I trying to export logical 1 indices of a matrix to another variable without altering their position. Below I am trying to explain my doubt using a example:
l = logical([1 0 1 1 ;...
1 1 1 0]);
A = [1 2 3 4;...
5 6 7 8];
B = zeros(size(A));
B = A(l)
produces:
B =
1
5
6
3
7
4
But what I am interested in getting is
B =
1 0 3 4
5 6 7 0
Can anyone help me? Thanks
While you could use #tim's approach for this specific example, a more general solution is to use the logical array to index both the thing you're retrieving values from and the array you're assigning into. This grabs the values in A at the TRUE locations in I and places them into the corresponding positions in B.
I = logical([1 0 1 1; 1 1 1 0]);
A = [1 2 3 4; 5 6 7 8];
B = zeros(size(A));
B(I) = A(I);
The element-wise multiplication approach won't work if you want the "default" values in B to be anything other than 0. For example.
% Initialize B to an array of 100's
B = 100 * ones(size(A));
% Replace the elements specified by the logical array
B(I) = A(I);
% 1 100 3 4
% 5 6 7 100
Alternately, if you just want to zero-out the values in A you can also use logical indexing to do this.
A(~I) = 0;
As a sidenote, try to avoid using l for a variable name as it is very difficult to distinguish l from the number 1.
l = logical([1 0 1 1 ;...
1 1 1 0]);
A = [1 2 3 4;...
5 6 7 8];
A .* l % element-wise multiplication
no prob, you are welcome ;-) Accept, question closed! xD
EDIT
I'm afraid Stackoverflow became a page where everyone tries to beat other's answers by trying to make a longer and more detailed answer, even though not related to WHAT WAS ORIGINALLY ASKED. And not the one's which give a quick, easy, simple solution within a small amount of time, to exactly that SPECIFIC QUESTION. Suever immediately becomes an upvote by answering a question which was NOT asked, just because it is longer.
I'll also play the game and edit my answer: If you want to have other default options then 0, one could also adopt my solution and use:
~l*default_value + A.*l
I just want to say: It IS possible.
EDIT2
tic;
for i = 1:1000000
B = A.*l;
end;
toc
>> Elapsed time is 2.18214 seconds.
tic;
for i = 1:1000000
B=zeros(size(A));
B(l)=A(l);
end;
toc
>>Elapsed time is 13.9691 seconds.
Choose for yourself.
EDIT3 (Default value != 0)
>> tic; for i = 1:1e6; B = A.*l+100*(~l); end; toc
Elapsed time is 4.17261 seconds.
>> tic; for i = 1:1e6; B=100*ones(size(A)); B(l)=A(l); end; toc
Elapsed time is 14.2126 seconds.
Related
I am trying to compare two vectors of different size. For instance when I run the code below:
A = [1 4 3 7 9];
B = [1 2 3 4 5 6 7 8 9];
myPadded = [A zeros(1,4)];
C = ismember(myPadded,B)
I get the following output:
C = 1 1 1 1 1 0 0 0 0
However, I want an output that will reflect the positions of the compared values, hence, I would like an output that is displayed as follows:
C = 1 0 1 1 0 0 1 0 1
Please, I need some help :)
There are 2 points. First, you are writing the inputs of ismember in the wrong order. Additionally, you do not need to grow your matrix. Simply try ismember(B, A) and you will get what you expect.
The function ismember(myPadded, B) returns a vector the same size of myPadded, indicating if the i-th element of myPadded is present in B.
To get what you want, just invert parameter order: ismember(B, myPadded).
A quick way of doing this is to use logical indexing. This will only work if the last digit of B is included in A.
A = [1 4 3 7 9];
c(A) = 1; % or true.
An assumption here is that you want to subindex a vector 1:N, so that B always is B = 1:N. In case the last digit is not one this is easy to fix. Just remember to return all to its previous state after you are done. It will be 2 rows extra though.
This solution is meant as a special case working on a very common problem.
