How to write a diagonal rectangular matrix

Question

Leonardo 2023-11-23

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2051182-how-to-write-a-diagonal-rectangular-matrix

评论： Dyuman Joshi 2023-11-23

采纳的回答： Chunru

I have to insert on matlab this matrix:

n = 100;

A = diag(21*ones(n,1)) + diag(-4*ones(n-1,1),-1)...

+ diag(-20*ones(n-1,1),1) + diag(ones(n-2,1),-2)...

+ diag(2*ones(n-2,1), 2);

I can generate it when it is squared, but now the exercise tells me to use the same numbers in a rectangular matrix having dimensions 100x98: how do I create the new matrix?

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Answer 1

Chunru 2023-11-23

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2051182-how-to-write-a-diagonal-rectangular-matrix#answer_1358517

编辑：Chunru 2023-11-23

在 MATLAB Online 中打开

You can use toeplitz function.

% Smaller n, m here
n = 10;
m = 8; 
A = diag(21*ones(n,1)) + diag(-4*ones(n-1,1),-1)...
    + diag(-20*ones(n-1,1),1) + diag(ones(n-2,1),-2)...
    + diag(2*ones(n-2,1), 2);
whos
  Name         Size            Bytes  Class     Attributes

  A           10x10              800  double              
  cmdout       1x33               66  char                
  m            1x1                 8  double              
  n            1x1                 8  double              
A
A = 10×10
    21   -20     2     0     0     0     0     0     0     0
    -4    21   -20     2     0     0     0     0     0     0
     1    -4    21   -20     2     0     0     0     0     0
     0     1    -4    21   -20     2     0     0     0     0
     0     0     1    -4    21   -20     2     0     0     0
     0     0     0     1    -4    21   -20     2     0     0
     0     0     0     0     1    -4    21   -20     2     0
     0     0     0     0     0     1    -4    21   -20     2
     0     0     0     0     0     0     1    -4    21   -20
     0     0     0     0     0     0     0     1    -4    21
c = zeros(n, 1);  c(1:3)=[21 -4 1];   % 1st column
r = zeros(m, 1);  r(1:3)=[21 -20 2];  % 1st row
B = toeplitz(c, r)
B = 10×8
    21   -20     2     0     0     0     0     0
    -4    21   -20     2     0     0     0     0
     1    -4    21   -20     2     0     0     0
     0     1    -4    21   -20     2     0     0
     0     0     1    -4    21   -20     2     0
     0     0     0     1    -4    21   -20     2
     0     0     0     0     1    -4    21   -20
     0     0     0     0     0     1    -4    21
     0     0     0     0     0     0     1    -4
     0     0     0     0     0     0     0     1
    

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Leonardo 2023-11-23

How can I remove the last two columns easily? @Dyuman Joshi

Dyuman Joshi 2023-11-23

在 MATLAB Online 中打开

% Smaller n, m here
n = 10;
m = 8; 
A = diag(21*ones(n,1)) + diag(-4*ones(n-1,1),-1)...
    + diag(-20*ones(n-1,1),1) + diag(ones(n-2,1),-2)...
    + diag(2*ones(n-2,1), 2)
A = 10×10
    21   -20     2     0     0     0     0     0     0     0
    -4    21   -20     2     0     0     0     0     0     0
     1    -4    21   -20     2     0     0     0     0     0
     0     1    -4    21   -20     2     0     0     0     0
     0     0     1    -4    21   -20     2     0     0     0
     0     0     0     1    -4    21   -20     2     0     0
     0     0     0     0     1    -4    21   -20     2     0
     0     0     0     0     0     1    -4    21   -20     2
     0     0     0     0     0     0     1    -4    21   -20
     0     0     0     0     0     0     0     1    -4    21
%Remove the last n-m columns
A(:,end-(1:n-m)) = []
A = 10×8
    21   -20     2     0     0     0     0     0
    -4    21   -20     2     0     0     0     0
     1    -4    21   -20     2     0     0     0
     0     1    -4    21   -20     2     0     0
     0     0     1    -4    21   -20     2     0
     0     0     0     1    -4    21   -20     0
     0     0     0     0     1    -4    21     0
     0     0     0     0     0     1    -4     2
     0     0     0     0     0     0     1   -20
     0     0     0     0     0     0     0    21