How to add columns of accumulated sum in a matrix

If a have this matrix:

A=[1:1:100]
B=[101:1:200]
M=[A(:), B(:)]

I need to add 20 columns to M which contain the summation of A values like:

C = summation of the row |i| + the row |i-1|,
D = summation of the row |i| + the row |i-1|+|i-2|,
E = summation of of the row |i| + the row |i-1|+|i-2|+|i-3|,.. etc

and M=[A(:), B(:), C(:), D(:), E(:) ...etc]

For example: it would be something like:

A  B  C  D  E.. etc -> until 20
1  101  1  1  1
2  102  3  3  3
3  103  5  6  6
4  104  7  9  10
5  105  9  12  14
6  106  11  15  18
7  107  13  18  22
8  108  15  21  26
9  109  17  24  30
10  110  19  27  34
11  111  21  30  38
12  112  13  33  42
.  .  .  .  .
.  .  .  .  .
.  .  .  .  .
etc  etc  etc  etc  etc ... etc -> until 20

[Star Strider]

Note: this is not homework. It’s meteorology or climatology research.

[Philippe Corner]

Yep, im trying to analyze some climate data. But for my bachelor thesis. I already did a cumsum, but there are too many columns, so im looking for a more automatic way to do it..

Thanks in advance Mr Star.

Answer 1

[Star Strider]

This seems to work for ‘C’, ‘D’ ... ‘T’.

This construction seems the only way to form your matrix (that I call ‘Ar’ here).

A = (1:100)';
Ar(1,:) = ones(1, 20);
for k1 = 2:numel(A)
    if k1 <= 20
        v1 = cumsum(A(k1:-1:max(1,k1-19)));
        Ar(k1,:) = [v1(2:end)' v1(end)*ones(1, 21-k1)];
    else
        v1 = cumsum(A(k1:-1:1));
        Ar(k1,:) = v1(2:21)';
    end
end

[Philippe Corner]

crack.

[Star Strider]

Thank you!

Answer 2

[Image Analyst]

Sounds like homework. See if you can figure out how to use the cumsum() function to do it. Let us know if you really can't figure it out.

[Philippe Corner]

I already did with cumsum(), but im trying to figure it out with more columns and im trying to automatize the code for that.