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Exponentially scaled modified Bessel functions of order zero and one.

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The functions are conventionally called i0e and i1e. The exponentially scaled version is more numerically stable. The standard Bessel functions can be obtained as i0(x) = exp(|x|) i0e(x)

The code is ported from Cephes and tested against SciPy.
This commit is contained in:
Michael Figurnov
2018-05-31 15:34:53 +01:00
parent 6af1433cb5
commit f216854453
12 changed files with 731 additions and 0 deletions
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46
unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsArrayAPI.h
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@@ -119,6 +119,52 @@ zeta(const Eigen::ArrayBase<DerivedX>& x, const Eigen::ArrayBase<DerivedQ>& q)
);
}
/** \returns an expression of the coefficient-wise i0e(\a x) to the given
* arrays.
*
* It returns the exponentially scaled modified Bessel
* function of order zero.
*
* \param x is the argument
*
* \note This function supports only float and double scalar types. To support
* other scalar types, the user has to provide implementations of i0e(T) for
* any scalar type T to be supported.
*
* \sa ArrayBase::i0e()
*/
template <typename Derived>
inline const Eigen::CwiseUnaryOp<
Eigen::internal::scalar_i0e_op<typename Derived::Scalar>, const Derived>
i0e(const Eigen::ArrayBase<Derived>& x) {
return Eigen::CwiseUnaryOp<
Eigen::internal::scalar_i0e_op<typename Derived::Scalar>,
const Derived>(x.derived());
}
/** \returns an expression of the coefficient-wise i1e(\a x) to the given
* arrays.
*
* It returns the exponentially scaled modified Bessel
* function of order one.
*
* \param x is the argument
*
* \note This function supports only float and double scalar types. To support
* other scalar types, the user has to provide implementations of i1e(T) for
* any scalar type T to be supported.
*
* \sa ArrayBase::i1e()
*/
template <typename Derived>
inline const Eigen::CwiseUnaryOp<
Eigen::internal::scalar_i1e_op<typename Derived::Scalar>, const Derived>
i1e(const Eigen::ArrayBase<Derived>& x) {
return Eigen::CwiseUnaryOp<
Eigen::internal::scalar_i1e_op<typename Derived::Scalar>,
const Derived>(x.derived());
}
} // end namespace Eigen
#endif // EIGEN_SPECIALFUNCTIONS_ARRAYAPI_H