RE: Simplify a module
- To: mathgroup at smc.vnet.net
- Subject: [mg39487] RE: Simplify a module
- From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
- Date: Wed, 19 Feb 2003 04:42:05 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Bobby, dcalc4[ein_] := Block[{a1, a2, a3, e = ein}, {T1, M1, T2, M2, T3, M3} = {2, 392, 3, 147, 47, 24}; Evaluate[sw /@ mytab]; Mod[a1*T1*M1 + a2*T2*M2 + a3*T3*M3, 1176]] does it. BTW, sw[{{a_, base_}, seq_}] := (a = Switch[Mod[e, base], Evaluate[Sequence @@ seq], _, 0]) Evaluate[a] is not needed after destructuring. Nonetheless, I'd not recommend this solution neither my dcalc2, as I hopefully have made clear in my first posting, more so something like in my PS, as e.g. ct1 = ctab[[All, 1, 2]]; (* get rid of hard-wired names *) ct2 = ctab[[All, 2]]; (* I'd not flatten this *) ct3 = {2, 3, 47}; (* perhaps better Transpose[{ct3,ct4}] ? *) ct4 = {392, 147, 24}; dcalc3x[e_] := Mod[#, 1176] &[ MapThread[ Switch[Mod[e, #1], Evaluate[Apply[Sequence, #2, {0, 1}]], _, 0 ] &, {ct1, ct2}].(ct3*ct4)] Now rework ct1,...,ct4 into a single structure and supply this as a second parameter to dcalc. -- Hartmut Wolf >-----Original Message----- >From: Dr Bob [mailto:drbob at bigfoot.com] To: mathgroup at smc.vnet.net >Sent: Tuesday, February 18, 2003 6:10 PM >To: Wolf, Hartmut; mathgroup at smc.vnet.net >Subject: [mg39487] Re: Simplify a module > > >Here's a marginally simpler solution: > >Cases[Hold[ > If[Mod[e, 3] == 1, a1 = 1]; If[Mod[e, 3] == 2, a1 = 2]; > If[Mod[e, 8] == 1, a2 = 1]; > If[Mod[e, 8] == 3, a2 = 3]; If[Mod[e, 8] == 5, a2 = 5]; > If[Mod[e, 8] == 7, a2 = 7]; > If[Mod[e, 49] == 1, a3 = 1]; If[Mod[e, 49] == 2, a3 = 25]; > If[Mod[e, 49] == 3, a3 = 33]; If[Mod[e, 49] == 4, a3 = 37]; > If[Mod[e, 49] == 5, a3 = 10]; If[Mod[e, 49] == 6, a3 = 41]; > If[Mod[e, 49] == 8, a3 = 43]; If[Mod[e, 49] == 9, a3 = 11]; > If[Mod[e, 49] == 10, a3 = 5]; If[Mod[e, 49] == 11, a3 = 9]; > If[Mod[e, 49] == 12, a3 = 45]; If[Mod[e, 49] == 13, a3 = 34]; > If[Mod[e, 49] == 15, a3 = 36]; If[Mod[e, 49] == 16, a3 = 46]; > If[Mod[e, 49] == 17, a3 = 26]; If[Mod[e, 49] == 18, a3 = 30]; > If[Mod[e, 49] == 19, a3 = 31]; If[Mod[e, 49] == 20, a3 = 27]; > If[Mod[e, 49] == 22, a3 = 29]; If[Mod[e, 49] == 23, a3 = 32]; > If[Mod[e, 49] == 24, a3 = 47]; If[Mod[e, 49] == 25, a3 = 2]; > If[Mod[e, 49] == 26, a3 = 17]; If[Mod[e, 49] == 27, a3 = 20]; > If[Mod[e, 49] == 29, a3 = 22]; If[Mod[e, 49] == 30, a3 = 18]; > If[Mod[e, 49] == 31, a3 = 19]; If[Mod[e, 49] == 32, a3 = 23]; > If[Mod[e, 49] == 33, a3 = 3]; If[Mod[e, 49] == 34, a3 = 13]; > If[Mod[e, 49] == 36, a3 = 15]; If[Mod[e, 49] == 37, a3 = 4]; > If[Mod[e, 49] == 38, a3 = 40]; If[Mod[e, 49] == 39, a3 = 44]; > If[Mod[e, 49] == 40, a3 = 38]; If[Mod[e, 49] == 41, a3 = 6]; > If[Mod[e, 49] == 