_dyy_", - "2d.coeffs/2d.cube.size4/coeff-dyy.store.c"); - -print_name_list_dcl(map(coeff_name, posn_list_2d_size4, "coeff_I_"), "fp", - "2d.coeffs/2d.cube.size4/coeff-I.dcl.c"); -print_name_list_dcl(map(coeff_name, posn_list_2d_size4, "coeff_dx_"), "fp", - "2d.coeffs/2d.cube.size4/coeff-dx.dcl.c"); -print_name_list_dcl(map(coeff_name, posn_list_2d_size4, "coeff_dy_"), "fp", - "2d.coeffs/2d.cube.size4/coeff-dy.dcl.c"); -print_name_list_dcl(map(coeff_name, posn_list_2d_size4, "coeff_dxx_"), "fp", - "2d.coeffs/2d.cube.size4/coeff-dxx.dcl.c"); -print_name_list_dcl(map(coeff_name, posn_list_2d_size4, "coeff_dxy_"), "fp", - "2d.coeffs/2d.cube.size4/coeff-dxy.dcl.c"); -print_name_list_dcl(map(coeff_name, posn_list_2d_size4, "coeff_dyy_"), "fp", - "2d.coeffs/2d.cube.size4/coeff-dyy.dcl.c"); - -print_interp_cmpt__lc_of_data(posn_list_2d_size4, - "result", "coeff_I_", "data_", - "2d.coeffs/2d.cube.size4/interp-I.compute.c"); -print_interp_cmpt__lc_of_data(posn_list_2d_size4, - "result", "coeff_dx_", "data_", - "2d.coeffs/2d.cube.size4/interp-dx.compute.c"); -print_interp_cmpt__lc_of_data(posn_list_2d_size4, - "result", "coeff_dy_", "data_", - "2d.coeffs/2d.cube.size4/interp-dy.compute.c"); -print_interp_cmpt__lc_of_data(posn_list_2d_size4, - "result", "coeff_dxx_", "data_", - "2d.coeffs/2d.cube.size4/interp-dxx.compute.c"); -print_interp_cmpt__lc_of_data(posn_list_2d_size4, - "result", "coeff_dxy_", "data_", - "2d.coeffs/2d.cube.size4/interp-dxy.compute.c"); -print_interp_cmpt__lc_of_data(posn_list_2d_size4, - "result", "coeff_dyy_", "data_", - "2d.coeffs/2d.cube.size4/interp-dyy.compute.c"); - -######################################## - -# -# generic stuff for 2d, cube, size=5 -# - -data_var_list_2d_size5 := map(data_var_name, posn_list_2d_size5, "data_"); - -print_name_list_dcl(data_var_list_2d_size5, "fp", - "2d.coeffs/2d.cube.size5/data-var.dcl.c"); -print_data_var_assign(posn_list_2d_size5, "data_", - "2d.coeffs/2d.cube.size5/data-var.assign.c"); - -print_interp_coeff_var_store(posn_list_2d_size5, "", "coeff_I_", - "2d.coeffs/2d.cube.size5/coeff-I.store.c"); -print_interp_coeff_var_store(posn_list_2d_size5, "factor", "coeff_dx_", - "2d.coeffs/2d.cube.size5/coeff-dx.store.c"); -print_interp_coeff_var_store(posn_list_2d_size5, "factor", "coeff_dy_", - "2d.coeffs/2d.cube.size5/coeff-dy.store.c"); -print_interp_coeff_var_store(posn_list_2d_size5, "factor", "coeff_dxx_", - "2d.coeffs/2d.cube.size5/coeff-dxx.store.c"); -print_interp_coeff_var_store(posn_list_2d_size5, "factor", "coeff_dxy_", - "2d.coeffs/2d.cube.size5/coeff-dxy.store.c"); -print_interp_coeff_var_store(posn_list_2d_size5, "factor", "coeff_dyy_", - "2d.coeffs/2d.cube.size5/coeff-dyy.store.c"); - -print_name_list_dcl(map(coeff_name, posn_list_2d_size5, "coeff_I_"), "fp", - "2d.coeffs/2d.cube.size5/coeff-I.dcl.c"); -print_name_list_dcl(map(coeff_name, posn_list_2d_size5, "coeff_dx_"), "fp", - "2d.coeffs/2d.cube.size5/coeff-dx.dcl.c"); -print_name_list_dcl(map(coeff_name, posn_list_2d_size5, "coeff_dy_"), "fp", - "2d.coeffs/2d.cube.size5/coeff-dy.dcl.c"); -print_name_list_dcl(map(coeff_name, posn_list_2d_size5, "coeff_dxx_"), "fp", - "2d.coeffs/2d.cube.size5/coeff-dxx.dcl.c"); -print_name_list_dcl(map(coeff_name, posn_list_2d