Re: make a set of conditions without the parameters

*To*: mathgroup at smc.vnet.net*Subject*: [mg57979] Re: make a set of conditions without the parameters*From*: "Ray Koopman" <koopman at sfu.ca>*Date*: Wed, 15 Jun 2005 05:58:12 -0400 (EDT)*References*: <d8jlkt$sum$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Guy Israeli wrote: > Hi, > > I have a big list made out of smaller lists. I want to filter out specific > smaller lists, for instance those who have 1 in the first place and 3 in the > 7th place. > > I know what item cannot be in what place for the condition described above > but the only thing i could do is to do those rules using string like this: > > > t2 = {{0, 0, 0, {3}, 0, {4}, 0, 0, 0}, {0, {7}, {3}, 0, 0, 0, {1}, {4}, 0}, > {{4}, > 0, 0, 0, {7}, 0, 0, 0, {6}}, {0, {9}, {5}, {4}, 0, {6}, 0, 0, 0}, {{8}, 0, > 0, 0, {9}, 0, 0, 0, {3}}, {0, {4}, {6}, {8}, 0, {1}, 0, 0, 0}, {{6}, 0, > 0, 0, 0, 0, 0, 0, {5}}, {0, {2}, {7}, 0, 0, 0, {3}, {8}, 0}, {0, 0, > 0, {5}, 0, {7}, 0, 0, 0}}; > rulesperline = Table[MapIndexed[ToString["#[["] <> ToString[#1] <> > ToString["]]!="] <> ToString[#2] &, (Part[#, i] & /@ Partition[Flatten[t2], > 9] ) // Flatten], {i, 1, 9}]; > > newrules = Fold[(#1 /. ToString["#[[0]]!={"] <> ToString[#2] <> > ToString["}"] -> X) &, > rulesperline, Range[9]] > > which will result in > > {{X, X, #[[4]]!={3}, X, #[[8]]!={5}, X, #[[6]]!={7}, X, X}, {X, #[[7]]!={2}, > X, #[[9]]!={4}, X, #[[4]]!={6}, X, #[[2]]!={8}, X}, {X, #[[3]]!={2}, > X, #[[5]]!={4}, X, #[[6]]!={6}, X, #[[7]]!={8}, X}, {#[[3]]!={1}, X, > X, #[[4]]!={4}, X, #[[8]]!={6}, X, X, #[[5]]!={9}}, {X, X, #[[7]]!={3}, > X, #[[9]]!={5}, X, X, X, X}, {#[[4]]!={1}, X, X, #[[6]]!={4}, > X, #[[1]]!={6}, X, X, #[[7]]!={9}}, {X, #[[1]]!={2}, X, X, X, X, > X, #[[3]]!={8}, X}, {X, #[[4]]!={2}, X, X, X, X, X, #[[8]]!={8}, X}, {X, > X, #[[6]]!={3}, X, #[[3]]!={5}, X, #[[5]]!={7}, X, X}} > > and then to cancel the underlines > > newrulesfull = Select[#, # != "X" &] & /@ newrules > > {{#[[4]]!={3}, #[[8]]!={5}, #[[6]]!={7}}, {#[[7]]!={2}, #[[9]]!={4}, \ > #[[4]]!={6}, #[[2]]!={8}}, {#[[3]]!={2}, #[[5]]!={4}, #[[6]]!={6}, \ > #[[7]]!={8}}, {#[[3]]!={1}, #[[4]]!={4}, #[[8]]!={6}, #[[5]]!={9}}, \ > {#[[7]]!={3}, #[[9]]!={5}}, {#[[4]]!={1}, #[[6]]!={4}, #[[1]]!={6}, \ > #[[7]]!={9}}, {#[[1]]!={2}, #[[3]]!={8}}, {#[[4]]!={2}, #[[8]]!={8}}, \ > {#[[6]]!={3}, #[[3]]!={5}, #[[5]]!={7}}} > > The X here is just to mark that it is unimportnat. > > however, each element is a string here. and now starts my problem > > I would want to do Select[somelist, And[newrulesfull [[1]]]&] meaning it > will give the elements in somelist that match the all of the conditions in > rulesperline[[1]]. But since it is a string it doesn't do much, and > everytime I do ToExpression it gives me a lot of errors because it doesn't > know what #[[4]] or some other number is. > > How can I make a list of rules like that so that I can use Select on those > conditions? Short answer: use x[[{positions}]] != {values} as your test. In[1]:= t2 = {{ 0, 0, 0, {3},0,{4},0, 0, 0 }, { 0,{7},{3}, 0, 0, 0,{1},{4},0 }, {{4},0, 0, 0,{7},0, 0, 0,{6}}, { 0,{9},{5},{4},0,{6},0, 0, 0 }, {{8},0, 0, 0,{9},0, 0, 0,{3}}, { 0,{4},{6},{8},0,{1},0, 0, 0 }, {{6},0, 0, 0, 0, 0, 0, 0,{5}}, { 0,{2},{7}, 0, 0, 0,{3},{8},0 }, { 0, 0, 0, {5},0,{7},0, 0, 0 }}; In[2]:= {u2,v2} = Transpose[Transpose@Select[ Transpose@{Range@Length@#,#},ListQ[#[[2]]]&]&/@t2] Out[2]= {{{4,6}, {2,3,7,8}, {1,5,9}, {2,3,4,6}, {1,5,9}, {2,3,4,6}, {1,9}, {2,3,7,8}, {4,6}}, {{{3},{4}}, {{7},{3},{1},{4}}, {{4},{7},{6}}, {{9},{5},{4},{6}}, {{8},{9},{3}}, {{4},{6},{8},{1}}, {{6},{5}}, {{2},{7},{3},{8}}, {{5},{7}}}} u2[[i]] gives the important positions in row i of t2. v2[[i]] gives the corresponding values. If the important elements in t2 were given as {x} only to mark them as important and to allow for {0}, and if the values in the to-be-inspected lists will all be simple scalars, then Flatten the rows of v2: In[3]:= v2 = Flatten/@v2 Out[3]= {{3,4}, {7,3,1,4}, {4,7,6}, {9,5,4,6}, {8,9,3}, {4,6,8,1}, {6,5}, {2,7,3,8}, {5,7}} In[4]:= x = Table[Random[Integer,9],{10^4},{9}]; In[5]:= Table[Length@Select[x,#[[u2[[i]]]] != v2[[i]]&],{i,Length@t2}] Out[5]= {9896, 10000, 9991, 9998, 9988, 9997, 9912, 9999, 9889} Here are the 9 lists that were rejected by rule 3: In[6]:= With[{i = 3}, Select[x, #[[u2[[i]]]] == v2[[i]]&]] Out[6]= {{4,5,6,8,7,8,4,5,6}, {4,8,9,8,7,6,2,4,6}, {4,7,8,6,7,9,5,8,6}, {4,1,2,7,7,6,0,3,6}, {4,0,1,3,7,3,3,3,6}, {4,2,4,5,7,7,4,9,6}, {4,2,8,0,7,8,3,5,6}, {4,1,3,6,7,8,4,0,6}, {4,2,3,6,7,0,9,2,6}}