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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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116
unsupported/test/cxx11_tensor_cuda.cu
View File

@@ -1208,6 +1208,116 @@ void test_cuda_betainc()
cudaFree(d_out);
}
template <typename Scalar>
void test_cuda_i0e()
{
Tensor<Scalar, 1> in_x(21);
Tensor<Scalar, 1> out(21);
Tensor<Scalar, 1> expected_out(21);
out.setZero();
Array<Scalar, 1, Dynamic> in_x_array(21);
Array<Scalar, 1, Dynamic> expected_out_array(21);
in_x_array << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0,
-2.0, 0.0, 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0;
expected_out_array << 0.0897803118848, 0.0947062952128, 0.100544127361,
0.107615251671, 0.116426221213, 0.127833337163, 0.143431781857,
0.16665743264, 0.207001921224, 0.308508322554, 1.0, 0.308508322554,
0.207001921224, 0.16665743264, 0.143431781857, 0.127833337163,
0.116426221213, 0.107615251671, 0.100544127361, 0.0947062952128,
0.0897803118848;
for (int i = 0; i < 21; ++i) {
in_x(i) = in_x_array(i);
expected_out(i) = expected_out_array(i);
}
std::size_t bytes = in_x.size() * sizeof(Scalar);
Scalar* d_in;
Scalar* d_out;
cudaMalloc((void**)(&d_in), bytes);
cudaMalloc((void**)(&d_out), bytes);
cudaMemcpy(d_in, in_x.data(), bytes, cudaMemcpyHostToDevice);
Eigen::CudaStreamDevice stream;
Eigen::GpuDevice gpu_device(&stream);
Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in(d_in, 21);
Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_out(d_out, 21);
gpu_out.device(gpu_device) = gpu_in.i0e();
assert(cudaMemcpyAsync(out.data(), d_out, bytes, cudaMemcpyDeviceToHost,
gpu_device.stream()) == cudaSuccess);
assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);
for (int i = 0; i < 21; ++i) {
VERIFY_IS_APPROX(out(i), expected_out(i));
}
cudaFree(d_in);
cudaFree(d_out);
}
template <typename Scalar>
void test_cuda_i1e()
{
Tensor<Scalar, 1> in_x(21);
Tensor<Scalar, 1> out(21);
Tensor<Scalar, 1> expected_out(21);
out.setZero();
Array<Scalar, 1, Dynamic> in_x_array(21);
Array<Scalar, 1, Dynamic> expected_out_array(21);
in_x_array << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0,
-2.0, 0.0, 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0;
expected_out_array << -0.0875062221833, -0.092036796872, -0.0973496147565,
-0.103697667463, -0.11146429929, -0.121262681384, -0.134142493293,
-0.152051459309, -0.178750839502, -0.215269289249, 0.0, 0.215269289249,
0.178750839502, 0.152051459309, 0.134142493293, 0.121262681384,
0.11146429929, 0.103697667463, 0.0973496147565, 0.092036796872,
0.0875062221833;
for (int i = 0; i < 21; ++i) {
in_x(i) = in_x_array(i);
expected_out(i) = expected_out_array(i);
}
std::size_t bytes = in_x.size() * sizeof(Scalar);
Scalar* d_in;
Scalar* d_out;
cudaMalloc((void**)(&d_in), bytes);
cudaMalloc((void**)(&d_out), bytes);
cudaMemcpy(d_in, in_x.data(), bytes, cudaMemcpyHostToDevice);
Eigen::CudaStreamDevice stream;
Eigen::GpuDevice gpu_device(&stream);
Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in(d_in, 21);
Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_out(d_out, 21);
gpu_out.device(gpu_device) = gpu_in.i1e();
assert(cudaMemcpyAsync(out.data(), d_out, bytes, cudaMemcpyDeviceToHost,
gpu_device.stream()) == cudaSuccess);
assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);
for (int i = 0; i < 21; ++i) {
VERIFY_IS_APPROX(out(i), expected_out(i));
}
cudaFree(d_in);
cudaFree(d_out);
}
void test_cxx11_tensor_cuda()
{
@@ -1280,5 +1390,11 @@ void test_cxx11_tensor_cuda()
CALL_SUBTEST_6(test_cuda_betainc<float>());
CALL_SUBTEST_6(test_cuda_betainc<double>());
CALL_SUBTEST_6(test_cuda_i0e<float>());
CALL_SUBTEST_6(test_cuda_i0e<double>());
CALL_SUBTEST_6(test_cuda_i1e<float>());
CALL_SUBTEST_6(test_cuda_i1e<double>());
#endif
}

40
unsupported/test/special_functions.cpp
View File

@@ -335,6 +335,46 @@ template<typename ArrayType> void array_special_functions()
ArrayType test = betainc(a, b + one, x) + eps;
verify_component_wise(test, expected););
}
// Test Bessel function i0e. Reference results obtained with SciPy.
{
ArrayType x(21);
ArrayType expected(21);
ArrayType res(21);
x << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0, 0.0,
2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0;
expected << 0.0897803118848, 0.0947062952128, 0.100544127361,
0.107615251671, 0.116426221213, 0.127833337163, 0.143431781857,
0.16665743264, 0.207001921224, 0.308508322554, 1.0, 0.308508322554,
0.207001921224, 0.16665743264, 0.143431781857, 0.127833337163,
0.116426221213, 0.107615251671, 0.100544127361, 0.0947062952128,
0.0897803118848;
CALL_SUBTEST(res = i0e(x);
verify_component_wise(res, expected););
}
// Test Bessel function i1e. Reference results obtained with SciPy.
{
ArrayType x(21);
ArrayType expected(21);
ArrayType res(21);
x << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0, 0.0,
2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0;
expected << -0.0875062221833, -0.092036796872, -0.0973496147565,
-0.103697667463, -0.11146429929, -0.121262681384, -0.134142493293,
-0.152051459309, -0.178750839502, -0.215269289249, 0.0, 0.215269289249,
0.178750839502, 0.152051459309, 0.134142493293, 0.121262681384,
0.11146429929, 0.103697667463, 0.0973496147565, 0.092036796872,
0.0875062221833;
CALL_SUBTEST(res = i1e(x);
verify_component_wise(res, expected););
}
#endif
}