find in list almost equal elements, make new list correspond to position or some list

Question

I have a list of elements called q and wish to compute Total Multiplicity of each element, and put these values in the list tm.

I need to search for almost equal elements, then list them as a new list with each element's position.

This new list would contain several lists, because there are many elements that are equal relative to each other.

Here is an example:

q list from 0 to 200 correspond to certain values in tm length 201 same as q.

q={0,....,200};
tm={1,3,3,7,3,1,7,8,4}

lst of 3 elements {q,tm}={{1,3},{2,3},{4,3}}

lst1 of 1 elements {q,tm}={{0,1},{5,1}}

and so on...

Here is my code: Look at the last line where tm is calculated.

n = 200; "Whole"
q = 200; "Whole"
na = 1; "System"
nb = 199; "Reservoir"


m[n_, q_] := N[(q + n - 1)!/(q!*(n - 1)!)];

qa = Table[q[j], {j, 0, q}]; 
qb = Reverse[Table[q[j], {j, 0, q}]]; 

qa1 = qa[[All,1]]; 
qb1 = qb[[All,1]]; 

"System Multiplicity"
ma = m[na, qa1]; 

"Reservoir Multiplicity"
mb = m[nb, qb1]; 

"Total Multiplicity"
tm = ma*mb

Answer 1

tm = {1, 3, 3, 7, 3, 1, 7, 8, 4};
A = GroupBy[Transpose[{Range[Length[tm]] - 1, tm}], Last]

<|1 -> {{0, 1}, {5, 1}}, 3 -> {{1, 3}, {2, 3}, {4, 3}}, 7 -> {{3, 7}, {6, 7}}, 8 -> {{7, 8}}, 4 -> {{8, 4}}|>

Values[A]

{{{0, 1}, {5, 1}}, {{1, 3}, {2, 3}, {4, 3}}, {{3, 7}, {6, 7}}, {{7, 8}}, {{8, 4}}}

Lookup[A, 1]

{{0, 1}, {5, 1}}

Lookup[A, 3]

{{1, 3}, {2, 3}, {4, 3}}

You say that you want to group "almost equal" elements. I'm not quite sure how you mean this, and propose to use Rounding of the grouping key. For example, grouping by rounding the elements to integer multiples of 3:

A = GroupBy[Transpose[{Range[Length[tm]] - 1, tm}], Round[Last[#], 3] &]

<|0 -> {{0, 1}, {5, 1}}, 3 -> {{1, 3}, {2, 3}, {4, 3}, {8, 4}}, 6 -> {{3, 7}, {6, 7}}, 9 -> {{7, 8}}|>