2×0 empty double matrix

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

Answer 1

[Voss]

"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.

[sxh]

Sharp eyes Voss! Many thanks

[Voss]

You're welcome!