I'm trying to elegantly split a vector. For example,
vec = [1 2 3 4 5 6 7 8 9 10]
According to another vector of 0's and 1's of the same length where the 1's indicate where the vector should be split - or rather cut:
cut = [0 0 0 1 0 0 0 0 1 0]
Giving us a cell output similar to the following:
[1 2 3] [5 6 7 8] [10]
Solution code
You can use cumsum & accumarray for an efficient solution -
%// Create ID/labels for use with accumarray later on
id = cumsum(cut)+1
%// Mask to get valid values from cut and vec corresponding to ones in cut
mask = cut==0
%// Finally get the output with accumarray using masked IDs and vec values
out = accumarray(id(mask).',vec(mask).',[],#(x) {x})
Benchmarking
Here are some performance numbers when using a large input on the three most popular approaches listed to solve this problem -
N = 100000; %// Input Datasize
vec = randi(100,1,N); %// Random inputs
cut = randi(2,1,N)-1;
disp('-------------------- With CUMSUM + ACCUMARRAY')
tic
id = cumsum(cut)+1;
mask = cut==0;
out = accumarray(id(mask).',vec(mask).',[],#(x) {x});
toc
disp('-------------------- With FIND + ARRAYFUN')
tic
N = numel(vec);
ind = find(cut);
ind_before = [ind-1 N]; ind_before(ind_before < 1) = 1;
ind_after = [1 ind+1]; ind_after(ind_after > N) = N;
out = arrayfun(#(x,y) vec(x:y), ind_after, ind_before, 'uni', 0);
toc
disp('-------------------- With CUMSUM + ARRAYFUN')
tic
cutsum = cumsum(cut);
cutsum(cut == 1) = NaN; %Don't include the cut indices themselves
sumvals = unique(cutsum); % Find the values to use in indexing vec for the output
sumvals(isnan(sumvals)) = []; %Remove NaN values from sumvals
output = arrayfun(#(val) vec(cutsum == val), sumvals, 'UniformOutput', 0);
toc
Runtimes
-------------------- With CUMSUM + ACCUMARRAY
Elapsed time is 0.068102 seconds.
-------------------- With FIND + ARRAYFUN
Elapsed time is 0.117953 seconds.
-------------------- With CUMSUM + ARRAYFUN
Elapsed time is 12.560973 seconds.
Special case scenario: In cases where you might have runs of 1's, you need to modify few things as listed next -
%// Mask to get valid values from cut and vec corresponding to ones in cut
mask = cut==0
%// Setup IDs differently this time. The idea is to have successive IDs.
id = cumsum(cut)+1
[~,~,id] = unique(id(mask))
%// Finally get the output with accumarray using masked IDs and vec values
out = accumarray(id(:),vec(mask).',[],#(x) {x})
Sample run with such a case -
>> vec
vec =
1 2 3 4 5 6 7 8 9 10
>> cut
cut =
1 0 0 1 1 0 0 0 1 0
>> celldisp(out)
out{1} =
2
3
out{2} =
6
7
8
out{3} =
10
For this problem, a handy function is cumsum, which can create a cumulative sum of the cut array. The code that produces an output cell array is as follows:
vec = [1 2 3 4 5 6 7 8 9 10];
cut = [0 0 0 1 0 0 0 0 1 0];
cutsum = cumsum(cut);
cutsum(cut == 1) = NaN; %Don't include the cut indices themselves
sumvals = unique(cutsum); % Find the values to use in indexing vec for the output
sumvals(isnan(sumvals)) = []; %Remove NaN values from sumvals
output = {};
for i=1:numel(sumvals)
output{i} = vec(cutsum == sumvals(i)); %#ok<SAGROW>
end
As another answer shows, you can use arrayfun to create a cell array with the results. To apply that here, you'd replace the for loop (and the initialization of output) with the following line:
output = arrayfun(#(val) vec(cutsum == val), sumvals, 'UniformOutput', 0);
That's nice because it doesn't end up growing the output cell array.
