defmodule Nx do
@moduledoc """
Numerical Elixir.
The `Nx` library is a collection of functions and data
types to work with Numerical Elixir. This module defines
the main entry point for building and working with said
data-structures. For example, to create an n-dimensional
tensor, do:
iex> t = Nx.tensor([[1, 2], [3, 4]])
iex> Nx.shape(t)
{2, 2}
`Nx` also provides the so-called numerical definitions under
the `Nx.Defn` module. They are a subset of Elixir tailored for
numerical computations. For example, it overrides Elixir's
default operators so they are tensor-aware:
defn softmax(t) do
Nx.exp(t) / Nx.sum(Nx.exp(t))
end
Code inside `defn` functions can also be given to custom compilers,
which can compile said functions just-in-time (JIT) to run on the
CPU or on the GPU.
## References
Here is a general outline of the main references in this library:
* For an introduction, see our [Intro to Nx](intro-to-nx.livemd) guide
* This module provides the main API for working with tensors
* `Nx.Defn` provides numerical definitions, CPU/GPU compilation, gradients, and more
* `Nx.LinAlg` provides functions related to linear algebra
* `Nx.Constants` declares many constants commonly used in numerical code
Continue reading this documentation for an overview of creating,
broadcasting, and accessing/slicing Nx tensors.
## Creating tensors
The main APIs for creating tensors are `tensor/2`, `from_binary/2`,
`iota/2`, `eye/2`, `random_uniform/2`, `random_normal/2`, and
`broadcast/3`.
The tensor types can be one of:
* unsigned integers (`u8`, `u16`, `u32`, `u64`)
* signed integers (`s8`, `s16`, `s32`, `s64`)
* floats (`f16`, `f32`, `f64`)
* brain floats (`bf16`)
* and complex numbers (`c64`, `c128`)
The types are tracked as tuples:
iex> Nx.tensor([1, 2, 3], type: {:f, 32})
#Nx.Tensor<
f32[3]
[1.0, 2.0, 3.0]
>
But a shortcut atom notation is also available:
iex> Nx.tensor([1, 2, 3], type: :f32)
#Nx.Tensor<
f32[3]
[1.0, 2.0, 3.0]
>
The tensor dimensions can also be named, via the `:names` option
available to all creation functions:
iex> Nx.iota({2, 3}, names: [:x, :y])
#Nx.Tensor<
s64[x: 2][y: 3]
[
[0, 1, 2],
[3, 4, 5]
]
>
Finally, for creating vectors and matrices, a sigil notation
is available:
iex> import Nx, only: :sigils
iex> ~V[1 2 3]f32
#Nx.Tensor<
f32[3]
[1.0, 2.0, 3.0]
>
iex> import Nx, only: :sigils
iex> ~M'''
...> 1 2 3
...> 4 5 6
...> '''s32
#Nx.Tensor<
s32[2][3]
[
[1, 2, 3],
[4, 5, 6]
]
>
All other APIs accept exclusively numbers or tensors, unless
explicitly noted otherwise.
## Broadcasting
Broadcasting allows operations on two tensors of different shapes
to match. For example, most often operations between tensors have
the same shape:
iex> a = Nx.tensor([1, 2, 3])
iex> b = Nx.tensor([10, 20, 30])
iex> Nx.add(a, b)
#Nx.Tensor<
s64[3]
[11, 22, 33]
>
Now let's imagine you want to multiply a large tensor of dimensions
1000x1000x1000 by 2. If you had to create a similarly large tensor
only to perform this operation, it would be inefficient. Therefore,
you can simply multiply this large tensor by the scalar 2, and Nx
will propagate its dimensions at the time the operation happens,
without allocating a large intermediate tensor:
iex> Nx.multiply(Nx.tensor([1, 2, 3]), 2)
#Nx.Tensor<
s64[3]
[2, 4, 6]
>
In practice, broadcasting is not restricted only to scalars; it
is a general algorithm that applies to all dimensions of a tensor.
When broadcasting, `Nx` compares the shapes of the two tensors,
starting with the trailing ones, such that:
* If the dimensions have equal size, then they are compatible
* If one of the dimensions have size of 1, it is "broadcast"
to match the dimension of the other
In case one tensor has more dimensions than the other, the missing
dimensions are considered to be of size one. Here are some examples
of how broadcast would work when multiplying two tensors with the
following shapes:
s64[3] * s64
#=> s64[3]
s64[255][255][3] * s64[3]
#=> s64[255][255][3]
s64[2][1] * s[1][2]
#=> s64[2][2]
s64[5][1][4][1] * s64[3][4][5]
#=> s64[5][3][4][5]
If any of the dimensions do not match or are not 1, an error is
raised.
## Access syntax (slicing)
Nx tensors implement Elixir's access syntax. This allows developers
to slice tensors up and easily access sub-dimensions and values.
