Tensor Basics
=============

The ATen tensor library backing PyTorch is a simple tensor library that exposes
the Tensor operations in Torch directly in C++17. ATen's API is auto-generated
from the same declarations PyTorch uses so the two APIs will track each other
over time.

Tensor types are resolved dynamically, such that the API is generic and does not
include templates. That is, there is one ``Tensor`` type. It can hold a CPU or
CUDA Tensor, and the tensor may have Doubles, Float, Ints, etc. This design
makes it easy to write generic code without templating everything.

See https://pytorch.org/cppdocs/api/namespace_at.html#functions for the provided
API. Excerpt:

.. code-block:: cpp

  Tensor atan2(const Tensor & other) const;
  Tensor & atan2_(const Tensor & other);
  Tensor pow(Scalar exponent) const;
  Tensor pow(const Tensor & exponent) const;
  Tensor & pow_(Scalar exponent);
  Tensor & pow_(const Tensor & exponent);
  Tensor lerp(const Tensor & end, Scalar weight) const;
  Tensor & lerp_(const Tensor & end, Scalar weight);
  Tensor histc() const;
  Tensor histc(int64_t bins) const;
  Tensor histc(int64_t bins, Scalar min) const;
  Tensor histc(int64_t bins, Scalar min, Scalar max) const;

In place operations are also provided, and always suffixed by `_` to indicate
they will modify the Tensor.

Efficient Access to Tensor Elements
-----------------------------------

When using Tensor-wide operations, the relative cost of dynamic dispatch is very
small. However, there are cases, especially in your own kernels, where efficient
element-wise access is needed, and the cost of dynamic dispatch inside the
element-wise loop is very high. ATen provides *accessors* that are created with
a single dynamic check that a Tensor is the type and number of dimensions.
Accessors then expose an API for accessing the Tensor elements efficiently.

Accessors are temporary views of a Tensor. They are only valid for the lifetime
of the tensor that they view and hence should only be used locally in a
function, like iterators.

Note that accessors are not compatible with CUDA tensors inside kernel functions.
Instead, you will have to use a *packed accessor* which behaves the same way but
copies tensor metadata instead of pointing to it.

It is thus recommended to use *accessors* for CPU tensors and *packed accessors*
for CUDA tensors.

CPU accessors
*************

.. code-block:: cpp

  torch::Tensor foo = torch::rand({12, 12});

  // assert foo is 2-dimensional and holds floats.
  auto foo_a = foo.accessor<float,2>();
  float trace = 0;

  for(int i = 0; i < foo_a.size(0); i++) {
    // use the accessor foo_a to get tensor data.
    trace += foo_a[i][i];
  }

CUDA accessors
**************


.. code-block:: cpp

  __global__ void packed_accessor_kernel(
      torch::PackedTensorAccessor64<float, 2> foo,
      float* trace) {
    int i = threadIdx.x;
    gpuAtomicAdd(trace, foo[i][i]);
  }

  torch::Tensor foo = torch::rand({12, 12});

  // assert foo is 2-dimensional and holds floats.
  auto foo_a = foo.packed_accessor64<float,2>();
  float trace = 0;

  packed_accessor_kernel<<<1, 12>>>(foo_a, &trace);

In addition to ``PackedTensorAccessor64`` and ``packed_accessor64`` there are
also the corresponding ``PackedTensorAccessor32`` and ``packed_accessor32``
which use 32-bit integers for indexing. This can be quite a bit faster on CUDA
but may lead to overflows in the indexing calculations.

Note that the template can hold other parameters such as the pointer restriction
and the integer type for indexing. See documentation for a thorough template
description of *accessors* and *packed accessors*.


Using Externally Created Data
-----------------------------

If you already have your tensor data allocated in memory (CPU or CUDA),
you can view that memory as a ``Tensor`` in ATen:

.. code-block:: cpp

  float data[] = { 1, 2, 3,
                   4, 5, 6 };
  torch::Tensor f = torch::from_blob(data, {2, 3});

These tensors cannot be resized because ATen does not own the memory, but
otherwise behave as normal tensors.

Scalars and zero-dimensional tensors
------------------------------------

In addition to the ``Tensor`` objects, ATen also includes ``Scalar``\s that
represent a single number. Like a Tensor, Scalars are dynamically typed and can
hold any one of ATen's number types. Scalars can be implicitly constructed from
C++ number types. Scalars are needed because some functions like ``addmm`` take
numbers along with Tensors and expect these numbers to be the same dynamic type
as the tensor. They are also used in the API to indicate places where a function
will *always* return a Scalar value, like ``sum``.

.. code-block:: cpp

  namespace torch {
  Tensor addmm(Scalar beta, const Tensor & self,
               Scalar alpha, const Tensor & mat1,
               const Tensor & mat2);
  Scalar sum(const Tensor & self);
  } // namespace torch

  // Usage.
  torch::Tensor a = ...
  torch::Tensor b = ...
  torch::Tensor c = ...
  torch::Tensor r = torch::addmm(1.0, a, .5, b, c);

In addition to ``Scalar``\s, ATen also allows ``Tensor`` objects to be
zero-dimensional. These Tensors hold a single value and they can be references
to a single element in a larger ``Tensor``. They can be used anywhere a
``Tensor`` is expected. They are normally created by operators like `select`
which reduce the dimensions of a ``Tensor``.

.. code-block:: cpp

  torch::Tensor two = torch::rand({10, 20});
  two[1][2] = 4;
  // ^^^^^^ <- zero-dimensional Tensor
