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create symmetric fixed rank polar factory #12

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@bamdevm bamdevm commented Apr 5, 2019

Creating the factory file for W = UBU' fixed rank geometry, where U is on the Stiefel and B is positive definite.

…in two places, and also added a tip regarding FD's for gradient.
…earch_hint. On the other hand, it does require a hint in the problem structure, so that is now provided by default. I don't understand how this did not create bugs before.....
…mit of this file (RLBFGS) was made because of a bug on my computer (I was working with two versions of manopt, so that rlbfgs was calling an older verison of linesearch_hint, and that was the reason for the code not working; this being said, the newer version should be more robust anyway.)
…rox of the Hessian in the checkhessian test.
…d by the user to explain what to expect in the case of FD approximations.
… call to a small built-in SVD -- using Brocket cost function. See if this is better numerically than the current truncated SVD in examples folder.
…ls that produce factories: all have M.tangent() defined.
@NicolasBoumal
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Hello Bamdev,

Thanks for the commits -- I have now reviewed your code and made a number of small and larger suggestions -- could you please check them out? Happy to discuss.

Best,
Nicolas

@NicolasBoumal
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Hello Bamdev,

Was there any issue with the recommendations I had made here?

Thanks,
Nicolas

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bamdevm commented Sep 17, 2019 via email

bamdevm and others added 6 commits September 17, 2019 09:17
Typos

Co-Authored-By: Nicolas Boumal <nicolasboumal@gmail.com>
fixed the typos that Nicolas suggeted
typos

Co-Authored-By: Nicolas Boumal <nicolasboumal@gmail.com>
Missing text

Co-Authored-By: Nicolas Boumal <nicolasboumal@gmail.com>
Co-Authored-By: Nicolas Boumal <nicolasboumal@gmail.com>
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bamdevm commented Sep 17, 2019 via email

bamdevm and others added 12 commits September 17, 2019 09:26
Co-Authored-By: Nicolas Boumal <nicolasboumal@gmail.com>
Adding description on the metric
to get matrix representation from the structure. and vice-versa.
symm(eta.B*(X.B\rgrad.B)) is same as  symm(eta.B*symm(egrad.B)*X.B). Therefore, we need only 1 such term.
Co-Authored-By: Nicolas Boumal <nicolasboumal@gmail.com>
Co-Authored-By: Nicolas Boumal <nicolasboumal@gmail.com>
Co-Authored-By: Nicolas Boumal <nicolasboumal@gmail.com>
Co-Authored-By: Nicolas Boumal <nicolasboumal@gmail.com>
Added " The total space is the Cartesian product of the Stiefel and symmetric
% positive definite manifolds. An element in the total space, therefore, is
% is also represented as a structure with two fields: U and B. This is
% also the output in M.tangent2ambient."
added semicolon.
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Moved to PR #12 as discussed in PR #6 .

@NicolasBoumal NicolasBoumal deleted the bmsymfixedrankpolarfactory branch May 20, 2020 17:31
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5 participants