I want to find all possible variations (combinations) of a vector, choosing various numbers of elements from that vector.
For example, suppose I have the vector:
x = [1 2 3 4 5];
I can determine the number of combinations for each number of chosen elements:
x = [1 2 3 4 5]';
n = numel(x);
for k = 1:n
combs(k) = nchoosek(n,k);
end
sum(combs)
This results in:
combs = 5 10 10 5 1
sum(combs) = 31
I want a way to store all 31 of these combinations in an array, for example a cell array, with n cells, within each is an array in which each row is a vector combination of the elements.
e.g. at k = 4:
combs{4} =
1 2 3 4
1 2 3 5
1 2 4 5
1 3 4 5
2 3 4 5
Is there an existing function that does this, or what would be the most simple approach to this?
Call nchoosek with a vector as first input, using arrayfun (or equivalently for) to loop over the number of picked elements:
n = 5;
combs = arrayfun(#(k) nchoosek(1:n,k), 1:n, 'UniformOutput', false);
Here is an approach using dec2bin , find and accumarray:
x = [1 2 3 4 5];
[a b] = find(dec2bin(1:2^numel(x)-1)=='1');
combs = accumarray(a,x(b),[],#(c){c});
Related
I have a Matrix of size M by N in which each row has some zero entries. I want to create M row vectors such that each of the vector contains the non zero elements of each row. For example if I have the following Matrix
A=[0 0 0 5;0 0 4 6;0 1 2 3;9 10 2 3]
I want four different row vectors of the following form
[5]
[4 6]
[1 2 3]
[9 10 2 3]
This can be done with accumarray using an anonymous function as fourth input argument. To make sure that the results are in the same order as in A, the grouping values used as first input should be sorted. This requires using (a linearized version of) A transposed as second input.
ind = repmat((1:size(A,2)).',1,size(A,2)).';
B = A.';
result = accumarray(ind(:), B(:), [], #(x){nonzeros(x).'});
With A = [0 0 0 5; 0 0 4 6; 0 1 2 3; 9 10 2 3]; this gives
result{1} =
5
result{2} =
4 6
result{3} =
1 2 3
result{4} =
9 10 2 3
Since Matlab doesn't support non-rectangular double arrays, you'll want to settle on a cell array. One quick way to get the desired output is to combine arrayfun with logical indexing:
nonZeroVectors = arrayfun(#(k) A(k,A(k,:)~=0),1:size(A,1),'UniformOutput',false);
I used the ('UniformOutput',false) name-value pair for the reasons indicated in the documentation (I'll note that the pair ('uni',0) also works, but I prefer verbosity). This input produces a cell array with the entries
>> nonZerosVectors{:}
ans =
5
ans =
4 6
ans =
1 2 3
ans =
9 10 2 3
I have a matrix that I'd like to create a new ordering of, for example,
vals = [1 2; 3 4]
I also have two matrices, new_x and new_y such that new_x(a,b) = j and new_x(a,b) = k means that I want the value at vals (a,b) to be mapped to new_vals(j,k).
For example, given
new_x = [1 2; 2 1]
new_y = [2 2; 1 1]
I'd want
new_vals = [4 3; 1 2]
I understand that I could just write two for loops to build the new array, but matlab is notoriously good at providing operations on entire matricies. My question is, how would I build new_vals without the for loops?
Basically you are trying to get a matrix that when indexed with new_x and new_y would give us vals, i.e. -
output(new_x(1,1),new_y(1,1)) must be equal to vals(1,1),
output(new_x(1,2),new_y(1,2)) must be equal to vals(1,2) and so on.
We will try to verify this later on. For now, here's one solution using linear indexing -
nrows = size(vals,1); %// Store number of rows
%// Calculate linear indices
idx = (new_x + (new_y-1)*nrows);
%// Trace/map back to sorted version of "1:numel(vals)"
[~,traced_back_idx] = sort(idx(:));
%// Index into vals with traced back linear indices & then reshape & transpose
out = reshape(vals(traced_back_idx),[],nrows).'
