C++ Concepts for C++ Concepts for Ill-posed Inverse Problems - - PowerPoint PPT Presentation

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Dec 01, 2023 121 likes •214 views

C++ Concepts for C++ Concepts for Ill-posed Inverse Problems Ill-posed Inverse Problems Or: How to do weird math stu at compile time Or: How to do weird math stu at compile time David Frank David Frank -- -- frankd@in.tum.de

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C++ Concepts for C++ Concepts for Ill-posed Inverse Problems Ill-posed Inverse Problems

Or: How to do weird math stu at compile time Or: How to do weird math stu at compile time

David Frank David Frank frankd@in.tum.de frankd@in.tum.de Complete code at Complete code at https://godbolt.org/z/EBuSA5 https://godbolt.org/z/EBuSA5

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SLIDE 2

What we'll be doing

Convert key ideas of elsa's* design, which currently does a lot at runtime, to work at compile time * You can find it at: https://gitlab.lrz.de/IP/elsa 2 / 9

SLIDE 3

What is an ill-posed Inverse Problem

Arise when, we want to compute information about hidden data from

utside

Can represent image processing or tomographic reconstruction task Check out the book Discrete Inverse Problems by Per Christian Hansen (Math heavy!!) 3 / 9

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What is an ill-posed Inverse Problem

Arise when, we want to compute information about hidden data from

utside

Can represent image processing or tomographic reconstruction task Check out the book Discrete Inverse Problems by Per Christian Hansen (Math heavy!!)

The concept Problem

Models mathematical optimization problem Incorporates logic, so an algorithm can find a solution (called a Solver) Currently elsa does all checks, if the Solver can actually handle the problem at run time. 4 / 9

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A base concept for a problem

template<class P_> concept Problem = requires(P_ p) { { p.dataTerm_ } -> Functional; requires requires (vector x) { { p.gradient(x) } -> convertible_to<vector>; }; };

How to read this: If a type has a member dataTerm_, which fulfills the concept Functional and has a member function gradient, which takes a vector and returns something, which is convertible to a vector, it satisfies the concept Problem 5 / 9

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Specialized Problems

For example, Conjugate Gradient * requires a data term in quadric from Introduce concepts, which require the original Problem and impose further restrictions * for the interested https://en.wikipedia.org/wiki/Conjugate_gradient_method 6 / 9

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Specialized Problems

For example, Conjugate Gradient * requires a data term in quadric from Introduce concepts, which require the original Problem and impose further restrictions

Concepts for Conjugate Gradient

template<class P_> concept QuadricProblem = Problem<P_> && requires(P_ p) { requires is_specialization<decltype(p.dataTerm_), quadric>; }; template<class P_> concept ConvertibleToQuadricProblem = Problem<P_> && requires(P_ p) { requires is_specialization<decltype(p.dataTerm_), l2_norm_pow2> && requires { { p.toQuadric() } -> QuadricProblem; }; };

* for the interested https://en.wikipedia.org/wiki/Conjugate_gradient_method 7 / 9

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A promising approach for elsa*

Remove flat polymorphic hierarchies Remove coupling between some components Describing mathematical constrains at compile time Personally, the approach of requiring something feels natural * and maybe for your project? 8 / 9

SLIDE 9

I hope you enjoyed my talk! I hope you enjoyed my talk!

David Frank David Frank frankd@in.tum.de frankd@in.tum.de Complete code at Complete code at https://godbolt.org/z/EBuSA5 https://godbolt.org/z/EBuSA5

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