RE: Re: Changing delayed formula

*To*: mathgroup at smc.vnet.net*Subject*: [mg35523] RE: [mg35487] Re: [mg35461] Changing delayed formula*From*: "DrBob" <majort at cox-internet.com>*Date*: Wed, 17 Jul 2002 02:09:21 -0400 (EDT)*Reply-to*: <drbob at bigfoot.com>*Sender*: owner-wri-mathgroup at wolfram.com

For large arrays, one method might be much faster than another, and we've gotten into little wars, looking for the fastest. Distribute is far more intuitive than the others, if the matrix isn't huge. If the matrix IS huge, you might need a more complicated solution than any of the ones you've seen so far. Bobby -----Original Message----- From: Julio Vera [mailto:jvera at adinet.com.uy] To: mathgroup at smc.vnet.net Subject: [mg35523] [mg35487] Re: [mg35461] Changing delayed formula Thanks, Bobby. This way it works exactly the same as Outer. It appears to me that there is only slight differences between certain Mathematica formulas, like Array, Outer, or Distribute. Julio ----- Original Message ----- From: "DrBob" <majort at cox-internet.com> To: mathgroup at smc.vnet.net Subject: [mg35523] [mg35487] RE: [mg35461] Changing delayed formula > I forgot you were trying to distribute And, rather than List: > > des = {{11, 12, 13, 14}, {21, 22, 23}, {31, 32}, {41, 42, 43, 44, 45}}; > Distribute[And @@ des, List] > > Bobby > > -----Original Message----- > From: Julio Vera [mailto:jvera at adinet.com.uy] To: mathgroup at smc.vnet.net > Sent: Saturday, July 13, 2002 2:49 AM > Subject: [mg35523] [mg35487] [mg35461] Changing delayed formula > > > Hi, > > I have a list of lists. it's length (the number of sublists it > contains) varies. > > In[1]:= des={{11,12,13,14},{21,22,23},{31,32},{41,42,43,44,45}} > > Out[1]:= {{11,12,13,14},{21,22,23},{31,32},{41,42,43,44,45}} > > The length of each of the sublists is arbitrary, too. So I have this > list of lengths. > > In[2]:= elems=Flatten[Table[Dimensions[des[[i]]],{i,Length[des]}]] > > Out[2]:= {4,3,2,5} > > I want to obtain the list of all combinations of one element of each > sublist, bounded by &&. This will be a list of 120 elements, each of > them with 4 components. I define a delayed formula, and apply Array to > it (the characters printed as bold are subscripts in the Mathematica > notebook). > > In[3]:= > cond4[a_,b_,g_,d_]:=des[[1,a]]&&des[[2,b]]&&des[[3,g]]&&des[[4,d]] > > In[4]:= combi=Flatten[Array[condLength[des],elems]] > > Out[4]:= > {11&&21&&31&&41,11&&21&&31&&42,11&&21&&31&&43,11&&21&&31&&44,... > > ...14&&23&&32&&42,14&&23&&32&&43,14&&23&&32&&44,14&&23&&32&&45} > > Since the length of des varies, I would have to define cond each time. > For instance: > > cond3[a_,b_,g_,d_]:=des[[1,a]]&&des[[2,b]]&&des[[3,g]] > > I would like to make a definition for cond that would adapt to these > changes automatically. > > I arrived to this solution, which is not rejected by Mathematica, but > does not work, either. > > In[5]:= d[a_,b_]:=des[[a,b<>"_"]] > > In[6]:= Unprotect[ReplaceAll] > > Out[6]:= {ReplaceAll} > > In[7]:= > condLength[des][Table[FromCharacterCode[944+i]<>"_",{i,Length[des]}]]/.{ > a__}=AEa:=Apply[And,Table[d[i,FromCharacterCode[944+i]<>"_"],{i,Length[d > es]}]] > > In fact, I quit the kernel and rerun all the cells except the one > written here as In[3]. If not, the definition for cond4 remains as it > was. I was not able to clear cond4 individually. > > Thanks very much for anything you can suggest. > > Best regards, > > Julio Vera > > > >