Error in svd in r2018a

Question

N/A 2022-7-17

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1761920-error-in-svd-in-r2018a

评论： Christine Tobler 2022-8-5

采纳的回答： Bruno Luong

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I only have access to r2018a, where there is an error in svd. I tried the recommended fix

[U,s,V] = svd(A + 1e-14*randn(size(A)));

but I still getting the same error every now and then. How do you recommend getting around this error without increasing the size of the perturbation? Could I increase the number of iterations to test convergence, if so how? Or something else?

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Walter Roberson 2022-7-17

The problem would continue if eps(A) > 1e-14 which would be the case if abs(A) > 100 or so

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Answer 1

Bruno Luong 2022-7-17

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https://ww2.mathworks.cn/matlabcentral/answers/1761920-error-in-svd-in-r2018a#answer_1009210

编辑：Bruno Luong 2022-7-17

在 MATLAB Online 中打开

As Walter has pointed out, the workwaround given by TMW might be still flawed because it ignores the scale of A.

A better solution would be

A = randi(100,4,6)
A = 4×6
    82     8    13    18    98    82
    77     8    10    61    29    85
    28    48    21    23    86    96
    70    94    98    63    60    33
[U,s,V] = svd(A + norm(A)*1e-14*randn(size(A)))
U = 4×4
   -0.5147    0.4562   -0.1289   -0.7144
   -0.4295    0.2837    0.7830    0.3493
   -0.4856    0.2094   -0.6069    0.5932
   -0.5610   -0.8170    0.0443   -0.1255
s = 4×6
  275.2436         0         0         0         0         0
         0  110.2492         0         0         0         0
         0         0   66.4140         0         0         0
         0         0         0   42.8050         0         0
V = 6×6
   -0.4656    0.0719    0.5394   -0.5573   -0.0481   -0.4174
   -0.3037   -0.5517   -0.2972    0.3213    0.2364   -0.5966
   -0.2767   -0.6068   -0.0339   -0.1317   -0.6095    0.4065
   -0.2978   -0.1917    0.5160    0.3314    0.5339    0.4619
   -0.5026    0.1989   -0.5943   -0.3829    0.3450    0.2984
   -0.5226    0.4959   -0.0125    0.5589   -0.4078   -0.0469

Or might be this cumbersome code that uses EIG (hopefully not buggy in your version) instead of SVD.

[m,n] = size(A);
AAc = A*A'; [U,s2u] = eig(1/2*(AAc+AAc'));
AcA = A'*A; [V,s2v] = eig(1/2*(AcA+AcA'));
[~, isu] = sort(sqrt(max(diag(s2u),0)),'descend');
[s, isv] = sort(sqrt(max(diag(s2v),0)),'descend');
U = U(:,isu);
S = diag(s);
if n < m
    S(m,1) = 0;
    isv = isv(1:n);
else
    S = S(1:m,:);
end
V = V(:,isv);
U
U = 4×4
    0.5147    0.4562    0.1289   -0.7144
    0.4295    0.2837   -0.7830    0.3493
    0.4856    0.2094    0.6069    0.5932
    0.5610   -0.8170   -0.0443   -0.1255
S
S = 4×6
  275.2436         0         0         0         0         0
         0  110.2492         0         0         0         0
         0         0   66.4140         0         0         0
         0         0         0   42.8050         0         0
V % Note the two last columns are arbitrary provided they span the same subspace and are orthogonal
V = 6×6
    0.4656    0.0719   -0.5394   -0.5573   -0.4065   -0.1064
    0.3037   -0.5517    0.2972    0.3213   -0.6239    0.1500
    0.2767   -0.6068    0.0339   -0.1317    0.4883   -0.5462
    0.2978   -0.1917   -0.5160    0.3314    0.3822    0.5936
    0.5026    0.1989    0.5943   -0.3829    0.2469    0.3836
    0.5226    0.4959    0.0125    0.5589    0.0110   -0.4103

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Christine Tobler 2022-8-5

Thank you for pointing this out, I have included scaling by norm(A) into the proposed workaround.

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Answer 2

Steven Lord 2022-7-17

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https://ww2.mathworks.cn/matlabcentral/answers/1761920-error-in-svd-in-r2018a#answer_1009120

Are you using Update 3 of release R2018a or a later Update, or are you using release R2018a (no Update) or Updates 1 or 2?

If you have not installed Update 3 or a later Update, please do.

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N/A 2022-7-17

编辑：N/A 2022-7-17

Thanks @Steven Lord. It's the version R2018a (9.4.0.813654) 64-bit (glnxa64) from Feb. 23, 2018. It's on a cluster where I don't have admin access (I'm not able to install a new version).

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