How to write a diagonal rectangular matrix

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Leonardo
Leonardo 2023-11-23
评论： Dyuman Joshi 2023-11-23
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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Chunru
Chunru 2023-11-23
编辑：Chunru 2023-11-23
Ran in:
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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Dyuman Joshi
Dyuman Joshi 2023-11-23
Ran in:
% 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

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