help with matrix concatenation

Hi Everyone, i am a beginner and i would like to ask if its possible to concatenate more than two matrices,please try and correct my code;

i am trying to swap a matrix then concanate all into one into one big matrice that will contain all swapped matrices so i can access them again.Is that possible and if it is how can i access the matrices later? thank you.

Allmatrix=zeros(length(main),length(main)*length(main));
for i=0:length(main)
    for swap=i:length(main)-1
        Axb=main;
        swaprow=Axb(:,1);
        Axb(:,1)=Axb(:,swap+1);
        Axb(:,swap+1)=swaprow;
    end 
    Allmatrix=Axb(i);
end

[DGM]

It's unclear what you're trying to do. You say "swap a matrix", but it appears that means "flip a row vector by permuting the individual elements pairwise". If that's the case, then what is "all swapped matrices"? Does that mean you want a array of all said permutations, or do you want an array of various fully flipped vectors?

[James Kamwela]

Hey thanks for getting back to me;i have explained what im trying to do below;

For example; we have 3*3 matrix A=[a1 a2 a3;b1 b2 b3;c1 c2 c3];

after swapping and concatenation A should look like

A=[a1 a2 a3;b1 b2 b3;c1 c2 c3;a2 a1 a3;b2 b1 b3;c2 c1 c3;a3 a2 a1;b3 b2 b1;c3 c2 c1];

i hope you can read the matrix and i hope i make sense

[DGM]

Well, let's start with that. This gives the permutation described by the example, as best fits the code provided:

A = [11 12 13; 21 22 23; 31 32 33];

s = size(A);
B = zeros([s(1)^2 s(2)]);
B(1:s(1),:) = A;
for r = 2:s(2)
    thisB = A;
    thisB(:,[1 r]) = thisB(:,[r 1]);
    B((r-1)*s(1)+1:r*s(1),:) = thisB;
end
B

B = 9×3

11 12 13 21 22 23 31 32 33 12 11 13 22 21 23 32 31 33 13 12 11 23 22 21 33 32 31

But while that looks fine for 3 columns, it doesn't generalize. Say A is wider (using a vector for compactness):

A = [1 2 3 4];

% this is unchanged
s = size(A);
B = zeros([s(1)^2 s(2)]);
B(1:s(1),:) = A;
for r = 2:s(2)
    thisB = A;
    thisB(:,[1 r]) = thisB(:,[r 1]);
    B((r-1)*s(1)+1:r*s(1),:) = thisB;
end
B

B = 4×4

1 2 3 4 2 1 3 4 3 2 1 4 4 2 3 1

Which is probably not what you want. There could be other ways to incrementally flip row vectors, but I miss how they would adhere to the examples. What should the incremental permutations look like for a 1x4 or 1x5 vector input?

I would imagine a flip process would look like this:

% initial
1 2 3 4
% first pass
2 1 3 4
3 1 2 4
4 1 2 3
% second pass
4 2 1 3
4 3 1 2
% third pass
4 3 2 1

And the result would be a sample from each pass, say the last sample from each pass

1 2 3 4
4 1 2 3
4 3 1 2
4 3 2 1

The example seems to use the first sample from each pass instead.

1 2 3 % this one

2 1 3 % this one
3 1 2

3 2 1 % this one

Is that what's intended?

[James Kamwela]

Thanks for investing your time to help, the first example is what i was looking for. However, you say it does not work if A is wider and that is also what i was wondering,if it can work if A was winder lets say 7*7,and if it can then how.

[DGM]

... That's what I was asking you. You have to define how the process should be generalized to wider arrays. In the last example I gave, there are two implied variations depending on how the loops are structured. For A = [1 2 3 4], you could either get

1 2 3 4 % case 1 (using last sample)
4 1 2 3
4 3 1 2
4 3 2 1

or you could get

1 2 3 4 % case 2 (using first sample)
2 1 3 4
4 2 1 3
4 3 2 1

or you could get something different yet depending on what you intended. This is an arbitrary subsampling of a process by which a vector is flipped by an arbitrary number of pairwise flips. It's not up to me to decide what the goals are.

EDIT:

If the first case meets the requirements, it simplifies very neatly:

A = [1 2 3 4 5 6 7]

s = size(A);
B = zeros([s(1)*s(2) s(2)]);
for rb = 1:s(2)
    B((rb-1)*s(1)+1:rb*s(1),:) = A(:,[s(2):-1:(s(2)-rb+2) 1:(s(2)-rb+1)]);
end
B

but this doesn't match the order in your smaller example.

Answer 1

[C B]

@James Kamwela is this what you expect as answer please check

main =[1 2 ; 3 4];

main =

1 2

3 4

Allmatrix=[];
 for i=1:size(main,2)
    for swap=1:size(main,1)-1
        Axb=main;
        swaprow=Axb(i,swap);
        Axb(i,swap)=Axb(i,swap+1);
        Axb(i,swap+1)=swaprow;
    end 
     Allmatrix=[Allmatrix Axb];
 end

Allmatrix =

2 1 1 2

3 4 4 3

[James Kamwela]

Thanks for your help, however this doesn`t fully answer my question.

For example; we have 3*3 matrix A=[a1 a2 a3;b1 b2 b3;c1 c2 c3];

after swapping and concatenation A should look like

A=[a1 a2 a3;b1 b2 b3;c1 c2 c3;a2 a1 a3;b2 b1 b3;c2 c1 c3;a3 a2 a1;b3 b2 b1;c3 c2 c1];

i hope you can read the matrix and i hope i make sense

Answer 2

[DGM]

I'm just going to post these two examples as an answer.

