How to calculate some statistical moments for every cell of a cell array?

Hello, I produced pairwise distances from some latitude and longitudes, then I want to calculate normal pdf and logarithmic pdf but I get an error message. My aim is to find if these distances are normally distributed or not. (Distances are produced according to the grid i defined onto a map). You can find the data, the code and the error message below:

clear all;
addpath('D:\Desktop\BOUN\JOB\Slip_Rates\Slip_Data\MAP');

LAT1=39; LAT2=42; LON1=29.0; LON2=41.0; sf = 1;

m_proj('albers equal-area','lat',[LAT1 LAT2],'long',[LON1 LON2],'rect','on');m_gshhs_h('color',[.5 .5 .5]);hold on; 
m_grid('linewi',1,'linest','none','tickdir','in','fontsize',10);

all = load('all_velocities.txt'); lon1=all(:,1); lat1=all(:,2); ve1=all(:,3); vn1=all(:,4);

% GRIDDING
dLO = .5*2; dLA = .3636*2;

lon = [LON1:dLO:LON2];
lat = [LAT1:dLA:LAT2];

nlat = length(lat); nlon = length(lon); DIST = cell(nlat, nlon);

for i = 1:nlat
    for j = 1:nlon
        ind = find(abs(lat1-lat(i))<dLA/2 & (abs(lon1-lon(j))<dLO/2)); 
        DENSITY(i,j) = length(ind);             % DENSITY OF THE GRIDS
        points = [reshape(lat1(ind),[],1), reshape(lon1(ind),[],1)];
        P{i,j} = points;                        % ELEMENTS IN EACH GRID
        DIST{i,j} = pdist(points, 'euclidean'); % PAIRWISE DISTANCE BETWEEN ELEMENTS IN EACH GRID
    end
end     

for i = 1:nlat
  for j = 1:nlon
      ind = DIST{i,j};      
      SDIST(i,j) = std(DIST{i,j});                      % STANDARD DEVIATION OF DISTANCES
      MDIST(i,j) = mean(DIST{i,j});                     % MEAN OF DISTANCES
      MEDIST(i,j) = median(DIST{i,j});                  % MEDIAN OF DISTANCES
      SDIST(isnan(SDIST))=0; MDIST(isnan(MDIST))=0; MEDIST(isnan(MEDIST))=0;
      LD(i,j) = exp(MDIST(i,j)+0.5*(SDIST(i,j).^2));    % CALCULATING LOGARITMIC PDF
      GD(i,j) = (1/((std(DIST{i,j})*sqrt(2*pi))))*exp(-((ind-mean(DIST{i,j})).^2)/(2*(std(DIST{i,j}).^2))); % CALCULATING GAUSSIAN PDF 
  end
end

C = abs(MDIST - MEDIST); m_pcolor(lon-dLO/2, lat-dLA/2, C); 
m_quiver(lon1,lat1,sf.*ve1,sf.*vn1,1,'w','filled','AutoScale','off','linewidth',1.5); hold off; 

Unable to perform assignment because the size of the left side is 1-by-1 and the size of the right side is 1-by-0.

Error in all_velocities4 (line 48)

GD(i,j) = (1/((std(DIST{i,j})*sqrt(2*pi))))*exp(-((ind-mean(DIST{i,j})).^2)/(2*(std(DIST{i,j}).^2))); % CALCULATING GAUSSIAN

PDF

[Sevil Cansu Yildirim]

That question has not been answered completely so I thought sending all code and the data would help. thank you.

[Stephen23]

"That question has not been answered completely..:"

I just closed your other question (which had no answers). It is preferred if you add more information to existing questions, rather than opening new questions. This is because it is easier for you and for us to keep track of what information you have provided, what clarifications you have provided, what data you have provided, and what answers you have been provided with.

[Sevil Cansu Yildirim]

I will keep in mind so thank you. Do you have any idea about my code?

[Stephen23]

"Do you have any idea about my code?"

1. Do not use all as a variable name, as then you shadow the very important inbuilt all function.
2. Your data file uses tabs for delimiters on the first line, but spaces on all of the other lines. Inconsistent files are more difficult to parse, and I strongly recommend fixing this inconsistent file format.
3. Prefer dlmread or readmatrix with a text file, rather than load.
4. Use absolute/relative filepaths, rather than adding data folders to the MATLAB Search Path.
5. Preallocation of the output arrays is strongly recommended (for efficiency and to avoid errors due to size/class incompatibilities).
6. Logical indexing is simpler and more efficient that using find like that.
7. Your code is not robustly written to handle cases where zero or multiple matches are found. This is likely the cause of your bug.

[Guillaume]

In your 2nd set of loops you have:

      ind = DIST{i,j};      
      %...
      GD(i,j) = (1/((std(DIST{i,j})*sqrt(2*pi))))*exp(-((ind-mean(DIST{i,j})).^2)/(2*(std(DIST{i,j}).^2))); % CALCULATING GAUSSIAN PDF 
      %ind is used here ----------------------------------^

What is the point of ind? First, why such a poor variable name which implies indices when it actually contains distances. Secondly, it's exactly the same as dist{i,j} and you use dist{i,j} everywhere but this one instance in the GD calculation. Why? As far as I can tell it just makes it harder to understand the expression and you could just get rid of the variable. i.e have DIST{i,j} = mean(DIST{i,j}) instead of ind - DIST{i, j}.

Unless ind is meant to be something else...

[Sevil Cansu Yildirim]

I corrected my code.

