I'd like to be able to create a column vector whose values in each row correspond to the column in a matrix with the max value in that specific row.
For example,
If I have a matrix such as:
A = [1,5,2;3,1,1;0,1,0];
I'd end up with the matrix:
maxValueColumns = transpose([2,1,2]);
Is there an easy/efficient way to do this?
You're looking for max():
A = [1,5,2;3,1,1;0,1,0];
[~, maxValueColumns] = max(A, [], 2); % 'maxValueColumns' will contain [2; 1; 2]
Related
I try to replace the array values at some specific row (row number 1, 10, 12, 20, 39 etc, not continuous) using the linear index from find. However I don't know how to proceed after this few lines of code:
[valmax, ~]=max(A); %Where A will consist of more than one MAX value
idxmax=find(A==valmax);
mclr=repmat([1 0 0],[10 1]); %Create the matrix of my value
mclr(idxmax,:)=[0 1 0]; %replace the value at idxmax index, this line won't work
Any idea how to fix this? Or there are other function instead of using find?
Thanks!
you can use ind2sub to convert the linear indexes into row indexes:
A = randi(5,[10 3]); % random matrix
[valmax, ~] = max(A(:)); %Where A will consist of more than one MAX value
idxmax = find(A == valmax);
% convert linear index into row index
[rowmax,colmax] = ind2sub(size(A),idxmax);
rowmax = unique(rowmax); % get unique rows
mclr = repmat([1 0 0],[10 1]); %Create the matrix of my value
mclr(rowmax,:) = repmat([0 1 0],[numel(rowmax) 1]); %replace the value at idxmax index
however it's more efficient to directly get the rows containing max values using any(X, 2):
rowmax = find(any(A == valmax,2));
I work on a matrix like this :
A=[1,2,3;5,4,6;9,8,7];
I want to get the index of each line. Here it is : Index = [1;2;3]
But how can I get this without a loop ?
I do this for the moment :
for k=1:length(A)
[~,Index(k)] = min(A(k,:));
end
From the documentation:
M = min(A,[],dim) returns the smallest elements along dimension dim. For example, if A is a matrix, then min(A,[],2) is a column vector containing the minimum value of each row.
Looking at output options, you can see
[M,I] = min(___) finds the indices of the minimum values of A and returns them in output vector I.
You were already using the second part of the above documentation notes, so just combine the two...
A=[1,2,3; 5,4,6; 9,8,7];
[~, idx] = min(A, [], 2);
% result: idx = [1; 2; 3];
I have sum of 3 cell arrays
A=72x1
B=72x720
C=72x90
resultant=A+B+C
size of resultant=72x64800
now when I find the minimum value with row and column indices I can locate the row element easily but how can I locate the column element in variables?
for example
after dong calculations for A,B,C I added them all and got a resultant in from of <72x(720x90)> or can say a matrix of integers of size <72x64800> then I found the minimum value of resultant with row and column index using the code below.
[minimumValue,ind]=min(resultant(:));
[row,col]=find(result== minimumValue);
then row got 14 and column got 6840 value..
now I can trace row 14 of all A,B,C variables easily but how can I know that the resultant column 6480 belongs to which combination of A,B,C?
Instead of using find, use the ind output from the min function. This is the linear index for minimumValue. To do that you can use ind2sub:
[r,c] = ind2sub(size(resultant),ind);
It is not quite clear what do you mean by resultant = A+B+C since you clearly don't sum them if you get a bigger array (72x64800), on the other hand, this is not a simple concatenation ([A B C]) since this would result in a 72x811 array.
However, assuming this is a concatenation you can do the following:
% get the 2nd dimension size of all matrices:
cols = cellfun(#(x) size(x,2),{A,B,C})
% create a vector with reapiting matrices names for all their columns:
mats = repelem(['A' 'B' 'C'],cols);
% get the relevant matrix for the c column:
mats(c)
so mats(c) will be the matrix with the minimum value.
EDIT:
From your comment I understand that your code looks something like this:
% arbitrary data:
A = rand(72,1);
B = rand(72,720);
C = rand(72,90);
% initializing:
K = size(B,2);
N = size(C,2);
counter = 1;
resultant = zeros(72,K*N);
% summing:
for k = 1:K
for n = 1:N
resultant(:,counter) = A + B(:,k) + C(:,n);
counter = counter+1;
end
end
% finding the minimum value:
[minimumValue,ind] = min(resultant(:))
and from the start of the answer you know that you can do this:
[r,c] = ind2sub(size(resultant),ind)
to get the row and column of minimumValue in resultant. So, in the same way you can do:
[Ccol,Bcol] = ind2sub([N,K],c)
where Bcol and Ccol is the column in B and C, respectively, so that:
minimumValue == A(r) + B(r,Bcol) + C(r,Ccol)
To see how it's working imagine that the loop above fills a matrix M with the value of counter, and M has a size of N-by-K. Because we fill M with a linear index, it will be filled in a column-major way, so the row will correspond to the n iterator, and the column will correspond to the k iterator. Now c corresponds to the counter where we got the minimum value, and the row and column of counter in M tells us the columns in B and C, so we can use ind2sub again to get the subscripts of the position of counter. Off course, we don't really need to create M, because the values within it are just the linear indices themselves.
