Using ALLCOMB for unknown number of vectors

Hello There!

I have N number of vectors recorded into workspace. I need to perform combination among themselves by using allcomb. How could I introduce the vectors into the command (allcomb) in the form of B = ALLCOMB(A1,A2,A3,...,AN).

Thanks inadvance....

[Adam]

How are your n vectors stored? If they are each in their own variable then what is wrong with just literally adding them all as input arguments as in the function signature?

[osman]

My variables are dynamic. the number of variables is continuously changing. I can not write them as you said. I have to define a set of variable like B = ALLCOMB(A1,A2,A3,...,AN). I do not know how to do this.

[John D'Errico]

READ THE RESPONSE BY BRUNO. Learn how to use cell arrays instead of dynamically naming your variables. Numbered variables is a terrible programming style, that if you continue to follow it, will continuously lead you into problems, just as you are having now.

Answer 1

[Bruno Luong]

Create a CELL array, and get rid of the method of naming your variables with number 1,2,....

C = {A1, A2, A3, ..., AN}
B = allcomb(C{:});

[osman]

That is very good idea. But it is not applicable. I had tried earlier. To create a cell like C, I have to use a for loop. But I do not know how to call the vectors from workspce in the for loop. Do you think I must use the numbers next to the alphabet. If so, I can not. Because the numbers are string.

[Bruno Luong]

"Do you think I must use the numbers next to the alphabet."

You can ask me or any experience MATLAB programmer, the answer is definitively NO.

[osman]

C=cell(size(U,1),1);
for k = 1:size(U,1)
   C{k}=eval(['V', int2str(k),' = U(k,:)']); %code resource; magic 
end
D=allcomb(C{:});

This is what I have done with my codes. The result ;

Error using repmat

Requested 12x12x12x12x12x12x12x12x12x12x12x12x12x12x12x12x12x12x12x12x12x11x11x11x11x11x11x11x11x11 (17179869184.0GB) array exceeds

maximum array size preference. Creation of arrays greater than this limit may take a long time and cause MATLAB to become unresponsive.

See array size limit or preference panel for more information.

Error in ndgrid (line 73)

varargout{i} = repmat(x,s);

Error in allcomb (line 109)

[A{ii}] = ndgrid(args{ii}) ;

[Jos (10584)]

Using EVAL is a very bad way to convert columns of a matrix into cells. Use mat2cell instead

C = mat2cell(U, size(U,1), ones(1,size(U,2))) ; % not tested

And than, what did you expect allcomb to return besides this gigantic matrix?

[Steven Lord]

Rethink your approach.

Even if you could generate this matrix (which is "only" about 1e33 elements, or more than the estimated number of bacterial cells on Earth) to process the combinations at one per second would require:

sizeOfOutput = [12, 12, 12, 12, 12, 12, 12, 12, 12, 12, ...
                12, 12, 12, 12, 12, 12, 12, 12, 12, 12, ...
                12, 11, 11, 11, 11, 11, 11, 11, 11, 11];
numberOfRows = prod(sizeOfOutput);
yearsAtOneCombinationPerSecond = years(seconds(numberOfRows))

about 3.4e24 years. According to the timeline of the far future that's after the estimated time until the Earth collides with the black dwarf Sun assuming it hadn't been engulfed by the Sun when it became a red giant about 7.6 billion years from now.

[osman]

Dear Jos (10584) !

Thanks you so much for your advice.

[Bruno Luong]

Something is odd that I don't get it.

If C come from rows of an array U:

C = mat2cell(U, size(U,1), ones(1,size(U,2)))

The NDGRID should return square hypercube where each side is of length == size(U,2) and not mixing between 11 and 12

12x12x12x12x12x12x12x12x12x12x12x12x12x12x12x12x12x12x12x12x12x11x11x11x11x11x11x11x11x11

[Bruno Luong]

Jos's replacement seems not correct either. The corresponding conversion of this code (BTW the assignment inside EVAL throw error in my MATLAB, might work in old MATLAB, I don't know)

C=cell(size(U,1),1);
for k = 1:size(U,1)
   C{k}=eval(['V', int2str(k),' = U(k,:)']); %code resource; magic 
end
D=allcomb(C{:});

is this code

C = mat2cell(U, ones(1,size(U,1)), size(U,2))

That might change a lot (or not). The number of combinations can be completely different. In one case is

size(U,2)^size(U,1)

in other is

size(U,1)^size(U,2)

It can makes billion year waiting for the calculation to finish estimated by Steve reduces to millions years. That's a whole difference. ;-)

[osman]

Dear Bruno !

First Thanks you! But I tried Jos's advice, It is very helpful. I am giving you the old form of my code below without eval.

C=cell(size(U,1),1);
for k = 1:size(U,1)
   C{k}=['V', int2str(k),' = U(k,:)']; 
end
D=allcomb(C{:});

As you can see, there is a for loop which takes a lot time. Now I give you the new one that I made by the help of Jos's advice.

C=mat2cell(U, size(U,1), ones(1,size(U,2)));
D=allcomb(C{:});

As you can see, there is no for loop. The result matrice (D) comes out promptly.

I have to emphasize that MatLab can not perform combination with a 30x30 matrice (,which is symbolized as U in code,) due to the memory shortage. So I reduced the dimension of the matrice. Now the matrice is 30x5.

[Bruno Luong]

Jos's command is wrong (well different than what you did) it splits U in separate columns. You splits in separate rows.

This is correct call of MAT2CELL as I said.

C = mat2cell(U, ones(1,size(U,1)), size(U,2));

The two give completely different combinations afterward.

For U of size 30x5

In one case (Jos's) the number of combinations is

>> 30^5

ans =

    24300000

the other (Your's) the number of combinations

>> 5^30

ans =

   9.3132e+20

It's not that one is faster than other. They compule two different things.

[osman]

This is the result with your and Jos's codes given above.

[Bruno Luong]

Do you understand when I wrote:

"They compule two different things."

% Example
U=bsxfun(@plus,(1:2),[0:2:6]')

% Your's
Your1 = allcomb(U(1,:),U(2,:),U(3,:),U(4,:))

% Your again
C=cell(size(U,1),1);
for k = 1:size(U,1)
   C{k}=eval('U(k,:)'); 
end
Your2 = allcomb(C{:})

% Jos's
C = mat2cell(U, size(U,1), ones(1,size(U,2)));
Jos = allcomb(C{:})

% Bruno's
C = mat2cell(U, ones(1,size(U,1)), size(U,2));
Bruno = allcomb(C{:})

[osman]

Thanks so much! I really appreciate about what you made me recognize.

[Jos (10584)]

Thanks Bruno, for correcting me, and thereby helping osman :-)