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Complex fixes #163

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The proposed changes aim to repair a few issues with levenberg_marquardt():

  • At present, it allows complex nonlinear variables. However, squared norm is not analytic, and optimizing it requires taking partial derivatives with respect to both z and conj(z). Best not to confuse users and simply disallow complex variables, recommending instead to treat them as pairs of real and imaginary parts.

  • It does not handle complex-valued Jacobian correctly

  • Computation of LM step involves forming normal equations, which squares the condition number.

@pkofod
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pkofod commented Oct 27, 2020

Thanks, I will try to look at this but I have been very busy lately unfortunately.

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pkofod commented Oct 28, 2020

This week is quite busy, but I promise to get back to you. Maybe @antoine-levitt has some comments in the mean time?

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I'm not familiar with the algorithm so I just left trivial style comments. Generally treating the complex optimization problem as real/imag is a good idea (sometimes it's unnecessary, but it's always a good fallback choice)

src/levenberg_marquardt.jl Outdated Show resolved Hide resolved
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