Re: Non-sequential composition of pure functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg127811] Re: Non-sequential composition of pure functions*From*: Earl Mitchell <earl.j.mitchell at gmail.com>*Date*: Thu, 23 Aug 2012 20:50:34 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <20120822062720.4DD8A6850@smc.vnet.net>

I ended up getting the solution to this guy earlier in the thread. I've resent it below for reference. If anyone is interested in taking on a side-M project (creating an M version of the RandomForest algorithm is the current task) send me a personal e-mail at earl.j.mitchell at gmail.com. This group is excellent, thanks again - Mitch On Wed, Aug 22, 2012 at 9:16 AM, Earl Mitchell <earl.j.mitchell at gmail.com>wrote: > Thanks again - I think I got it. The solution - slightly modified from > what Albert sent - was this (and if there are obvious improvements to what > I do here I'd love to hear them, learning a lot even though I program in M > every day!): > > originalconds = {If[#1[[4]] <= 6, 4.52] &, > If[(#1[[4]] <= 6) && (#1[[4]] <= 0), 4.47] &, > If[(#1[[4]] <= 6) && (#1[[4]] <= 0) && (#1[[5]] <= 0), 4.40] &, > If[(#1[[4]] <= 6) && (#1[[4]] <= 0) && (#1[[5]] <= 0) && (#1[[1]] <= 0), > 4.02] &, > If[(#1[[4]] <= 6) && (#1[[4]] <= 0) && (#1[[5]] <= 0) && (#1[[1]] <= > 0) && (#1[[3]] <= 0), 4.30] &} > > > out472:= Join[{originalconds[[1]]}, > Table[ > With[{ > condlist = Take[originalconds, i] > }, > With[{ > action = First@Last[condlist /. If[c_, a_] :> (a) /. Function -> > List] > }, > If @@@ (Function @@ {Join[ > And @@@ > Hold @@ {Flatten[ > Hold @@ Cases[condlist, Function[If[c_, a_]] :> Hold[c], > {1}]]}, > Hold[action]]})]], {i, 2, Length[originalconds]}]] > > > out472= {If[#1[[4]] <= 6, 4.52] &, > If[#1[[4]] <= 6 && (#1[[4]] <= 6 && #1[[4]] <= 0), 4.47] &, > If[#1[[4]] <= 6 && (#1[[4]] <= 6 && #1[[4]] <= 0) && (#1[[4]] <= 6 && > #1[[4]] <= 0 && #1[[5]] <= 0), 4.4] &, > > If[#1[[4]] <= > 6 && (#1[[4]] <= 6 && #1[[4]] <= 0) && (#1[[4]] <= 6 && #1[[4]] <= > 0 && #1[[5]] <= 0) && (#1[[4]] <= 6 && #1[[4]] <= 0 && #1[[5]] <= > 0 && #1[[1]] <= 0), 4.02] &, > If[#1[[4]] <= > 6 && (#1[[4]] <= 6 && #1[[4]] <= 0) && (#1[[4]] <= 6 && #1[[4]] <= > 0 && #1[[5]] <= 0) && (#1[[4]] <= 6 && #1[[4]] <= 0 && #1[[5]] <= > 0 && #1[[1]] <= 0) && (#1[[4]] <= 6 && #1[[4]] <= 0 && #1[[5]] <= > 0 && #1[[1]] <= 0 && #1[[3]] <= 0), 4.3] &} > > > Thanks again! > > > Mitch > On Wed, Aug 22, 2012 at 9:05 AM, Sseziwa Mukasa <mukasa at gmail.com> wrote: > >> On approach: >> >> Extract the list of conditions from the functions: >> >> (Debug) In[49]:= >> list = {(If[cond1[#[[1]]], action]) &, (If[cond2[#[[2]]], >> action]) &, (If[cond3[#[[3]]], action]) &}; >> >> (Debug) In[50]:= list /. (If[cond_, action_] &) -> (cond &) >> >> (Debug) Out[50]= {cond1[#1[[1]]] &, cond2[#1[[2]]] &, >> cond3[#1[[3]]] &} >> >> Then you can use Through and And to evaluate all the conditions: >> >> (Debug) In[53]:= And @@ >> Through[(list /. (If[cond_, action_] &) -> (cond &))[{arg1, arg2, >> arg3}]] >> >> (Debug) Out[53]= cond1[arg1] && cond2[arg2] && cond3[arg3] >> >> At this point all you need to do is extract the action from one of the >> functions, or all of them if they are different, and perform based on the >> result of the conditional. Putting it all together: >> >> (Debug) In[55]:= >> combineConditionalFunctions[functions_ {If[_, _] & ..}, >> arguments_ {__}] := >> Module[{performAction = >> And @@ Through[(functions /. (If[cond_, action_] &) -> (cond &))[ >> arguments]], >> action = functions[[1]] /. (If[_, action_]) & -> action}, >> If[performAction, action]] >> >> (Debug) In[56]:= combineConditionalFunctions[list, {arg1, arg2, arg3}] >> >> (Debug) Out[56]= If[ >> cond1[arg1] && cond2[arg2] && cond3[arg3], action$900] >> >> >> On Wed, Aug 22, 2012 at 2:27 AM, Earl Mitchell <earl.j.mitchell at gmail.com >> > wrote: >> >>> >>> Hi All, >>> >>> I have a list of pure functions (If[Conditional[#[[1]]],Action]& >>> statements) and I want to compose them into one large pure function >>> >>> If[FirstConditional[#[[1]]]&&SecondConditional[#[[6]]]&&ThirdConditional[#[[foo]]],Action]&. >>> They are to be applied to a list of values, and the conditionals checked >>> for multiple columns for a given element of a list. >>> >>> I'm having problems joining these things together - to the point that >>> I've >>> considered converting them all to strings and doing the tedious >>> (hackie) string manipulations to get the final function in the right >>> form. >>> Any recommendations on how to do this? I found Composition[] but it >>> nests >>> the functions - and I want to combine them. >>> >>> Thanks! >>> >>> Mitch >>> >> >> >

**References**:**Non-sequential composition of pure functions***From:*Earl Mitchell <earl.j.mitchell@gmail.com>