How can I reshape a square matrix to a rectangular matrix based on its adjacency list?

Question

Nadatimuj 2022-3-23

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1678359-how-can-i-reshape-a-square-matrix-to-a-rectangular-matrix-based-on-its-adjacency-list

评论： Nadatimuj 2022-3-23

How can I reshape a square matrix to a rectangular matrix based on its adjacency list? Let's say I have the following 14x14 matrix A. If it is a graph, each node has a maximum neighbors = 6. I want to create a matrix which will be 14x6. So, each row will have maximum 6 items and the values will be the non-zero items (keeping original sequence) from the original matrix, followed by zero padding.

A =
  -1     0     0     0     0    -2    -2     0     0     0     0     0     2
    -1     0     0     0     0     0     0     0     2     0     0     0     2     2
   0     0    -1     2    -1     0     0     0     0     0     0     0    -2
   0    -1     0     2     0     0     0     0     0     0     0     0     0
   0     2     2     0     0     0     0     0     0     0     0     1     2
   0    -1     0     0     0    -1     0     0     2     0     0     0    -2
    -2     0     0     0     0    -1     0    -1     0     2     0     0     0     0
    -2     0     0     0     0     0    -1     0    -1     0     2     0     0     0
   2     0     0     0     0     0    -1     0     0     2     0    -1     0
   0     0     0     0     2     2     0     0     0    -1     2     0     0
   0     0     0     0     0     0     2     2    -1     0     2     0     0
   0     0     0     0     0     0     0     0     2     2     0    -1     2
   2     0     0     1     0     0     0    -1     0     0    -1     0     0
   2    -2     0     2    -2     0     0     0     0     0     2     0     0

Now it's adjacency list will be (I got it from Mathematica):

 {{2, 7, 8, 14}},
 {{1, 9, 13, 14}},
 {{4, 5, 6, 14}},
 {{3, 5}},
 {{3, 4, 13, 14}},
 {{3, 7, 10, 14}},
 {{1, 6, 8, 10}},
 {{1, 7, 9, 11}},
 {{2, 8, 11, 13}},
 {{6, 7, 11, 12}},
 {{8, 9, 10, 12}},
 {{10, 11, 13, 14}},
 {{2, 5, 9, 12}},
 {{1, 2, 3, 5, 6, 12}}

Now I need the output matrix will be:

 A_reshaped =
    -1    -2    -2     2     0     0
    -1     2     2     2     0     0
    -1     2    -1    -2     0     0
    -1     2     0     0     0     0
     2     2     1     2     0     0
    -1    -1     2    -2     0     0
    -2    -1    -1     2     0     0
    -2    -1    -1     2     0     0
     2    -1     2    -1     0     0
     2     2    -1     2     0     0
     2     2    -1     2     0     0
     2     2    -1     2     0     0
     2     1    -1    -1     0     0
     2     2    -2     2    -2     2

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Answer 1

Matt J 2022-3-23

1
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1678359-how-can-i-reshape-a-square-matrix-to-a-rectangular-matrix-based-on-its-adjacency-list#answer_924834

编辑：Matt J 2022-3-23

在 MATLAB Online 中打开

A=[  0    -1     0     0     0     0    -2    -2     0     0     0     0     0     2
    -1     0     0     0     0     0     0     0     2     0     0     0     2     2
     0     0     0    -1     2    -1     0     0     0     0     0     0     0    -2
     0     0    -1     0     2     0     0     0     0     0     0     0     0     0
     0     0     2     2     0     0     0     0     0     0     0     0     1     2
     0     0    -1     0     0     0    -1     0     0     2     0     0     0    -2
    -2     0     0     0     0    -1     0    -1     0     2     0     0     0     0
    -2     0     0     0     0     0    -1     0    -1     0     2     0     0     0
     0     2     0     0     0     0     0    -1     0     0     2     0    -1     0
     0     0     0     0     0     2     2     0     0     0    -1     2     0     0
     0     0     0     0     0     0     0     2     2    -1     0     2     0     0
     0     0     0     0     0     0     0     0     0     2     2     0    -1     2
     0     2     0     0     1     0     0     0    -1     0     0    -1     0     0
     2     2    -2     0     2    -2     0     0     0     0     0     2     0     0];
     
     
 At=A.';
 
 I0=(At~=0);
 
 I = sort(I0,1,'descend');
Areshaped=zeros(size(At));
Areshaped(I)=At(I0);
Areshaped=Areshaped(any(Areshaped,2),:)'
Areshaped = 14×6
    -1    -2    -2     2     0     0
    -1     2     2     2     0     0
    -1     2    -1    -2     0     0
    -1     2     0     0     0     0
     2     2     1     2     0     0
    -1    -1     2    -2     0     0
    -2    -1    -1     2     0     0
    -2    -1    -1     2     0     0
     2    -1     2    -1     0     0
     2     2    -1     2     0     0

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Nadatimuj 2022-3-23

Thank you!

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Answer 2

Arif Hoq 2022-3-23

3
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1678359-how-can-i-reshape-a-square-matrix-to-a-rectangular-matrix-based-on-its-adjacency-list#answer_924819

编辑：Arif Hoq 2022-3-23

在 MATLAB Online 中打开

try this:

A =[0     1     0     1     0
 1     0     1     1     0
 0     1     0     1     1
 1     1     1     0     1
 0     0     1     1     0];
output=sort(A,2,'descend');
output(:,end)=[]
output = 5×4
     1     1     0     0
     1     1     1     0
     1     1     1     0
     1     1     1     1
     1     1     0     0

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Arif Hoq 2022-3-23

在 MATLAB Online 中打开

or try this:

A =[0    -1     0     0     0     0    -2    -2     0     0     0     0     0     2
-1     0     0     0     0     0     0     0     2     0     0     0     2     2
0     0     0    -1     2    -1     0     0     0     0     0     0     0    -2
0     0    -1     0     2     0     0     0     0     0     0     0     0     0
0     0     2     2     0     0     0     0     0     0     0     0     1     2
0     0    -1     0     0     0    -1     0     0     2     0     0     0    -2
-2     0     0     0     0    -1     0    -1     0     2     0     0     0     0
-2     0     0     0     0     0    -1     0    -1     0     2     0     0     0
0     2     0     0     0     0     0    -1     0     0     2     0    -1     0
0     0     0     0     0     2     2     0     0     0    -1     2     0     0
0     0     0     0     0     0     0     2     2    -1     0     2     0     0
0     0     0     0     0     0     0     0     0     2     2     0    -1     2
0     2     0     0     1     0     0     0    -1     0     0    -1     0     0
2     2    -2     0     2    -2     0     0     0     0     0     2     0     0];
b= size(A, 1);
[~, Y] = sort(A == 0, 2);
output= A((1:b).' + (Y - 1) * b);
output( :, ~any(output,1) ) = []
output = 14×6
    -1    -2    -2     2     0     0
    -1     2     2     2     0     0
    -1     2    -1    -2     0     0
    -1     2     0     0     0     0
     2     2     1     2     0     0
    -1    -1     2    -2     0     0
    -2    -1    -1     2     0     0
    -2    -1    -1     2     0     0
     2    -1     2    -1     0     0
     2     2    -1     2     0     0