How do I apply a function to each cell in a matrix which is dependent on surrounding cells?

For instance: I have a matrix

A = [1 2 1; 2 3 2; 4 1 2]

I need to write a function presumably using arrayfun that will create a new matrix (same dimensions)

Ignoring Matlab syntax I would imagine the function to look like this :

xy2 = (.25*x(n-1)y + .5*xy1 + .25*x(n+1)y)

The function would create a new value in the same position in a new matrix that would take into account values that occurred before and after the cell at hand.

Thank you in advance for the help!

[Athena Jones]

Using the example array the new array would be

A2 = [1 1.5 1; 1.75 2.5 1.75; 2.25 2 1.25]

[Azzi Abdelmalek]

This is not clear. How A is used ?

[Athena Jones]

A is used as the production of a commodity y values are by year and x values vary by preservative used to treat the commodity. A2 is hypothetically the disposal of the commodity

Answer 1

[per isakson]

My guess:

A = [1 2 1; 2 3 2; 4 1 2];
%%xy2 = (.25*x(n-1)y + .5*xy1 + .25*x(n+1)y) 
B = cat( 2, zeros(size(A,1),1), A, zeros(size(A,1),1) );
C = arrayfun( @(n) (B(:,n-1)/4 + B(:,n)/2 + B(:,n+1)/4), [2,3,4], 'uni',false );
D = cell2mat(C);
A2 = [1 1.5 1; 1.75 2.5 1.75; 2.25 2 1.25];
if all(all(D==A2))
    disp('Success')
else
    disp('Failure')
end

which returns

Success