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
Related
I have a vector like this:
h = [1,2,3,4,5,6,7,8,9,10,11,12]
And I want to repeat every third element like so:
h_rep = [1,2,3,3,4,5,6,6,7,8,9,9,10,11,12,12]
How do I accomplish this elegantly in MATLAB? The actual arrays are huge, so ideally I don't want to write a for loop. Is there a vectorized way to do this?
One way to do this would be to use the recent repelem function that was released in version R2015b where you can repeat each element in a vector a certain amount of times. In this case, specify a vector where every third element is a 2 with the rest of the values being a 1 as the number of times to repeat the corresponding element, then use the function:
N = numel(h);
rep = ones(1, N);
rep(3:3:end) = 2;
h_rep = repelem(h, rep);
Using your example: h = 1 : 12, we thus get:
>> h_rep
h_rep =
1 2 3 3 4 5 6 6 7 8 9 9 10 11 12 12
If repelem is not available to you, then a clever use of cumsum may help. Basically, note that for every three elements, the next one is a copy of the previous element. If we had an indicator vector of [1 1 1 0] where 1 is the position that we want to copy and 0 tells us to copy the last value, using cumulative sum or cumsum on repeated versions of this vector - exactly 1 + (numel(h) / 4) will give us exactly where we would need to index into h. Therefore, create a vector of ones that is the length of h added with 1 + (numel(h) / 4 to ensure that we make space for the duplicate elements, then make sure every fourth element is set to 0 before applying the cumsum:
N = numel(h);
rep = ones(1, N + 1 + (N / 4));
rep(4:4:end) = 0;
rep = cumsum(rep);
h_rep = h(rep);
Thus:
>> h_rep
h_rep =
1 2 3 3 4 5 6 6 7 8 9 9 10 11 12 12
One last suggestion (thanks to user #bremen_matt) would be to reshape your vector into a matrix so that it has 3 rows, duplicate the last row, then reshape the resulting duplicated matrix back to a single vector:
h_rep = reshape(h, 3, []);
h_rep = reshape([h_rep; h_rep(end,:)], 1, []);
We again get:
>> h_rep
h_rep =
1 2 3 3 4 5 6 6 7 8 9 9 10 11 12 12
Of course the obvious caveat with the above code is that the length of vector h is evenly divisible by 4.
(Modified according to rayryeng's correct observations)...
Another solution is to play around with the reshape function. If you reshape the matrix to a 3xn matrix first...
B = reshape(h,3,[])
And then copy the last row
B = [B;B(end,:)]
And finally vectorize the solution...
B(:).'
You can use just indexing:
h = [1,2,3,4,5,6,7,8,9,10,11,12]; % initial data
n = 3; % step for repetition
h_rep = h(ceil(n/(n+1):n/(n+1):end));
An index-based approach (using sort):
h_rep = h(sort([1:numel(h) 3:3:numel(h)]));
Or a slightly shorter syntax...
h_rep = h(sort([1:end 3:3:end]));
I think this will do it:
h = [1,2,3,4,5,6,7,8,9,10,11,12];
h0=kron(h,[1 1])
h_rep=h0(mod(1:length(h0),2)==0 | mod(1:length(h0),3)==2)
Answer:
1 2 3 3 4 5 6 6 7 8 9 9 10 11 12 12
Explanation:
After duplicating every element, you select only those that you wants. You can extend this idea to duplicate second and third. etc..
I am trying to remove array values whose difference is a member of that array in MATLAB. For example, if I have an array defined as
x = [1 2 4 3 7];
I would like to remove 2, because it can be achieved from 4 - 2. I would also like to remove 4 because it can be achieved from 7 - 3. I would then like to store these values (2 and 4, respectively) into a matrix. The latter is easy. I just have a hard time doing this checker for summation.
I know you can use
ismember(*any 2 differences*),x(:))
to check if the differences are in the array. However, I don't know how to code my function to try out all the combinations of element subtraction.
Seemed like a good setup to use bsxfun -
abs_diffs = abs(bsxfun(#minus,x(:),x(:).')) %//'
unq_abs_diffs = unique(abs_diffs)
out = x(~any(bsxfun(#eq,unq_abs_diffs(:),x(:).'),1)) %//'
%// OR x(~ismember(x,unq_abs_diffs))
Sample run -
>> x
x =
1 2 4 3 7
>> abs_diffs = abs(bsxfun(#minus,x(:),x(:).'))
abs_diffs =
0 1 3 2 6
1 0 2 1 5
3 2 0 1 3
2 1 1 0 4
6 5 3 4 0
>> unq_abs_diffs = unique(abs_diffs)
unq_abs_diffs =
0
1
2
3
4
5
6
>> out = x(~any(bsxfun(#eq,unq_abs_diffs(:),x(:).'),1))
out =
7
So, in [1 2 4 3 7], only 7 seemed like the one that could not be removed.
