```Python
chebyshev_polynomial_v(input, n, *, out=None) -> Tensor
```
Chebyshev polynomial of the third kind $V_{n}(\text{input})$.
```Python
chebyshev_polynomial_w(input, n, *, out=None) -> Tensor
```
Chebyshev polynomial of the fourth kind $W_{n}(\text{input})$.
```Python
legendre_polynomial_p(input, n, *, out=None) -> Tensor
```
Legendre polynomial $P_{n}(\text{input})$.
```Python
shifted_chebyshev_polynomial_t(input, n, *, out=None) -> Tensor
```
Shifted Chebyshev polynomial of the first kind $T_{n}^{\ast}(\text{input})$.
```Python
shifted_chebyshev_polynomial_u(input, n, *, out=None) -> Tensor
```
Shifted Chebyshev polynomial of the second kind $U_{n}^{\ast}(\text{input})$.
```Python
shifted_chebyshev_polynomial_v(input, n, *, out=None) -> Tensor
```
Shifted Chebyshev polynomial of the third kind $V_{n}^{\ast}(\text{input})$.
```Python
shifted_chebyshev_polynomial_w(input, n, *, out=None) -> Tensor
```
Shifted Chebyshev polynomial of the fourth kind $W_{n}^{\ast}(\text{input})$.
Pull Request resolved: https://github.com/pytorch/pytorch/pull/78304
Approved by: https://github.com/mruberry
Adds:
```Python
bessel_j0(input, *, out=None) -> Tensor
```
Bessel function of the first kind of order $0$, $J_{0}(\text{input})$.
```Python
bessel_j1(input, *, out=None) -> Tensor
```
Bessel function of the first kind of order $1$, $J_{1}(\text{input})$.
```Python
bessel_j0(input, *, out=None) -> Tensor
```
Bessel function of the second kind of order $0$, $Y_{0}(\text{input})$.
```Python
bessel_j1(input, *, out=None) -> Tensor
```
Bessel function of the second kind of order $1$, $Y_{1}(\text{input})$.
```Python
modified_bessel_i0(input, *, out=None) -> Tensor
```
Modified Bessel function of the first kind of order $0$, $I_{0}(\text{input})$.
```Python
modified_bessel_i1(input, *, out=None) -> Tensor
```
Modified Bessel function of the first kind of order $1$, $I_{1}(\text{input})$.
```Python
modified_bessel_k0(input, *, out=None) -> Tensor
```
Modified Bessel function of the second kind of order $0$, $K_{0}(\text{input})$.
```Python
modified_bessel_k1(input, *, out=None) -> Tensor
```
Modified Bessel function of the second kind of order $1$, $K_{1}(\text{input})$.
Pull Request resolved: https://github.com/pytorch/pytorch/pull/78451
Approved by: https://github.com/mruberry
Adds:
```Python
chebyshev_polynomial_t(input, n, *, out=None) -> Tensor
```
Chebyshev polynomial of the first kind $T_{n}(\text{input})$.
If $n = 0$, $1$ is returned. If $n = 1$, $\text{input}$ is returned. If $n < 6$ or $|\text{input}| > 1$ the recursion:
$$T_{n + 1}(\text{input}) = 2 \times \text{input} \times T_{n}(\text{input}) - T_{n - 1}(\text{input})$$
is evaluated. Otherwise, the explicit trigonometric formula:
$$T_{n}(\text{input}) = \text{cos}(n \times \text{arccos}(x))$$
is evaluated.
## Derivatives
Recommended $k$-derivative formula with respect to $\text{input}$:
$$2^{-1 + k} \times n \times \Gamma(k) \times C_{-k + n}^{k}(\text{input})$$
where $C$ is the Gegenbauer polynomial.
