Classifying things into kinds

Increasingly often I want to do the following, so I want a simple vectorised way to do it - no "for" loops.

I have n things. Each thing is of one of m types. Coding the things as 1:n and the types as 1:m I can describe this data by an n-vector x where each x(j) is an integer in 1:m saying what type thing j has.

E.g. let n=7, m=5, then x = [2 3 1 3 5 1 2] says thing 1 has type 2, thing 2 has type 3 etc.

I want to convert between this form and the (obviously equivalent) form of a *partition* of 1:n into m subsets where the i'th subset lists all the things that have type i. This shall be a cell vector c of length m where c{i} is the set {j such that x(j)=i}, written as an ordinary vector in ascending order.

For the example, c is {[3], [1 7], [2 4], [] ,[5]}. Note c{4} is the empty vector because type 4 wasn't used.

Obviously, one can convert x to c and c to x by simple "for" loops but I want to avoid it.

I can do "x to c" by

c = arrayfun(@(i)find(x==i),1:m,'UniformOutput',false);

but (1) it looks clumsy, (2) implicitly it applies "find" to x a total of m times whereas a single pass through x should do.

Imagine n=10,000 and m=10, say. I welcome a better solution.

[John Pryce]

Sorry I should have written c is {[3 6], [1 7], [2 4], [] ,[5]}.

[John Pryce]

Thanks! This is just what I was looking for.

Answer 1

[Ameer Hamza]

You can use accumarray()

x = [2 3 1 3 5 1 2];
c = accumarray(x(:), (1:numel(x)), [], @(x) {x})

Result

>> c{:}
ans =
     3
     6
ans =
     1
     7
ans =
     2
     4
ans =
     []
ans =
     5