Re: Replacement rules that contain function arguments (evaluation
- To: mathgroup at smc.vnet.net
- Subject: [mg105386] Re: Replacement rules that contain function arguments (evaluation
- From: dh <dh at metrohm.com>
- Date: Tue, 1 Dec 2009 04:11:44 -0500 (EST)
- References: <heqesv$1k7$1@smc.vnet.net>
Leo Alekseyev wrote:
> Dear Mathgroup,
>
> I am trying to understand what happens when a pattern from function
> definition appears in the list of replacement rules. In particular,
> consider this:
>
> (* Example (A): *)
> Clear[foo,kij,k];
> foo[k_] := kij /. {kij :> Table[k[[i]] k[[j]], {i, 1, 3}, {j, 1, 3}]}
> foo[{1, 1, 1}]
> (* gives {{1, 1, 1}, {1, 1, 1}, {1, 1, 1}} as expected *)
>
> (* But now, let's put replacement rules into a variable: *)
> (* Example (B): *)
> rrules := {kij :> Table[k[[i]] k[[j]], {i, 1, 3}, {j, 1, 3}]}
> foo[k_] := kij /. rrules
> foo[{1, 1, 1}]
> (* rrules gets evaluated first, hence this fails *)
>
> My question is -- is there a good way to control evaluation such that
> even though rules are defined in a variable, evaluation proceeds as in
> Example (A)?
>
> Below are a couple of things I found to work, but they are somewhat
> syntactically cumbersome.
>
> (* Example (C): works, but have to manually turn off messages *)
> foo[k_] := Evaluate[Off[Part::"partd"]; kij /. rrules]; On[
> Part::"partd"]
> foo[{1, 1, 1}]
>
> (* Example (D): works, but have to rename function argument and wrap
> in a block *)
> foo[kk_] := Block[{k = kk}, kij /. rrules];
> foo[{1, 1, 1}]
>
> Thanks,
> --Leo
>
Hi Leo,
in: rrules := {kij :> Table[k[[i]] k[[j]], {i, 1, 3}, {j, 1, 3}]}
k is a global variable, but in: foo[k_] := kij /.... k it is la local one.
What you can do is to make k local in both cases. E.g.:
Clear[foo, kij, k];
rrules[k_] := {kij :> Table[k[[i]] k[[j]], {i, 1, 3}, {j, 1, 3}]}
foo[k_] := (kij /. rrules[k])
foo[{1, 1, 1}]
Daniel