Recommended $k$-derivative formula with respect to $\text{n}$:
$$\text{arccos}(\text{input})^{k} \times \text{cos}(\frac{k \times \pi}{2} + n \times \text{arccos}(\text{input})).$$
## Example
```Python
x = torch.linspace(-1, 1, 256)
matplotlib.pyplot.plot(x, torch.special.chebyshev_polynomial_t(x, 10))
```
Pull Request resolved: https://github.com/pytorch/pytorch/pull/78196
Approved by: https://github.com/mruberry
Euler beta function:
```Python
torch.special.beta(input, other, *, out=None) → Tensor
```
`reentrant_gamma` and `reentrant_ln_gamma` implementations (using Stirling’s approximation) are provided. I started working on this before I realized we were missing a gamma implementation (despite providing incomplete gamma implementations). Uses the coefficients computed by Steve Moshier to replicate SciPy’s implementation. Likewise, it mimics SciPy’s behavior (instead of the behavior in Cephes).
Pull Request resolved: https://github.com/pytorch/pytorch/pull/78031
Approved by: https://github.com/mruberry
Summary:
Reference https://github.com/pytorch/pytorch/issues/50345
`zeta` was already present in the codebase to support computation of `polygamma`.
However, `zeta` only had `double(double, double)` signature **for CPU** before the PR (which meant that computation `polygamma` were always upcasted to `double` for zeta part).
With this PR, float computations will take place in float and double in double.
Have also refactored the code and moved the duplicate code from `Math.cuh` to `Math.h`
**Note**: For scipy, q is optional, and if it is `None`, it defaults `1` which corresponds to Reimann-Zeta. However, for `torch.specia.zeta`, I made it mandatory cause for me it feels odd without `q` this is Reimann-Zeta and with `q` it is the general Hurwitz Zeta. I think sticking to just general made more sense as passing `1` for q sounds trivial.
Verify:
* [x] Docs https://14234587-65600975-gh.circle-artifacts.com/0/docs/special.html#torch.special.zeta
Pull Request resolved: https://github.com/pytorch/pytorch/pull/59623
Reviewed By: ngimel
Differential Revision: D29348269
Pulled By: mruberry
fbshipit-source-id: a3f9ebe1f7724dbe66de2b391afb9da1cfc3e4bb
Summary:
Reference: https://github.com/pytorch/pytorch/issues/50345
Changes:
* Add `i0e`
* Move some kernels from `UnaryOpsKernel.cu` to `UnarySpecialOpsKernel.cu` to decrease compilation time per file.
Time taken by i0e_vs_scipy tests: around 6.33.s
<details>
<summary>Test Run Log</summary>
```
(pytorch-cuda-dev) kshiteej@qgpu1:~/Pytorch/pytorch_module_special$ pytest test/test_unary_ufuncs.py -k _i0e_vs
======================================================================= test session starts ========================================================================
platform linux -- Python 3.8.6, pytest-6.1.2, py-1.9.0, pluggy-0.13.1
rootdir: /home/kshiteej/Pytorch/pytorch_module_special, configfile: pytest.ini
plugins: hypothesis-5.38.1
collected 8843 items / 8833 deselected / 10 selected
test/test_unary_ufuncs.py ...sss.... [100%]
========================================================================= warnings summary =========================================================================
../../.conda/envs/pytorch-cuda-dev/lib/python3.8/site-packages/torch/backends/cudnn/__init__.py:73
test/test_unary_ufuncs.py::TestUnaryUfuncsCUDA::test_special_i0e_vs_scipy_cuda_bfloat16
/home/kshiteej/.conda/envs/pytorch-cuda-dev/lib/python3.8/site-packages/torch/backends/cudnn/__init__.py:73: UserWarning: PyTorch was compiled without cuDNN/MIOpen support. To use cuDNN/MIOpen, rebuild PyTorch making sure the library is visible to the build system.
warnings.warn(
-- Docs: https://docs.pytest.org/en/stable/warnings.html
===================================================================== short test summary info ======================================================================
SKIPPED [3] test/test_unary_ufuncs.py:1182: not implemented: Could not run 'aten::_copy_from' with arguments from the 'Meta' backend. This could be because the operator doesn't exist for this backend, or was omitted during the selective/custom build process (if using custom build). If you are a Facebook employee using PyTorch on mobile, please visit https://fburl.com/ptmfixes for possible resolutions. 'aten::_copy_from' is only available for these backends: [BackendSelect, Named, InplaceOrView, AutogradOther, AutogradCPU, AutogradCUDA, AutogradXLA, UNKNOWN_TENSOR_TYPE_ID, AutogradMLC, AutogradNestedTensor, AutogradPrivateUse1, AutogradPrivateUse2, AutogradPrivateUse3, Tracer, Autocast, Batched, VmapMode].
