I have an array A of 1s and 0s and want to see if the larger array of bits B contains those bits in that exact order?
Example: A= [0 1 1 0 0 0 0 1]
B= [0 1 0 0 1 1 0 0 0 0 1 0 1 0 1]
would be true as A is contained in B
Most solutions I have found only determine if a value IS contained in another matrix, this is no good here as it is already certain that both matrices will be 1s and 0s
Thanks
One (albeit unusual) option, since you're dealing with integer values, is to convert A and B to character arrays and use the contains function:
isWithin = contains(char(B), char(A));
There are some obtuse vectorized ways to to do this, but by far the easiest, and likely just as efficient, is to use a loop with a sliding window,
A = [0 1 1 0 0 0 0 1];
B = [0 1 0 0 1 1 0 0 0 0 1 0 1 0 1];
vec = 0:(numel(A)-1);
for idx = 1:(numel(B)-numel(A)-1)
if all(A==B(idx+vec))
fprintf('A is contained in B\n');
break; % exit the loop as soon as 1 match is found
end
end
Or if you want to know the location(s) in B (of potentially multiple matches) then,
A = [0 1 1 0 0 0 0 1];
B = [0 1 0 0 1 1 0 0 0 0 1 0 1 0 1];
C = false(1,numel(B)-numel(A)-1);
vec = 0:(numel(A)-1);
for idx = 1:numel(C)
C(idx) = all(A==B(idx+vec));
end
if any(C)
fprintf('A is contained in B\n');
end
In this case
>> C
C =
1×6 logical array
0 0 0 1 0 0
You can use the cross-correlation between two signals for this, as a measure of local similarity.
For achieving good results, you need to shift A and B so that you don't have the value 0 any more. Then compute the correlation between the two of them with conv (keeping in mind that the convolution is the cross-correlation with one signal flipped), and normalize with the energy of A so that you get a perfect match whenever you get the value 1:
conv(B-0.5, flip(A)-0.5, 'valid')/sum((A-0.5).^2)
In the normalization term, flipping is removed as it does not change the value.
It gives:
[0 -0.5 0.25 1 0 0 -0.25 0]
4th element is 1, so starting from index equal to 4 you get a perfect match.
Related
I've got logical array(zeros and ones) 1500x700
I want to find "1" in every column and when there are more than one "1" in column i should choose the middle one.
Is that possible to do it? I know how to find "1", but don't know how to extract the middle "1" if there's couple of "1" in one column.
The find function returns the indices of your ones.
>> example=[1,0,0,1,0,1,1];
>> indices=find(example)
indices =
1 4 6 7
>> indices(floor(numel(indices)/2))
ans =
4
Do this for each column and you have a solution.
You can
Get the row and column indices of ones with find;
Apply accumarray with a custom function to get the middle row index for each column.
x = [1 0 0 0 0; 0 0 1 0 0; 1 0 1 0 0; 1 0 0 1 0]; % example
[ii, jj] = find(x); % step 1
result = accumarray(jj, ii, [size(x,2) 1], #(x) x(ceil(end/2)), NaN); % step 2
Note that:
For an even number of ones this gives the first of the two middle indices. If you prefer the average of the two middle indices replace #(x) x(ceil(end/2)) by #median.
For a column without ones this gives NaN as result. If you prefer a different value, replace the input fifth argument of accumarray by that.
Example:
x =
1 0 0 0 0
0 0 1 0 0
1 0 1 0 0
1 0 0 1 0
result =
3
NaN
2
4
NaN
I basically want to use the function ismember, but for a range. For example, I want to know what data points in array1 are within n distance to array2, for each element in array2.
I have the following:
array1 = [1,2,3,4,5]
array2 = [2,2,3,10,20,40,50]
I want to know what values in array2 are <= 2 away from array1:
indices(1,:) (where array1(1) = 1) = [1 1 1 0 0 0 0]
indices(2,:) (where array1(2) = 2) = [1 1 1 0 0 0 0]
indices(3,:) (where array1(3) = 3) = [1 1 1 0 0 0 0]
indices(4,:) (where array1(4) = 4) = [1 1 1 0 0 0 0]
indices(5,:) (where array1(5) = 5) = [0 0 1 0 0 0 0]
Drawbacks:
My array1 is 496736 elements, my array2 is 9268 elements, so aI would rather not use a loop.
Looping is a valid option here. Intialise an array output to the size of array1 X array2, then loop over all elements in array1 an subtract array2 from that, then check whether the absolute value is less than or equal to 2:
array1 = [1,2,3,4,5];
array2 = [2,2,3,10,20,40,50];
output = zeros(numel(array1), numel(array2),'logical');
for ii = 1:numel(array1)
output(ii,:) = abs(array1(ii)-array2)<=2;
end
output =
1 1 1 0 0 0 0
1 1 1 0 0 0 0
1 1 1 0 0 0 0
1 1 1 0 0 0 0
0 0 1 0 0 0 0
i.e. loops are not the problem.