Answer 1

[Jakob B. Nielsen]

A good way to troubleshoot is to insert a keyboard line - it pauses the code, and allows you to see "what matlab sees" mid-execution.

keyboard      
GD(i,j) = (1/((std(DIST{i,j})*sqrt(2*pi))))*exp(-((ind-mean(DIST{i,j})).^2)/(2*(std(DIST{i,j}).^2))); % CALCULATING GAUSSIAN PDF 

If you pause it here, when i=1 and j=1 std(DIST{i,j}) gives 0. That means you try to divide by zero, never a good idea. However, matlab prints it as NaN and that goes into your GD variable.

However, when i=1 and j=2, DIST{i,j} is an empty double. So you try to place an empty double (1x0 dimension) into GD(1,2) (a 1,1 position within GD).

The root of your problem seems to be with this part of your code. For i=1, j=2 your ind findes no indexes that live up to your limits. That gives your empty cell which goes on to give your error later.

for i = 1:nlat
    for j = 1:nlon
        ind = find(abs(lat1-lat(i))<dLA/2 & (abs(lon1-lon(j))<dLO/2)); 
        DENSITY(i,j) = length(ind);             % DENSITY OF THE GRIDS
        points = [reshape(lat1(ind),[],1), reshape(lon1(ind),[],1)];
        P{i,j} = points;                        % ELEMENTS IN EACH GRID
        DIST{i,j} = pdist(points, 'euclidean'); % PAIRWISE DISTANCE BETWEEN ELEMENTS IN EACH GRID
        keyboard %I inserted a keyboard here, as well
    end
end  

[Sevil Cansu Yildirim]

I understood the problem with empty double. How to avoid?

[Guillaume]

The question is not how to avoid, but rather what you want to do in the case where no point fits your hconditions. What should the value of GD be in that case?

[Guillaume]

Sevil Cansu Yildirim's comment moved here:

I changed the code like this, now I dont get any error message. But GD is 5x13 zero matrix.

for i = 1:nlat
  for j = 1:nlon  
      SDIST(i,j) = std(DIST{i,j});                      % STANDARD DEVIATION OF DISTANCES
      MDIST(i,j) = mean(DIST{i,j});                     % MEAN OF DISTANCES
      MEDIST(i,j) = median(DIST{i,j});                  % MEDIAN OF DISTANCES
      SDIST(isnan(SDIST))=0; MDIST(isnan(MDIST))=0; MEDIST(isnan(MEDIST))=0;
      LD(i,j) = exp(MDIST(i,j)+0.5*(SDIST(i,j).^2));    % CALCULATING LOGARITMIC PDF
      if length(DIST{i,j})>1 & SDIST>0
          GD(i,j) = (1/((std(DIST{i,j})*sqrt(2*pi))))*exp(-((DIST{i,j}-mean(DIST{i,j})).^2)/(2*(std(DIST{i,j}).^2))); % CALCULATING GAUSSIAN PDF
      elseif length(DIST{i,j})<1 & SDIST<0
          GD(i,j) = 1;
      end
  end
end

[Guillaume]

But GD is 5x13 zero matrix.

Since nlat is 5 and nlon is 13, this is exactly what it should be. It's not clear why it is a problem. What size did you expect?

[Sevil Cansu Yildirim]

GD should be the answer of pdf function. not all zero.

Answer 2

[Guillaume]

"GD should be the answer of pdf function. not all zero."

Ah, I thought you were complaining about the size of the output, not its content.

There's two problems about the code you've posted but first some advice:

Never end a if...elseif... without a plain else... to catch the conditions you may have forgotten, e.g.

if somecondition
    %do something
elseif someothercondition
    %do something else
elseif anothercondition
   %do another thing
else
   error('There''s a problem. Review the conditions');
end

If you'd done that you would have found that neither your if condition or your elseif condition was true. This explains why GD is all zeros, you never put anything in it.

Second advice, if your elseif condition is supposed to be the exact opposite of the if condition, then you don't need an elseif. You already know that if the if condition is not true, the opposite is always true. So instead of

if somecondition
    %do something
elseif oppositeof_somecondition
    %dosomething else
end

Just write

if somecondition
    %do something
else
    %do something else
end

This is clearer and crucially saves you from having to write the opposite condition correctly. That's your first problem, the opposite of A > 1 & C > 0 is not A < 1 & B < 0 but A <= 1 | B <= 0.

The second problem is that the expression

GD(i,j) = (1/((std(DIST{i,j})*sqrt(2*pi))))*exp(-((DIST{i,j}-mean(DIST{i,j})).^2)/(2*(std(DIST{i,j}).^2)))

can only work if DIST{i, j} is scalar. If it is not, then DIST{i,j}-mean(DIST{i,j}) will be a vector or matrix (same size as DIST{i, J}) and you'll be trying to store that into the scalar GD(i, j).

So you need to review your equation, it's still not right.

[Sevil Cansu Yildirim]

So you need to review your equation, it's still not right.

Can you help with the equation?

In normal probability density function, I need to substract mean value of the data from every data itself. (note: formula I try to use is: f(x)=e−(x−μ)2/(2σ2)σ√2π which is GD in my code)

So, my data is DIST{i,j} (every cell contains distances, thus some cells are empty, some are zero and some are 1 x [] double). I need to substract mean(DIST{i,j}) from every element of DIST{i,j}.

[Guillaume]

"I need to substract mean(DIST{i,j}) from every element of DIST{i,j}."

It looks like that's what your code is doing. If that is what you want, it is not possible to store that result as an element of a matrix since matrix elements must be scalar and the result of the above is going to be a vector or matrix the same size as DIST{i, j}.

Perhaps GD should be a cell array?

[Sevil Cansu Yildirim]

I think LD would be cell array then.