BackendSelect: fallthrough registered at ../aten/src/ATen/core/BackendSelectFallbackKernel.cpp:3 [backend fallback]
Named: registered at ../aten/src/ATen/core/NamedRegistrations.cpp:7 [backend fallback]
InplaceOrView: fallthrough registered at ../aten/src/ATen/core/VariableFallbackKernel.cpp:56 [backend fallback]
AutogradOther: registered at ../torch/csrc/autograd/generated/VariableType_4.cpp:8761 [autograd kernel]
AutogradCPU: registered at ../torch/csrc/autograd/generated/VariableType_4.cpp:8761 [autograd kernel]
AutogradCUDA: registered at ../torch/csrc/autograd/generated/VariableType_4.cpp:8761 [autograd kernel]
AutogradXLA: registered at ../torch/csrc/autograd/generated/VariableType_4.cpp:8761 [autograd kernel]
UNKNOWN_TENSOR_TYPE_ID: registered at ../torch/csrc/autograd/generated/VariableType_4.cpp:8761 [autograd kernel]
AutogradMLC: registered at ../torch/csrc/autograd/generated/VariableType_4.cpp:8761 [autograd kernel]
AutogradNestedTensor: registered at ../torch/csrc/autograd/generated/VariableType_4.cpp:8761 [autograd kernel]
AutogradPrivateUse1: registered at ../torch/csrc/autograd/generated/VariableType_4.cpp:8761 [autograd kernel]
AutogradPrivateUse2: registered at ../torch/csrc/autograd/generated/VariableType_4.cpp:8761 [autograd kernel]
AutogradPrivateUse3: registered at ../torch/csrc/autograd/generated/VariableType_4.cpp:8761 [autograd kernel]
Tracer: registered at ../torch/csrc/autograd/generated/TraceType_4.cpp:9348 [kernel]
Autocast: fallthrough registered at ../aten/src/ATen/autocast_mode.cpp:250 [backend fallback]
Batched: registered at ../aten/src/ATen/BatchingRegistrations.cpp:1016 [backend fallback]
VmapMode: fallthrough registered at ../aten/src/ATen/VmapModeRegistrations.cpp:33 [backend fallback]
==================================================== 7 passed, 3 skipped, 8833 deselected, 2 warnings in 6.33s =====================================================
```
</details>
TODO:
* [x] Check rendered docs (https://11743402-65600975-gh.circle-artifacts.com/0/docs/special.html)
Pull Request resolved: https://github.com/pytorch/pytorch/pull/54409
Reviewed By: jbschlosser
Differential Revision: D27760472
Pulled By: mruberry
fbshipit-source-id: bdfbcaa798b00c51dc9513c34626246c8fc10548
Summary:
Related to https://github.com/pytorch/pytorch/issues/52256
Use autosummary instead of autofunction to create subpages for autograd functions. I left the autoclass parts intact but manually laid out their members.
Also the Latex formatting of the spcecial page emitted a warning (solved by adding `\begin{align}...\end{align}`) and fixed alignment of equations (by using `&=` instead of `=`).
zou3519
Pull Request resolved: https://github.com/pytorch/pytorch/pull/55672
Reviewed By: jbschlosser
Differential Revision: D27736855
Pulled By: zou3519
fbshipit-source-id: addb56f4f81c82d8537884e0ff243c1e34969a6e
Summary:
Reference: https://github.com/pytorch/pytorch/issues/50345
Chages:
* Alias for sigmoid and logit
* Adds out variant for C++ API
* Updates docs to link back to `special` documentation
Pull Request resolved: https://github.com/pytorch/pytorch/pull/54759
Reviewed By: mrshenli
Differential Revision: D27615208
Pulled By: mruberry
fbshipit-source-id: 8bba908d1bea246e4aa9dbadb6951339af353556
