How to perform operations on time matrices

Ok so my problem stems from the analysis of measurements taken from images.

I have an excel sheet where I have a table of measurements where each column is a different cell (replicate) and the rows are the different time points in which the measurements were taken.

I now want to polish the data, exclude replicates (columns) when necessary and do multiple different operations with the values: i.e. calculating the mean value at time 1 between all of the columns and subtracting that to every element of the matrix; translate the column values to the top in order for them to start with the first positive number and eliminating any negative number after that by 'pushing together' the values below.

I.e. my matrix would be a = 0 2.3450 3.4570

1.0000 3.4670 4.8750

2.0000 4.6350 5.8350

I would first like to calculate the mean of the values of the first row (2.345 and 3.457) = 2.901

Then substract that to every value of the matrix i.e. a = 0 -0.5560 0.5560

1.0000 0.5660 1.9740

2.0000 1.7340 2.9340

Then I eliminate any negative value by filling the gaps with the lower values on the column i.e. a= 0 0.5660 0.5560

1.0000 1.7340 1.9740

2.0000 0 2.9340

If the matrix instead was c = 0 0.5660 0.5560

1.0000 1.7340 -1.6460

2.0000 0 2.9340

I would want the matrix to become c = 0 0.5660 0.5560

1.0000 1.7340 2.9340

2.0000 0 0

Is there any function or operation that could help me do those kind of modifications to the matrix?

Thank you!

Answer 1

[Stephen23]

a = [0,2.3450,3.4570;1,3.4670,4.8750;2,4.6350,5.8350]

a = 3×3

0 2.3450 3.4570 1.0000 3.4670 4.8750 2.0000 4.6350 5.8350

m = a(:,2:end)-mean(a(1,2:end));
[~,x] = sort(m<0,1);
for k = 1:size(m,2)
    m(:,k) = m(x(:,k),k);
end
a(:,2:end) = max(0,m)

a = 3×3

0 0.5660 0.5560 1.0000 1.7340 1.9740 2.0000 0 2.9340

[LORENZO DAVIDE DODI]

Would you be able to explain how this works precisely?

I understand the comparison function (max) but i'm still not clear about the line

   [~,x] = sort(m<0,1)

and the for loop

    for k = 1:size(m,2)
        m(:,k) = m(x(:,k),k);
    end

How can I generalize this for different criterias?

Many thanks in advance

[Stephen23]

"Would you be able to explain how this works precisely?"

m = a(:,2:end)-mean(a(1,2:end)); % subtract mean of the first row
[~,x] = sort(m<0,1); % sort columns of matrix of true/false (negative/positive values)
for k = 1:size(m,2)
    m(:,k) = m(x(:,k),k); % sort data matrix columns according to the column indices x
end
a(:,2:end) = max(0,m) % replace negative values with 0

The concept is very simple: the logical comparison provides FALSE (i.e. positive values) and TRUE (i.e. negative values) in a logical matrix. Then SORT simply moves the TRUEs (corresponding to negative values) to the bottom of each column of the logical matrix. The loop just takes the sorted column indices and applies them column-by-column to the original data matrix.

" How can I generalize this for different criterias?"

I have no idea what "different criterias" you might want to change, nor how you want to "generalize" them.

[LORENZO DAVIDE DODI]

Ok perfect that makes a lot of sense.

I will try to explain myself a bit better:

In this case the criteria for the first value is for it to be non negative: this is achievable by sorting down the negative values. If I wanted to achieve this without considering any negative values further along in the column and therefore leaving any negative values unscathed how could the code be modified.

Another exaple is to have another criteria for the first value: instead of the non-negativity it being a set amount less then the next value in the column: here an example

a=[2,3,2;2.5,3.8,1.8;5,3,2;6,8,2.4;7,10,7;8,11,9]

a =
    
        2.0000    3.0000    2.0000
        2.5000    3.8000    1.8000
        5.0000    3.0000    2.0000
        6.0000    8.0000    2.4000
        7.0000   10.0000    7.0000
        8.0000   11.0000    9.0000

If the criteria for example for the first 'acceptable' element of the column was the one which had a higher delta then i.e. 2 from the previous one, and therefore something which would return something like this:

        a =
        
        2.5000    3.0000    2.4000
        5.0000    8.0000    7.0000
        6.0000   10.0000    9.0000
        7.0000   11.0000         0
        8.0000         0         0
        0              0         0

Would this be possible to tweak into the existing code or would I need something completely different?

Thank you very much in advance

[Stephen23]

"Would this be possible to tweak into the existing code"

You will need to generate a suitable matrix (it does not have to be a logical matrix) which somehow encodes the "criteria" that you want to sort based on (this itself might require a loop), and then SORT that matrix. Most likely the FOR-loop can stay much the same.