Replacing zeros in a matrix with an interpolation

I have a matrix, on which the values become larger as columns go, but some values in that matrix are zero.

E.g. [1,1,1;2,0,2;3,3,3]

I want to replace the values that are zero with an interpolation. In this example theres an increment of 1 per line, so the value zero should become the previous value in that column (1) plus the average increment value (1). Therefore becoming the value 2.

Returning the matrix [1,1,1;2,2,2;3,3,3]

So how can I do this given any matrix, with whatever values.

EDIT: Okay I probably got myself misunderstood, I dont want the zero values to be always the previous value + 1. Let me illustrate further:

M = [1,10;1,0;1,0;1,22]

-Values m(2,2) and m(3,2) are both zero.

-Values m(1,2) and m(4,2) are 10 and 22 which means in 3 rows there was an increment of 12 values, averaging and increment of 4 values per row.

-Interpolating, the values for m(2,2) and m(3,2) should be 14 and 18 respectively.

Thanks alot for you help, appreciated.

[Azzi Abdelmalek]

What if 0 is in the first line

[Bob Choy]

This shouldnt be a problem, there are never zeros in the first line, meaning I only want to do this for the second line and forth.

Thank you.

Answer 1

[Azzi Abdelmalek]

Ok, if the first line is different from zero

a= [1,1,1;2,0,2;0,3,3]
inc=1;
idx=find(~a)
a(idx)=a(idx-1)+inc

[Bob Choy]

Please check my edit on the original question, thank you for your effort so far.

[Azzi Abdelmalek]

 M = [1,10;1,0;1,0;1,22];
[n,m]=size(M);
for k=1:m
    m=M(:,k);
    inc=(m(n)-m(1))/(n-1);
    for l=1:n
        if m(l)==0
            M(l,k)=M(l-1,k)+inc;
        end
    end
end

[Azzi Abdelmalek]

You said the average increment is, for example for the first column:

 (30-1)/4= 7.25,

why are you expecting inc to be 4?

[Bob Choy]

Nevermind what I said before, I have a new problem though, Im doing this with a big with lots of zeros to be replaced, and everytime it replaces a zero it returns that matrix, resulting in the program returning thousands of matrixes until it finally gets to the final one with all zeros replaced, this process takes a huge amount of time. How can I tell matlab to return only the final matrix and not show me every one of them?

[Azzi Abdelmalek]

Bob, If you have a new problem, post a new question, and make it as clear as possible