I've two matrix a and b and I'd like to combine the rows in a way that in the first row I got no duplicate value and in the second value, columns in a & b which have the same row value get added together in new matrix. i.e.
a =
1 2 3
8 2 5
b =
1 2 5 7
2 4 6 1
Desired outputc =
1 2 3 5 7
10 6 5 6 1
Any help is welcomed,please.
For two-row matrices
You want to add second-row values corresponding to the same first-row value. This is a typical use of unique and accumarray:
[ii, ~, kk] = unique([a(1,:) b(1,:)]);
result = [ ii; accumarray(kk(:), [a(2,:) b(2,:)].').'];
General case
If you need to accumulate columns with an arbitrary number of columns (based on the first-row value), you can use sparse as follows:
[ii, ~, kk] = unique([a(1,:) b(1,:)]);
r = repmat((1:size(a,1)-1).', 1, numel(kk));
c = repmat(kk.', size(a,1)-1, 1);
result = [ii; full(sparse(r,c,[a(2:end,:) b(2:end,:)]))];
Related
I have a 2D matrix where the № of columns is always a multiple of 3 (e.g. 250×27) - due to a repeating organisation of the results (A,B,C, A,B,C, A,B,C, and so forth). I wish to reshape this matrix to create a new matrix with 3 columns - each containing the aggregated data for each type (A,B,C) (e.g. 2250×3).
So in a matrix of 250×27, all the data in columns 1,4,7,10,13,16,19,22,25 would be merged to form the first column of the resulting reshaped matrix.
The second column in the resulting reshaped matrix would contain all the data from columns 2,5,8,11,14,17,20,23,26 - and so forth.
Is there a simple way to do this in MATLAB? I only know how to use reshape if the columns I wanted to merge were adjacent (1,2,3,4,5,6) rather than non-adjacent (1,4,7,10,13,16) etc.
Shameless steal from #Divakar:
B = reshape( permute( reshape(A,size(A,1),3,[]), [1,3,2]), [], 3 );
Let A be your matrix. You can save every third column in one matrix like:
(Note that you don't have to save them as matrices separately but it makes this example easier to read).
A = rand(27); %as test
B = A(:,1:3:end);
C = A(:,2:3:end);
D = A(:,3:3:end);
Then you use reshape:
B = reshape(B,[],1);
C = reshape(C,[],1);
D = reshape(D,[],1);
And finally put it all together:
A = [B C D];
You can just treat every set of columns as a single item and do three reshapes together. This should do the trick:
[save as "reshape3.m" file in your Matlab folder to call it as a function]
function out = reshape3(in)
[~,C]=size(in); % determine number of columns
if mod(C,3) ~=0
error('ERROR: Number of rows must be a multiple of 3')
end
R_out=numel(in)/3; % number of rows in output
% Reshape columns 1,4,7 together as new column 1, column 2,5,8 as new col 2 and so on
out=[reshape(in(:,1:3:end),R_out,1), ...
reshape(in(:,2:3:end),R_out,1), ...
reshape(in(:,3:3:end),R_out,1)];
end
Lets suppose you have a 3x6 matrix A
A = [1 2 3 4 5 6;6 5 4 3 2 1;2 3 4 5 6 7]
A =
1 2 3 4 5 6
6 5 4 3 2 1
2 3 4 5 6 7
you extract the size of the matrix
b =size(A)
and then extract each third column for a single row
c1 = A((1:b(1)),[1:3:b(2)])
c2 = A((1:b(1)),[2:3:b(2)])
c3 = A((1:b(1)),[3:3:b(2)])
and put them in one matrix
A_result = [c1(:) c2(:) c3(:)]
A_result =
1 2 3
6 5 4
2 3 4
4 5 6
3 2 1
5 6 7
My 2 cents:
nRows = size(matrix, 1);
nBlocks = size(matrix, 2) / 3;
matrix = reshape(matrix, [nRows 3 nBlocks]);
matrix = permute(matrix, [1 3 2]);
matrix = reshape(matrix, [nRows * nBlocks 1 3]);
matrix = reshape(matrix(:), [nRows * nBlocks 3]);
Here's my 2 minute take on it:
rv = #(x) x(:);
ind = 1:3:size(A,2);
B = [rv(A(:,ind)) rv(A(:,ind+1)) rv(A(:,ind+2))];
saves a few ugly reshapes, may be a bit slower though.
