diff options
Diffstat (limited to 'src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.maple')
-rw-r--r-- | src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.maple | 170 |
1 files changed, 170 insertions, 0 deletions
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.maple b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.maple new file mode 100644 index 0000000..a5b197c --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.maple @@ -0,0 +1,170 @@ +# 2d.maple -- compute Lagrange interpolation coefficients in 2-D +# $Header$ + +################################################################################ + +# +# 2d, cube, order=1, smoothing=0 (size=2) +# + +# interpolating polynomial +interp_2d_cube_order1_smooth0 + := Lagrange_polynomial_interpolant(fn_2d_order1, coeffs_list_2d_order1, + coords_list_2d, posn_list_2d_size2); + +# I +coeffs_as_lc_of_data(%, posn_list_2d_size2); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "2d.coeffs/2d.cube.order1.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_2d_cube_order1_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_2d_size2); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "2d.coeffs/2d.cube.order1.smooth0/coeffs-dx.compute.c"); + +# d/dy +simplify( diff(interp_2d_cube_order1_smooth0,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size2); +print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", + "2d.coeffs/2d.cube.order1.smooth0/coeffs-dy.compute.c"); + +################################################################################ + +# +# 2d, cube, order=2, smoothing=0 (size=3) +# + +# interpolating polynomial +interp_2d_cube_order2_smooth0 + := Lagrange_polynomial_interpolant(fn_2d_order2, coeffs_list_2d_order2, + coords_list_2d, posn_list_2d_size3); + +# I +coeffs_as_lc_of_data(%, posn_list_2d_size3); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "2d.coeffs/2d.cube.order2.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_2d_cube_order2_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_2d_size3); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "2d.coeffs/2d.cube.order2.smooth0/coeffs-dx.compute.c"); + +# d/dy +simplify( diff(interp_2d_cube_order2_smooth0,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size3); +print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", + "2d.coeffs/2d.cube.order2.smooth0/coeffs-dy.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_2d_cube_order2_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_2d_size3); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "2d.coeffs/2d.cube.order2.smooth0/coeffs-dxx.compute.c"); + +# d^2/dxdy +simplify( diff(interp_2d_cube_order2_smooth0,x,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size3); +print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", + "2d.coeffs/2d.cube.order2.smooth0/coeffs-dxy.compute.c"); + +# d^2/dy^2 +simplify( diff(interp_2d_cube_order2_smooth0,y,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size3); +print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", + "2d.coeffs/2d.cube.order2.smooth0/coeffs-dyy.compute.c"); + +################################################################################ + +# +# 2d, cube, order=3, smoothing=0 (size=4) +# + +# interpolating polynomial +interp_2d_cube_order3_smooth0 + := Lagrange_polynomial_interpolant(fn_2d_order3, coeffs_list_2d_order3, + coords_list_2d, posn_list_2d_size4); + +# I +coeffs_as_lc_of_data(%, posn_list_2d_size4); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "2d.coeffs/2d.cube.order3.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_2d_cube_order3_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_2d_size4); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "2d.coeffs/2d.cube.order3.smooth0/coeffs-dx.compute.c"); + +# d/dy +simplify( diff(interp_2d_cube_order3_smooth0,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size4); +print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", + "2d.coeffs/2d.cube.order3.smooth0/coeffs-dy.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_2d_cube_order3_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_2d_size4); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "2d.coeffs/2d.cube.order3.smooth0/coeffs-dxx.compute.c"); + +# d^2/dxdy +simplify( diff(interp_2d_cube_order3_smooth0,x,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size4); +print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", + "2d.coeffs/2d.cube.order3.smooth0/coeffs-dxy.compute.c"); + +# d^2/dy^2 +simplify( diff(interp_2d_cube_order3_smooth0,y,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size4); +print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", + "2d.coeffs/2d.cube.order3.smooth0/coeffs-dyy.compute.c"); + +################################################################################ + +# +# 2d, cube, order=4, smoothing=0 (size=5) +# + +# interpolating polynomial +interp_2d_cube_order4_smooth0 + := Lagrange_polynomial_interpolant(fn_2d_order4, coeffs_list_2d_order4, + coords_list_2d, posn_list_2d_size5); + +# I +coeffs_as_lc_of_data(%, posn_list_2d_size5); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "2d.coeffs/2d.cube.order4.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_2d_cube_order4_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_2d_size5); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "2d.coeffs/2d.cube.order4.smooth0/coeffs-dx.compute.c"); + +# d/dy +simplify( diff(interp_2d_cube_order4_smooth0,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size5); +print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", + "2d.coeffs/2d.cube.order4.smooth0/coeffs-dy.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_2d_cube_order4_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_2d_size5); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "2d.coeffs/2d.cube.order4.smooth0/coeffs-dxx.compute.c"); + +# d^2/dxdy +simplify( diff(interp_2d_cube_order4_smooth0,x,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size5); +print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", + "2d.coeffs/2d.cube.order4.smooth0/coeffs-dxy.compute.c"); + +# d^2/dy^2 +simplify( diff(interp_2d_cube_order4_smooth0,y,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size5); +print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", + "2d.coeffs/2d.cube.order4.smooth0/coeffs-dyy.compute.c"); + +################################################################################ |