I have two arrays:
A=[1 1 2 2 3 3 3];
B=[1 3];
Is there any function that can remove elements which are contained in B from A?
The result should be
C=[1 2 2 3 3];
The order is not important, but if there is more specific elements like two times 1 in A, then I need operation that removes (from A) only as many of these specific elements is in B (in this case only one of 1 and one of 3; meaning other 1 and 3 should remain in final product C). This function should be analogous to setdiff, with the difference that it should take care of multiple instances of array elements. This analogy can hold because my B only contains elements that are in A.
For loop solution:
C = A;
for ii = 1:length(B)
C(find(C == B(ii), 1,'first')) = [];
end
Result
C =
1 2 2 3 3
Here's a vectorized solution using accumarray and repelem:
maxValue = max([A B]);
counts = accumarray(A(:), 1, [maxValue 1])-accumarray(B(:), 1, [maxValue 1]);
C = repelem(1:maxValue, max(counts, 0));
And the result for your sample data A = [1 1 2 2 3 3 3]; B = [1 3];:
C =
1 2 2 3 3
This will even work for cases where there are values in B not in A (like B = [1 4];) or more of a given value in B than in A (like B = [1 1 1];).
Note: The above works sinceA and B contain integers. If they were to contain floating-point values, you could map the unique values to integers first using unique and ismember. Let's say we had the following sample data:
A = [0 0 pi pi 2*pi 2*pi 2*pi];
B = [0 2*pi];
Here's a variant of the above code that can handle this:
uniqueValues = unique([A B]);
[~, A] = ismember(A, uniqueValues);
[~, B] = ismember(B, uniqueValues);
maxValue = max([A B]);
counts = accumarray(A(:), 1, [maxValue 1])-accumarray(B(:), 1, [maxValue 1]);
C = uniqueValues(repelem(1:maxValue, max(counts, 0)));
And the results:
C =
0 3.1416 3.1416 6.2832 6.2832 % [0 pi pi 2*pi 2*pi]
Related
I have two vectors, and I'm trying to find ALL coincidences of one on the other within a certain tolerance without using a for loop.
By tolerance I mean for example if I have the number 3, with tolerance 2, I will want to keep values within 3±2, so (1,2,3,4,5).
A = [5 3 4 2]; B = [2 4 4 4 6 8];
I want to obtain a cell array containing on each cell the numbers of all the coincidences with a tolerance of 1 (or more) units. (A = B +- 1)
I have a solution with zero units (A = B), which would look something like this:
tol = 0;
[tf, ia] = ismembertol(B,A,tol,'DataScale',1); % For tol = 0, this is equivalent to using ismember
idx = 1:numel(B);
ib = accumarray(nonzeros(ia), idx(tf), [], #(x){x}) % This gives the cell array
The output is:
ib =
[]
[]
[2 3 4]
[1]
Which is as desired.
If I change the tolerance to 1, the code doesn't work as intended. It outputs instead:
tol = 1
[tf, ia] = ismembertol(B,A,tol,'DataScale',1); % For tolerance = 1, this is equivalent to using ismember
idx = 1:numel(B);
ib = accumarray(nonzeros(ia), idx(tf), [], #(x){x}) % This gives the cell array
ib =
[5]
[2 3 4]
[]
[1]
When I would expect to obtain:
ib =
[2 3 4 5]
[1 2 3 4]
[2 3 4]
[1]
What am I doing wrong? Is there an alternative solution?
Your problem is that, in the current state of your code, ismembertol only outputs 1 index per element of B found in A, so you lose information in the cases where an element can be found several times within tolerance.
As per the documentation You can use the 'OutputAllIndices',true value pair argument syntax, to output what you want in ia with just a call to ismembertol:
A = [5 3 4 2]; B = [2 4 4 4 6 8];
tol = 0;
[tf, ia] = ismembertol(A,B,tol,'DataScale',1,'OutputAllIndices',true);
celldisp(ia) % tol = 0
ia{1} =
0
ia{2} =
0
ia{3} =
2
3
4
ia{4} =
1
celldisp(ia) % tol = 1
ia{1} =
2
3
4
5
ia{2} =
1
2
3
4
ia{3} =
2
3
4
ia{4} =
1
Here is a manual approach, just to provide another method. It computes an intermediate matrix of all absolute differences (using implicit expansion), and from the row and column indices of the entries that are less than the tolerance it builds the result:
A = [5 3 4 2];
B = [2 4 4 4 6 8];
tol = 1;
[ii, jj] = find(abs(A(:).'-B(:))<=tol);
ib = accumarray(jj, ii, [numel(A) 1], #(x){x});
Note that this approach
may be memory-intensive, because of the intermediate matrix;
can be made to work in old Matlab versions, because it doesn't use ismembertol; but then implicit expansion has to be replaced by explicitly calling bsxfun:
[ii, jj] = find(abs(bsxfun(#minus, A(:).', B(:)))<=tol);
ib = accumarray(jj, ii, [numel(A) 1], #(x){x});
I have a matrix where each row is a combination of two numbers, like A = [1 2; 2 5; 3 4; 4 6; 5 6]
A is built so that, for each row, the first elements is always smaller than the second one.