If you have the Image Processing Toolbox, im2col is a very handy solution:
out = im2col(A,[1 4], 'distinct').'
Try Matlab function mat2cell, I think this form is allowed.
X is the "start matrix"
C = mat2cell(X, [n], [3, 3, 3]); %n is the number of rows, repeat "3" as many times as you nedd
%extract every matrix
C1 = C{1,1}; %first group of 3 columns
C2 = C{1,2}; %second group of 3 columns
%repeat for all your groups
%join the matrix with vertcat
Cnew = vertcat(C1,C2,C3); %join as many matrix n-by-3 as you have
I will try to explain what I need through an example.
Suppose you have a matrix x as follows:
1 2 3
4 5 6
And another matrix y as follows:
1 4 5
7 4 8
What I need is (without looping over the rows) to perform an intersection between each 2 corresponding rows in x & y. So I wish to get a matrix z as follows:
1
4
The 1st rows in x and y only have 1 as the common value. The 2nd rows have 4 as the common value.
EDIT:
I forgot to add that in my case, it is guaranteed that the intersection results will have the same length and the length is always 1 actually.
I am thinking bsxfun -
y(squeeze(any(bsxfun(#eq,x,permute(y,[1 3 2])),2)))
Sample runs -
Run #1:
>> x
x =
1 2 3
4 5 6
>> y
y =
1 4 5
7 4 8
>> y(squeeze(any(bsxfun(#eq,x,permute(y,[1 3 2])),2)))
ans =
1
4
Run #2:
>> x
x =
3 5 7 9
2 7 9 0
>> y
y =
6 4 3
6 0 2
>> y(squeeze(any(bsxfun(#eq,x,permute(y,[1 3 2])),2)))
ans =
0
3
2
The idea is to put the matrices together and to look for duplicates in the rows. One idea to find duplicated numeric values is to diff them; the duplicates will be marked by the value 0 in result.
Which leads to:
%'Initial data'
A = [1 2 3; 8 5 6];
B = [1 4 5; 7 4 8];
%'Look in merged data'
V = sort([A,B],2); %'Sort matrix values in rows'
R = V(diff(V,1,2)==0); %'Find duplicates in rows'
This should work with any number of matrices that can be concatenated horizontally. It will detect all the duplicates, but it will return a column the same size as the number of rows only if there is one and only one duplicate per row in the matrices.
I am working on matlab and have an array:
a =
2 1 5 3 2 1 2 1
You can see there may be one value multiple times. I want a function that will give me an array for each of those value that contains the index(s) of that value in the array as output.
Using the above example, the output would be:
(1 5 7)
(2 6 8)
(3)
(4)
(1 5 7) are the indexes of 2 in the input array. Same happens for 1,5 and 3.
This can be done using for loops etc. I just want to know if there is some in-built function for this in matlab.
**** EDIT ****
There may be two columns as following.
2 1 5 3 2 1 2 1
3 4 3 2 4 4 3 4
In that case output will be
(1 7)
(2 6 8)
(3)
(4)
(5)
Use the third output of unique to get unique labels for each column of a, and then apply accumarray with a custom function:
[~, ~, kk] = unique(a.', 'rows', 'stable'); %'
result = accumarray(kk, (1:numel(kk)).', [], #(x) {sort(x).'});
This works for any number of rows. For your two-row example
a = [2 1 5 3 2 1 2 1
3 4 3 2 4 4 3 4];
the result is
result{1} =
1 7
result{2} =
2 6 8
result{3} =
3
result{4} =
4
result{5} =
5
If element order is not important, you can simplify the code a little:
[~, ~, kk] = unique(a.', 'rows'); %'
result = accumarray(kk, (1:numel(kk)).', [], #(x) {x.'});
which gives
result{1} =
2 8 6
result{2} =
7 1
result{3} =
5
result{4} =
4
result{5} =
3
I don't think there is a buit-in function to do that, but you can do it in one line with unique and arrayfun:
Res = arrayfun(#(x) find(x==a), unique (x, 'stable'), 'UniformOutput', false);
Best,
Extend Ratbert's nice answer to arrive at a more general one which addresses the "edited" request:
[~, ~, J]= unique(a.', 'rows');
Res = cellfun(#str2num,accumarray(J,[1:size(a,2)]',[], #(x)num2str(x),'uni',0);
Use of conversion from double to char and back is clunky, but it works with Octave 3.6.4, and should also work on MATLAB. In MATLAB a more elegant answer with accumarray is likely possible.