43, a3 = 8]; If[Mod[e, 49] == 44, a3 = 39]; > If[Mod[e, 49] == 45, a3 = 12]; If[Mod[e, 49] == 46, a3 = 16]; > If[Mod[e, 49] == 47, a3 = 24]; If[Mod[e, 49] == 48, a3 = 48];], > If[ > Mod[_, g_] == h_, ax_ = k_] :> {ax, g, h, k}, Infinity]; >split = Split[%, #1[[1]] === #2[[1]] &]; >mytab = {#[[1, {1, 2}]], Flatten[#[[All, {3, 4}]]]} & /@ split; >dcalc3[e_] := Block[{a1, a2, a3}, {T1, M1, T2, M2, T3, M3} = >{2, 392, 3, >147, 47, 24}; > (Evaluate[#[[1, 1]]] = Switch[Mod[e, #[[ > 1, 2]]], Evaluate[Sequence @@ #[[2]]], _, 0]) & /@ mytab; > Mod[a1*T1*M1 + a2*T2*M2 + a3*T3*M3, 1176]] > >dcalc3@# == dcalc2@# & /@ Range[1176]; >And @@ % > >True > >Could someone explain why something like the following doesn't >work? I've >tried several versions and haven't been able to use a named >function like >sw in place of the identical in-line function. > >sw[{{a_, base_}, seq_}] := (Evaluate[a] = Switch[Mod[e, base], >Evaluate[Sequence @@ seq], _, 0]) >dcalc4[e_] := Block[{a1, a2, > a3}, {T1, M1, T2, M2, T3, M3} = {2, 392, 3, 147, 47, 24}; > Evaluate[sw /@ mytab]; > Mod[a1*T1*M1 + a2*T2*M2 + a3*T3*M3, 1176]] > >Bobby > >On Mon, 17 Feb 2003 18:17:34 -0500 (EST), Wolf, Hartmut ><Hartmut.Wolf@t- >systems.com> wrote: > >> >>> -----Original Message----- >>> From: flip [mailto:flip_alpha at safebunch.com] To: mathgroup at smc.vnet.net >> To: mathgroup at smc.vnet.net >>> Sent: Sunday, February 16, 2003 12:14 PM >>> To: mathgroup at smc.vnet.net >>> Subject: [mg39487] Simplify a module >>> >>> >>> Hi All, >>> >>> Can someone recommend a simplification to this module (just >a bunch of >>> if >>> checks). >>> >>> It was specified to be done that way (and I know how to >sove the problem >>> using PowerMod in one step, so please bear with me here). >>> >>> Thanks, Flip >>> >>> (* to email me remove "_alpha" *) >>> >>> Anyway, here goes. >>> >>> dcalc[ein_] := Module[{e = ein, a1 = 0, a2 = 0, a3 = 0}, >>> {T1, M1, T2, M2, T3, M3} = {2, 392, 3, 147, 47, 24}; >>> If[Mod[e, 3] == 1, a1 = 1]; If[Mod[e, 3] == 2, a1 = 2]; >>> If[Mod[e, 8] == 1, a2 = 1]; >>> If[Mod[e, 8] == 3, a2 = 3]; If[Mod[e, 8] == 5, a2 = 5]; >>> If[Mod[e, 8] == 7, a2 = 7]; >>> If[Mod[e, 49] == 1, a3 = 1]; If[Mod[e, 49] == 2, a3 = 25]; >>> If[Mod[e, 49] == 3, a3 = 33]; If[Mod[e, 49] == 4, a3 = 37]; >>> If[Mod[e, 49] == 5, a3 = 10]; If[Mod[e, 49] == 6, a3 = 41]; >>> If[Mod[e, 49] == 8, a3 = 43]; If[Mod[e, 49] == 9, a3 = 11]; >>> If[Mod[e, 49] == 10, a3 = 5]; If[Mod[e, 49] == 11, a3 = 9]; >>> If[Mod[e, 49] == 12, a3 = 45]; If[Mod[e, 49] == 13, a3 = 34]; >>> If[Mod[e, 49] == 15, a3 = 36]; If[Mod[e, 49] == 16, a3 = 46]; >>> If[Mod[e, 49] == 17, a3 = 26]; If[Mod[e, 49] == 18, a3 = 30]; >>> If[Mod[e, 49] == 19, a3 = 31]; If[Mod[e, 49] == 20, a3 = 27]; >>> If[Mod[e, 49] == 22, a3 = 29]; If[Mod[e, 49] == 