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)
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've always been told that almost all for loops can be omitted in MATLAB and that they in general slow down the process. So is there a way to do so here?:
I have a cell-array (tsCell). tsCell stores time-arrays with varying length. I want to find an intersecting time-array for all time-arrays (InterSection):
InterSection = tsCell{1}.time
for i = 2:length{tsCell};
InterSection = intersect(InterSection,tsCell{i}.time);
end
Here's another way. This also assumes there are no duplicates within each original vector.
tsCell_time = {[1 6 4 5] [4 7 1] [1 4 3] [4 3 1 7]}; %// example data (from Divakar)
t = [tsCell_time{:}]; %// concat into a single vector
u = unique(t); %// get unique elements
ind = sum(bsxfun(#eq, t(:), u), 1)==numel(tsCell_time); %// indices of unique elements
%// that appear maximum number of times
result = u(ind); %// output those elements
Here's a vectorized approach using unique and accumarray, assuming there are no duplicates within each cell of the input cell array -
[~,~,idx] = unique([tsCell_time{:}],'stable')
out = tsCell_time{1}(accumarray(idx,1) == length(tsCell_time))
Sample run -
>> tsCell_time = {[1 6 4 5],[4 7 1],[1 4 3],[4 3 1 7]};
>> InterSection = tsCell_time{1};
for i = 2:length(tsCell_time)
InterSection = intersect(InterSection,tsCell_time{i});
end
>> InterSection
InterSection =
1 4
>> [~,~,idx] = unique([tsCell_time{:}],'stable');
out = tsCell_time{1}(accumarray(idx,1) == length(tsCell_time));
>> out
out =
1 4
I have an array a = [6 8 2 1 9] and b = [1 2 6]. I want a function which returns 2 since a(2)=8 which is the smallest element of a not in b.
What I have tried so far:
[A,I] = sort(a);
index = I(find(~ismember(A,b),1))
I would like something faster as this piece of code has to run many times and the arrays involved are very large.
Thanks in advance!
Another (faster, I believe) solution would be:
a = [6 8 2 1 9];
b = [1 2 6];
[d,I] = setdiff(a,b); % d is the set difference, I is the indices of d elements in a
[m,J] = min(d); % m is the minimum in d, J is it's index
I(J) % This is the index of m in d (the value that you want)
ans =
2
Does this do what you need?
>> a = [6 8 2 1 9];
>> b = [1 2 6];
>> min(a(~ismember(a,b)))
ans =
8
Edit:
Oops - I meant
>> find(a==min(a(~ismember(a,b))),1)
ans =
2
This finds the index as you requested, rather than the value, which the first answer gives.
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]
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));