Thanks to Rahnema1's suggestion, you can initialise output directly as a logical matrix:
output = zeros(numel(array1),numel(array2),'logical');
whose size is just 4.3GB.
On timings: Hans' code runs in a matter of seconds for array1 = 5*rand(496736,1); array2 = 25*rand(9286,1);, the looped solution takes about 15 times longer. Both solutions are equal to one another. obcahrdon's ismembertol solution is somewhere in between on my machine.
On RAM usage:
Both implicit expansion, as per Hans' answer, as well as the loop suggested in mine work with just 4.3GB RAM on your expanded problem size (496736*9286)
pdist2 as per Luis' answer and bsxfun as per Hans' on the other hand try to create an intermediate double matrix of 34GB (which doesn't even fit in my RAM, so I cannot compare timings).
obchardon's ismembertol solution outputs a different form of the solution, and takes ~5.04GB (highly dependent on the amount of matches found, the more, the larger this number will be).
In general this leads me to the conclusion that implicit expansion should be your option of choice, but if you have R2016a or earlier, ismembertol or a loop is the way to go.
Using implicit expansion, introduced in MATLAB R2016b, you can simply write:
abs(array1.' - array2) <= 2
ans =
1 1 1 0 0 0 0
1 1 1 0 0 0 0
1 1 1 0 0 0 0
1 1 1 0 0 0 0
0 0 1 0 0 0 0
For earlier MATLAB versions, you can get this using the bsxfun function:
abs(bsxfun(#minus, array1.', array2)) <= 2
ans =
1 1 1 0 0 0 0
1 1 1 0 0 0 0
1 1 1 0 0 0 0
1 1 1 0 0 0 0
0 0 1 0 0 0 0
Hope that helps!
P.S. On the "MATLAB is slow for loops" myth, please have a look at that blog post for example.
EDIT: Please read Adriaan's answer on the RAM consumption using this and/or his approach!
If you have the Statistics Toolbox, you can use pdist2 to compute the distance matrix:
result = pdist2(array1(:), array2(:)) <= 2;
As noted by #Adriaan, this is not efficient for large input sizes. In that case a better approach is a loop with preallocation of the logical matrix output, as in his answer.
You can also use ismembertol with some specific option:
A = [1,2,3,4,5];
B = [2,2,3,10,20,40,5000];
tol = 2;
[~,ind] = ismembertol([A-tol;A+tol].',[B-tol;B+tol].',tol, 'ByRows', true, ...
'OutputAllIndices', true, 'DataScale', [1,Inf])
It will create a 5x1 cell array containing the corresponding linear indice
ind{1} = [1,2,3]
ind{2} = [1,2,3]
...
ind{5} = [3]
In this case using linear indices instead of logical indices will greatly reduce the memory consumption.
I'm trying to remove the rows which has duplicates in sequence. I have only 2 possible values which are 0 and 1. I have nXm which n shows possible number of bits and m is not important for my question. My goal is to find an matrix which is nX(m-a). The rows a which has the property which includes duplicates in sequence. For example:
My matrix is :
A=[0 1 0 1 0 1;
0 0 0 1 1 1;
0 0 1 0 0 1;
0 1 0 0 1 0;
1 0 0 0 1 0]
I want to remove the rows has t duplicates in sequence for 0. In this question let's assume t is 3. So I want the matrix which:
B=[0 1 0 1 0 1;
0 0 1 0 0 1;
0 1 0 0 1 0]
2nd and 5th rows are removed.
I probably need to use diff.
So you want to remove rows of A that contain at least t zeros in sequence.
How about a single line?
B = A(~any(conv2(1,ones(1,t),2*A-1,'valid')==-t, 2),:);
How this works:
Transform A to bipolar form (2*A-1)
Convolve each row with a sequence of t ones (conv2(...))
Keep only rows for which the convolution does not contain -t (~any(...)). The presence of -t indicates a sequence of t zeros in the corresponding row of A.
To remove rows that contain at least t ones, just change -t to t:
B = A(~any(conv2(1,ones(1,t),2*A-1,'valid')==t, 2),:);
Here is a generalized approach which removes any rows which has given number of consecutive duplicates (not just zero. could be any number).
t = 3;
row_mask = ~any(all(~diff(reshape(im2col(A,[1 t],'sliding'),t,size(A,1),[]))),3);
out = A(row_mask,:)
Sample Run:
>> A
A =
0 1 0 1 0 1
0 0 1 5 5 5 %// consecutive 3 5's
0 0 1 0 0 1
0 1 0 0 1 0
1 1 1 0 0 1 %// consecutive 3 1's
>> out
out =
0 1 0 1 0 1
0 0 1 0 0 1
0 1 0 0 1 0
How about an approach using strings? This is certainly not as fast as Luis Mendo's method where you work directly with the numerical array, but it's thinking a bit outside of the box. The basis of this approach is that I consider each row of A to be a unique string, and I can search each string for occurrences of a string of 0s by regular expressions.
