In addition to igamma(a, x), this code implements:
* igamma_der_a(a, x) = d igamma(a, x) / da -- derivative of igamma with respect to the parameter
* gamma_sample_der_alpha(alpha, sample) -- reparameterization derivative of a Gamma(alpha, 1) random variable sample with respect to the alpha parameter
The derivatives are computed by forward mode differentiation of the igamma(a, x) code. Although gamma_sample_der_alpha can be implemented via igamma_der_a, a separate function is more accurate and efficient due to analytical cancellation of some terms. All three functions are implemented by a method parameterized with "mode" that always computes the derivatives, but does not return them unless required by the mode. The compiler is expected to (and, based on benchmarks, does) skip the unnecessary computations depending on the mode.
This commit enables the use of Eigen on HIP kernels / AMD GPUs. Support has been added along the same lines as what already exists for using Eigen in CUDA kernels / NVidia GPUs.
Application code needs to explicitly define EIGEN_USE_HIP when using Eigen in HIP kernels. This is because some of the CUDA headers get picked up by default during Eigen compile (irrespective of whether or not the underlying compiler is CUDACC/NVCC, for e.g. Eigen/src/Core/arch/CUDA/Half.h). In order to maintain this behavior, the EIGEN_USE_HIP macro is used to switch to using the HIP version of those header files (see Eigen/Core and unsupported/Eigen/CXX11/Tensor)
Use the "-DEIGEN_TEST_HIP" cmake option to enable the HIP specific unit tests.
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.
Check for nan inputs and propagate them immediately. Limit the number of internal iterations to 2000 (same number as used by scipy.special.gammainc). This prevents an infinite loop when the function is called with nan or very large arguments.
Original change by mfirgunov@google.com
Changes:
* Removed unnecessary types from the Functor by inferring from its types
* Removed inputs() function reference, replaced with .rows()
* Updated the forward constructor to use variadic templates
* Added optional parameters to the Fuctor for passing parameters,
control signals, etc
* Has been tested with fixed size and dynamic matricies
Ammendment by chtz: overload operator() for compatibility with not fully conforming compilers
