Re: Non-sequential composition of pure functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg127805] Re: Non-sequential composition of pure functions*From*: Earl Mitchell <earl.j.mitchell at gmail.com>*Date*: Thu, 23 Aug 2012 20:48:34 -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>

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>