Access accepts integers:
iex> t = Nx.tensor([[1, 2], [3, 4]])
iex> t[0]
#Nx.Tensor<
s64[2]
[1, 2]
>
iex> t[1]
#Nx.Tensor<
s64[2]
[3, 4]
>
iex> t[1][1]
#Nx.Tensor<
s64
4
>
If a negative index is given, it accesses the element from the back:
iex> t = Nx.tensor([[1, 2], [3, 4]])
iex> t[-1][-1]
#Nx.Tensor<
s64
4
>
Out of bound access will raise:
iex> Nx.tensor([1, 2])[2]
** (ArgumentError) index 2 is out of bounds for axis 0 in shape {2}
iex> Nx.tensor([1, 2])[-3]
** (ArgumentError) index -3 is out of bounds for axis 0 in shape {2}
The index can also be another tensor but in such cases it must be
a scalar between 0 and the dimension size. Out of bound dynamic indexes
are always clamped to the tensor dimensions:
iex> two = Nx.tensor(2)
iex> t = Nx.tensor([[1, 2], [3, 4]])
iex> t[two][two]
#Nx.Tensor<
s64
4
>
For example, a `minus_one` dynamic index will be clamped to zero:
iex> minus_one = Nx.tensor(-1)
iex> t = Nx.tensor([[1, 2], [3, 4]])
iex> t[minus_one][minus_one]
#Nx.Tensor<
s64
1
>
Access also accepts ranges. Ranges in Elixir are inclusive:
iex> t = Nx.tensor([[1, 2], [3, 4], [5, 6], [7, 8]])
iex> t[0..1]
#Nx.Tensor<
s64[2][2]
[
[1, 2],
[3, 4]
]
>
Ranges can receive negative positions and they will read from
the back. In such cases, the range step must be explicitly given
and the right-side of the range must be equal or greater than
the left-side:
iex> t = Nx.tensor([[1, 2], [3, 4], [5, 6], [7, 8]])
iex> t[1..-2//1]
#Nx.Tensor<
s64[2][2]
[
[3, 4],
[5, 6]
]
>
As you can see, accessing with a range does not eliminate the
accessed axis. This means that, if you try to cascade ranges,
you will always be filtering the highest dimension:
iex> t = Nx.tensor([[1, 2], [3, 4], [5, 6], [7, 8]])
iex> t[1..-1//1] # Drop the first "row"
#Nx.Tensor<
s64[3][2]
[
[3, 4],
[5, 6],
[7, 8]
]
>
iex> t[1..-1//1][1..-1//1] # Drop the first "row" twice
#Nx.Tensor<
s64[2][2]
[
[5, 6],
[7, 8]
]
>
Therefore, if you want to slice across multiple dimensions, you can wrap
the ranges in a list:
iex> t = Nx.tensor([[1, 2], [3, 4], [5, 6], [7, 8]])
iex> t[[1..-1//1, 1..-1//1]] # Drop the first "row" and the first "column"
#Nx.Tensor<
s64[3][1]
[
[4],
[6],
[8]
]
>
You can also use `..` as the full-slice range, which means you want to
keep a given dimension as is:
iex> t = Nx.tensor([[1, 2], [3, 4], [5, 6], [7, 8]])
iex> t[[.., 1..-1//1]] # Drop only the first "column"
#Nx.Tensor<
s64[4][1]
[
[2],
[4],
[6],
[8]
]
>
You can mix both ranges and integers in the list too:
iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]])
iex> t[[1..2, 2]]
#Nx.Tensor<
s64[2]
[6, 9]
>
If the list has less elements than axes, the remaining dimensions
are returned in full:
iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]])
iex> t[[1..2]]
#Nx.Tensor<
s64[2][3]
[
[4, 5, 6],
[7, 8, 9]
]
>
The access syntax also pairs nicely with named tensors. By using named
tensors, you can pass only the axis you want to slice, leaving the other
axes intact:
iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]], names: [:x, :y])
iex> t[x: 1..2]
#Nx.Tensor<
s64[x: 2][y: 3]
[
[4, 5, 6],
[7, 8, 9]
]
>
iex> t[x: 1..2, y: 0..1]
#Nx.Tensor<
s64[x: 2][y: 2]
[
[4, 5],
[7, 8]
]
>
iex> t[x: 1, y: 0..1]
#Nx.Tensor<
s64[y: 2]
[4, 5]
>
For a more complex slicing rules, including strides, you
can always fallback to `Nx.slice/4`.
## Backends
The `Nx` library has built-in support for multiple backends.
A tensor is always handled by a backend, the default backend
being `Nx.BinaryBackend`, which means the tensor is allocated
as a binary within the Erlang VM.
Most often backends are used to provide a completely different
implementation of tensor operations, often accelerated to the GPU.
In such cases, you want to guarantee all tensors are allocated in
the new backend. This can be done by configuring your runtime:
# config/runtime.exs
import Config
config :nx, default_backend: EXLA.Backend
In your notebooks and on `Mix.install/2`, you might:
Mix.install(
[
{:nx, ">= 0.0.0"}
],
config: [nx: [default_backend: EXLA.Backend]]
)
Or by calling `Nx.global_default_backend/1` (less preferrable):
Nx.global_default_backend(EXLA.Backend)
To pass options to the backend, replacing `EXLA.Backend` by
`{EXLA.Backend, client: :cuda}` or similar. See the documentation
for [EXLA](https://hexdocs.pm/exla) and [Torchx](https://hexdocs.pm/torchx)
for installation and GPU support.
To implement your own backend, check the `Nx.Tensor` behaviour.
"""
import Nx.Shared
import Nx.Defn.Kernel, only: [keyword!: 2]
alias Nx.Tensor, as: T
@typedoc """
Represents a numerical value.
Can be a plain number, a `Complex` number or an `Nx.Tensor`.
See also: `is_tensor/1`
"""
@type t :: number | Complex.t() | Nx.Tensor.t()
@type shape :: number() | Nx.Tensor.t() | Nx.Tensor.shape()
@type axis :: Nx.Tensor.axis()
@type axes :: Nx.Tensor.axes()
@type template :: Nx.Tensor.t(%Nx.TemplateBackend{})
@file_prefix <<?n, ?x>>
@file_version 1
@non_finite [:neg_infinity, :infinity, :nan]
@doc """
Checks whether the value is a valid numerical value.
Returns true if the value is a `number`, a non-finite atom (like `:infinity`),
a `Complex` number or an `Nx.Tensor`.
See also: `t:t/0`
"""
@doc type: :guards
defguard is_tensor(t)
when is_number(t) or is_struct(t, T) or is_struct(t, Complex) or t in @non_finite
## Creation API
@doc """
Builds a tensor.
The argument must be one of:
* a tensor
* a number (which means the tensor is scalar/zero-dimensional)
* a boolean (also scalar/zero-dimensional)
* an arbitrarily nested list of numbers and booleans
If a new tensor has to be allocated, it will be allocated in
`Nx.default_backend/0`, unless the `:backend` option is given,
which overrides the default one.
