Calculating a matrix from other matrices

조회 수: 16(최근 30일)
편집: Matt J 15 Feb 2021
How can I write the following matrix?
M = [C*B;
C*A*B + C*B;
C*A^2*B + C*A*B + C*B;
.
.
.
C*A^(N-1)*B + C*A^(N-2)*B + ... + C*B];
A, B, and C are 2D arrays with size(A)=(n,n), size(B)=(n,p), and size(C)=(q,n). N is a positive integer.
댓글 수: 1표시숨기기 없음
Walter Roberson 15 Feb 2021
I posted code for the 2D version of this a couple of years ago, where the values were being copied down the diagonals.
Unfortunately it has been far too long for me to recall the key words that would needed to find it within my other posts :(

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답변(1개)

Matt J 15 Feb 2021
Q=eye(n);
Mcell=cell(n,1);
for i=1:N
Mcell{i}=C*Q*B;
Q=A*Q+Q;
end
M=cell2mat(Mcell);
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Matt J 15 Feb 2021
Sorry, it should be
N = 4;
A = rand(4);
B = rand(4,1);
C = rand(1,4);
[n,p] = size(B);
R = [C*B;
C*A*B + C*B;
C*A^2*B + C*A*B + C*B;
C*A^3*B + C*A^2*B + C*A*B + C*B];
[Q,Q0]=deal(eye(n));
Mcell=cell(n,1);
for i=1:N
Mcell{i}=C*Q*B;
Q=A*Q+Q0;
end
M=cell2mat(Mcell);
difference=norm(R-M)
difference = 1.8310e-15

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