You could do it like this:
n = length(a);
differences = meshgrid(a,a) - meshgrid(a,a)'; % get differences between elements
differences(1:n+1:n*n) = []; % remove diagonal
a(ismember(a,differences)) = []; % remove elements in differences
I'm assuming that you only want differences between unique elements. If you want to allow the difference between an element of a and itself, then remove the 3rd line.
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,:)]))];
I wish to locate the first position of each unique number from a vector but without a for loop:
e.g
a=[1 1 2 2 3 4 2 1 3 4];
and I can obtain the unique number by having:
uniq=unique(a);
where uniq = [1 2 3 4]
What I want is to obtain each number's first appearance location, any ideas????
first_pos = [1 3 5 6]
where 1 is firstly appear in position 1, 4 is firstly appear in the sixth position from the vector
ALSO, what about the position of the second appearance??
second_pos = [2 4 9 10]
Thank you very much
Use the second output of unique, and use the 'first' option:
>> A = [1 1 2 2 3 4 2 1 3 4];
>> [a,b] = unique(A, 'first')
a =
1 2 3 4 %// the unique values
b =
1 3 5 6 %// the first indices where these values occur
To find the locations of the second occurrences,
%// replace first occurrences with some random number
R = rand;
%// and do the same as before
A(b) = R;
[a2,b2] = unique(A, 'first');
%// Our random number is NOT part of original vector
b2(a2==R)=[];
a2(a2==R)=[];
with this:
b2 =
2 4 9 10
Note that there will have to be at least 2 occurrences of each number in the vector A if the sizes of b and b2 are to agree (this was not the case before your edit).
I have quite big array. To make things simple lets simplify it to:
A = [1 1 1 1 2 2 3 3 3 3 4 4 5 5 5 5 5 5 5 5];
So, there is a group of 1's (4 elements), 2's (2 elements), 3's (4 elements), 4's (2 elements) and 5's (8 elements). Now, I want to keep only columns, which belong to group of 3 or more elements. So it will be like:
B = [1 1 1 1 3 3 3 3 5 5 5 5 5 5 5 5];
I was doing it using for loop, scanning separately 1's, 2's, 3's and so on, but its extremely slow with big arrays...
Thanks for any suggestions how to do it in more efficient way :)
Art.
A general approach
If your vector is not necessarily sorted, then you need to run to count the number of occurrences of each element in the vector. You have histc just for that:
elem = unique(A);
counts = histc(A, elem);
B = A;
B(ismember(A, elem(counts < 3))) = []
The last line picks the elements that have less than 3 occurrences and deletes them.
An approach for a grouped vector
If your vector is "semi-sorted", that is if similar elements in the vector are grouped together (as in your example), you can speed things up a little by doing the following:
start_idx = find(diff([0, A]))
counts = diff([start_idx, numel(A) + 1]);
B = A;
B(ismember(A, A(start_idx(counts < 3)))) = []
Again, note that the vector need not to be entirely sorted, just that similar elements are adjacent to each other.
Here is my two-liner
counts = accumarray(A', 1);
B = A(ismember(A, find(counts>=3)));
accumarray is used to count the individual members of A. find extracts the ones that meet your '3 or more elements' criterion. Finally, ismember tells you where they are in A. Note that A needs not be sorted. Of course, accumarray only works for integer values in A.
What you are describing is called run-length encoding.
There is software for this in Matlab on the FileExchange. Or you can do it directly as follows:
len = diff([ 0 find(A(1:end-1) ~= A(2:end)) length(A) ]);
val = A(logical([ A(1:end-1) ~= A(2:end) 1 ]));
Once you have your run-length encoding you can remove elements based on the length. i.e.
idx = (len>=3)
len = len(idx);
val = val(idx);
And then decode to get the array you want:
i = cumsum(len);
j = zeros(1, i(end));
j(i(1:end-1)+1) = 1;
j(1) = 1;
B = val(cumsum(j));
Here's another way to do it using matlab built-ins.
% Set up
A=[1 1 1 1 2 2 3 3 3 3 4 4 5 5 5 5 5];
threshold=2;
% Get the unique elements of the array
uniqueElements=unique(A);
% Count haw many times each unique element occurs
counts=histc(A,uniqueElements);
% Write which elements should be kept
toKeep=uniqueElements(counts>threshold);
% Make a logical index
indexer=false(size(A));
for i=1:length(toKeep)
% For every unique element we want to keep select the indices in A that
% are equal
indexer=indexer|(toKeep(i)==A);
end
% Apply index
B=A(indexer);