How to add matrices with different dimensions

hello, I want the shortest way to add matrices with different dimensions. I know the easiest way but it is not appropriate for big matrices like 10*10 or bigger please see the picture to understand what I mean Sorry there was a problem with the picture. I provide an example. I hope it is clear now.

[Azzi Abdelmalek]

How? post a short numeric example with the expected result

[Joseph Cheng]

wha? Am i missing something? K1 looks to be 4x4 that has a mosaic of k sub nxm following row column numbering. K2 is a 4x4 with a mosaic of k sub nxm with a specified pattern. However a 4x4 +4x4 should still be a 4x4? how does it go to 6x6? or is that K=K1+K2 = 36?

[Azzi Abdelmalek]

Mohammed you don't need a picture to post an example

[Mohammed]

Hi Aziz The example in the picture Do you see the picture or not?

[Azzi Abdelmalek]

Mohammed my name is Azzi, and I meant, for your case, you don't need to add a picture, just write your example

[Mohammed]

Hi Azzi, sorry for writing your name wrongly and thank you for your advice.

Answer 1

[Joseph Cheng]

That makes more sense now. you can do something like this.

k1=reshape([1:16],4,4)';
k2=reshape(17:32,4,4)';

K1=zeros(6,6);
K2=K1;

K1(1:length(k1),1:length(k1))= k1;
k2pattern= [5:6 1:2];
K2(k2pattern,k2pattern) = k2;

K=K1+K2

not the most efficient way nor did i supply how to vary depending on the size of the matrix. However this was <5 min of thinking without knowing what to with k2 for larger sizes. Just substitute the k2pattern with what its column labeling.

[Mohammed]

Thank you a lot. I think this is the best answer. I am still practicing to understand and I may need your help again. Thank you a lot. I appreciate your help.

[Joseph Cheng]

Just run through it line by line and see the output.

[Mohammed]

Hi Joseph I run it and ot was correct, but I don't know how you did that Imagine you have three matrices, k1=4*4 (1 2 5 6) and k2=3*3 (4 1 2) k3=4*4 (3 4 7 8) k= k1 + k2 +k3=8*8 regardless of the values inside the matrices, could you please tell me how you will add them?

[Joseph Cheng]

Very similar manner. As i did in the 2 matrices version i made a zero filled matrix for each with the size of the output labeling them as K#. in the capital K variable i did K1(indexpattern,indexpattern). and you show the indexing pattern in your text above. K1([1 2 5 6],[1 2 5 6]) = k1, K2(pattern,pattern)=k2. etc.

What is happening here is when i go K1(pattern,pattern) i'm specifying which rows and columns to put it in. The pattern I noticed from your examples allows us to go this route. Like i said before step through it line by line and look at how the K# are being formed. What is happening here is

[Joseph Cheng]

As a off example example when i do:

A = zeros(10,10);
A([1 2 3 4],[5 6 7 8])= 1;

makes the rows 1,2,3and 4 the number one for columns 5,6,7 and 8. the indexes is the permutation of the two arrays and fills in what you say. (1,5),(1,6),(1,7)...(3,5),(3,6)...(4,8).

similarly if i go

A = zeros(10,10); A(1:2:end,2:2:end)=1

which will make every odd column 1 for every even column.

So for your example you have a 4x4 which when you look at the generic case K1 = some matrix filled with a permutation of the pattern.

[Mohammed]

Hi Joseph Sorry for my questions. I try to do it in MatLab and I cannot find the answer because the program said it is out of the dimensions could please show me how you create the matrix?

Answer 2

[Image Analyst]

Just extract all the values and add them.

K = zeros(6); % Initialize
K(1,1) = K1(1,1) + K2(3, 1); % Sum up k11 values.
K(1,2) = K1(1,2) + K2(3, 2); % Sum up k12 values.

and so on for all 36 values. It's not rocket surgery - just pluck them out of where they're defined to be in each matrix and add them together. Simple as that.

[Mohammed]

Thank you for the answer, but when I have 20*20 matrices, it will take time