## Examples
A number returns a tensor of zero dimensions:
iex> Nx.tensor(0)
#Nx.Tensor<
s64
0
>
iex> Nx.tensor(1.0)
#Nx.Tensor<
f32
1.0
>
Giving a list returns a vector (a one-dimensional tensor):
iex> Nx.tensor([1, 2, 3])
#Nx.Tensor<
s64[3]
[1, 2, 3]
>
iex> Nx.tensor([1.2, 2.3, 3.4, 4.5])
#Nx.Tensor<
f32[4]
[1.2000000476837158, 2.299999952316284, 3.4000000953674316, 4.5]
>
The type can be explicitly given. Integers and floats
bigger than the given size overflow:
iex> Nx.tensor([300, 301, 302], type: :s8)
#Nx.Tensor<
s8[3]
[44, 45, 46]
>
Mixed types give higher priority to floats:
iex> Nx.tensor([1, 2, 3.0])
#Nx.Tensor<
f32[3]
[1.0, 2.0, 3.0]
>
Boolean values are also accepted, where `true` is
converted to `1` and `false` to `0`, with the type
being inferred as `{:u, 8}`
iex> Nx.tensor(true)
#Nx.Tensor<
u8
1
>
iex> Nx.tensor(false)
#Nx.Tensor<
u8
0
>
iex> Nx.tensor([true, false])
#Nx.Tensor<
u8[2]
[1, 0]
>
Multi-dimensional tensors are also possible:
iex> Nx.tensor([[1, 2, 3], [4, 5, 6]])
#Nx.Tensor<
s64[2][3]
[
[1, 2, 3],
[4, 5, 6]
]
>
iex> Nx.tensor([[1, 2], [3, 4], [5, 6]])
#Nx.Tensor<
s64[3][2]
[
[1, 2],
[3, 4],
[5, 6]
]
>
iex> Nx.tensor([[[1, 2], [3, 4], [5, 6]], [[-1, -2], [-3, -4], [-5, -6]]])
#Nx.Tensor<
s64[2][3][2]
[
[
[1, 2],
[3, 4],
[5, 6]
],
[
[-1, -2],
[-3, -4],
[-5, -6]
]
]
>
## Floats and complex numbers
Besides single-precision (32 bits), floats can also have
half-precision (16) or double-precision (64):
iex> Nx.tensor([1, 2, 3], type: :f16)
#Nx.Tensor<
f16[3]
[1.0, 2.0, 3.0]
>
iex> Nx.tensor([1, 2, 3], type: :f64)
#Nx.Tensor<
f64[3]
[1.0, 2.0, 3.0]
>
Brain-floating points are also supported:
iex> Nx.tensor([1, 2, 3], type: :bf16)
#Nx.Tensor<
bf16[3]
[1.0, 2.0, 3.0]
>
In all cases, the non-finite values negative infinity (-Inf),
infinity (Inf), and "not a number" (NaN) can be represented by
the atoms `:neg_infinity`, `:infinity`, and `:nan` respectively:
iex> Nx.tensor([:neg_infinity, :nan, :infinity])
#Nx.Tensor<
f32[3]
[-Inf, NaN, Inf]
>
Finally, complex numbers are also supported in tensors:
iex> Nx.tensor(Complex.new(1, -1))
#Nx.Tensor<
c64
1.0-1.0i
>
## Naming dimensions
You can provide names for tensor dimensions. Names are atoms:
iex> Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:x, :y])
#Nx.Tensor<
s64[x: 2][y: 3]
[
[1, 2, 3],
[4, 5, 6]
]
>
Names make your code more expressive:
iex> Nx.tensor([[[1, 2, 3], [4, 5, 6], [7, 8, 9]]], names: [:batch, :height, :width])
#Nx.Tensor<
s64[batch: 1][height: 3][width: 3]
[
[
[1, 2, 3],
[4, 5, 6],
[7, 8, 9]
]
]
>
You can also leave dimension names as `nil`:
iex> Nx.tensor([[[1, 2, 3], [4, 5, 6], [7, 8, 9]]], names: [:batch, nil, nil])
#Nx.Tensor<
s64[batch: 1][3][3]
[
[
[1, 2, 3],
[4, 5, 6],
[7, 8, 9]
]
]
>
However, you must provide a name for every dimension in the tensor:
iex> Nx.tensor([[[1, 2, 3], [4, 5, 6], [7, 8, 9]]], names: [:batch])
** (ArgumentError) invalid names for tensor of rank 3, when specifying names every dimension must have a name or be nil
## Tensors
Tensors can also be given as inputs:
iex> Nx.tensor(Nx.tensor([1, 2, 3]))
#Nx.Tensor<
s64[3]
[1, 2, 3]
>
If the `:backend` and `:type` options are given, the tensor will
compared against those values and raise in case of mismatch:
iex> Nx.tensor(Nx.tensor([1, 2, 3]), type: :f32)
** (ArgumentError) Nx.tensor/2 expects a tensor with type :f32 but it was given a tensor of type {:s, 64}
The `:backend` option will check only against the backend name
and not specific backend configuration such as device and client.
In case the backend differs, it will also raise.
The names in the given tensor are always discarded but Nx will raise
in case the tensor already has names that conflict with the assigned ones:
iex> Nx.tensor(Nx.tensor([1, 2, 3]), names: [:row])
#Nx.Tensor<
s64[row: 3]
[1, 2, 3]
>
iex> Nx.tensor(Nx.tensor([1, 2, 3], names: [:column]))
#Nx.Tensor<
s64[3]
[1, 2, 3]
>
iex> Nx.tensor(Nx.tensor([1, 2, 3], names: [:column]), names: [:row])
** (ArgumentError) cannot merge name :column on axis 0 with name :row on axis 0
## Options
* `:type` - sets the type of the tensor. If one is not given,
one is automatically inferred based on the input.
* `:names` - dimension names. If you wish to specify dimension
names you must specify a name for every dimension in the tensor.
Only `nil` and atoms are supported as dimension names.