I need to return, from A, the lists of chained elements (in the case above, the lists of chained elements are 1 2 5 6 and 3 4 6). These lists are essentially built by considering a row, and checking is the last number is the first number of another row. Do you have any suggestion on how to do this?
If I got the question correctly, assuming A as the input array, you can use bsxfun -
mask = bsxfun(#eq,A(:,1),A(:,2).');
out = unique(A(any(mask,1).' | any(mask,2),:))
Sample run -
>> A
A =
1 2
3 4
2 5
5 6
>> mask = bsxfun(#eq,A(:,1),A(:,2).');
>> unique(A(any(mask,1).' | any(mask,2),:))
ans =
1
2
5
6
You can also use ismember, like so -
out = unique(A(ismember(A(:,1),A(:,2)) | ismember(A(:,2),A(:,1)),:))
Third option would be to use intersect to solve it, like so -
[~,idx1,idx2] = intersect(A(:,1),A(:,2));
out = unique(A([idx1,idx2],:))
The following seems to work. It builds a matrix (B) that tells which elements are connected (by 1 step). It then extends that matrix ( C) to include 0-step, 1-step, ..., (n-1)-step connections, where n is the number of nodes.
From that matrix, groups of connected elements are obtained (R). Finally, only "maximal" groups are kept (that is, those, not contained in other groups).
A = [1 2; 3 4; 2 5; 4 6; 5 6]; %// data
n = max(A(:));
B = full(sparse(A(:,1), A(:,2), 1, n, n )); %// matrix of 1-step connections
C = eye(n) | B; %// initiallize with 0-step and 1-step connections
for k = 1:n-1
C = C | C*B; %// add k-step connections, up to k=n-1
end
[ii, jj] = find(C);
R = accumarray(ii, jj, [], #(x) {sort(x).'}); %'// all groups (maximal or not)
[xx, yy] = ndgrid(1:n);
C = cellfun(#(x,y) all(ismember(x, y)), R(xx), R(yy) ); %// group included in another?
result = R(all(~C | eye(n), 2)); %// keep only groups that are not included in others
This gives
>> result{:}
ans =
1 2 5 6
ans =
3 4 6
Given the values in C, I want to count how many times I encounter each of these values in the vector B. For example, if C = [1 2], I'd like to count how many "1"s are in B and how many "2"s are in B by checking the elements of array C.
However, the code I have seems to count up to 5, but what the true output should be is that the number of 1s is 2 and the number of 2s is 3.
The code I wrote is shown below. Any help would be certainly appreciated.
My code :
B = [ 1 2 1 4 5 2 2 ]
C = [ 1 2 ]
lb = length(B)
lc = length(C)
for i = 1:length(B)
for j = 1:length(C)
if B(1,i)==C(1,j)
c=c+1
A(i)=c
end
end
end
Santhan Salai gave the corrected answer if you want to stick with loops. However, for efficiency, you could achieve what you want with bsxfun and sum if you don't want to loop:
>> B = [ 1 2 1 4 5 2 2 ];
>> C = [ 1 2 ];
>> D = sum(bsxfun(#eq, B, C.'), 2)
D =
2
3
bsxfun is a nice tool that allows you to broadcast data across singleton dimensions. In our case, I used the equals functions to check for element-wise equality and I transposed C so that it becomes a column vector. What will be produced is a matrix where we have as many rows as there are in C and as many columns as there are in B. Each row of this output matrix tells you which elements were equal to each corresponding element in C. C is broadcasted such that we get a matrix of a bunch of [1;2] columns mashed together for as many elements as there are in B and B is broadcasted such that we get replicates of B with as many rows as there are in C. By doing element-wise equality, we would produce a logical matrix where each element for a row tells you which elements were equal to the corresponding value of C. All you have to do now is sum over the columns to get how many elements were equal to each value in C, hence the sum call over the second dimension.
If you want overkill, you can also use accumarray. Assuming that B and C only consist of integers, do:
>> B = [ 1 2 1 4 5 2 2 ];
>> C = [ 1 2 ];
>> D = accumarray(B.', 1);
D =
2
3
0
1
1
This however computes the frequency of all unique values in B, and so you'd just want the first two entries in D.
One more alternative is to use histc:
>> B = [ 1 2 1 4 5 2 2 ];
>> C = [ 1 2 ];
>> D = histc(B, C)
D =
2 3
What you are basically computing is a histogram of B at specified bins, which are denoted at C.
Using arrayfun could be one alternate to your loop
out = arrayfun(#(x) sum(ismember(B,x)), C)
Here is your corrected loop
count = zeros(1,numel(C));
for ii = 1:numel(C)
for jj = 1:numel(B)
if (C(ii) == B(jj))
count(ii) = count(ii) + 1;
end
end
end
I am trying to create all possible 1xM vectors (word) from a 1xN vector (alphabet) in MATLAB. N is > M. For example, I want to create all possible 2x1 "words" from a 4x1 "alphabet" alphabet = [1 2 3 4];
I expect a result like:
[1 1]
[1 2]
[1 3]
[1 4]
[2 1]
[2 2]
...
