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-rw-r--r--src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.maple248
1 files changed, 248 insertions, 0 deletions
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.maple b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.maple
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+++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.maple
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+# 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, coeffs_list_3d_order1,
+ coords_list_3d, posn_list_3d_size2);
+
+# I
+coeffs_as_lc_of_data(%, posn_list_3d_size2);
+print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp",
+ "3d.coeffs/3d.cube.order1.smooth0/coeffs-I.compute.c");
+
+# d/dx
+simplify( diff(interp_3d_cube_order1_smooth0,x) );
+coeffs_as_lc_of_data(%, posn_list_3d_size2);
+print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp",
+ "3d.coeffs/3d.cube.order1.smooth0/coeffs-dx.compute.c");
+
+# d/dy
+simplify( diff(interp_3d_cube_order1_smooth0,y) );
+coeffs_as_lc_of_data(%, posn_list_3d_size2);
+print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp",
+ "3d.coeffs/3d.cube.order1.smooth0/coeffs-dy.compute.c");
+
+# d/dz
+simplify( diff(interp_3d_cube_order1_smooth0,z) );
+coeffs_as_lc_of_data(%, posn_list_3d_size2);
+print_coeffs__lc_of_data(%, "coeffs_dz->coeff_", "fp",
+ "3d.coeffs/3d.cube.order1.smooth0/coeffs-dz.compute.c");
+
+################################################################################
+
+#
+# 3d, cube, order=2, smoothing=0 (size=3)
+#
+
+# interpolating polynomial
+interp_3d_cube_order2_smooth0
+ := Lagrange_polynomial_interpolant(fn_3d_order2, coeffs_list_3d_order2,
+ coords_list_3d, posn_list_3d_size3);
+
+# I
+coeffs_as_lc_of_data(%, posn_list_3d_size3);
+print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp",
+ "3d.coeffs/3d.cube.order2.smooth0/coeffs-I.compute.c");
+
+# d/dx
+simplify( diff(interp_3d_cube_order2_smooth0,x) );
+coeffs_as_lc_of_data(%, posn_list_3d_size3);
+print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp",
+ "3d.coeffs/3d.cube.order2.smooth0/coeffs-dx.compute.c");
+
+# d/dy
+simplify( diff(interp_3d_cube_order2_smooth0,y) );
+coeffs_as_lc_of_data(%, posn_list_3d_size3);
+print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp",
+ "3d.coeffs/3d.cube.order2.smooth0/coeffs-dy.compute.c");
+
+# d/dz
+simplify( diff(interp_3d_cube_order2_smooth0,z) );
+coeffs_as_lc_of_data(%, posn_list_3d_size3);
+print_coeffs__lc_of_data(%, "coeffs_dz->coeff_", "fp",
+ "3d.coeffs/3d.cube.order2.smooth0/coeffs-dz.compute.c");
+
+# d^2/dx^2
+simplify( diff(interp_3d_cube_order2_smooth0,x,x) );
+coeffs_as_lc_of_data(%, posn_list_3d_size3);
+print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp",
+ "3d.coeffs/3d.cube.order2.smooth0/coeffs-dxx.compute.c");
+
+# d^2/dxdy
+simplify( diff(interp_3d_cube_order2_smooth0,x,y) );
+coeffs_as_lc_of_data(%, posn_list_3d_size3);
+print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp",
+ "3d.coeffs/3d.cube.order2.smooth0/coeffs-dxy.compute.c");
+
+# d^2/dxdz
