diff options
Diffstat (limited to 'src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/fns.maple')
| -rw-r--r-- | src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/fns.maple | 266 |
1 files changed, 266 insertions, 0 deletions
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/fns.maple b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/fns.maple new file mode 100644 index 0000000..6995524 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/fns.maple @@ -0,0 +1,266 @@ +# Maple code to define Lagrange interpolating functions/coords/coeffs +# $Header$ + +################################################################################ + +# +# 1-D 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; + +######################################## + +# coordinates for 1-D interpolating functions +coords_list_1d := [x]; + +######################################## + +# +# coefficients in 1-D interpolating functions +# + +coeffs_list_1d_order1 := [c0, c1]; +coeffs_list_1d_order2 := [c0, c1, c2]; +coeffs_list_1d_order3 := [c0, c1, c2, c3]; +coeffs_list_1d_order4 := [c0, c1, c2, c3, c4]; +coeffs_list_1d_order5 := [c0, c1, c2, c3, c4, c5]; +coeffs_list_1d_order6 := [c0, c1, c2, c3, c4, c5, c6]; + +################################################################################ + +# +# 2-D interpolating functions (maximum degree) +# + +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; + +######################################## + +# coordinates for 2-D interpolating functions +coords_list_2d := [x,y]; + +######################################## + +# +# coefficients in 2-D interpolating functions (maximum degree) +# + +coeffs_list_2d_order1 := [ + c01, + c00, c10 + ]; +coeffs_list_2d_order2 := [ + c02, + c01, c11, + c00, c10, c20 + ]; +coeffs_list_2d_order3 := [ + c03, + c02, c12, + c01, c11, c21, + c00, c10, c20, c30 + ]; +coeffs_list_2d_order4 := [ + c04, + c03, c13, + c02, c12, c22, + c01, c11, c21, c31, + c00, c10, c20, c30, c40 + ]; + +################################################################################ + +# +# 3-D interpolating functions (maximum degree) +# + +fn_3d_order1 := +proc(x,y,z) +# z^0 ----------- ++ c010*y ++ c000 + c100*x +# z^1 ----------- ++ c001*z +end proc; + +fn_3d_order2 := +proc(x,y,z) +# z^0 -------------------------- ++ c020*y^2 ++ c010*y + c110*x*y ++ c000 + c100*x + c200*x^2 +# z^1 -------------------------- ++ c011*y*z ++ c001*z + c101*x*z +# z^2 -------------------------- ++ c002*z^2 +end proc; + +fn_3d_order3 := +proc(x,y,z) +# z^0 ------------------------------------------- ++ c030*y^3 ++ c020*y^2 + c120*x*y^2 ++ c010*y + c110*x*y + c210*x^2*y ++ c000 + c100*x + c200*x^2 + c300*x^3 +# z^1 ------------------------------------------- ++ c021*y^2*z ++ c011*y *z + c111*x*y*z ++ c001 *z + c101*x *z + c201*x^2*z +# z^2 ------------------------------------------- ++ c012*y*z^2 ++ c002 *z^2 + c102*x*z^2 +# z^3 ------------------------------------------- ++ c003 *z^3 +end proc; + +fn_3d_order4 := +proc(x,y,z) +# z^0 -------------------------------------------------------- ++ c040*y^4 ++ c030*y^3 + c130*x*y^3 ++ c020*y^2 + c120*x*y^2 + c220*x^2*y^2 ++ c010*y + c110*x*y + c210*x^2*y + c310*x^3*y ++ c000 + c100*x + c200*x^2 + c300*x^3 + c400*x^4 +# z^1 ------------------------------------------- ++ c031*y^3*z ++ c021*y^2*z + c121*x*y^2*z ++ c011*y *z + c111*x*y *z + c211*x^2*y*z ++ c001 *z + c101*x *z + c201*x^2 *z + c301*x^3*z +# z^2 ------------------------------------------- ++ c022*y^2*z^2 ++ c012*y *z^2 + c112*x*y*z^2 ++ c002 *z^2 + c102*x *z^2 + c202*x^2*z^2 +# z^3 ------------------------------------------- ++ c013*y *z^3 ++ c003 *z^3 + c103*x *z^3 +# z^4 ------------------------------------------- ++ c004 *z^4 +end; + +######################################## + +# coordinates for 3-D interpolating functions +coords_list_3d := [x,y,z]; + +######################################## + +# +# coefficients in 3-D interpolating functions (maximum degree) +# + +coeffs_list_3d_order1 := [ + # z^0 ----- + c010, + c000, c100, + # z^1 ----- + c001 + ]; +coeffs_list_3d_order2 := [ + # z^0 ----------- + c020, + c010, c110, + c000, c100, c200, + # z^1 ----------- + c011, + c001, c101, + # z^2 ----------- + c002 + ]; +coeffs_list_3d_order3 := [ + # z^0 ---------------- + c030, + c020, c120, + c010, c110, c210, + c000, c100, c200, c300, + # z^1 ---------------- + c021, + c011, c111, + c001, c101, c201, + # z^2 ---------------- + c012, + c002, c102, + # z^3 ---------------- + c003 + ]; +coeffs_list_3d_order4 := [ + # z^0 ----------------------- + c040, + c030, c130, + c020, c120, c220, + c010, c110, c210, c310, + c000, c100, c200, c300, c400, + # z^1 ----------------------- + c031, + c021, c121, + c011, c111, c211, + c001, c101, c201, c301, + # z^2 ----------------------- + c022, + c012, c112, + c002, c102, c202, + # z^3 ----------------------- + c013, + c003, c103, + # z^4 ----------------------- + c004 + ]; + +################################################################################ |