Submatrices into a Structured Larger Matrix

Hi,

I need a code to create a lower triangular matrix consisting of several submatrices, where each submatrix has its own coordinates [between (xi_0,yi_0) and (xi_f,yi_f)] without any use of for loop.

i.e. Submatrices A, B and C are each 3x3 matrices. I want to create a D matrix as: [A zeros(3x3);B C]

Any help could be useful.

Thanks in advance!

[Akan Selim]

My first attempt is:

A=randn(3,18);

B=zeros(3,27);

layers=[1:3 10:15 19:27];

B(:,layers)=A

C=mat2cell(B,ones(1,1)*3,ones(3,1)*9)

vertcat(C{:})

[David Hill]

Hard to understand what you want. Please provide a simple example of A,B,C and the desired output.

[Akan Selim]

In this simple example, there are 3 matrices, mainly A, B and C.

I want to place these matrices into a lower triangular matrix form:

[A zeros(3x3);

B C]

A=[1 2 3;4 5 6;7 8 9]

B=[10 11 12;13 14 15;16 17 18]

C=[19 20 21;22 23 24;25 26 27]

Output: [1 2 3 0 0 0;

4 5 6 0 0 0;

7 8 9 0 0 0;

10 11 12 19 20 21

13 14 15 22 23 24

16 17 18 25 26 27]

In general form, I have over hundreds of matrices (A1, A2, A3, A4, ... A100) that should be placed as follows:

[A1

A2 A3

A4 A5 A6

...]

Thank you!

Answer 1

[David Hill]

Adjust as necessary. Need 105 3x3 matrices to fill described pattern above. I assume all A matrices are the same size (3x3).

for k=1:105
    A{k}=randi(100,3);%fill A cell array with 3x3 matrices. Recommend you place all your matrices into a cell array or 3D array
    A2(:,:,k)=randi(100,3);%3D array instead of cell array
end
B=zeros(1,42);
B2=B;
c=1;
for m=1:14
   for n=1:m
       B((m-1)*3+1:3*m,(n-1)*3+1:3*n)=A{c};%either storage system will work (A or A2)
       B2((m-1)*3+1:3*m,(n-1)*3+1:3*n)=A2(:,:,c);
       c=c+1;
   end
end

[Akan Selim]

I was looking for a way that doesn't utilize any for loops, like in this example I gave earlier:

A=randn(3,18);
B=zeros(3,27);
layers=[1:3 10:15 19:27]; (columns 4:9, 16:18 are zeros)
B(:,layers)=A
C=mat2cell(B,ones(1,1)*3,ones(3,1)*9)
vertcat(C{:})

Thanks for the answer though.

[David Hill]

There is nothing wrong with loops, especially when having to index into a variable. You should never label variables like A1, A2, A3, ......, A100, but rather store then into an array that can be indexed.

[Walter Roberson]

Why are you looking for a way that doesn't utilize any for loops? mat2cell() uses for loops internally -- you can read the source code.