If you want to sample the process at the end of each pass, the structure is more simple:

A = [1 2 3 4 5 6 7];

s = size(A);
B = zeros([s(1)*s(2) s(2)]);
for rb = 1:s(2)
    B((rb-1)*s(1)+1:rb*s(1),:) = A(:,[s(2):-1:(s(2)-rb+2) 1:(s(2)-rb+1)]);
end
B

B = 7×7

1 2 3 4 5 6 7 7 1 2 3 4 5 6 7 6 1 2 3 4 5 7 6 5 1 2 3 4 7 6 5 4 1 2 3 7 6 5 4 3 1 2 7 6 5 4 3 2 1

but this doesn't match the order in your smaller example.

A = [11 12 13; 21 22 23; 31 32 33];

s = size(A);
B = zeros([s(1)^2 s(2)]);
for rb = 1:s(2)
    B((rb-1)*s(1)+1:rb*s(1),:) = A(:,[s(2):-1:(s(2)-rb+2) 1:(s(2)-rb+1)]);
end
B

B = 9×3

11 12 13 21 22 23 31 32 33 13 11 12 23 21 22 33 31 32 13 12 11 23 22 21 33 32 31

If you want to sample the process at the beginning of each pass, the pattern isn't as neat and the code accordingly isn't as simple.

A = [1 2 3 4 5 6 7];

s = size(A);
B = zeros([s(1)*s(2) s(2)]);
B(1:s(1),:) = A;
B(end-s(1)+1:end,:) = fliplr(A);
for rb = 2:s(2)-1
    B((rb-1)*s(1)+1:rb*s(1),:) = A(:,[s(2):-1:(s(2)-rb+3) 2 1 3:(s(2)-rb+2)]);
end
B

B = 7×7

1 2 3 4 5 6 7 2 1 3 4 5 6 7 7 2 1 3 4 5 6 7 6 2 1 3 4 5 7 6 5 2 1 3 4 7 6 5 4 2 1 3 7 6 5 4 3 2 1

but this does match your example...

A = [11 12 13; 21 22 23; 31 32 33];

s = size(A);
B = zeros([s(1)*s(2) s(2)]);
B(1:s(1),:) = A;
B(end-s(1)+1:end,:) = fliplr(A);
for rb = 2:s(2)-1
    B((rb-1)*s(1)+1:rb*s(1),:) = A(:,[s(2):-1:(s(2)-rb+3) 2 1 3:(s(2)-rb+2)]);
end
B

B = 9×3

11 12 13 21 22 23 31 32 33 12 11 13 22 21 23 32 31 33 13 12 11 23 22 21 33 32 31

Answer 3

[James Kamwela]

so i guess it doesnt continue after the third swap,So now that i cant concatenate more than 3 matrices i would like to ask another question, lets suppose A = [11 12 13; 21 22 23; 31 32 33]; we swap each column with column one however after the swap i want the product of the diagonal stored in B, so that should make B a (1,3) vector,

this is actually what i was struggling with, i am able to swap the columns but B only stores the value of the last swap diagonal product, so what i think happens is that it finishes all the swaps then calculates the diagonal product of the last matrix

i hope i made sense and thank you for your help

[DGM]

If A is 3x3, then B is 9x3. The diagonal of B is the diagonal of the first 3x3 block. The first 3x3 block is a copy of A, so the diagonal of B is the diagonal of A.

B = [11 12 13;21 22 23;31 32 33;13 11 12;23 21 22;33 31 32;13 12 11;23 22 21;33 32 31]

B = 9×3

11 12 13 21 22 23 31 32 33 13 11 12 23 21 22 33 31 32 13 12 11 23 22 21 33 32 31

d = diag(B)

d = 3×1

11 22 33

p = prod(d)

p = 7986

I don't know where this is going

[James Kamwela]

No thats not what i asked, i will try to explain again A=[11 12 13;21 22 23;31 32 33]; B=zeros(1,length(n))

step1--->so the first action will be B=A(i,i)-->B1=prod(B)--->the product of diagonal coefficints in this case (11,22,33)

step2--->then it will swap columns-->column 1 will be column 2 and column 2 will be column 1

A will look the same but columns 1 and 2 will have swapped places

calculate B2 again

step 3--->A will default to its original

then it will swap columns-->column 1 will be column 3 and column 3 will be column 1

then it will calculate B3 again

step4---> this process will continue to the length(A)-1(if matrix was larger)

calculate B(n)

step5---> so taking A as reference,after the process finishesat step 3.that will mean that B has three values since A is a 3*3 matrix.my problem is that i am not able to store the value of of B somewhere after every calculation

this is what i want to happen

step1---find B1

step2---find B2

step2---find B3

Barray=(B1 B2 B3);

i think i am clear now,sorry ive taken so long.

[DGM]

Assuming that A is square, then

% these are copied from the main example so i don't ahve to repaste everything
s = [3 3];
B = [11 12 13;21 22 23;31 32 33;12 11 13;22 21 23;32 31 33;13 12 11;23 22 21;33 32 31]

B = 9×3

11 12 13 21 22 23 31 32 33 12 11 13 22 21 23 32 31 33 13 12 11 23 22 21 33 32 31

Bd = cellfun(@diag,mat2cell(B,repmat(s(1),[s(2) 1]),s(2)),'uniform',false);
Bd = prod(cell2mat(Bd.'),1)

Bd = 1×3

7986 8316 8866

Those are the products of the diagonals of the 3x3 sub-blocks within B.