How to get the union of the two 3D matrix? - matlab

I have two 3D matrix A and B. The size of A and B are both 40*40*20 double.
The values in matrix A and B are either 0 or 1. The number of "1" in A are 100,
the number of "1" in B are 50. The "1" in matrix A and B may or may not be in
the same coordinates. I want to get the union of matrix A and B, called C. The values in 3D matrix C is either "1" or "0". The number of "1" in C is less than or equal to 150. My question is how to get the 3D matrix C in Matlab?

You can use the operator or, which is a logical or. So or(a,b) is equivalent to the logical operation a | b.
C = or(A,B);
C = a | b;
| and or are the same operator in MatLab, it's just two different way to call it.
I think this is the best solution as long as it's integrated into MatLab. However, you have plenty different ways to do it.
Just as an example, you can do
C = logical(a+b);
logical is an operator that convert every value into logical values. Long story short, it will replace any value different of 0 by 1.

You can approach it in 2 ways. The more efficient one is using vectors but you can also do it in classical nested for loops.
A = rand(40,40,20);
A = A > 0.01; # Get approximate 320 ones and rest zeros
B = rand(40,40,20);
B = B > 0.005; # Get approximate 160 ones and rest zeros
C = zeros(size(A));
for iter1 = 1:size(A,1)
for iter2 = 1:size(A,2)
for iter3 = 1:size(A,3)
C(iter1,iter2,iter3) = A(iter1,iter2,iter3)|B(iter1,iter2,iter3)
end
end
end
This method will be very slow. You can vectorized it to improve performance
C = A|B

Related

Matlab - indexing

I have a matrix A which is 21x1 and contains only ones and twos.
Then I have a matrix B which is 6 * 600 matrix of numbers ranging between 0 and 21.
I want to generate a matrix C which is 6 * 600 matrix containing ones and twos such that:
If B matrix has a zero, matrix C should have a zero on that place. If B matrix has number 5, then matrix C should have the element on row 5 of matrix A and so on and so forth.
Please let me know if this is not clear.
Let us generate some sample inputs:
A = randi(2,21,1);
B = randi(22,6,600)-1;
The output C will then be:
C = B*0; %// preallocation + take care of the elements that need to be 0
C(B>0) = A(B(B>0)); %// logical indexing
The explanation of the 2nd line is as follows:
RHS
B>0 - return a logical array the size of B which has the meaning of whether this specific element of B is larger-than-0 value.
B(B>0) - return the elements of B for which there are true values in B>0 (i.e. numbers that can be used to index into A).
A(...) - return the elements of A that correspond to the valid indices from B.
% Generate matrices fitting the description
A = round(rand(21,1))+1;
B = round(rand(6,600)*21);
C = zeros(6,600);
% Indexing impossible since zeroes cannot be used as index. So treat per element using linear indexing.
for ii = 1:(6*600)
if B(ii) == 0
C(ii) = 0;
else
C(ii) = A(B(ii));
end
end
Although the piece of code could be optimized further this is the most clear way of creating understanding and speed is not needed if it's only this small matrix evaluated a limited number of times.

How to vectorize this Matlab loop

I need some help to vectorize the following operation since I'm a little confused.
So, I have a m-by-2 matrix A and n-by-1 vector b. I want to create a n-by-1 vector c whose entries should be the values of the second column of A whose line is given by the line where the correspondent value of b would fall...
Not sure if I was clear enough. Anyway, the code below does compute c correctly so you can understand what is my desired output. However, I want to vectorize this function since my real n and m are in the order of many thousands.
Note that values of bare non-integer and not necessarily equal to any of those in the first column of A (these ones could be non-integers too!).
m = 5; n = 10;
A = [(0:m-1)*1.1;rand(1,m)]'
b = (m-1)*rand(n,1)
[bincounts, ind] = histc(b,A(:,1))
for i = 1:n
c(i) = A(ind(i),2);
end
All you need is:
c = A(ind,2);