+simplify( diff(interp_3d_cube_order2_smooth0,x,z) );
+coeffs_as_lc_of_data(%, posn_list_3d_size3);
+print_coeffs__lc_of_data(%, "coeffs_dxz->coeff_", "fp",
+ "3d.coeffs/3d.cube.order2.smooth0/coeffs-dxz.compute.c");
+
+# d^2/dy^2
+simplify( diff(interp_3d_cube_order2_smooth0,y,y) );
+coeffs_as_lc_of_data(%, posn_list_3d_size3);
+print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp",
+ "3d.coeffs/3d.cube.order2.smooth0/coeffs-dyy.compute.c");
+
+# d^2/dydz
+simplify( diff(interp_3d_cube_order2_smooth0,y,z) );
+coeffs_as_lc_of_data(%, posn_list_3d_size3);
+print_coeffs__lc_of_data(%, "coeffs_dyz->coeff_", "fp",
+ "3d.coeffs/3d.cube.order2.smooth0/coeffs-dyz.compute.c");
+
+# d^2/dz^2
+simplify( diff(interp_3d_cube_order2_smooth0,z,z) );
+coeffs_as_lc_of_data(%, posn_list_3d_size3);
+print_coeffs__lc_of_data(%, "coeffs_dzz->coeff_", "fp",
+ "3d.coeffs/3d.cube.order2.smooth0/coeffs-dzz.compute.c");
+
+################################################################################
+
+#
+# 3d, cube, order=3, smoothing=0 (size=4)
+#
+
+# interpolating polynomial
+interp_3d_cube_order3_smooth0
+ := Lagrange_polynomial_interpolant(fn_3d_order3, coeffs_list_3d_order3,
+ coords_list_3d, posn_list_3d_size4);
+
+# I
+coeffs_as_lc_of_data(%, posn_list_3d_size4);
+print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp",
+ "3d.coeffs/3d.cube.order3.smooth0/coeffs-I.compute.c");
+
+# d/dx
+simplify( diff(interp_3d_cube_order3_smooth0,x) );
+coeffs_as_lc_of_data(%, posn_list_3d_size4);
+print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp",
+ "3d.coeffs/3d.cube.order3.smooth0/coeffs-dx.compute.c");
+
+# d/dy
+simplify( diff(interp_3d_cube_order3_smooth0,y) );
+coeffs_as_lc_of_data(%, posn_list_3d_size4);
+print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp",
+ "3d.coeffs/3d.cube.order3.smooth0/coeffs-dy.compute.c");
+
+# d/dz
+simplify( diff(interp_3d_cube_order3_smooth0,z) );
+coeffs_as_lc_of_data(%, posn_list_3d_size4);
+print_coeffs__lc_of_data(%, "coeffs_dz->coeff_", "fp",
+ "3d.coeffs/3d.cube.order3.smooth0/coeffs-dz.compute.c");
+
+# d^2/dx^2
+simplify( diff(interp_3d_cube_order3_smooth0,x,x) );
+coeffs_as_lc_of_data(%, posn_list_3d_size4);
+print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp",
+ "3d.coeffs/3d.cube.order3.smooth0/coeffs-dxx.compute.c");
+
+# d^2/dxdy
+simplify( diff(interp_3d_cube_order3_smooth0,x,y) );
+coeffs_as_lc_of_data(%, posn_list_3d_size4);
+print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp",
+ "3d.coeffs/3d.cube.order3.smooth0/coeffs-dxy.compute.c");
+
+# d^2/dxdz
+simplify( diff(interp_3d_cube_order3_smooth0,x,z) );
+coeffs_as_lc_of_data(%, posn_list_3d_size4);
+print_coeffs__lc_of_data(%, "coeffs_dxz->coeff_", "fp",
+ "3d.coeffs/3d.cube.order3.smooth0/coeffs-dxz.compute.c");
+
+# d^2/dy^2
+simplify( diff(interp_3d_cube_order3_smooth0,y,y) );
+coeffs_as_lc_of_data(%, posn_list_3d_size4);
+print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp",
+ "3d.coeffs/3d.cube.order3.smooth0/coeffs-dyy.compute.c");
+
+# d^2/dydz
+simplify( diff(interp_3d_cube_order3_smooth0,y,z) );
