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MathGroup Archive 2007

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Intersection question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75172] Intersection question
  • From: János <janos.lobb at yale.edu>
  • Date: Thu, 19 Apr 2007 04:33:35 -0400 (EDT)

Hi,

I have a nested list with 250 elements, where the elements of the 
list are also nested lists - down 4th deep.  The first element in the 
list has 249 elements, the second element has 248 elements, etc...

Here is how the 246, 247, 248, 249 and 250 elements of the list are 
for illustration:

In[116]:=
vch[[246]]
Out[116]=
{{{}, {}, {}, {{120}},
    {{22}, {71}, {113}, {179},
     {182}, {250}, {286},
     {359}, {439}, {448},
     {451}, {455}},
    {{35}, {46}, {51}, {63},
     {75}, {83}, {88}, {92},
     {95}, {96}, {101}, {119},
     {131}, {141}, {143},
     {152}, {168}, {184},
     {204}, {217}, {247},
     {258}, {259}, {274},
     {275}, {291}, {294},
     {295}, {302}, {318},
     {327}, {342}, {344},
     {346}, {365}, {367},
     {369}, {378}, {391},
     {405}, {420}, {423},
     {430}, {438}, {442}},
    {{16}, {18}, {19}, {24},
     {26}, {44}, {84}, {85},
     {144}, {188}, {191},
     {205}, {216}, {221},
     {238}, {251}, {260},
     {264}, {292}, {332},
     {336}, {339}, {348},
     {352}, {376}, {379},
     {392}, {398}, {404},
     {411}, {412}, {419}},
    {{45}, {268}, {446}}, {},
    {}, {}}, {{}, {}, {}, {},
    {}, {}, {}, {}, {}, {},
    {}}, {{}, {}, {}, {}, {},
    {}, {}, {}, {}, {}, {}},
   {{}, {}, {}, {}, {}, {},
    {}, {}, {}, {}, {}}}

In[121]:=
vch[[247]]
Out[121]=
{{{}, {}, {}, {}, {}, {}, {},
    {}, {}, {}, {}},
   {{}, {}, {}, {}, {}, {},
    {}, {}, {}, {}, {}},
   {{}, {}, {}, {}, {}, {},
    {}, {}, {}, {}, {}}}



In[56]:=
vch[[248]]
Out[56]=
{{{}, {}, {}, {}, {}, {}, {},
    {}, {}, {{130}}, {{263}},
    {{233}}, {}, {}, {},
    {{198}}, {}, {}, {}, {}},
   {{}, {}, {}, {}, {}, {},
    {}, {}, {}, {}, {}, {},
    {}, {}, {}, {}, {}, {},
    {}}}

In[61]:=
vch[[249]]
Out[61]=
{{{}, {}, {}, {}, {{87}},
    {{11}, {58}, {242}},
    {{5}, {22}, {77}, {81},
     {107}, {116}, {167},
     {182}, {196}, {227},
     {275}, {335}, {367},
     {394}}, {{28}, {45},
     {68}, {126}, {129},
     {145}, {175}, {185},
     {213}, {218}, {245},
     {294}, {329}, {336},
     {352}, {407}, {458}},
    {{2}, {48}, {85}, {189},
     {200}, {282}, {300},
     {345}, {357}}, {{293}},
    {{60}}, {{6}, {101}},
    {{429}}, {{296}}, {{302}},
    {}, {}, {}, {}}}

In[66]:=
vch[[250]]
Out[66]=
{}

The "numbers" shown in the outputs above are identifiers or name tags.
To find out where let say ID=1 occurs in the vch list, I do the 
following:

In[79]:=
Position[vch, {1}]
Out[79]=
{{3, 1, 9, 1}, {5, 1, 10, 1},
   {10, 1, 10, 1}, {15, 1, 9,
    1}, {25, 1, 7, 1},
   {29, 1, 9, 1}, {61, 1, 9,
    1}, {70, 1, 10, 1},
   {79, 1, 10, 1}, {81, 1, 12,
    1}, {86, 1, 13, 1},
   {90, 1, 9, 1}, {129, 1, 9,
    1}, {143, 1, 8, 1},
   {147, 1, 11, 1},
   {164, 1, 13, 1},
   {169, 1, 11, 1},
   {182, 1, 10, 1},
   {186, 1, 14, 1},
   {221, 1, 14, 1},
   {227, 1, 12, 1},
   {232, 1, 9, 1}}

To find out where let say ID=2 occurs in the vch list I do the 
following:

In[88]:=
Position[vch, {2}]
Out[88]=
{{6, 1, 9, 1}, {6, 2, 9, 1},
   {7, 1, 9, 1}, {21, 1, 8,
    1}, {27, 1, 7, 1},
   {29, 1, 11, 1}, {31, 1, 12,
    1}, {42, 1, 13, 1},
   {42, 2, 13, 1}, {43, 1, 13,
    1}, {61, 1, 12, 1},
   {68, 1, 10, 1}, {82, 1, 10,
    1}, {93, 1, 13, 1},
   {95, 1, 15, 1},
   {113, 1, 13, 1},
   {123, 1, 10, 1},
   {136, 1, 12, 1},
   {139, 1, 11, 1},
   {141, 1, 13, 1},
   {174, 1, 13, 1},
   {188, 1, 8, 1},
   {198, 1, 10, 1},
   {203, 1, 10, 1},
   {219, 1, 9, 1},
   {230, 1, 15, 1},
   {249, 1, 9, 1}}

If I am just interested in not in the exact occurrence like {6, 1, 9, =

1}, but just in the first element of this result - the 6 -,  I do the =

following for IDs 1 and 2:

In[93]:=
First /@ Position[vch, {1}]
Out[93]=
{3, 5, 10, 15, 25, 29, 61,
   70, 79, 81, 86, 90, 129,
   143, 147, 164, 169, 182,
   186, 221, 227, 232}

In[94]:=
First /@ Position[vch, {2}]
Out[94]=
{6, 6, 7, 21, 27, 29, 31, 42,
   42, 43, 61, 68, 82, 93, 95,
   113, 123, 136, 139, 141,
   174, 188, 198, 203, 219,
   230, 249}

The Intersection of these two lists would show me those list elements =

in vch where the two IDs can be found together:

In[50]:=
Intersection[First /@
    Position[vch, {1}],
   First /@ Position[vch, {2}]]
Out[50]=
{29, 61}

Now, I would like to know this result not just for IDs 1 and 2, but 
for any pairs of IDS from 1 to 459.  For me, being a newbie, the 
simplest thing to do is to create a nested table like:

ti = Table[Table[Length[
       Intersection[First /@
         Position[vch, {i}],
        First /@ Position[vch,
          {j}]]], {j, 1,
       Length[spsplit]}],
     {i, 1, Length[spsplit]}];

Length[spsplit] is 459.

On my 2Ghz G5 with two processors this nested table creation takes 2 
days.  I am wondering if there is another way to get the same result 
from vch...... FASTer.

Thanks ahead,

J=E1nos









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