* `:backend` - the backend to allocate the tensor on. It is either
an atom or a tuple in the shape `{backend, options}`. It defaults
to `Nx.default_backend/0` for new tensors
"""
@doc type: :creation
def tensor(arg, opts \\ [])
def tensor(%Nx.Tensor{} = tensor, opts) do
opts = keyword!(opts, [:type, :names, :backend])
tensor =
if backend = opts[:backend] do
case backend!(backend) do
{backend, _options} when tensor.data.__struct__ == backend ->
tensor
{backend, _} ->
raise ArgumentError,
"Nx.tensor/2 wants to allocate on backend #{inspect(backend)} " <>
"but it was given a tensor allocated on #{inspect(tensor.data.__struct__)}"
end
else
tensor
end
tensor =
if type = opts[:type] do
if tensor.type == Nx.Type.normalize!(type) do
tensor
else
raise ArgumentError,
"Nx.tensor/2 expects a tensor with type #{inspect(type)} " <>
"but it was given a tensor of type #{inspect(tensor.type)}"
end
else
tensor
end
# We merge to check for conflicts but ultimately discard the tensor.names for consistency
names =
if names = opts[:names] do
names = Nx.Shape.named_axes!(names, tensor.shape)
_ = Nx.Shape.merge_names!(tensor.names, names)
names
else
List.duplicate(nil, tuple_size(tensor.shape))
end
%{tensor | names: names}
end
def tensor(arg, opts) do
opts = keyword!(opts, [:type, :names, :backend])
type = Nx.Type.normalize!(opts[:type] || infer_type(arg))
tensor(arg, type, opts)
end
defp infer_type([head | tail]) when is_list(tail) do
Enum.reduce(tail, infer_type(head), &Nx.Type.merge(infer_type(&1), &2))
end
defp infer_type(number)
when is_number(number) or is_struct(number, Complex) or number in @non_finite or
is_boolean(number) do
Nx.Type.infer(number)
end
defp infer_type(%Nx.Tensor{} = value) do
raise ArgumentError,
"invalid value given to Nx.tensor/1. If you want to create a tensor from other tensors, " <>
"consider using Nx.concatenate/2 or Nx.stack/2 instead. Got: #{inspect(value)}"
end
defp infer_type(value) do
raise ArgumentError, "invalid value given to Nx.tensor/1, got: #{inspect(value)}"
end
defp tensor(true, type, opts), do: tensor(1, type, opts)
defp tensor(false, type, opts), do: tensor(0, type, opts)
defp tensor(arg, type, opts) when is_number(arg) do
names = Nx.Shape.named_axes!(opts[:names], {})
{backend, backend_options} = backend_from_options!(opts) || default_backend()
backend.constant(%T{shape: {}, type: type, names: names}, arg, backend_options)
end
defp tensor(%Complex{} = arg, {:c, size}, opts) do
names = Nx.Shape.named_axes!(opts[:names], {})
{backend, backend_options} = backend_from_options!(opts) || default_backend()
backend.constant(%T{shape: {}, type: {:c, size}, names: names}, arg, backend_options)
end
defp tensor(%Complex{}, type, _) do
raise ArgumentError,
"invalid type for complex number. Expected {:c, 64} or {:c, 128}, got: #{inspect(type)}"
end
defp tensor(arg, type, opts) when arg in @non_finite do
names = Nx.Shape.named_axes!(opts[:names], {})
{backend, backend_options} = backend_from_options!(opts) || default_backend()
data = number_to_binary(arg, type)
backend.from_binary(%T{shape: {}, type: type, names: names}, data, backend_options)
end
defp tensor(arg, type, opts) when is_list(arg) do
{shape, data} = flatten_list(arg, type)
if data == "" do
raise "cannot build empty tensor"
end
names = Nx.Shape.named_axes!(opts[:names], shape)
{backend, backend_options} = backend_from_options!(opts) || default_backend()
backend.from_binary(%T{shape: shape, type: type, names: names}, data, backend_options)
end
defp flatten_list(list, type) do
{dimensions, acc} = flatten_list(list, type, [], [])
{dimensions |> Enum.reverse() |> List.to_tuple(),
acc |> Enum.reverse() |> :erlang.list_to_binary()}
end
defp flatten_list([], _type, dimensions, acc) do
{[0 | dimensions], acc}
end
defp flatten_list([head | rest], type, parent_dimensions, acc) when is_list(head) do
{child_dimensions, acc} = flatten_list(head, type, [], acc)
{n, acc} =
Enum.reduce(rest, {1, acc}, fn list, {count, acc} ->
case flatten_list(list, type, [], acc) do
{^child_dimensions, acc} ->
{count + 1, acc}
{other_dimensions, _acc} ->
raise ArgumentError,
"cannot build tensor because lists have different shapes, got " <>
inspect(List.to_tuple(child_dimensions)) <>
" at position 0 and " <>
inspect(List.to_tuple(other_dimensions)) <> " at position #{count + 1}"
end
end)
{child_dimensions ++ [n | parent_dimensions], acc}
end
defp flatten_list(list, type, dimensions, acc) do
{[length(list) | dimensions],
Enum.reduce(list, acc, &[tensor_or_number_to_binary(&1, type) | &2])}
end
defp tensor_or_number_to_binary(true, type), do: tensor_or_number_to_binary(1, type)
defp tensor_or_number_to_binary(false, type), do: tensor_or_number_to_binary(0, type)
defp tensor_or_number_to_binary(number, type)
when is_number(number)
when is_struct(number, Complex)
when number in @non_finite do
number_to_binary(number, type)
end
defp tensor_or_number_to_binary(value, _type) do
raise ArgumentError, "invalid value given to Nx.tensor/1, got: #{inspect(value)}"
end
@doc """
Creates a tensor template.
You can't perform any operation on this tensor.
It exists exclusively to define APIs that say
a tensor with a certain type, shape, and names
is expected in the future.
## Examples
iex> Nx.template({2, 3}, :f32)
#Nx.Tensor<
f32[2][3]
Nx.TemplateBackend
>
iex> Nx.template({2, 3}, {:f, 32}, names: [:rows, :columns])
#Nx.Tensor<
f32[rows: 2][columns: 3]
Nx.TemplateBackend
>
Although note it is impossible to perform any operation on a tensor template:
iex> t = Nx.template({2, 3}, {:f, 32}, names: [:rows, :columns])
iex> Nx.abs(t)
** (RuntimeError) cannot perform operations on a Nx.TemplateBackend tensor
To convert existing tensors to templates, use `to_template/1`.
"""
@doc type: :creation
def template(shape, type, opts \\ []) when is_tuple(shape) do
opts = keyword!(opts, [:names])
type = Nx.Type.normalize!(type)
names = Nx.Shape.named_axes!(opts[:names], shape)
%T{shape: shape, type: type, names: names, data: %Nx.TemplateBackend{}}
end
for t <- [:u8, :u16, :u32, :u64, :s8, :s16, :s32, :s64, :bf16, :f16, :f32, :f64] do
@doc """
Short-hand function for creating tensor of type `#{t}`.
This is just an alias for `Nx.tensor(tensor, type: #{t})`.
"""
@doc type: :creation
def unquote(t)(tensor), do: Nx.tensor(tensor, type: unquote(t))
end
@doc """
Converts a tensor (or tuples and maps of tensors) to tensor templates.
Templates are useful when you need to pass types and shapes to
operations and the data is not yet available.
For convenience, this function accepts tensors and any container
(such as maps and tuples as defined by the `Nx.LazyContainer` protocol)
and recursively converts all tensors to templates.