The key feature of this routine is the variable cutsum, which ends up looking like this:
cutsum =
0 0 0 NaN 1 1 1 1 NaN 2
Then all we need to do is use it to create indices to pull the data out of the original vec array. We loop from zero to max and pull matching values. Notice that this routine handles some situations that may arise. For instance, it handles 1 values at the very beginning and very end of the cut array, and it gracefully handles repeated ones in the cut array without creating empty arrays in the output. This is because of the use of unique to create the set of values to search for in cutsum, and the fact that we throw out the NaN values in the sumvals array.
You could use -1 instead of NaN as the signal flag for the cut locations to not use, but I like NaN for readability. The -1 value would probably be more efficient, as all you'd have to do is truncate the first element from the sumvals array. It's just my preference to use NaN as a signal flag.
The output of this is a cell array with the results:
output{1} =
1 2 3
output{2} =
5 6 7 8
output{3} =
10
There are some odd conditions we need to handle. Consider the situation:
vec = [1 2 3 4 5 6 7 8 9 10 11 12 13 14];
cut = [1 0 0 1 1 0 0 0 0 1 0 0 0 1];
There are repeated 1's in there, as well as a 1 at the beginning and end. This routine properly handles all this without any empty sets:
output{1} =
2 3
output{2} =
6 7 8 9
output{3} =
11 12 13
You can do this with a combination of find and arrayfun:
vec = [1 2 3 4 5 6 7 8 9 10];
N = numel(vec);
cut = [0 0 0 1 0 0 0 0 1 0];
ind = find(cut);
ind_before = [ind-1 N]; ind_before(ind_before < 1) = 1;
ind_after = [1 ind+1]; ind_after(ind_after > N) = N;
out = arrayfun(#(x,y) vec(x:y), ind_after, ind_before, 'uni', 0);
We thus get:
>> celldisp(out)
out{1} =
1 2 3
out{2} =
5 6 7 8
out{3} =
10
So how does this work? Well, the first line defines your input vector, the second line finds how many elements are in this vector and the third line denotes your cut vector which defines where we need to cut in our vector. Next, we use find to determine the locations that are non-zero in cut which correspond to the split points in the vector. If you notice, the split points determine where we need to stop collecting elements and begin collecting elements.
However, we need to account for the beginning of the vector as well as the end. ind_after tells us the locations of where we need to start collecting values and ind_before tells us the locations of where we need to stop collecting values. To calculate these starting and ending positions, you simply take the result of find and add and subtract 1 respectively.
Each corresponding position in ind_after and ind_before tell us where we need to start and stop collecting values together. In order to accommodate for the beginning of the vector, ind_after needs to have the index of 1 inserted at the beginning because index 1 is where we should start collecting values at the beginning. Similarly, N needs to be inserted at the end of ind_before because this is where we need to stop collecting values at the end of the array.
Now for ind_after and ind_before, there is a degenerate case where the cut point may be at the end or beginning of the vector. If this is the case, then subtracting or adding by 1 will generate a start and stopping position that's out of bounds. We check for this in the 4th and 5th line of code and simply set these to 1 or N depending on whether we're at the beginning or end of the array.
The last line of code uses arrayfun and iterates through each pair of ind_after and ind_before to slice into our vector. Each result is placed into a cell array, and our output follows.
We can check for the degenerate case by placing a 1 at the beginning and end of cut and some values in between:
vec = [1 2 3 4 5 6 7 8 9 10];
cut = [1 0 0 1 0 0 0 1 0 1];
Using this example and the above code, we get:
>> celldisp(out)
out{1} =
1
out{2} =
2 3
out{3} =
5 6 7
out{4} =
9
out{5} =
10
Yet another way, but this time without any loops or accumulating at all...
lengths = diff(find([1 cut 1])) - 1; % assuming a row vector
lengths = lengths(lengths > 0);
data = vec(~cut);
result = mat2cell(data, 1, lengths); % also assuming a row vector
The diff(find(...)) construct gives us the distance from each marker to the next - we append boundary markers with [1 cut 1] to catch any runs of zeros which touch the ends. Each length is inclusive of its marker, though, so we subtract 1 to account for that, and remove any which just cover consecutive markers, so that we won't get any undesired empty cells in the output.