I want to make M an input to my routine and I do not know it beforehand. Otherwise, I could easily do this using nested for-loops. Anyway to do this?
Try
[d1 d2] = ndgrid(alphabet);
[d2(:) d1(:)]
To parameterize on M:
d = cell(M, 1);
[d{:}] = ndgrid(alphabet);
for i = 1:M
d{i} = d{i}(:);
end
[d{end:-1:1}]
In general, and in languages that don't have ndgrid in their library, the way to parameterize for-loop nesting is using recursion.
[result] = function cartesian(alphabet, M)
if M <= 1
result = alphabet;
else
recursed = cartesian(alphabet, M-1)
N = size(recursed,1);
result = zeros(M, N * numel(alphabet));
for i=1:numel(alphabet)
result(1,1+(i-1)*N:i*N) = alphabet(i);
result(2:M,1+(i-1)*N:i*N) = recursed; % in MATLAB, this line can be vectorized with repmat... but in MATLAB you'd use ndgrid anyway
end
end
end
To get all k-letter combinations from an arbitrary alphabet, use
n = length(alphabet);
aux = dec2base(0:n^k-1,n)
aux2 = aux-'A';
ind = aux2<0;
aux2(ind) = aux(ind)-'0'
aux2(~ind) = aux2(~ind)+10;
words = alphabet(aux2+1)
The alphabet may consist of up to 36 elements (as per dec2base). Those elements may be numbers or characters.
How this works:
The numbers 0, 1, ... , n^k-1 when expressed in base n give all groups of k numbers taken from 0,...,n-1. dec2base does the conversion to base n, but gives the result in form of strings, so need to convert to the corresponding number (that's part with aux and aux2). We then add 1 to make the numbers 1,..., n. Finally, we index alphabet with that to use the real letters of numbers of the alphabet.
Example with letters:
>> alphabet = 'abc';
>> k = 2;
>> words
words =
aa
ab
ac
ba
bb
bc
ca
cb
cc
Example with numbers:
>> alphabet = [1 3 5 7];
>> k = 2;
>> words
words =
1 1
1 3
1 5
1 7
3 1
3 3
3 5
3 7
5 1
5 3
5 5
5 7
7 1
7 3
7 5
7 7
use ndgrid function in Matlab
[a,b] = ndgrid(alphabet)
Let's say I have a one-dimensional array:
a = [1, 2, 3];
Is there a built-in Matlab function that takes an array and an integer n and replicates each
element of the array n times?
For example calling replicate(a, 3) should return [1,1,1,2,2,2,3,3,3].
Note that this is not at all the same as repmat. I can certainly implement replicate by doing repmat on each element and concatenating the result, but I am wondering if there is a built in function that is more efficient.
I'm a fan of the KRON function:
>> a = 1:3;
>> N = 3;
>> b = kron(a,ones(1,N))
b =
1 1 1 2 2 2 3 3 3
You can also look at this related question (which dealt with replicating elements of 2-D matrices) to see some of the other solutions involving matrix indexing. Here's one such solution (inspired by Edric's answer):
>> b = a(ceil((1:N*numel(a))/N))
b =
1 1 1 2 2 2 3 3 3
a = [1 2 3];
N = 3;
b = reshape(repmat(a,N,1), 1, [])
As of R2015a, there is a built-in and documented function to do this, repelem:
repelem Replicate elements of an array.
W = repelem(V,N), with vector V and scalar N, creates a vector W where each element of V is repeated N times.
The second argument can also be a vector of the same length as V to specify the number of replications for each element. For 2D replication:
B = repelem(A,N1,N2)
No need for kron or other tricks anymore!
UPDATE: For a performance comparison with other speedy methods, please see the Q&A Repeat copies of array elements: Run-length decoding in MATLAB.
>> n=3;
>> a(floor((0:size(a,2)*n-1)/n)+1)
ans =
1 1 1 2 2 2 3 3 3
Some exotic alternatives. Admittedly more funny than useful:
Assign the (first) result of meshgrid to a vector:
b = NaN(1,numel(a)*n); %// pre-shape result
b(:) = meshgrid(a,1:n);
Build a matrix that multiplied by a gives the result:
b = a * fliplr(sortrows(repmat(eye(numel(a)),n,1))).';
Use ind2sub to generate the indices:
[~, ind] = ind2sub([n 1],1:numel(a)*n);
b = a(ind);
If you have the image processing toolbox, there is another alternative:
N = 3;
imresize(a, [1 N*numel(a)],'nearest')
% To get b = [1 1 1 2 2 2 3 3 3]
N = 3;
a = [1 2 3];
temp_a = a(ones(N,1),:);
b = reshape(temp_a,1,numel(temp_a));
% To get b = [1 2 3 1 2 3 1 2 3]
N = 3;
a = [1 2 3];
temp_a = a(ones(N,1),:);
b = reshape(temp_a',1,numel(temp_a));