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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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54
unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsFunctors.h
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@@ -229,6 +229,60 @@ struct functor_traits<scalar_erfc_op<Scalar> >
};
};
/** \internal
* \brief Template functor to compute the exponentially scaled modified Bessel
* function of order zero
* \sa class CwiseUnaryOp, Cwise::i0e()
*/
template <typename Scalar>
struct scalar_i0e_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_i0e_op)
EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& x) const {
using numext::i0e;
return i0e(x);
}
typedef typename packet_traits<Scalar>::type Packet;
EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& x) const {
return internal::pi0e(x);
}
};
template <typename Scalar>
struct functor_traits<scalar_i0e_op<Scalar> > {
enum {
// On average, a Chebyshev polynomial of order N=20 is computed.
// The cost is N multiplications and 2N additions.
Cost = 20 * NumTraits<Scalar>::MulCost + 40 * NumTraits<Scalar>::AddCost,
PacketAccess = packet_traits<Scalar>::HasI0e
};
};
/** \internal
* \brief Template functor to compute the exponentially scaled modified Bessel
* function of order zero
* \sa class CwiseUnaryOp, Cwise::i1e()
*/
template <typename Scalar>
struct scalar_i1e_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_i1e_op)
EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& x) const {
using numext::i1e;
return i1e(x);
}
typedef typename packet_traits<Scalar>::type Packet;
EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& x) const {
return internal::pi1e(x);
}
};
template <typename Scalar>
struct functor_traits<scalar_i1e_op<Scalar> > {
enum {
// On average, a Chebyshev polynomial of order N=20 is computed.
// The cost is N multiplications and 2N additions.
Cost = 20 * NumTraits<Scalar>::MulCost + 40 * NumTraits<Scalar>::AddCost,
PacketAccess = packet_traits<Scalar>::HasI1e
};
};
} // end namespace internal
} // end namespace Eigen