For the data, we mask out any elements corresponding to markers, so we just have the valid parts we want to partition up. Finally, with the data ready to split and the lengths into which to split it, that's precisely what mat2cell is for.
Also, using #Divakar's benchmark code;
-------------------- With CUMSUM + ACCUMARRAY
Elapsed time is 0.272810 seconds.
-------------------- With FIND + ARRAYFUN
Elapsed time is 0.436276 seconds.
-------------------- With CUMSUM + ARRAYFUN
Elapsed time is 17.112259 seconds.
-------------------- With mat2cell
Elapsed time is 0.084207 seconds.
...just sayin' ;)
Here's what you need:
function spl = Splitting(vec,cut)
n=1;
j=1;
for i=1:1:length(b)
if cut(i)==0
spl{n}(j)=vec(i);
j=j+1;
else
n=n+1;
j=1;
end
end
end
Despite how simple my method is, it's in 2nd place for performance:
-------------------- With CUMSUM + ACCUMARRAY
Elapsed time is 0.264428 seconds.
-------------------- With FIND + ARRAYFUN
Elapsed time is 0.407963 seconds.
-------------------- With CUMSUM + ARRAYFUN
Elapsed time is 18.337940 seconds.
-------------------- SIMPLE
Elapsed time is 0.271942 seconds.
Unfortunately there is no 'inverse concatenate' in MATLAB. If you wish to solve a question like this you can try the below code. It will give you what you looking for in the case where you have two split point to produce three vectors at the end. If you want more splits you will need to modify the code after the loop.
The results are in n vector form. To make them into cells, use num2cell on the results.
pos_of_one = 0;
% The loop finds the split points and puts their positions into a vector.
for kk = 1 : length(cut)
if cut(1,kk) == 1
pos_of_one = pos_of_one + 1;
A(1,one_pos) = kk;
end
end
F = vec(1 : A(1,1) - 1);
G = vec(A(1,1) + 1 : A(1,2) - 1);
H = vec(A(1,2) + 1 : end);
I believe most functions in MATLAB should be able to receive matrix input and return the output in the form of matrix.
For example sqrt([1 4 9]) would return [1 2 3].
However, when I tried this recurring factorial function:
function k = fact(z)
if z ~= 0
k = z * fact(z-1);
else
k = 1;
end
end
It works perfectly when a number is input into fact. However, when a matrix is input into fact, it returns the matrix itself, without performing the factorial function.
E.g.
fact(3) returns 6
fact([1 2 3]) returns [1 2 3] instead of [1 2 6].
Any help is appreciated. Thank you very much!
Since MATLAB is not known to be good with recursive functions, how about a vectorized approach? Try this for a vector input -
mat1 = repmat([1:max(z)],[numel(z) 1])
mat1(bsxfun(#gt,1:max(z),z'))=1
output1 = prod(mat1,2)
Sample run -
z =
1 2 7
output1 =
1
2
5040
For the sake of answering your original question, here's the annoying loopy code for a vector or 2D matrix as input -
function k1 = fact1(z1)
k1 = zeros(size(z1));
for ii = 1:size(z1,1)
for jj = 1:size(z1,2)
z = z1(ii,jj);
if z ~= 0
k1(ii,jj) = z .* fact1(z-1);
else
k1(ii,jj) = 1;
end
end
end
return
Sample run -
>> fact1([1 2 7;3 2 1])
ans =
1 2 5040
6 2 1
You can use the gamma function to compute the factorial without recursion:
function k = fact(z)
k = gamma(z+1);
Example:
>> fact([1 2 3 4])
ans =
1 2 6 24
Not sure if all of you know, but there is an actual factorial function defined in MATLAB that can take in arrays / matrices of any size, and computes the factorial element-wise. For example:
k = factorial([1 2 3 4; 5 6 7 8])
k =
1 2 6 24
120 720 5040 40320
Even though this post is looking for a recursive implementation, and Divakar has provided a solution, I'd still like to put my two cents in and suggest an alternative. Also, let's say that we don't have access to factorial, and we want to compute this from first principles. What I would personally do is create a cell array that's the same size as the input matrix, but each element in this cell array would be a linear index array from 1 up to the number defined for each location in the original matrix. You would then apply prod to each cell element to compute the factorial. A precondition is that no number is less than 1, and that all elements are integers. As such:
z1 = ... ; %// Define input matrix here
z1_matr = arrayfun(#(x) 1:x, z1, 'uni', 0);
out = cellfun(#prod, z1_matr);
If z1 = [1 2 3 4; 5 6 7 8];, from my previous example, we get the same output with the above code:
out =
1 2 6 24
120 720 5040 40320
This will obviously be slower as there is an arrayfun then cellfun call immediately after, but I figured I'd add another method for the sake of just adding in another method :) Not sure how constructive this is, but I figured I'd add my own method and join Divakar and Luis Mendo :)
I'm looking for a fast / concise way to check whether some matrix contains given vector, e.g.:
bigMatrix = [1 1 1; 2 2 2; 4 4 4; 5 5 5];
someFunction(bigMatrix, [1 1 1]) % = true
someFunction(bigMatrix, [3 3 3]) % = false
Is there such function/operator, or I need a loop?
I would suggest the following solution:
bigMatrix = [1 1 1; 2 2 2; 4 4 4; 5 5 5];
Vec = [2 2 2];
Index = ismember(bigMatrix, Vec, 'rows');
The result?
Index =
0
1
0
0
ismember is an incredibly useful function that checks whether the elements of one set are in another set. Here, I exploit the rows option to force the function to compare rows, rather than individual elements.
UPDATE: On the other hand, it is always worth doing a few speed tests! I just compared the ismember approach to the following alternative method:
N = size(bigMatrix, 1);
Index2 = zeros(N, 1);
for n = 1:N
if all(bigMatrix(n, :) == Vec)
Index2(n) = 1;
end
end
My findings? The size of bigMatrix matters! In particular, if bigMatrix is on the small side (somewhat of a misnomer), then the loop is much faster. The first approach is preferable only when bigMatrix becomes big. Further, the results are also dependent on how many columns bigMatrix has, as well as rows! I suggest you test both approaches for your application and then go with whichever is faster. (EDIT: This was on R2011a)
General Note: I am continually surprised by how much faster Matlab's loops have gotten in the last few years. Methinks vectorized code is no longer the holy grail that it once was.
I have a matrix A with size (nr,nc), a vector of column indices B (so B has size (nr,1) and every element in B is an integer between 1 and nc), and I want to do something to every element in A that is of the form A(i,B(i)) for i between 1 and nr, efficiency being the key concern.
For concreteness, say C is a vector of size (nr,1), the goal is to do
for i=1:nr
A(i,B(i))=A(i,B(i))+C(i)
end
more efficiently. The context is usually that nr>>nc (because when nr is large vectorization is efficient for many operations). I have gotten a factor 3 speedup by using an indicator function approach:
for k=1:nc
A(:,k)=A(:,k)+(k==B).*C
end
Are there other ways (more efficient hopefully) to do this?
I guess this is similar to many questions on double-indexing, but it's concretely one I run into all the time.
Use linear indexing:
idx = sub2ind(size(A), 1:nr, B');
A(idx) = A(idx) + C';
or (edited version with one less transpose)
idx = sub2ind(size(A), (1:nr)', B);
A(idx) = A(idx) + C;
One way would be to use linear indexing of the matrix. You will need a vector v holding the offsets of the first element in each line, then index using A(v + B). For example:
>A=[1 2 3; 4 5 6; 7 8 9]
A =
1 2 3
4 5 6
7 8 9
>B = [1 2 3] % we want the 1st element of row 1, 2nd of row 2, 3rd of row 3
>ii = [0 3 6] + B
>a(ii)
1 5 9
Note: As groovingandi had shown, it is also possible (and more readable) to use sub2ind to generate the ii linear indices vector. The idea is essentially the same.