Re: Functional programming
- To: mathgroup at smc.vnet.net
- Subject: [mg27149] Re: Functional programming
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Thu, 8 Feb 2001 04:40:39 -0500 (EST)
- Organization: Universitaet Leipzig
- References: <95qsgd$spr@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
it is a bit hard to improve the source code when no
input data given.
So only a few comments:
> NDMatrixPower[M_/;And[MatrixQ[M], Length[M]] == Length[M[[1]]], t_
> /; Or[NumericQ[t], Head[t] == Symbol]] :=
> Module[{v, w, r, EigenTable, Multiplicidad, A, B, Sol, k},
(* You don't need to Clear[] the variables in a module because
new unique symbols names are generated when Module is called *)
> Clear[v, w, r, EigenTable, Multiplicidad, Sol, k];
> v = Eigenvalues[M];
(* Why Union[{v,v}] the Union [v] will work and is faster *)
> w = Union[v, v];
(* Hmm what is the task of evaluating w[[1]] but don't use the result ..
*)
> w[[1]];
(* Try
{First[#], Length[#]} & /@ Split[Eigenvalues]
and forget the line below and the Union[]. You Don't need to Sort
the eigenvalues because Eigenvalues[] return already a sorted
list.
*)
> EigenTable = Table[{w[[i]], Count[v, w[[i]]]}, {i, 1,
> Length[w]}];
(* I'm not sure about that, but
Flatten[Table[i - 1, {i, Length[#]}] & /@ Split[v]]
will do the same. *)
> Multiplicidad = Join@@Table[i, {j, 1, Length[EigenTable]},
> {i, 1, EigenTable[[j, 2]]}] - 1;
> A = Table[D[Power[r, j - 1], {r, Multiplicidad[[i]]}] /. r
> -> v[[i]], {i, 1, Length[M]}, {j, 1, Length[M]}];
> B = Table[D[Power[r, k], {r, Multiplicidad[[i]]}] /. r ->
> v[[i]], {i, 1, Length[M]}, {j, 1, 1}];
> Sol = Transpose[LinearSolve[A, B]][[1]];
> Plus@@Table[MatrixPower[M, i - 1]*Sol[[i]], {i, 1,
> Length[v]}] /. k -> t];
For the rest I would like to see the original formulas.
Hope that helps
Jens