23, a3 = 32]; >>> If[Mod[e, 49] == 24, a3 = 47]; If[Mod[e, 49] == 25, a3 = 2]; >>> If[Mod[e, 49] == 26, a3 = 17]; If[Mod[e, 49] == 27, a3 = 20]; >>> If[Mod[e, 49] == 29, a3 = 22]; If[Mod[e, 49] == 30, a3 = 18]; >>> If[Mod[e, 49] == 31, a3 = 19]; If[Mod[e, 49] == 32, a3 = 23]; >>> If[Mod[e, 49] == 33, a3 = 3]; If[Mod[e, 49] == 34, a3 = 13]; >>> If[Mod[e, 49] == 36, a3 = 15]; If[Mod[e, 49] == 37, a3 = 4]; >>> If[Mod[e, 49] == 38, a3 = 40]; If[Mod[e, 49] == 39, a3 = 44]; >>> If[Mod[e, 49] == 40, a3 = 38]; If[Mod[e, 49] == 41, a3 = 6]; >>> If[Mod[e, 49] == 43, a3 = 8]; If[Mod[e, 49] == 44, a3 = 39]; >>> If[Mod[e, 49] == 45, a3 = 12]; If[Mod[e, 49] == 46, a3 = 16]; >>> If[Mod[e, 49] == 47, a3 = 24]; If[Mod[e, 49] == 48, a3 = 48]; >>> Return[Mod[a1*T1*M1 + a2*T2*M2 + a3*T3*M3, 1176]]] >>> >>> >>> >>> >>> >>> >>> >>> >> Flip, >> >> to "simplify" your module, resort to metaprogramming, i.e. >write another >> program that constructs that module from data you supply >from a table. >> >> The following is a somewhat foolish example, just to show >the idea. To >> begin with, I cut out part of your coding... >> >> In[2]:= >> Cases[Hold[If[Mod[e, 3] == 1, a1 = 1]; If[Mod[e, 3] == 2, a1 = 2]; >> If[Mod[e, 8] == 1, a2 = 1]; >> ......,and so on...... >> If[Mod[e, 49] == 47, a3 = 24]; If[Mod[e, 49] == 48, a3 = 48];], >> If[Mod[_, g_] == h_, ax_ = k_] :> {ax, g, h, k}, Infinity]; >> >> ...to extract your data >> >> In[3]:= Split[%, #1[[1]] === #2[[1]] &]; >> >> ...group, and transform it to a handy structure >> >> In[4]:= ctab = {#[[1, {1, 2}]], #[[All, {3, 4}]]} & /@ %; >> >> >> Of course in future you'll just start with ctab, or >something similar. >> >> >> >> In[5]:= dcalc2[e_] := Block[{a1, a2, a3}, {T1, M1, T2, M2, >T3, M3} = {2, >> 392, 3, 147, 47, 24}; >> (Evaluate[#[[1, 1]]] = Switch[Mod[e, #[[1, 2]]], >Evaluate[Apply[Sequence, >> #[[2, All]], {0, 1}]], _, 0 ]) & /@ ctab; >> Mod[a1*T1*M1 + a2*T2*M2 + a3*T3*M3, 1176]] >> >> In[6]:= d100 = dcalc /@ Range[100]; >> In[7]:= d100x = dcalc2 /@ Range[100]; >> In[8]:= d100 == d100x >> Out[8]= True >> >> As said, just to get an idea; this is not a suggestion as >how to code it, >> don't use the hard-wired symbols a1, a2, a3 between ctab and dcalc2 >> (generate them as needed) or thread, avoid global T1, M2, etc. Your >> exercise. >> >> -- >> Hartmut >> >> >> PS, perhaps something like >> >> dcalc3[e_] := Mod[Plus @@ MapThread[ >> Switch[Mod[e, #1[[1, 2]]], Evaluate[Apply[Sequence, #1[[2, >All]], {0, >> 1}]], >> _, 0 ]*#2*#3 &, {ctab, {2, 3, 47}, {392, 147, 24}}], 1176] >> >> (a1, etc. not used) >> >> >> > > > >-- >majort at cox-internet.com >Bobby R. Treat >
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- Re: RE: Simplify a module
- From: Dr Bob <drbob@bigfoot.com>
- Re: RE: Simplify a module