拉格朗日函数如何定义？

daphne_wj

比如

1. Clear["Global`*"]
   
2. \[Xi]\[Xi] = {-1, 0, 1}
   
3. i = 1;
   
4. lagrange[\[Xi]_] = 1.;
   
5. Do[If[j != i,
   
6.   lagrange[\[Xi]_] =
   
7.    lagrange[\[Xi]] (\[Xi] - \[Xi]\[Xi][[j]])/(\[Xi]\[Xi][] - \[Xi]\
   
8. \[Xi][[j]])], {j, 1, 3}]

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但是我想实现i同时作为自变量，比如


但这样行不通

chyanog

1. lagrPoly[A_, B_] := Table[Product[If[i != j, (x - j)/(i - j), 1], {j, A}], {i, A}].B;
   
2. lagrPoly2[pts_] :=
   
3. With[{k = Length[pts]},
   
4.   Sum[pts[[j, 2]]* Product[If[j != m, (x - pts[[m, 1]])/(pts[[j, 1]] - pts[[m, 1]]), 1], {m, 1, k}], {j, 1, k}]]
   
5. 
   
6. p = {{1, 2, 3, 4}, {1, 1, 2, 3}};
   
7. pt = Transpose[p]
   
8. lagrPoly @@ p // Simplify
   
9. lagrPoly2@p1 // Simplify
   
10. InterpolatingPolynomial[p1, x] // Simplify

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