_size5, "coeff_dxy_"), "fp", - "2d.coeffs/2d.cube.size5/coeff-dxy.dcl.c"); -print_name_list_dcl(map(coeff_name, posn_list_2d_size5, "coeff_dyy_"), "fp", - "2d.coeffs/2d.cube.size5/coeff-dyy.dcl.c"); - -print_interp_cmpt__lc_of_data(posn_list_2d_size5, - "result", "coeff_I_", "data_", - "2d.coeffs/2d.cube.size5/interp-I.compute.c"); -print_interp_cmpt__lc_of_data(posn_list_2d_size5, - "result", "coeff_dx_", "data_", - "2d.coeffs/2d.cube.size5/interp-dx.compute.c"); -print_interp_cmpt__lc_of_data(posn_list_2d_size5, - "result", "coeff_dy_", "data_", - "2d.coeffs/2d.cube.size5/interp-dy.compute.c"); -print_interp_cmpt__lc_of_data(posn_list_2d_size5, - "result", "coeff_dxx_", "data_", - "2d.coeffs/2d.cube.size5/interp-dxx.compute.c"); -print_interp_cmpt__lc_of_data(posn_list_2d_size5, - "result", "coeff_dxy_", "data_", - "2d.coeffs/2d.cube.size5/interp-dxy.compute.c"); -print_interp_cmpt__lc_of_data(posn_list_2d_size5, - "result", "coeff_dyy_", "data_", - "2d.coeffs/2d.cube.size5/interp-dyy.compute.c"); - - -################################################################################ - -# -# 2d, cube, order=1, smoothing=0 (size=2) -# - -# interpolating polynomial -interp_2d_cube_order1_smooth0 - := polynomial_interpolant(fn_2d_order1, coeff_list_2d_order1, - coord_list_2d, posn_list_2d_size2); - -# I -coeff_as_lc_of_data(%, posn_list_2d_size2); -print_coeff__lc_of_data(%, "coeff_I_", "fp", - "2d.coeffs/2d.cube.order1.smooth0/coeff-I.compute.c"); - -# d/dx -simplify( diff(interp_2d_cube_order1_smooth0,x) ); -coeff_as_lc_of_data(%, posn_list_2d_size2); -print_coeff__lc_of_data(%, "coeff_dx_", "fp", - "2d.coeffs/2d.cube.order1.smooth0/coeff-dx.compute.c"); - -# d/dy -simplify( diff(interp_2d_cube_order1_smooth0,y) ); -coeff_as_lc_of_data(%, posn_list_2d_size2); -print_coeff__lc_of_data(%, "coeff_dy_", "fp", - "2d.coeffs/2d.cube.order1.smooth0/coeff-dy.compute.c"); - -######################################## - -# -# 2d, cube, order=2, smoothing=0 (size=3) -# - -# interpolating polynomial -interp_2d_cube_order2_smooth0 - := polynomial_interpolant(fn_2d_order2, coeff_list_2d_order2, - coord_list_2d, posn_list_2d_size3); - -# I -coeff_as_lc_of_data(%, posn_list_2d_size3); -print_coeff__lc_of_data(%, "coeff_I_", "fp", - "2d.coeffs/2d.cube.order2.smooth0/coeff-I.compute.c"); - -# d/dx -simplify( diff(interp_2d_cube_order2_smooth0,x) ); -coeff_as_lc_of_data(%, posn_list_2d_size3); -print_coeff__lc_of_data(%, "coeff_dx_", "fp", - "2d.coeffs/2d.cube.order2.smooth0/coeff-dx.compute.c"); - -# d/dy -simplify( diff(interp_2d_cube_order2_smooth0,y) ); -coeff_as_lc_of_data(%, posn_list_2d_size3); -print_coeff__lc_of_data(%, "coeff_dy_", "fp", - "2d.coeffs/2d.cube.order2.smooth0/coeff-dy.compute.c"); - -# d^2/dx^2 -simplify( diff(interp_2d_cube_order2_smooth0,x,x) ); -coeff_as_lc_of_data(%, posn_list_2d_size3); -print_coeff__lc_of_data(%, "coeff_dxx_", "fp", - "2d.coeffs/2d.cube.order2.smooth0/coeff-dxx.compute.c"); - -# d^2/dxdy -simplify( diff(interp_2d_cube_order2_smooth0,x,y) ); -coeff_as_lc_of_data(%, posn_list_2d_size3); -print_coeff__lc_of_data(%, "coeff_dxy_", "fp", - "2d.coeffs/2d.cube.order2.smooth0/coeff-dxy.compute.c"); - -# d^2/dy^2 -simplify( diff(interp_2d_cube_order2_smooth0,y,y) ); -coeff_as_lc_of_data(%, posn_list_2d_size3); -print_coeff__lc_of_data(%, "coeff_dyy_", "fp", - "2d.coeffs/2d.cube.order2.smooth0/coeff-dyy.compute.c"); - -######################################## - -# -# 2d, cube, order=3, smoothing=0 (size=4) -# - -# interpolating polynomial -interp_2d_cube_order3_smooth0 - := polynomial_interpolant(fn_2d_order3, coeff_list_2d_order3, - coord_list_2d, posn_list_2d_size4); - -# I -coeff_as_lc_of_data(%, posn_list_2d_size4); -print_coeff__lc_of_data(%, "coeff_I_", "fp", - "2d.coeffs/2d.cube.order3.smooth0/coeff-I.compute.c"); - -# d/dx -simplify( diff(interp_2d_cube_order3_smooth0,x) ); -coeff_as_lc_of_data(%, posn_list_2d_size4); -print_coeff__lc_of_data(%, "coeff_dx_", "fp", - "2d.coeffs/2d.cube.order3.smooth0/coeff-dx.compute.c"); - -# d/dy -simplify( diff(interp_2d_cube_order3_smooth0,y) ); -coeff_as_lc_of_data(%, posn_list_2d_size4); -print_coeff__lc_of_data(%, "coeff_dy_", "fp", - "2d.coeffs/2d.cube.order3.smooth0/coeff-dy.compute.c"); - -# d^2/dx^2 -simplify( diff(interp_2d_cube_order3_smooth0,x,x) ); -coeff_as_lc_of_data(%, posn_list_2d_size4); -print_coeff__lc_of_data(%, "coeff_dxx_", "fp", - "2d.coeffs/2d.cube.order3.smooth0/coeff-dxx.compute.c"); - -# d^2/dxdy -simplify( diff(interp_2d_cube_order3_smooth0,x,y) ); -coeff_as_lc_of_data(%, posn_list_2d_size4); -print_coeff__lc_of_data(%, "coeff_dxy_", "fp", - "2d.coeffs/2d.cube.order3.smooth0/coeff-dxy.compute.c"); - -# d^2/dy^2 -simplify( diff(interp_2d_cube_order3_smooth0,y,y) ); -coeff_as_lc_of_data(%, posn_list_2d_size4); -print_coeff__lc_of_data(%, "coeff_dyy_", "fp", - "2d.coeffs/2d.cube.order3.smooth0/coeff-dyy.compute.c"); - -######################################## - -# -# 2d, cube, order=4, smoothing=0 (size=5) -# - -# interpolating polynomial -interp_2d_cube_order4_smooth0 - := polynomial_interpolant(fn_2d_order4, coeff_list_2d_order4, - coord_list_2d, posn_list_2d_size5); - -# I -coeff_as_lc_of_data(%, posn_list_2d_size5); -print_coeff__lc_of_data(%, "coeff_I_", "fp", - "2d.coeffs/2d.cube.order4.smooth0/coeff-I.compute.c"); - -# d/dx -simplify( diff(interp_2d_cube_order4_smooth0,x) ); -coeff_as_lc_of_data(%, posn_list_2d_size5); -print_coeff__lc_of_data(%, "coeff_dx_", "fp", - "2d.coeffs/2d.cube.order4.smooth0/coeff-dx.compute.c"); - -# d/dy -simplify( diff(interp_2d_cube_order4_smooth0,y) ); -coeff_as_lc_of_data(%, posn_list_2d_size5); -print_coeff__lc_of_data(%, "coeff_dy_", "fp", - "2d.coeffs/2d.cube.order4.smooth0/coeff-dy.compute.c"); - -# d^2/dx^2 -simplify( diff(interp_2d_cube_order4_smooth0,x,x) ); -coeff_as_lc_of_data(%, posn_list_2d_size5); -print_coeff__lc_of_data(%, "coeff_dxx_", "fp", - "2d.coeffs/2d.cube.order4.smooth0/coeff-dxx.compute.c"); - -# d^2/dxdy -simplify( diff(interp_2d_cube_order4_smooth0,x,y) ); -coeff_as_lc_of_data(%, posn_list_2d_size5); -print_coeff__lc_of_data(%, "coeff_dxy_", "fp", - "2d.coeffs/2d.cube.order4.smooth0/coeff-dxy.compute.c"); - -# d^2/dy^2 -simplify( diff(interp_2d_cube_order4_smooth0,y,y) ); -coeff_as_lc_of_data(%, posn_list_2d_size5); -print_coeff__lc_of_data(%, "coeff_dyy_", "fp", - "2d.coeffs/2d.cube.order4.smooth0/coeff-dyy.compute.c"); - -################################################################################ |