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Decomposition - symmetric and anti-symmetric #62

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Decomposition - symmetric and anti-symmetric #62

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Decomposition - symmetric and anti-symmetric
AnhMai-bit Apr 24, 2022
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Update - Decomposition
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Update reproducing.m
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Update - Apr 27 - Symm Decomp
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Update - Decomp - Include checks for accuracy
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Update - Decomp - Reshape
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Decom - Update - May 4
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Expand Up @@ -349,6 +349,14 @@
%% Pg. 55, SCM-BCR
%% Pg. 56, Decomposition into symmetric and anti-symmetric parts

b = dec2bin(2^4-1:-1:0)-'0';
b1 = b(:,1); b2 = b(:,2); b3 = b(:,3); b4 = b(:,4);

f=b1.*b2 + b2.*b3 + b3.*b4 - 4*b1.*b2.*b3;

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It would be better if this example had the following:

  • 1 linear term with a coefficient of +1,
  • 1 quadratic terms with a coefficient of +2,
  • 1 cubic term with a coefficient of -4, and
  • one quartic term with a coefficient of +2.

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I will add that asap.

f_sym = (1/2)*(f + f.');
f_anti = (1/2)*(f - f.');

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This makes no sense. I don't see why you did f.'.

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This is to make the transpose of the matrix.

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@ndattani my alternative solution is below. I will add that to the code if you approve.

% f_sym = (1/2)(f(b) + (1-f(b))
f_sym = (1/2)(f + (1-f))

% f_anti = (1/2)(f(b) - (1-f(b))
f_anti = (1/2)(f - (1-f))

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@ndattani ndattani Apr 27, 2022 •
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Anyone who has used MATLAB for as long as me would know that f.' does the transpose of f, but what made you think that it would be a good idea to do the transpose?

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I looked into how decomposition into symmetric and antisymmetric would be and I see there are 2 ways to do it. One this by adding and subtracting transpose into f, divided by two. Source: https://www.mathworks.com/matlabcentral/answers/401295-how-to-find-the-symmetric-and-skew-symmetric-part-of-a-specified-matrix.

The other is from the paper attached to the part in the book: https://www.maths.lth.se/matematiklth/vision/publdb/reports/pdf/kahl-strandmark-iccv-11.pdf. Notation: f - (1-transpose of f), divided by 2.

Can you please explain the difference between those 2? Thank you.

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The second example doesn't use the transpose.

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It seems like I confused myself somewhere, my apologies. I will fix that tomorrow since I currently have to prepare to move.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
QUANTUM GADGETS
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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