How can I average multiple matrices by element to create a new matrix of the same size?

I have 31 matrices, each of size 72x144, and each representing a day of the month of January. I would like to have a 32nd matrix, also of size 72x144, which includes the average value for each element in the original 31 matrices. For example, if I have:

A=[1,2,3|2,3,4|3,4,5] B=[2,3,4|3,4,5|4,5,6] C=[3,4,5|4,5,6|5,6,7]

I want:

D=[2,3,4|3,4,5|4,5,6] (the average by element of the originals)

What is the easiest way for me to do this? I have found a few threads here which have answers I don't really understand, as I am relatively unfamiliar with writing codes, for MATLAB or otherwise. I need something easy to understand.

Thanks, Patrick

[Azzi Abdelmalek]

How those matrices are represented? A,B,C,D,E,...

[Patrick]

Azzi, please see my comment in reply to Image Analyst's answer. I was mistakenly unclear about the file names, and that adds some value to the correct answer, I presume. Thanks for your help!

Answer 1

[Image Analyst]

meanMatrix = (matrix1 + matrix2 + matrix3 + .... etc...... + matrix 30 + matrix31)/31;

[Patrick]

Awesome, and thank you so much for the quick reply! However, is there an easier way than that, even? I should have been more clear - the matrix .txt files are for the month of January 2004, and are written in the format "WP20040101.txt", "WP20040102.txt", etc.

And, on that topic - I am ultimately going to need to find an average matrix of the same size using data for the whole year (366 files, since 2004 was a leap year). After "WP20040131.txt", I have "WP20040201.txt". The answer you have provided would require me to type the file names for 366 separate matrices.

Since they are in chronological order, is there an easier way to write the code?

Thanks, Patrick

[Image Analyst]

If you don't already have them in arrays, then you can use the code in the FAQ to read in the arrays from a bunch of files: http://matlab.wikia.com/wiki/FAQ#How_can_I_process_a_sequence_of_files.3F

myFolder = 'C:\Documents and Settings\yourUserName\My Documents\My Data Files';
if ~isdir(myFolder)
  errorMessage = sprintf('Error: The following folder does not exist:\n%s', myFolder);
  uiwait(warndlg(errorMessage));
  return;
end
filePattern = fullfile(myFolder, '*.txt');
txtFiles = dir(filePattern);
for k = 1:length(txtFiles)
  baseFileName = txtFiles(k).name;
  fullFileName = fullfile(myFolder, baseFileName);
  fprintf(1, 'Now reading %s\n', fullFileName);
  thisArray = csvread(fullFileName); % Or however you read them in.
  if k == 1
    sumArray = thisArray;
  else
    sumArray = sumArray
  end
end
meanArray = sumArray / length(txtFiles);

Answer 2

[Azzi Abdelmalek]

M={A,B,C,D,E};
B=cat(3,M{:})
out=mean(B,3)

Answer 3

[Matt J]

Read the matrices into the slices A(:,:,i) of a 3D array and do

 Amean=mean(A,3);

Answer 4

[Tope Oyelade]

Just add a dot before the '/' as below and you are good to go!

meanMatrix = (matrix1 + matrix2 + matrix3 + .... etc...... + matrix30 + matrix31)./31

[Image Analyst]

Tope, the dot is not needed before division by a scalar, such as 31. It is only needed if you need to do an element-by-element division by an array.

[Tope Oyelade]

Thanks @Image Analyst. I have just tried it out and the division works without the 'dot'...but the matrices being the same size adds up by just using the + sign and division by the number of matrices gave me the average of each elemment within the matrices.

Thanks again

[Image Analyst]

Of course adding and dividing gives you the average - not sure why you said "but" as if something is different from what I said.

[Sebastian Garzon]

I have a similar problem, but I want to disregard zero values from each cell when calculating the average. For instance, if i am summing 31 matrices two of the matrices have a zero value in cell 1X1 then the cell 1X1 from the resulting matrix would be the sum of the 29 remaining values divided by 29 rather than 31.

[Bruno Luong]

@Sebastian Garzon Replace 0 with NaN the use 'omitnan' argumant

A(A==0) = NaN;
meanA = mean(A, 3, 'omitnan')

Or non destructive way:

meanA = sum(A,3) ./ sum(A~=0,3)

[Image Analyst]

@Sebastian Garzon with Bruno's way you'd need to create A as a 3-D matrix:

A = cat(3, matrix1, matrix2, matrix3, .... etc...... , matrix30, matrix31);
A(A==0) = NaN;
meanA = mean(A, 3, 'omitnan')

Here's another way:

countMatrix = (matrix1 ~= 0 + matrix2 ~= 0 + matrix3 ~= 0 + .... etc...... + matrix30 ~= 0 + matrix31 ~= 0);
sumMatrix = (matrix1 + matrix2 + matrix3 + .... etc...... + matrix30 + matrix31);
averageMatrix = sumMatrix ./ countMatrix;