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AbsFunctions added #1976

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@fmwatson fmwatson commented Nov 6, 2024

Description

Methodology for converting a CIL Function H(x) into the same Function applied to the magnitude of data G(z):=H(|z|), in particular for complex-valued problems. The New CIL Function can be used as
function = SomeCILFunction() fun_applied_to_magnitude = FunctionOfAbs(function)

.proximal() (and .proximal_conjugate()) will be correctly modified for use with Algorithms such as PDHG

For mathematical details see https://doi.org/10.48550/arXiv.2410.22161

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jakobsj commented Nov 7, 2024

Thanks very much @fmwatson for adding this absolute value feature! As also discussed in person, it would be a great help for reviewing this if you could add some very basic demonstration code of how a user might use this. One potential (but possibly slightly too simplistic) case could be a complex random valued square MatrixOperator A mapping a vectordata x to a vectordata b and then use the functionality to do ||A* abs(x) - b||_2^2

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