## Examples
iex> Nx.iota({2, 3}) |> Nx.to_template()
#Nx.Tensor<
s64[2][3]
Nx.TemplateBackend
>
iex> {int, float} = Nx.to_template({1, 2.0})
iex> int
#Nx.Tensor<
s64
Nx.TemplateBackend
>
iex> float
#Nx.Tensor<
f32
Nx.TemplateBackend
>
Although note it is impossible to perform any operation on a tensor template:
iex> t = Nx.iota({2, 3}) |> Nx.to_template()
iex> Nx.abs(t)
** (RuntimeError) cannot perform operations on a Nx.TemplateBackend tensor
To build a template from scratch, use `template/3`.
"""
@doc type: :conversion
def to_template(tensor_or_container) do
tensor_or_container
|> Nx.LazyContainer.traverse(:ok, fn template, _fun, :ok -> {template, :ok} end)
|> then(fn {template, :ok} -> template end)
end
@doc false
@deprecated "Use Nx.Random.uniform/2 instead"
def random_uniform(tensor_or_shape, opts \\ []) do
random_uniform(tensor_or_shape, 0.0, 1.0, opts)
end
@doc false
@deprecated "Use Nx.Random.uniform/2 instead"
def random_uniform(tensor_or_shape, min, max, opts \\ []) do
opts = keyword!(opts, [:type, :names, :backend])
%T{type: min_type, shape: min_shape} = min = to_tensor(min)
%T{type: max_type, shape: max_shape} = max = to_tensor(max)
Nx.Shared.raise_vectorization_not_supported(min, __ENV__.function)
Nx.Shared.raise_vectorization_not_supported(max, __ENV__.function)
shape = shape(tensor_or_shape)
names = Nx.Shape.named_axes!(opts[:names] || names!(tensor_or_shape), shape)
range_type = Nx.Type.merge(min_type, max_type)
type = Nx.Type.normalize!(opts[:type] || range_type)
unless min_shape == {} and max_shape == {} do
raise ArgumentError,
"random_uniform/3 expects min and max to be scalars, got:" <>
" min shape: #{inspect(min_shape)} and max shape: #{inspect(max_shape)}"
end
unless Nx.Type.float?(type) or (Nx.Type.integer?(type) and Nx.Type.integer?(range_type)) do
raise ArgumentError,
"random_uniform/3 expects compatible types, got: #{inspect(type)}" <>
" with range #{inspect(range_type)}"
end
{backend, backend_options} = backend_from_options!(opts) || default_backend()
backend.random_uniform(%T{shape: shape, type: type, names: names}, min, max, backend_options)
end
@doc false
@deprecated "Use Nx.Random instead"
def random_normal(tensor_or_shape, opts \\ []) do
random_normal(tensor_or_shape, 0.0, 1.0, opts)
end
@doc false
@deprecated "Use Nx.Random instead"
def random_normal(tensor_or_shape, mu, sigma, opts \\ []) do
opts = keyword!(opts, [:type, :names, :backend])
%T{type: mu_type, shape: mu_shape} = mu = to_tensor(mu)
%T{type: sigma_type, shape: sigma_shape} = sigma = to_tensor(sigma)
Nx.Shared.raise_vectorization_not_supported(mu, __ENV__.function)
Nx.Shared.raise_vectorization_not_supported(sigma, __ENV__.function)
shape = shape(tensor_or_shape)
names = Nx.Shape.named_axes!(opts[:names] || names!(tensor_or_shape), shape)
type = Nx.Type.normalize!(opts[:type] || {:f, 32})
unless mu_shape == {} and sigma_shape == {} do
raise ArgumentError,
"random_normal/3 expects mu and sigma to be scalars" <>
" got: mu shape: #{inspect(mu_shape)} and sigma shape: #{inspect(sigma_shape)}"
end
unless Nx.Type.float?(mu_type) and Nx.Type.float?(sigma_type) do
raise ArgumentError,
"random_normal/3 expects mu and sigma to be float types," <>
" got: mu type: #{inspect(mu_type)} and sigma type: #{inspect(sigma_type)}"
end
unless Nx.Type.float?(type) do
raise ArgumentError, "random_normal/3 expects float type, got: #{inspect(type)}"
end
{backend, backend_options} = backend_from_options!(opts) || default_backend()
backend.random_normal(%T{shape: shape, type: type, names: names}, mu, sigma, backend_options)
end
@doc false
@deprecated "Use Nx.Random.shuffle/2 instead"
def shuffle(tensor, opts \\ []) do
opts = keyword!(opts, [:axis])
%T{shape: shape, names: names} = tensor = to_tensor(tensor)
if axis = opts[:axis] do
axis = Nx.Shape.normalize_axis(shape, axis, names)
size = Nx.axis_size(tensor, axis)
permutation = random_uniform({size}) |> Nx.argsort()
Nx.take(tensor, permutation, axis: axis)
else
flattened = Nx.flatten(tensor)
permutation = flattened |> random_uniform() |> Nx.argsort()
flattened |> Nx.take(permutation) |> Nx.reshape(tensor)
end
end
@doc """
Creates a tensor with the given shape which increments
along the provided axis. You may optionally provide dimension
names.
If no axis is provided, index counts up at each element.
If a tensor or a number are given, the shape and names are taken from the tensor.
## Options
* `:type` - the type of the tensor
* `:axis` - an axis to repeat the iota over
* `:names` - the names of the tensor dimensions
* `:backend` - the backend to allocate the tensor on. It is either
an atom or a tuple in the shape `{backend, options}`. This option
is ignored inside `defn`
* `:vectorized_axes` - a keyword list of `axis_name: axis_size`.
If given, the resulting tensor will be vectorized accordingly.
Vectorization is not supported via tensor inputs.
