Create diagonals along a block matrix

Good Morning,

I have a 4x4 matrix containing values only in the first column and all 0's in the remaining spaces. The values contained in each cell are actually vectors of multiple values.

I'd like to make the first value (vector) of the first row be carried over to the second row of the second column, the third row of the third column, and so on. I would like to do the same for the second value (vector) of the first row, which should be reported in the third row of the second column, and so on, in order to create diagonals along the matrix containing the same values.

How can I do this?

Thank you so much!!

[Jan]

"I have a 4x4 matrix containing values only in the first column and all 0's in the remaining spaces"

X = [rand(4, 1), zeros(4, 3)];

"The values contained in each cell are actually vectors of multiple values"

Here is no cell. Which values do you mean? What is a vector of multiple values?

"I would like to do the same for the second value (vector) of the first row"

The 2nd value of the first row is 0. What does carrying over mean?

Currently the description as text is not useful enough. Please edit the question and insert some code, which clarifies what the inputs are and what you want as output.

[sc]

I have a matrix of this type:

A =
[0,0]
[1,1]
[2,1]
[3,3]

and I would like to create a matrix (B) with the diagonals carrying the vectors, ie:

B =
[0,0] [0,0] [0,0] [0,0]
[1,1] [0,0] [0,0] [0,0]
[2,1] [1,1] [0,0] [0,0]
[3,3] [2,1] [1,1] [0,0]

I tried using the command:

B=blkdiag(A{:}); 

but the problem is that it creates an array of this type:

B =
0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0
0 0 0 0 2 1 0 0
0 0 0 0 0 0 3 3

And it is not what i want to obtain.

[Jan]

Sorry, this is a Matlab forum. This is not a Matlab matrix:

A =
[0,0]
[1,1]
[2,1]
[3,3]

Please use Matlab syntax, because this is the common convention here. Thanks.

A matrix has 2 diagonals only. I assume you mean the sub- and super-diagonals?

"B=blkdiag(A{:})" - Now A is a cell array? Sorry for beeing nitpicking, but the more the readers have to guess, the more unlikely is a useful answer.

[sc]

Unfortunately, I haven't used Matlab for very long, so I'm struggling to make myself understood. Anyway, I mean that A is a cell matrix, where each cell contains a vector. I would like to get another cell matrix (called B), which as shown in the code above, presents the cells diagonally. Is it possible to do this?

Answer 1

[Jan]

With some bold guessing and knowing, that this might be more confusing than useful:

The input A is a cell vector and the wanted output B a cell matrix:

A = {[0,0]; ...
     [1,1]; ...
     [2,1]; ...
     [3,3]};

H = flipud(hankel(4:-1:1))   % The display is cropped:

H = 4×4

1 0 0 0 2 1 0 0 3 2 1 0 4 3 2 1

B = cell(numel(A), numel(A));
B(H ~= 0) = A(H(H~= 0))

B = 4×4 cell array
    {[0 0]}    {0×0 double}    {0×0 double}    {0×0 double}
    {[1 1]}    {[     0 0]}    {0×0 double}    {0×0 double}
    {[2 1]}    {[     1 1]}    {[     0 0]}    {0×0 double}
    {[3 3]}    {[     2 1]}    {[     1 1]}    {[     0 0]}

% Or maybe:
H2 = max(1, flipud(hankel(4:-1:1)))   % The display is cropped:

H2 = 4×4

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

B2 = A(H2)

B2 = 4×4 cell array
    {[0 0]}    {[0 0]}    {[0 0]}    {[0 0]}
    {[1 1]}    {[0 0]}    {[0 0]}    {[0 0]}
    {[2 1]}    {[1 1]}    {[0 0]}    {[0 0]}
    {[3 3]}    {[2 1]}    {[1 1]}    {[0 0]}

[sc]

Thank you, the second approach is the correct one!