feat(ratf): Added rational functions support and implemented Pade approximation #66
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- Created new file `ALFI/ALFI/ratf.h` with `alfi::ratf` namespace for rational function. - Implemented a `std::pair`-interchangeable class `RationalFunction`.
- Replaced `RationalFunction` class with an alias for `std::pair<Container<Number>, Container<Number>>`. - Added `alfi::util::numeric::binpow` function for binary exponentiation. - Added `val`, `val_mul`, and `val_div` functions in `alfi::ratf` for scalars and vectors.
- Created new file `ALFI/ALFI/util/poly.h` for utility functions for polynomial operations. - Implemented `normalize`, `mul`, `div`, and `extended_euclid` functions in `alfi::util::poly`. - Implemented `alfi::ratf::pade` function using `extended_euclid`.
This is done to fix false negative results, for example, with the [2/2] approximation of x^5. It also simplifies the code and improves performance.
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Types of changes
Description
New features:
ALFI/ALFI/ratf.hwithalfi::ratfnamespace for rational functions.RationalFunctiontype as an alias forstd::pair<Container<Number>, Container<Number>>.val,val_mul, andval_divfunctions for scalars and vectors.padefunction for computing Pade approximant aboutNew utility functions:
ALFI/ALFI/util/poly.hwith utility functions for polynomial operations.normalize,mul, anddivfunctions inalfi::util::poly.alfi::util::numeric::binpowfunction for binary exponentiation.Added documentation for all new functions and namespaces.
Implemented basic tests and benchmarks for rational functions and Pade approximation.