How to unfold a Matrix on Matlab?

问题

I have a given matrix H and I would like to unfold (expand) it to find a matrix B by following the method below :

Let H be a matrix of dimension m × n. Let x = gcd (m,n)

The matrix H is cut in two parts.
The cutting pattern being such that :

The "diagonal cut" is made by alternately moving c = n/x units to the right (we move c units to the right several times).
We alternately move c-b = m/x units down (i.e. b = (n-m)/x) (we move b units down several times).

After applying this "diagonal cut" of the matrix, we copy and paste the two parts repeatedly to obtain the matrix B.

Exemple : Let the matrix H of dimension m × n = 5 × 10 defined by :

 1 0 1 1 1 0 1 1 0 0  
 0 1 1 0 0 1 1 0 1 1  
 1 1 0 1 1 1 0 1 0 0  
 0 1 1 0 1 0 1 0 1 1  
 1 0 0 1 0 1 0 1 1 1

Let's calculate x = gcd (m,n) = gcd (5,10) = 5,
Alternatively move to the right : c = n/x = 10/5 = 2,
Alternatively move down : b = (n-m)/x = (10-5)/5 = 1.

Diagonal cutting diagram : The matrix H is cut in two parts. The cutting pattern is such that :

We move c = 2 units to the right several times c = 2 units to the right,
We repeatedly move c - b = 1 unit downwards.

We get :

After applying this "diagonal cut" of the matrix, we copy and paste the two parts repeatedly to obtain the matrix :

Remark : In the matrices X, X1 and X2 the dashes are zeros.

The resulting matrix B is (L is factor) :

Any suggestions?

回答1:

This can be done by creating a logical mask with the cutting pattern, and then element-wise multiplying the input by the mask and by its negation. Repeating by L can be done with blkdiag.

H = [1 0 1 1 1 0 1 1 0 0
     0 1 1 0 0 1 1 0 1 1
     1 1 0 1 1 1 0 1 0 0
     0 1 1 0 1 0 1 0 1 1
     1 0 0 1 0 1 0 1 1 1];
L = 2;
[m, n] = size(H);
x = gcd(m, n);
c = n / x;
b = (n-m)/x;
mask = repelem(tril(true(m/b)), b, c);
A = [H.*mask; H.*~mask];
A = repmat({A}, L, 1);
B = blkdiag(A{:});

来源：https://stackoverflow.com/questions/65049810/how-to-unfold-a-matrix-on-matlab

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arrays

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matrix