Here's another and possibly faster way -
out = nan(size(vals));
out((new_x + (new_y-1)*nrows)) = vals;
out = out.'
As discussed earlier for verification, let's index into out with new_x and new_y and that should match up with vals. Here's a code to do so -
for ii = 1:size(out,1)
for jj = 1:size(out,2)
check_back(ii,jj) = out(new_y(ii,jj),new_x(ii,jj));
end
end
Sample runs -
Case #1 (sample from question):
vals =
1 2
3 4
new_x =
1 2
2 1
new_y =
2 2
1 1
new_vals =
4 3
1 2
out =
4 3
1 2
check_back = (must be same as vals)
1 2
3 4
Case #2:
vals =
1 2 5
3 4 5
6 8 3
new_x =
1 2 3
3 1 2
3 2 1
new_y =
2 2 3
2 1 1
1 3 3
out =
4 5 6
1 2 3
3 8 5
check_back = (must be same as vals)
1 2 5
3 4 5
6 8 3
I think i see what you are trying to do here. new_x and new_y are just coordinates for the new_val matrix rigth? The problem is tha what you are trying to do only works for vectors, not for matrix, so the only way is to transform the matrix into a vector, reorder the values and then go back to matrix like:
vals = [1 ,2; 3, 4];
A=reshape(vals,1,4); % A is a vector [ 1 3 2 4]
new_coord=[2,3,4,1];
B(new_c)=A; %B is [4 1 3 2]
new_val=reshape(B,2,2) %back to matrix
Obtainig new_val=[4 3; 1 2]. Also B=A(new_c) is also allowed but with different coordinates, eventhoug is much easy to think the rigth coordinates in that way.
I am sure there must be a way to include the new_x matrix and transform everything into new_coord
What I'm trying to do: given a 2D matrix, get the column indices of the elements in each row that satisfy some particular condition.
For example, say my matrix is
M = [16 2 3 13; 5 11 10 8; 9 7 6 12; 4 14 15 1]
and my condition is M>6. Then my desired output would be something like
Indices = {[1 4]'; [2 3 4]'; [1 2 4]'; [2 3]';}
After reading the answers to this similar question I came up with this partial solution using find and accumarray:
[ix, iy] = find(M>6);
Indices = accumarray(ix,iy,[],#(iy){iy});
This gives very nearly the results I want -- in fact, the indices are all right, but they're not ordered the way I expected. For example, Indices{2} = [2 4 3]' instead of [2 3 4]', and I can't understand why. There are 3 occurrences of 2 in ix, at indices 3, 6, and 9. The corresponding values of iy at those indices are 2, 3, and 4, in that order. What exactly is creating the observed order? Is it just arbitrary? Is there a way to force it to be what I want, other than sorting each element of Indices afterwards?
Here's one way to solve it with arrayfun -
idx = arrayfun(#(x) find(M(x,:)>6),1:size(M,1),'Uni',0)
Display output wtih celldisp(idx) -
idx{1} =
1 4
idx{2} =
2 3 4
idx{3} =
1 2 4
idx{4} =
2 3
To continue working with accumarray, you can wrap iy with sort to get your desired output which doesn't look too pretty maybe -
Indices = accumarray(ix,iy,[],#(iy){sort(iy)})
Output -
>> celldisp(Indices)
Indices{1} =
1
4
Indices{2} =
2
3
4
Indices{3} =
1
2
4
Indices{4} =
2
3
accumarray is not guaranteed to preserve order of each chunk of its second input (see here, and also here). However, it does seem to preserve it when the first input is already sorted:
[iy, ix] = find(M.'>6); %'// transpose and reverse outputs, to make ix sorted
Indices = accumarray(ix,iy,[],#(iy){iy}); %// this line is the same as yours
produces
Indices{1} =
1
4
Indices{2} =
2
3
4
Indices{3} =
1
2
4
Indices{4} =
2
3
I’ve a matrix A = (4*4) and a cell array B {4,1}. I’d like to find all the values of B in A, searching row by row and after I’d like to delete the correspondent column associated to this particular value. I’ve a problem using bsxfun o cellfun and find function with a matrix and a cell array. I‘ve tried to convert the cell array into a matrix but I don’t have more the exact correspondence.
