Dear Bibhuti,

First of all, we can start to compare two different matrices, say A =[aij] and B= [bij ], 

take the difference matrix C=[aij -bij ]= [cij ]

Now if cij =0, then the cell remains unchanged and if cij < 0, then the cell is increased, otherwise it is decreasing. Similarly, you can construct a program to compare all given matrices mutually.

If a given function generates the data of the cells, say 

A = [ aij(x,y,z,...)], then you can study the variation of the cells using calculus of several variables which give a direct answer to your problem.

Best wishes    

Thank you Hasan Keles, I will read the papers from your profile. 

Thank you Issam. I understood the first part i.e., knowing the difference and getting an idea of the direction and amount of the change.  

I also plan to cluster the cells which got changed in similar way ( direction and amount) and further analyse the effect of the factor that brought change. Could you elaborate more on your idea?

Thanks a lot. 

I wouldn't reinvent the wheel. try the subtract function in scipy.numpy and identify non-nulls indicating cells that changed.

https://docs.scipy.org/doc/numpy/reference/generated/numpy.subtract.html

Dear Bibhuti,

Are the data of the matrix cells (entries) random? Is there a generator of the data?

Your reply decides the approach how to tackle your question.

Best regards

Hi Bibhuti,

Certainly, you can do it with numpy/scipy package if all matrices are in the same dimension easily by matrix subtraction or if the dimensions are different, you can also write your own code either in R or Python or any other programming too. You need to read all matrices and save into a dictionary or matrix in your coding language, and then in a for loop you can compare cell by cell and calculate the differences, then save and write it into a csv file. It might not be efficient, but I usually do that way ;-)

Best Regards

Hi , 

Thank you for replying. 

Issam: htank you.  They are not necessarily random. 

Elnaz, yes, this will help me tackle with the 'large matrix" part. Thank you.

Simplifying my question  :

1. let's say I have 5 matrices of n X n dimension, each representing the data from 5 weekdays. I want to compare the changes in cells of matrices. What can be a good measure ? I am new in this field, and the measures I am aware of , from literature, are R^2, %RMSE, Igen value based measure etc.  These measures will tell me how different one matrix is to another (matrices as a whole), but I get no information on how my cells within the matrices are affected by the change in days (thus time). I want to use a measure which lets me account the changes within matrices. 

2. Once  I find the technique, I need a way to do it for comparing 100 different matrices, where n X n could be 20000 X 20000. This is where programming would help me. Thank you for suggesting numpy/scipy for this. 

How to deal with (1) ? Any further suggestions?

Hi Peter,

Thank you for detailed explanation. This makes things more clearer to me.

It is not always memory to be considered but also time.

Hi there,

I just wanted t ask u; won't it be easy to imagine a 2000*2000 matrix as a vector with (4 * 10^6) dimentions. And if so compaing vectors can be done easily. Then why not convert it. 

Its just a guess. I 'm completely not sure if thats suitable for ur application.

Regards.

Dear Devang,

The matrix is a vector regardless how to arrange the components.

Best

Dear Issam, matrix is a representation of data so is a vector; yes they can be converted from one format to another; but many operations can't be carried out when they are in one of the form. E.g. u cant carry out elementary row operations on a vector.

Regards