Edit: The following is a more elegant answer with accumarray (see the MATLAB documentation for more details) - equivalent to LuisMendo's answer.
[~, ~, J]= unique(a.', 'rows');
Res = accumarray(J,[1:numel(J)]',[],#(x){x});
Given a vector
X = [1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3]
I would like to generate a vector such
Y = [1 2 3 4 5 1 2 3 4 5 6 1 2 3 4 5]
So far what I have got is
idx = find(diff(X))
Y = [1:idx(1) 1:idx(2)-idx(1) 1:length(X)-idx(2)]
But I was wondering if there is a more elegant(robust) solution?
One approach with diff, find & cumsum for a generic case -
%// Initialize array of 1s with the same size as input array and an
%// intention of using cumsum on it after placing "appropriate" values
%// at "strategic" places for getting the final output.
out = ones(size(X))
%// Find starting indices of each "group", except the first group, and
%// by group here we mean run of identical numbers.
idx = find(diff(X))+1
%// Place differentiated and subtracted values of indices at starting locations
out(idx) = 1-diff([1 idx])
%// Perform cumulative summation for the final output
Y = cumsum(out)
Sample run -
X =
1 1 1 1 2 2 3 3 3 3 3 4 4 5
Y =
1 2 3 4 1 2 1 2 3 4 5 1 2 1
Just for fun, but customary bsxfun based alternative solution -
%// Logical mask with each column of ones for presence of each group elements
mask = bsxfun(#eq,X(:),unique(X(:).')) %//'
%// Cumulative summation along columns and use masked values for final output
vals = cumsum(mask,1)
Y = vals(mask)
Here's another approach:
Y = sum(triu(bsxfun(#eq, X, X.')), 1);
This works as follows:
Compare each element with all others (bsxfun(...)).
Keep only comparisons with current or previous elements (triu(...)).
Count, for each element, how many comparisons are true (sum(..., 1)); that is, how many elements, up to and including the current one, are equal to the current one.
Another method is using the function unique
like this:
[unqX ind Xout] = unique(X)
Y = [ind(1):ind(2) 1:ind(3)-ind(2) 1:length(X)-ind(3)]
Whether this is more elegant is up to you.
A more robust method will be:
[unqX ind Xout] = unique(X)
for ii = 1:length(unqX)-1
Y(ind(ii):ind(ii+1)-1) = 1:(ind(ii+1)-ind(ii));
end
I am looking for non-repeated rows in a matrix.
Assume:
A =
8 1
2 2
2 2
2 2
2 2
3 6
5 7
5 7
I would like to get "B" which is:
B=
8 1
3 6
Please mind C=unique(A,'rows') will give us unique rows of "A" which include repeated and non-repeated arrays and only remove repetitious rows. It means:
C =
2 2
3 6
5 7
8 1
"C" is not the one that I am looking for.
Any help would be greatly appreciated!
Use the second and third outputs of unique as follows:
[~, ii, jj] = unique(A,'rows');
kk = find(histc(jj,unique(jj))==1);
B = A(sort(ii(kk)),:);
Or use this more direct bsxfun-based approach:
B = A(sum(squeeze(all(bsxfun(#eq, A.', permute(A, [2 3 1])))))==1,:);
These two approaches work in quite generally: A may have any number of columns, and may contain non-integer values.
If A always has two columns and contains only integer values, you can also do it with accumarray, using the sparse option (sixth input argument) to save memory in case of large values:
[ii jj] = find(accumarray(A, 1, [], #sum, 0, true)==1);
B = [ii jj];
Or you can use sparse instead of accumarray:
[ii jj] = find(sparse(A(:,1),A(:,2),1)==1);
B = [ii jj];
If you don't care about the order of the rows, try this -
[C,~,ic] = unique(A,'rows','legacy')
B = C(histc(ic,unique(ic))==1,:)