## Examples
iex> Nx.iota({})
#Nx.Tensor<
s64
0
>
iex> Nx.iota({5})
#Nx.Tensor<
s64[5]
[0, 1, 2, 3, 4]
>
iex> Nx.iota({3, 2, 3}, names: [:batch, :height, :width])
#Nx.Tensor<
s64[batch: 3][height: 2][width: 3]
[
[
[0, 1, 2],
[3, 4, 5]
],
[
[6, 7, 8],
[9, 10, 11]
],
[
[12, 13, 14],
[15, 16, 17]
]
]
>
iex> Nx.iota({3, 3}, axis: 1, names: [:batch, nil])
#Nx.Tensor<
s64[batch: 3][3]
[
[0, 1, 2],
[0, 1, 2],
[0, 1, 2]
]
>
iex> Nx.iota({3, 3}, axis: -1)
#Nx.Tensor<
s64[3][3]
[
[0, 1, 2],
[0, 1, 2],
[0, 1, 2]
]
>
iex> Nx.iota({3, 4, 3}, axis: 0, type: :f64)
#Nx.Tensor<
f64[3][4][3]
[
[
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0]
],
[
[1.0, 1.0, 1.0],
[1.0, 1.0, 1.0],
[1.0, 1.0, 1.0],
[1.0, 1.0, 1.0]
],
[
[2.0, 2.0, 2.0],
[2.0, 2.0, 2.0],
[2.0, 2.0, 2.0],
[2.0, 2.0, 2.0]
]
]
>
iex> Nx.iota({1, 3, 2}, axis: 2)
#Nx.Tensor<
s64[1][3][2]
[
[
[0, 1],
[0, 1],
[0, 1]
]
]
>
iex> Nx.iota({2, 3}, axis: 0, vectorized_axes: [x: 1, y: 2])
#Nx.Tensor<
vectorized[x: 1][y: 2]
s64[2][3]
[
[
[
[0, 0, 0],
[1, 1, 1]
],
[
[0, 0, 0],
[1, 1, 1]
]
]
]
>
"""
@doc type: :creation
def iota(tensor_or_shape, opts \\ []) do
opts = keyword!(opts, [:axis, :names, :backend, :vectorized_axes, type: {:s, 64}])
vectorized_axes = opts[:vectorized_axes]
if not is_tuple(tensor_or_shape) do
IO.warn("passing a tensor as shape to iota/2 is deprecated. Please call Nx.shape/2 before")
vectorized_axes =
case tensor_or_shape do
%T{vectorized_axes: tensor_axes} -> vectorized_axes || tensor_axes
_ -> vectorized_axes
end
if vectorized_axes do
raise ArgumentError, "vectorization is only supported for shape inputs"
end
end
shape = shape(tensor_or_shape)
names = Nx.Shape.named_axes!(opts[:names] || names!(tensor_or_shape), shape)
type = Nx.Type.normalize!(opts[:type])
{backend, backend_options} = backend_from_options!(opts) || default_backend()
output =
if axis = opts[:axis] do
axis = Nx.Shape.normalize_axis(shape, axis, names)
backend.iota(%T{type: type, shape: shape, names: names}, axis, backend_options)
else
backend.iota(%T{type: type, shape: shape, names: names}, nil, backend_options)
end
if not is_nil(vectorized_axes) and vectorized_axes != [] do
base_shape =
List.to_tuple(List.duplicate(1, length(vectorized_axes)) ++ Tuple.to_list(shape))
output_shape = List.to_tuple(Keyword.values(vectorized_axes) ++ Tuple.to_list(shape))
output
|> reshape(base_shape)
|> broadcast(output_shape)
|> vectorize(vectorized_axes)
else
output
end
end
@doc """
Creates the identity matrix of size `n`.
## Options
* `:type` - the type of the tensor
* `:names` - the names of the tensor dimensions
* `:backend` - the backend to allocate the tensor on. It is either
an atom or a tuple in the shape `{backend, options}`. This option
is ignored inside `defn`
* `:vectorized_axes` - a keyword list of `axis_name: axis_size`.
If given, the resulting tensor will be vectorized accordingly.
Vectorization is not supported via tensor inputs.
## Examples
iex> Nx.eye(2)
#Nx.Tensor<
s64[2][2]
[
[1, 0],
[0, 1]
]
>
iex> Nx.eye(3, type: :f32, names: [:height, :width])
#Nx.Tensor<
f32[height: 3][width: 3]
[
[1.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, 1.0]
]
>
The first argument can also be a shape of a matrix:
iex> Nx.eye({1, 2})
#Nx.Tensor<
s64[1][2]
[
[1, 0]
]
>
The shape can also represent a tensor batch. In this case,
the last two axes will represent the same identity matrix.
iex> Nx.eye({2, 4, 3})
#Nx.Tensor<
s64[2][4][3]
[
[
[1, 0, 0],
[0, 1, 0],
[0, 0, 1],
[0, 0, 0]
],
[
[1, 0, 0],
[0, 1, 0],
[0, 0, 1],
[0, 0, 0]
]
]
>
## Vectorized tensors
If given, vectorized axes, are added as leading dimensions to the tensor,
effectively broadcasting the base shape along them.
iex> Nx.eye({3}, vectorized_axes: [x: 1, y: 2])
#Nx.Tensor<
vectorized[x: 1][y: 2]
s64[3]
[
[
[1, 0, 0],
[1, 0, 0]
]
]
>
iex> Nx.eye({2, 3}, vectorized_axes: [x: 2])
#Nx.Tensor<
vectorized[x: 2]
s64[2][3]
[
[
[1, 0, 0],
[0, 1, 0]
],
[
[1, 0, 0],
[0, 1, 0]
]
]
>
"""
@doc type: :creation
def eye(n_or_tensor_or_shape, opts \\ [])
def eye(n, opts) when is_integer(n) and n > 0 do
eye({n, n}, opts)
end
def eye(shape, opts) when is_tuple(shape) and tuple_size(shape) >= 1 do
opts = keyword!(opts, [:names, :backend, :vectorized_axes, type: {:s, 64}])
names = Nx.Shape.named_axes!(opts[:names], shape)
type = Nx.Type.normalize!(opts[:type] || {:s, 64})
vectorized_axes = opts[:vectorized_axes] || []
{backend, backend_options} = backend_from_options!(opts) || default_backend()
if vectorized_axes != [] do
{vec_names, vec_sizes} = Enum.unzip(vectorized_axes)
out_shape = List.to_tuple(vec_sizes ++ Tuple.to_list(shape))
names = vec_names ++ names
out =
case shape do
{n} ->
intermediate_shape = Tuple.duplicate(1, tuple_size(out_shape) - 1) |> Tuple.append(n)
backend.eye(
%T{type: type, shape: intermediate_shape, names: names},
backend_options
)
|> broadcast(out_shape, names: names)
_ ->
backend.eye(
%T{type: type, shape: out_shape, names: names},
backend_options
)
end
vectorize(out, vectorized_axes)
else
if tuple_size(shape) < 2 do
raise ArgumentError,
"eye/2 expects a shape with at least 2 dimensions or an integer, got: #{inspect(shape)}"
end
backend.eye(%T{type: type, shape: shape, names: names}, backend_options)
end
end
def eye(shape, _opts) when is_tuple(shape) do
raise ArgumentError,
"eye/2 expects a shape with at least 2 dimensions or an integer, got: #{inspect(shape)}"
end
def eye(tensor, opts) do
IO.warn("passing a tensor as shape to eye/2 is deprecated. Please call Nx.shape/2 before")
Nx.Shared.raise_vectorization_not_supported(tensor, __ENV__.function)
eye(Nx.shape(tensor), opts)
end
@doc """
Lower triangle of a matrix.
