How to calculate a Poisson matrix in Matlab analogous to Excel or R and summarize certain parts?

I already posted a similar question on this link, but it didn't work out maybe because I haven't expressed myself clearly enough or I haven't been able to understand the answer. However, this question is more precise since I have realized my project using R (R Studio). Unfortunately, I have recognized that R Studio calculates my Poisson-Matrix as slow as Excel, which is why I am forced to do my project using Matlab.

R code:

a <- Table$ValueA
b <- Table1$ValueB
lapply(a,function(a) {lapply(b,function(b) {outer(dpois(0:20,a), dpois(0:20,b))})})

Excel calculation:


, where a and yes they are variables to which all pairs of input values ​​are assigned, one after another. X It is a variable that goes from 0 to 20.
Then, for each input-value pair register (a, b) (located in two columns) I want to create a Matrix that is based on previous Poisson calculations, with X from 0 to 20.

Then p. The first result in the matrix, in cell (1,1) is based on the following calculation:


The following graphic shows the matrix in Excel:

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Finally, I want to summarize three parts of that matrix and present these three values ​​next to the two columns (which contain the input values a and yes) for each input value register:

1) Sum of: The diagonal from the upper left corner to the lower right corner
2) Sum of: The el upper rest of the matrix
3) Sum of: The lower rest of the matrix

It would be great if there was someone to help, since I really hope to increase performance with Matlab!