A=[0 1 0 1 0 1;
0 0 0 1 1 1;
0 0 1 0 0 1;
0 1 0 0 1 0;
1 0 0 0 1 0];
t = 3;
B = sprintfc('%s', char('0' + A));
ind = cellfun('isempty', regexp(B, repmat('0', [1 t])));
B(~ind) = [];
B = double(char(B) - '0');
We get:
B =
0 1 0 1 0 1
0 0 1 0 0 1
0 1 0 0 1 0
Explanation
Line 1: Convert each line of the matrix A into a string consisting of 0s and 1s. Each line becomes a cell in a cell array. This uses the undocumented function sprintfc to facilitate this cell array conversion.
Line 2: I use regular expressions to find any occurrences of a string of 0s that is t long. I first use repmat to create a search string that is full of 0s and is t long. After, I determine if each line in this cell array contains this sequence of characters (i.e. 000....). The function regexp helps us perform regular expressions and returns the locations of any matches for each cell in the cell array. Alternatively, you can use the function strfind for more recent versions of MATLAB to speed up the computation, but I chose regexp so that the solution is compatible with most MATLAB distributions out there.
Continuing on, the output of regexp/strfind is a cell array of elements where each cell reports the locations of where we found the particular string. If we have a match, there should be at least one location that is reported at the output, so I check to see if any matches are empty, meaning that these are the rows we don't want to remove. I want to turn this into a logical array for the purposes of removing rows from A, and so this is wrapped with a cellfun call to determine the cells that are empty. Therefore, this line returns a logical array where a 0 means that remove this row and a 1 means that we don't.
Line 3: I take the logical array from Line 2 and invert it because that's what we really want. We use this inverted array to index into the cell array and remove those strings.
Line 4: The output is still a cell array, so I convert it back into a character array, and finally back into a numerical array.
I have an array of binary data with long stretches of ones and zeros and I want to find the indices of when it changes.
a = [ 1 1 1 1 1 0 0 0 0 0 0 1 1]
I want to search for [1 0] and [0 1] to find the transition points. I'd like to avoid long loops to find these if possible. Any ideas?
Something like this should do the job:
b = diff(a); % (assuming 'a' is a vector)
oneFromZero = find(b == 1) + 1; % vector of indices of a '1' preceded by a '0'
zeroFromOne = find(b == -1) + 1; % vector of indices of a '0' preceded by a '1'
Depending on what you want exactly, you may or may not want to add 1 to the resulting arrays of indices.
I'd go with
d = a(1:end-1) - a(2:end);
ind = find(d);
Here, d will be 1 where you have a ... 1 0 ... in your bit string and it will be -1 where you have a ... 0 1 .... All the other elements in d will be 0, since, at those positions, the bits are equal to their neighbour.
With this in place, you can use find to get the indices where these two patterns occur. The whole procedure is of O(n) complexity, where n=length(a), since it requires two passes through a.
For a = [ 1 1 1 1 1 0 0 0 0 0 0 1 1] the above code computes ind = [5 11].
To search for an arbitrary pattern of zeros and ones:
You can compute a convolution (conv) of the two sequences in bipolar (±1) form and then find the maxima. Since the convolution flips one of the inputs, it has to be flipped to undo that:
a = [ 1 1 1 1 1 0 0 0 0 0 0 1 1];
pattern = [0 1 1];
result = find(conv(2*a-1, 2*pattern(end:-1:1)-1, 'valid')==numel(pattern));
In this example
result =
11
which means that [0 1 1] appears in a only once, namely at index 11.
A simpler approach is to use strfind, exploiting the undocumented fact that this function can be applied to numeric vectors:
result = strfind(a, pattern);
I am trying to write a svm code, but i am literally a beginner in matlab.
So in my code, in a for loop, i should store predictions. The data is like this:
testIdx = [1 1 1 0 0 0 0 0 1 0 1 1]'; % i wrote it like this but it says logical
and
pred = [1 1 1 0 1 0]'; % again logical
So i want to form a 12 length array and turn its 1st,2nd,3rd,9th,11th,12th elements into 1 1 1 0 1 0, and likewise rest of test elements into another set of 0/1s in other iteration.
If possible let it be a normal array, not logical. Thanks in advance
I did it myself old style but there must be a shorter direct way right?
Y = zeros ( size(testIdx,1), 1) ;
a=1;
for i = 1:size(testIdx,1)
if testIdx(i) ==1
Y(i) = pred(a);
a=a+1;
end
end
If you create testIdx and pred the way you specified, then they are double and not logical type. To use logical indexing, it is easiest if testIdx is converted to the logical type. Then you can simply use
testIdx = [1 1 1 0 0 0 0 0 1 0 1 1]';
pred = [1 1 1 0 1 0]';
Y = zeros(size(testIdx));
Y(logical(testIdx)) = pred;
With Y(logical(testIdx), you select all indexes which are set to 1 in the testIdx vector and then write predto these indexes.