## Options
* `k` - The diagonal above which to zero elements. Default: 0.
## Examples
iex> Nx.tril(Nx.tensor([[1, 2, 3], [4, 5, 6], [7, 8, 9]]))
#Nx.Tensor<
s64[3][3]
[
[1, 0, 0],
[4, 5, 0],
[7, 8, 9]
]
>
iex> Nx.tril(Nx.tensor([[1, 2, 3], [4, 5, 6], [7, 8, 9]]), k: 1)
#Nx.Tensor<
s64[3][3]
[
[1, 2, 0],
[4, 5, 6],
[7, 8, 9]
]
>
iex> Nx.tril(Nx.iota({2, 3, 4}))
#Nx.Tensor<
s64[2][3][4]
[
[
[0, 0, 0, 0],
[4, 5, 0, 0],
[8, 9, 10, 0]
],
[
[12, 0, 0, 0],
[16, 17, 0, 0],
[20, 21, 22, 0]
]
]
>
iex> Nx.tril(Nx.iota({6}))
** (ArgumentError) tril/2 expects a tensor with at least 2 dimensions, got: #Nx.Tensor<
s64[6]
[0, 1, 2, 3, 4, 5]
>
"""
@doc type: :creation
def tril(tensor, opts \\ []) do
opts = keyword!(opts, k: 0)
if rank(tensor) < 2 do
raise ArgumentError,
"tril/2 expects a tensor with at least 2 dimensions, got: #{inspect(tensor)}"
end
mask = tri(axis_size(tensor, -2), axis_size(tensor, -1), k: opts[:k])
mask = extend_mask(tensor, mask)
select(mask, tensor, 0)
end
@doc """
Upper triangle of an array.
## Options
* `k` - The diagonal below which to zero elements. Default: 0.
## Examples
iex> Nx.triu(Nx.tensor([[1, 2, 3], [4, 5, 6], [7, 8, 9]]))
#Nx.Tensor<
s64[3][3]
[
[1, 2, 3],
[0, 5, 6],
[0, 0, 9]
]
>
iex> Nx.triu(Nx.tensor([[1, 2, 3], [4, 5, 6], [7, 8, 9]]), k: 1)
#Nx.Tensor<
s64[3][3]
[
[0, 2, 3],
[0, 0, 6],
[0, 0, 0]
]
>
iex> Nx.triu(Nx.iota({2, 3, 4}))
#Nx.Tensor<
s64[2][3][4]
[
[
[0, 1, 2, 3],
[0, 5, 6, 7],
[0, 0, 10, 11]
],
[
[12, 13, 14, 15],
[0, 17, 18, 19],
[0, 0, 22, 23]
]
]
>
iex> Nx.triu(Nx.iota({6}))
** (ArgumentError) triu/2 expects a tensor with at least 2 dimensions, got: #Nx.Tensor<
s64[6]
[0, 1, 2, 3, 4, 5]
>
"""
@doc type: :creation
def triu(tensor, opts \\ []) do
opts = keyword!(opts, k: 0)
if rank(tensor) < 2 do
raise ArgumentError,
"triu/2 expects a tensor with at least 2 dimensions, got: #{inspect(tensor)}"
end
mask = tri(axis_size(tensor, -2), axis_size(tensor, -1), k: opts[:k] - 1)
mask = extend_mask(tensor, mask)
select(mask, 0, tensor)
end
@doc """
An array with ones at and below the given diagonal and zeros elsewhere.
## Options
* `k` - The diagonal above which to zero elements. Default: 0.
## Examples
iex> tensor = Nx.tensor([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
iex> {num_rows, num_cols} = Nx.shape(tensor)
iex> Nx.tri(num_rows, num_cols)
#Nx.Tensor<
u8[3][3]
[
[1, 0, 0],
[1, 1, 0],
[1, 1, 1]
]
>
iex> tensor = Nx.tensor([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
iex> {num_rows, num_cols} = Nx.shape(tensor)
iex> Nx.tri(num_rows, num_cols, k: 1)
#Nx.Tensor<
u8[3][3]
[
[1, 1, 0],
[1, 1, 1],
[1, 1, 1]
]
>
"""
@doc type: :creation
def tri(n, m, opts \\ []) do
opts = keyword!(opts, k: 0)
greater_equal(iota({n, 1}), subtract(iota({1, m}), opts[:k]))
end
defp extend_mask(tensor, mask) do
to_duplicate = rank(tensor) - 2
shape = List.to_tuple(List.duplicate(1, to_duplicate) ++ Tuple.to_list(shape(mask)))
reshape(mask, shape) |> broadcast(tensor)
end
@doc """
Extracts the diagonal of batched matrices.
Converse of `make_diagonal/2`.
## Examples
Given a matrix without offset:
iex> Nx.take_diagonal(Nx.tensor([
...> [0, 1, 2],
...> [3, 4, 5],
...> [6, 7, 8]
...> ]))
#Nx.Tensor<
s64[3]
[0, 4, 8]
>
And if given a matrix along with an offset:
iex> Nx.take_diagonal(Nx.iota({3, 3}), offset: 1)
#Nx.Tensor<
s64[2]
[1, 5]
>
iex> Nx.take_diagonal(Nx.iota({3, 3}), offset: -1)
#Nx.Tensor<
s64[2]
[3, 7]
>
Given batched matrix:
iex> Nx.take_diagonal(Nx.iota({3, 2, 2}))
#Nx.Tensor<
s64[3][2]
[
[0, 3],
[4, 7],
[8, 11]
]
>
iex> Nx.take_diagonal(Nx.iota({3, 2, 2}), offset: -1)
#Nx.Tensor<
s64[3][1]
[
[2],
[6],
[10]
]
>
## Options
* `:offset` - offset used for extracting the diagonal.