Say I have a nxm matrix and want to treat each row as vectors in a function. So, if I have a function that adds vectors, finds the Cartesian product of vectors or for some reason takes the input of several vectors, I want that function to treat each row in a matrix as a vector.
This sounds like a very operation in Matlab. You can access the ith row of a matrix A using A(i, :). For example, to add rows i and j, you would do A(i, :) + A(j, :).
Given an nxm matrix A:
If you want to edit a single column/row you could use the following syntax: A(:, i) for the ith-column and A(i, :) for ith-row.
If you want to edit from a column/row i to a column/row j, you could use that syntax: A(:, i:j) or A(i:j, :)
If you want to edit (i.e.) from the penultimate column/row to the last one, you could you: A(:, end-1:end) or A(end-1:end, :)
EDIT:
I can't add a comment above because I don't have 50 points, but you should post the function setprod. I think you should be able to do what you want to do, by iterating the matrix you're passing as an argument, with a for-next statement.
I think you're going to have to loop:
Input
M = [1 2;
3 4;
5 6];
Step 1: Generate a list of all possible row pairs (row index numbers)
n = size(M,1);
row_ind = nchoosek(1:n,2)
Step 2: Loop through these indices and generate the product set:
S{n,n} = []; //% Preallocation of cell matrix
for pair = 1:size(row_ind,1)
p1 = row_ind(pair,1);
p2 = row_ind(pair,2);
S{p1,p2} = setprod(M(p1,:), M(p2,:))
end
Transform the matrix into a list of row vectors using these two steps:
Convert the matrix into a cell array of the matrix rows, using mat2cell.
Generate a comma-separated list from the cell array, using linear indexing of the cell contents.
Example: let
v1 = [1 2];
v2 = [10 20];
v3 = [11 12];
M = [v1; v2; v3];
and let fun be a function that accepts an arbitrary number of vectors as its input. Then
C = mat2cell(M, ones(1,size(M,1)));
result = fun(C{:});
is the same as result = fun(v1, v2, v3).
I have a matrix A which holds integers in a bounded range (0..255) and I need to build a table mapping a value (0..255) to all the coordinates in the matrix which hold this value.
What is the best way to achieve this? - I thought about using containers.Map for the task but Map doesn't support multiple values per key. I could have used lists but that would seem inefficient as I would have to create a new list on each iteration.
A vectorized solution, which gives the same output as the solution from Mikhail, is to sort all the pixel values in your image using the SORT function, convert the linear indices returned from SORT into subscripted indices using the function IND2SUB, and collect them together into a single cell array using the functions ACCUMARRAY and MAT2CELL:
A = randi([0 255],[5 5],'uint8'); %# A sample matrix
[values,indices] = sort(double(A(:))); %# Sort all the pixel values
[y,x] = ind2sub(size(A),indices); %# Convert linear index to subscript
counts = accumarray(values+1,1,[256 1]); %# Count number of each value
map = mat2cell([y x],counts); %# Create a 256-by-1 cell array
Now, for a given integer value iValue you can get the N-by-2 matrix containing the y (first column) and x (second column) coordinates for the N pixels in the image with that value by doing the following:
key = double(iValue)+1; %# Need to use double to avoid integer saturation
points = map{key}; %# An N-by-2 coordinate matrix
In addition, just in case you're interested, you could also make map a structure array with fields x and y using the function STRUCT:
map = struct('x',mat2cell(x,counts),'y',mat2cell(y,counts));
And you can then access the x and y coordinates for pixels with a value iValue as follows:
key = double(iValue)+1;
x = map(key).x;
y = map(key).y
What about using a cell array? You can index it with integers. For example:
map = {[1,1;13,56], [], [4,5]};
In this example index 0 is in the matrix in 1,1 and 13,56, index 1 in none and index 2 in 4,5
Your cell would have 256 elements (mine has 3) and to acces you would simply add 1 to the index.
You could also store indices linearly so the code to fill the table would be:
for ii = 0:255
map{ii+1} = find( mat(:)==ii )
end
Well, I wrote the following and it seems to work in reasonable time. I think the thing that does the trick is preallocating the cell arrays based on the histogram for each value:
[H, W] = size(A);
histogram = hist(A, 256);
AGT = arrayfun(#(avg) {0 cell(1, histogram(avg))}, 1:256, 'UniformOutput', false);
for y = 1:H
for x = 1:W
idx = A(y, x) + 1;
count = AGT{idx}{1};
AGT{idx}{2}{count + 1} = [y x];
AGT{idx}{1} = count + 1;
end
end
Accessing the table is a bit annoyting though :
AGT{200}{2}{:}
to access all coordinates with value 200.