element by element matrix multiplication in Matlab

So I have the following matrices:
A = [1 2 3; 4 5 6];
B = [0.5 2 3];
I'm writing a function in MATLAB that will allow me to multiply a vector and a matrix by element as long as the number of elements in the vector matches the number of columns. In A there are 3 columns:
1 2 3
4 5 6
B also has 3 elements so this should work. I'm trying to produce the following output based on A and B:
0.5 4 9
2 10 18
My code is below. Does anyone know what I'm doing wrong?
function C = lab11(mat, vec)
C = zeros(2,3);
[a, b] = size(mat);
[c, d] = size(vec);
for i = 1:a
for k = 1:b
for j = 1
C(i,k) = C(i,k) + A(i,j) * B(j,k);
end
end
end
end
MATLAB already has functionality to do this in the bsxfun function. bsxfun will take two matrices and duplicate singleton dimensions until the matrices are the same size, then perform a binary operation on the two matrices. So, for your example, you would simply do the following:
C = bsxfun(#times,mat,vec);
Referencing MrAzzaman, bsxfun is the way to go with this. However, judging from your function name, this looks like it's homework, and so let's stick with what you have originally. As such, you need to only write two for loops. You would use the second for loop to index into both the vector and the columns of the matrix at the same time. The outer most for loop would access the rows of the matrix. In addition, you are referencing A and B, which are variables that don't exist in your code. You are also initializing the output matrix C to be 2 x 3 always. You want this to be the same size as mat. I also removed your checking of the length of the vector because you weren't doing anything with the result.
As such:
function C = lab11(mat, vec)
[a, b] = size(mat);
C = zeros(a,b);
for i = 1:a
for k = 1:b
C(i,k) = mat(i,k) * vec(k);
end
end
end
Take special note at what I did. The outer-most for loop accesses the rows of mat, while the inner-most loop accesses the columns of mat as well as the elements of vec. Bear in mind that the number of columns of mat need to be the same as the number of elements in vec. You should probably check for this in your code.
If you don't like using the bsxfun approach, one alternative is to take the vector vec and make a matrix out of this that is the same size as mat by stacking the vector vec on top of itself for as many times as we have rows in mat. After this, you can do element-by-element multiplication. You can do this stacking by using repmat which repeats a vector or matrices a given number of times in any dimension(s) you want. As such, your function would be simplified to:
function C = lab11(mat, vec)
rows = size(mat, 1);
vec_mat = repmat(vec, rows, 1);
C = mat .* vec_mat;
end
However, I would personally go with the bsxfun route. bsxfun basically does what the repmat paradigm does under the hood. Internally, it ensures that both of your inputs have the same size. If it doesn't, it replicates the smaller array / matrix until it is the same size as the larger array / matrix, then applies an element-by-element operation to the corresponding elements in both variables. bsxfun stands for Binary Singleton EXpansion FUNction, which is a fancy way of saying exactly what I just talked about.
Therefore, your function is further simplified to:
function C = lab11(mat, vec)
C = bsxfun(#times, mat, vec);
end
Good luck!

Average part of a multidimensional array based on another array (Matlab)

B = randn(1,25,10);
Z = [1;1;1;2;2;3;4;4;4;3];
Ok, so, I want to find the locations where Z=1(or any numbers that are equal to each other), then average across each of the 25 points at these specific locations. In the example you would end with a 1*25*4 array.
Is there an easy way to do this?
I'm not the most versed in Matlab.
First things first: break down the problem.
Define the groups (i.e. the set of unique Z values)
Find elements which belong to these groups
Take the average.
Once you have done that, you can begin to see it's a pretty standard for loop and "Select columns which meet criteria".
Something along the lines of:
B = randn(1,25,10);
Z = [1;1;1;2;2;3;4;4;4;3];
groups = unique(Z); %//find the set of groups
C = nan(1,25,length(groups)); %//predefine the output space for efficiency
for gi = 1:length(groups) %//for each group
idx = Z == groups(gi); %//find it's members
C(:,:,gi) = mean(B(:,:,idx), 3); %//select and mean across the third dimension
end
If B = randn(10,25); then it's very easy because Matlab function usually works down the rows.
Using logical indexing:
ind = Z == 1;
mean(B(ind,:));
If you're dealing with multiple dimensions use permute (and reshape if you actually have 3 dimensions or more) to get yourself to a point where you're averaging down the rows as above:
B = randn(1,25,10);
BB = permute(B, [3,2,1])
continue as above

Maximum of a subset of array (MATLAB)

Suppose in MATLAB I have a real matrix A which is n x m and a binary matrix B of the same size. The latter matrix defines the optimization set (all indices for which the element of B equals one): over this set I would like to find the maximal element of A. How can I do this?
The first idea I had is that I consider C = A.*B and look for the maximal element of C. This works fine for all matrices A which have at least one positive element, however it does not work for matrices with all negative elements.
You can do
C = A(B==1);
to give you an array of just the values of A corresponding to a value of 1 in B. And
max( C )
will give you the maximum value of A where B is 1
With this method you don't run into a problem when all values of A are negative as the zeros don't appear in C.
Obviously you can condense this to
desiredValue = max(A(B(:)==1));
I am using the colon operator to make sure that the result of A(B(:)==1) is a column vector - if B is all ones I am not sure if Matlab would return a vector or a nxm matrix (and I can't confirm right now).
update to get the index of the value, you can do:
f = find(B==1);
[m mi] = max(A(f));
maxIndex = f(mi);
And to get that back to the 2D elements:
[i j] = ind2sub(size(A), maxIndex);