2×0 empty double matrix

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sxh
sxh 2024-9-4
评论： Voss 2024-9-5
Ran in:
trying to calculate a function with matrix arguments and matrix output: Question 1: is the following code the right way to do it? Question 2: why is SAB21 returning " 2×0 empty double matrix"?
A = magic(4)
A = 4x4
16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1
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S = anti_eye(4)
S = 4x4
0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0
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S = star (S, A) %should return A
SAB11 = 2x2
11 5 2 16
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SAB12 = 2x2
10 8 3 13
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SAB21 = 2x0 empty double matrix
SAB22 = 2x2
6 12 15 1
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S = 4x4
11 5 10 8 2 16 3 13 0 0 6 12 0 0 15 1
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function SAB = star(SA,SB)
% Redheffer Star Product
SAB11 = SA (1:2,1:2,:) + SA (1:2,3:4,:) *((eye(2) - SB (1:2,1:2,:)* SA (3:4,3:4,:))^(-1)) *SB (1:2,1:2,:) *SA (3:4,1:2,:)
SAB12 = SA (1:2,3:4,:) *((eye(2) - SB (1:2,1:2,:) *SA (3:4,3:4,:))^(-1)) *SB(1:2,3:4,:)
SAB21 = SB (3:4,1:2,:) *((eye(2) - SA (3:4,3:4,:) *SB (1:2,1:2,:))^(-1)) *SA(3:4,2:1,:)
SAB22 = SB (3:4,3:4,:) + SB (3:4,1:2,:) *((eye(2) - SA (3:4,3:4,:) *SB (1:2,1:2,:))^(-1)) *SA (3:4,3:4,:) *SB (1:2,3:4,:)
SAB (1:2, 1:2 ,:) = SAB11;
SAB (1:2, 3:4 ,:) = SAB12;
SAB (3:4, 2:1, :) = SAB21;
SAB (3:4, 3:4, :) = SAB22;
end
function ans = anti_eye(n)
% anti Identity matrix
flipud(eye(n));
end

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采纳的回答

Voss
Voss 2024-9-4
编辑：Voss 2024-9-4
Ran in:
"why is SAB21 returning " 2×0 empty double matrix"?"
Because the expression 2:1 evaluates to an empty vector.
SAB21 = SB (3:4,1:2,:) *((eye(2) - SA (3:4,3:4,:) *SB (1:2,1:2,:))^(-1)) *SA(3:4,2:1,:)
% ^^^
2:1
ans = 1x0 empty double row vector
I guess you meant 2:-1:1, or simpler, [2 1]:
2:-1:1
ans = 1x2
2 1
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[2 1]
ans = 1x2
2 1
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Example:
M = magic(4)
M = 4x4
16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1
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M(3:4,2:1,:)
ans = 2x0 empty double matrix
M(3:4,[2 1],:)
ans = 2x2
7 9 14 4
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https://www.mathworks.com/help/matlab/ref/colon.html
And by the way, the colon indexing in the third dimension, e.g.:
SA(3:4,[2 1],:)
% ^^
is not necessary anywhere in the code because all the arrays are two-dimensional (i.e., matrices). That is, you can just write
SA(3:4,[2 1])
etc.

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