For example:
A =
1 5 10 23
2 4 2 18
3 3 5 14
1 9 10 4
B =
1
2 4
3 3 14
1
To obtain:
C =
10
2
5
10
Thanks in advance,
L.
Here's how:
C = cellfun(#(x, y){sparse(1,find(ismember(x,y),numel(y)),true,1,size(A,2))}, ...
mat2cell(A, ones(size(A, 1), 1), size(A, 2)), B(:));
C = A(:, all(~vertcat(C{:})));
The cellfun is fed with two cell arrays: the first one contains the rows of A and second one is B. The anonymous function is the tricky part; it operates on a pair of two corresponding rows as follows:
It employs ismember to check which columns in A contain any of the elements in B.
It uses find to pick only the first N ones, with respect to the number of elements in the B.
It uses sparse as a fancy way of zeroing out the rest of the elements.
For your example it would look like this:
A = [1 5 10 23; 2 4 2 18; 3 3 5 14; 1 9 10 4];
B = {1; [2 4]; [3 3 14]; 1};
C = cellfun(#(x, y){sparse(1,find(ismember(x,y),numel(y)),true,1,size(A,2))}, ...
mat2cell(A, ones(size(A, 1), 1), size(A, 2)), B(:));
which yields:
C =
{
[1 0 0 0]
[1 1 0 0]
[1 1 0 1]
[1 0 0 0]
}
After that, it's a simple matter of logical indexing to pick the resulting columns:
C = A(:, all(~vertcat(C{:})));
which in this case should be:
C =
10
2
5
10
just lets make it simple, assume that I have a 10x3 matrix in matlab. The numbers in the first two columns in each row represent the x and y (position) and the number in 3rd columns show the corresponding value. For instance, [1 4 12] shows that the value of function in x=1 and y=4 is equal to 12. I also have same x, and y in different rows, and I want to average the values with same x,y. and replace all of them with averaged one.
For example :
A = [1 4 12
1 4 14
1 4 10
1 5 5
1 5 7];
I want to have
B = [1 4 12
1 5 6]
I really appreciate your help
Thanks
Ali
Like this?
A = [1 4 12;1 4 14;1 4 10; 1 5 5;1 5 7];
[x,y] = consolidator(A(:,1:2),A(:,3),#mean);
B = [x,y]
B =
1 4 12
1 5 6
Consolidator is on the File Exchange.
Using built-in functions:
sparsemean = accumarray(A(:,1:2), A(:,3).', [], #mean, 0, true);
[i,j,v] = find(sparsemean);
B = [i.' j.' v.'];
A = [1 4 12;1 4 14;1 4 10; 1 5 5;1 5 7]; %your example data
B = unique(A(:, 1:2), 'rows'); %find the unique xy pairs
C = nan(length(B), 1);
% calculate means
for ii = 1:length(B)
C(ii) = mean(A(A(:, 1) == B(ii, 1) & A(:, 2) == B(ii, 2), 3));
end
C =
12
6
The step inside the for loop uses logical indexing to find the mean of rows that match the current xy pair in the loop.
Use unique to get the unique rows and use the returned indexing array to find the ones that should be averaged and ask accumarray to do the averaging part:
[C,~,J]=unique(A(:,1:2), 'rows');
B=[C, accumarray(J,A(:,3),[],#mean)];
For your example
>> [C,~,J]=unique(A(:,1:2), 'rows')
C =
1 4
1 5
J =
1
1
1
2
2
C contains the unique rows and J shows which rows in the original matrix correspond to the rows in C then
>> accumarray(J,A(:,3),[],#mean)
ans =
12
6
returns the desired averages and
>> B=[C, accumarray(J,A(:,3),[],#mean)]
B =
1 4 12
1 5 6
is the answer.