How to avoid counting elements in each row of matrix multiple times?

I have written this function to calculate the location distribution in a form of a grid pattern(2D map of distribution).

x&y which are coordinates of each points are as follows:

X: is a matrix that each row contins a x position of points which creats an individual trajectory.(number of rows)

Y: is a matrix that each row contins a y position of points corresponding to x positions.

Note: each rows of X or Y contains a trajectory with a specified length and the rest of row is filled with NaNs:

X=[0.3 0.18 1.2 2.3 nan nan nan ,....,nan ;

0.1 0.12 0.5 2.6 nan nan nan ,....,nan ;

.......]

the same thing for Y.

=====================================

Question: the N matrix calculated in "for loop" below counts points multiple times if they are belong to one trajectory(one row of X) but pass through one grid multiple times. how can I modify the code to avoid counting points multiple times if they belong to the same trajectory but pass through the grid multiple times?

=====================================

function [binx,biny,dx,dy,N] = myfunc(X,Y,Nbin,[Xmin Xmax Ymin Ymax])
%Nbin=number of bins to create 2D matrix of N
lim(1)=Xmin;
lim(2)=Xmax;
lim(3)=Ymin;
lim(4)=Ymax;

% change to 1D arrays
X = X(:);
Y = Y(:);

%exclude nans
X = X(find(~isnan(X)));
Y = Y(find(~isnan(Y)));

%variable range
if isempty(lim)
    in1 = min(X(:));
    en1 = max(X(:));
    in2 = min(Y(:));
    en2 = max(Y(:));
else
    in1 = lim(1);
    en1 = lim(2);
    in2 = lim(3);
    en2 = lim(4);
end

%initialise bin sizes
dx = abs(en1-in1)/Nbin;
dy = abs(en2-in2)/Nbin;

binx = [in1+dx/2:dx:en1-dx/2];
biny = [in2+dy/2:dy:en2-dy/2];

%compute N matrix of 2D-map
N = zeros(Nbin,Nbin);

for ii = 1:length(X)
      
        %check if variables fall within the domain
        if X(ii) >= binx(1)-dx/2 && X(ii) <= binx(end)+dx/2 && Y(ii) >= biny(1)-dy/2 && Y(ii) <= biny(end)+dy/2
            %find bin
            indx = find(binx+dx/2 >= X(ii));
            indx = indx(1);
            indy = find(biny+dy/2 >= Y(ii));
            indy = indy(1);
            
            N(indy,indx) = N(indy,indx) + 1;
            
        end
    
end

[Matt J]

What does it mean to "pass through the grid"? What is "the grid"?

[Voss]

Please provide sample inputs to myfunc, as well as the value of the output N you would like myfunc to return for those inputs.

Also, please provide a definition of myfunc that runs; e.g., lim is undefined, and this is incorrect function definition syntax:

%                                              you can't use [ ] in the inputs of a function definition
function [binx,biny,dx,dy,N] = myfunc(X,Y,Nbin,[Xmin Xmax Ymin Ymax])

Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for mismatched delimiters.

end

[Ham Man]

grids mean: each box of N matrix which is supposed to be filled with the number of locations.(e.g Nbin=50 generates a grid pattern of 50X50)

[Ham Man]

lim was defined in the code

[Ham Man]

The file size in large to upload here:40MB (zip file)

[Walter Roberson]

%Nbin=number of bins to create 2D matrix of N
% lim(1)=Xmin
% lim(2)=Xmax
% lim(3)=Ymin
% lim(4)=Ymax

Those are comments. They do not define lim

if isempty(lim)

lim is used there without it having been defined.

[Ham Man]

[DGM]

Is it possible that a single trajectory can land two (or more) sequential samples in the same bin without actually crossing? If so, are those counts to be included, or is a single trajectory to produce a map of strictly singular bin counts (i.e. a binary map of the bins that it occupies)?

[Ham Man]

many trajectories can pass through one bin and this is fine, but if one trajectory cross itself in a bin multiple times it should be counted one time. map is supposed to be created by many of such trajectories.

[Matt J]

Yes, but that wasn't the question. The question was, what happens when one trajectory occupies the same bin multiple times, but doesn't cross itself, like what occurs in bins (4,2) and (5,3) in the drawing below? Are these bins to be counted only once, as well?

[Ham Man]

Thank you Matt, yes that should be counted once as well.

[Matt J]

Then see my answer below.

Answer 1

[Matt J]

Xedges=linspace(Xmin,Xmax, Nbin+1);
Yedges=linspace(Ymin,Ymax, Nbin+1);
 
N=0;
for i=1:height(X)
    
 deltaN = histcounts2(X(i,:),Y(i,:),Xedges,Yedges);
 
 N=N+logical(deltaN);
 
end