+coeffs_as_lc_of_data(%, posn_list_3d_size4);
+print_coeffs__lc_of_data(%, "coeffs_dyz->coeff_", "fp",
+ "3d.coeffs/3d.cube.order3.smooth0/coeffs-dyz.compute.c");
+
+# d^2/dz^2
+simplify( diff(interp_3d_cube_order3_smooth0,z,z) );
+coeffs_as_lc_of_data(%, posn_list_3d_size4);
+print_coeffs__lc_of_data(%, "coeffs_dzz->coeff_", "fp",
+ "3d.coeffs/3d.cube.order3.smooth0/coeffs-dzz.compute.c");
+
+################################################################################
+
+#
+# 3d, cube, order=4, smoothing=0 (size=5)
+#
+
+# interpolating polynomial
+interp_3d_cube_order4_smooth0
+ := Lagrange_polynomial_interpolant(fn_3d_order4, coeffs_list_3d_order4,
+ coords_list_3d, posn_list_3d_size5);
+
+# I
+coeffs_as_lc_of_data(%, posn_list_3d_size5);
+print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp",
+ "3d.coeffs/3d.cube.order4.smooth0/coeffs-I.compute.c");
+
+# d/dx
+simplify( diff(interp_3d_cube_order4_smooth0,x) );
+coeffs_as_lc_of_data(%, posn_list_3d_size5);
+print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp",
+ "3d.coeffs/3d.cube.order4.smooth0/coeffs-dx.compute.c");
+
+# d/dy
+simplify( diff(interp_3d_cube_order4_smooth0,y) );
+coeffs_as_lc_of_data(%, posn_list_3d_size5);
+print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp",
+ "3d.coeffs/3d.cube.order4.smooth0/coeffs-dy.compute.c");
+
+# d/dz
+simplify( diff(interp_3d_cube_order4_smooth0,z) );
+coeffs_as_lc_of_data(%, posn_list_3d_size5);
+print_coeffs__lc_of_data(%, "coeffs_dz->coeff_", "fp",
+ "3d.coeffs/3d.cube.order4.smooth0/coeffs-dz.compute.c");
+
+# d^2/dx^2
+simplify( diff(interp_3d_cube_order4_smooth0,x,x) );
+coeffs_as_lc_of_data(%, posn_list_3d_size5);
+print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp",
+ "3d.coeffs/3d.cube.order4.smooth0/coeffs-dxx.compute.c");
+
+# d^2/dxdy
+simplify( diff(interp_3d_cube_order4_smooth0,x,y) );
+coeffs_as_lc_of_data(%, posn_list_3d_size5);
+print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp",
+ "3d.coeffs/3d.cube.order4.smooth0/coeffs-dxy.compute.c");
+
+# d^2/dxdz
+simplify( diff(interp_3d_cube_order4_smooth0,x,z) );
+coeffs_as_lc_of_data(%, posn_list_3d_size5);
+print_coeffs__lc_of_data(%, "coeffs_dxz->coeff_", "fp",
+ "3d.coeffs/3d.cube.order4.smooth0/coeffs-dxz.compute.c");
+
+# d^2/dy^2
+simplify( diff(interp_3d_cube_order4_smooth0,y,y) );
+coeffs_as_lc_of_data(%, posn_list_3d_size5);
+print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp",
+ "3d.coeffs/3d.cube.order4.smooth0/coeffs-dyy.compute.c");
+
+# d^2/dydz
+simplify( diff(interp_3d_cube_order4_smooth0,y,z) );
+coeffs_as_lc_of_data(%, posn_list_3d_size5);
+print_coeffs__lc_of_data(%, "coeffs_dyz->coeff_", "fp",
+ "3d.coeffs/3d.cube.order4.smooth0/coeffs-dyz.compute.c");
+
+# d^2/dz^2
+simplify( diff(interp_3d_cube_order4_smooth0,z,z) );
+coeffs_as_lc_of_data(%, posn_list_3d_size5);
+print_coeffs__lc_of_data(%, "coeffs_dzz->coeff_", "fp",
+ "3d.coeffs/3d.cube.order4.smooth0/coeffs-dzz.compute.c");
+
+################################################################################
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