Using Accumarray with @maxk instead of @max?

Hi,

Say you have three vectors:

a = [1;2;3;4;5;1;3;1;4];
b = [100;200;300;400;500;400;300;200;100];
c = [123;456;221;111;800;1000;10;25;150];

And you use accumarray so that:

maxval = sparse(accumarray(a(:,1),max(b,c),[],@max))

You get:

maxval =

   (1,1)           1000
   (2,1)            456
   (3,1)            300
   (4,1)            400
   (5,1)            800

Now lets, say I have a whole lot of variables for each subs (something like 2000 each), and I want the average of the top 3 values using the same method. How can I accomplish this? For example, in the same problem, I want my output to be:

The top three values with subs 1 are: 100,400 and 200, so their average is 233.33 and the first row in my sparse matrix is:

maxval =

   (1,1)           1000

and so on.

Is it maybe possible to use maxk as a function handle?

Answer 1

[Walter Roberson]

accumarray(a(:,1), max(b,c), [], @(v) mean(maxk(v,3)), 0, true)   %final parameter is sparse flag

[Ayman Al-Sukhon]

Sorry for the late reply, had a few other kinks to work out. This is a very solid answer and exactly what I was looking for. Can you explain the @v to me?

[dpb]

@() is the preamble to define an anonymous function. The v is the dummy argument variable name Walter chose; you'll see it reflected in the argument to maxk().

All the details about anonymous functions is in the documentation under the general subject of functions.

[Ayman Al-Sukhon]

I see, thank you very much dpb!

Answer 2

[dpb]

Don't see anyway around with accumarray because the VAL parameter must be 1:1 with rows of SUBS; use findgroups/splitapply or varfun (altho latter must be table or timetable).

g=findgroups(a);
mnk=splitapply(@(x) mean(maxk(x,3)),b,g);

yields

>> mnk =
  233.3333
  200.0000
  300.0000
  250.0000
  500.0000
>> 

[Walter Roberson]

This is not needed. accumarray() with non-default function, uses the subs as a grouping variable, records all of the values with the same value of the grouping variable, and applies the given function to the valaues. (With the default function of sum(), it can take the short-cut of just totaling the values instead of having to record them all in a vector first.)

[dpb]

Ah, yeah, good point...got sidetracked to implement the request rather than just solving the problem.

For things needing something other than the sum() as a starting point, however, may need to collect the inputs first .

[Sean de Wolski]

Oftentimes this can be worked around by 1:numel(vals) as the vals vector and then indexing into the original data with the index rather than having accumarray using vals directly.

[dpb]

That's good tip, too, Sean. If I follow you, it takes the grouping vector (or its equivalent however it's generated) above to do that lookup though, correct?

[Walter Roberson]

If you were going to do something like

idxcells = accumarray(Subs, (1:numel(Subs)).', [], @(v) {v}, {}, true);

so as to get the indices associated with each subs, and then

[r, c, s] = find(idxcells);
mean3 = sparse(r, c, cellfun(@(x) mean(maxk(Values(x),3))), s));

then you might as well use splitapply() with findgroups(), or the accumarray() that I suggested.

[dpb]

What it looked like to me, too, Walter.

Your's works for the specific instance (or anywhere sum is the needed intemediary); however in the followup here I was thinking of the more general cases where the function needs the elements rather than a single result.

[Ayman Al-Sukhon]

Just wanted to thank everyone else for the help. All the suggestions were good, however Walter's got right to the point for me.