Use offset > 0 for diagonals above the main diagonal,
and offset < 0 for diagonals below the main diagonal.
Defaults to 0.
## Error cases
iex> Nx.take_diagonal(Nx.tensor([0, 1, 2]))
** (ArgumentError) take_diagonal/2 expects tensor of rank 2 or higher, got tensor of rank: 1
iex> Nx.take_diagonal(Nx.iota({3, 3}), offset: 3)
** (ArgumentError) offset must be less than length of axis 1 when positive, got: 3
iex> Nx.take_diagonal(Nx.iota({3, 3}), offset: -4)
** (ArgumentError) absolute value of offset must be less than length of axis 0 when negative, got: -4
"""
@doc type: :creation
def take_diagonal(tensor, opts \\ []) do
tensor = to_tensor(tensor)
opts = keyword!(opts, offset: 0)
{batch_shape, matrix_shape} = Nx.Shape.take_diagonal(tensor.shape)
offset = opts[:offset]
Nx.Shape.validate_diag_offset!(matrix_shape, offset)
t = Nx.gather(tensor, diag_indices(tensor.shape, offset))
if batch_shape == {} do
t
else
diag_length = div(Nx.size(t), Tuple.product(batch_shape))
Nx.reshape(t, Tuple.append(batch_shape, diag_length))
end
end
@doc """
Creates a diagonal tensor from a 1D tensor.
Converse of `take_diagonal/2`.
The returned tensor will be a square matrix of dimensions equal
to the size of the tensor. If an offset is given, the absolute value
of the offset is added to the matrix dimensions sizes.
## Options
* `:offset` - offset used for making the diagonal.
Use offset > 0 for diagonals above the main diagonal,
and offset < 0 for diagonals below the main diagonal.
Defaults to 0.
## Examples
Given a 1D tensor:
iex> Nx.make_diagonal(Nx.tensor([1, 2, 3, 4]))
#Nx.Tensor<
s64[4][4]
[
[1, 0, 0, 0],
[0, 2, 0, 0],
[0, 0, 3, 0],
[0, 0, 0, 4]
]
>
Given a 1D tensor with an offset:
iex> Nx.make_diagonal(Nx.tensor([1, 2, 3]), offset: 1)
#Nx.Tensor<
s64[4][4]
[
[0, 1, 0, 0],
[0, 0, 2, 0],
[0, 0, 0, 3],
[0, 0, 0, 0]
]
>
iex> Nx.make_diagonal(Nx.tensor([1, 2, 3]), offset: -1)
#Nx.Tensor<
s64[4][4]
[
[0, 0, 0, 0],
[1, 0, 0, 0],
[0, 2, 0, 0],
[0, 0, 3, 0]
]
>
You can also have offsets with an abs greater than the tensor length:
iex> Nx.make_diagonal(Nx.tensor([1, 2, 3]), offset: -4)
#Nx.Tensor<
s64[7][7]
[
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[1, 0, 0, 0, 0, 0, 0],
[0, 2, 0, 0, 0, 0, 0],
[0, 0, 3, 0, 0, 0, 0]
]
>
iex> Nx.make_diagonal(Nx.tensor([1, 2, 3]), offset: 4)
#Nx.Tensor<
s64[7][7]
[
[0, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 2, 0],
[0, 0, 0, 0, 0, 0, 3],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0]
]
>
### Vectorized tensors
iex> t = Nx.vectorize(Nx.tensor([[1, 2], [3, 4]]), :x)
iex> Nx.make_diagonal(t, offset: 1)
#Nx.Tensor<
vectorized[x: 2]
s64[3][3]
[
[
[0, 1, 0],
[0, 0, 2],
[0, 0, 0]
],
[
[0, 3, 0],
[0, 0, 4],
[0, 0, 0]
]
]
>
iex> Nx.make_diagonal(t, offset: -1)
#Nx.Tensor<
vectorized[x: 2]
s64[3][3]
[
[
[0, 0, 0],
[1, 0, 0],
[0, 2, 0]
],
[
[0, 0, 0],
[3, 0, 0],
[0, 4, 0]
]
]
>
## Error cases
iex> Nx.make_diagonal(Nx.tensor([[0, 0], [0, 1]]))
** (ArgumentError) make_diagonal/2 expects tensor of rank 1, got tensor of rank: 2
"""
@doc type: :creation
def make_diagonal(tensor, opts \\ []) do
base_shape = shape(tensor)
apply_vectorized(tensor, fn tensor ->
%{shape: shape} = tensor = to_tensor(tensor)
opts = keyword!(opts, offset: 0)
{len} = Nx.Shape.make_diagonal(base_shape)
offset = opts[:offset]
diag_len = len + Kernel.abs(offset)
batch_shape = shape |> Tuple.delete_at(tuple_size(shape) - 1) |> Tuple.to_list()
diag_shape = List.to_tuple(batch_shape ++ [diag_len, diag_len])
0
|> broadcast(diag_shape)
|> indexed_put(diag_indices(diag_shape, offset), Nx.flatten(tensor))
end)
end
@doc """
Puts the individual values from a 1D diagonal into the diagonal indices
of the given 2D tensor.
See also: `take_diagonal/2`, `make_diagonal/2`.
## Examples
Given a 2D tensor and a 1D diagonal:
iex> t = Nx.broadcast(0, {4, 4})
#Nx.Tensor<
s64[4][4]
[
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]
]
>
iex> Nx.put_diagonal(t, Nx.tensor([1, 2, 3, 4]))
#Nx.Tensor<
s64[4][4]
[
[1, 0, 0, 0],
[0, 2, 0, 0],
[0, 0, 3, 0],
[0, 0, 0, 4]
]
>
iex> t = Nx.broadcast(0, {4, 3})
#Nx.Tensor<
s64[4][3]
[
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0]
]
>
iex> Nx.put_diagonal(t, Nx.tensor([1, 2, 3]))
#Nx.Tensor<
s64[4][3]
[
[1, 0, 0],
[0, 2, 0],
[0, 0, 3],
[0, 0, 0]
]
>
Given a 2D tensor and a 1D diagonal with a positive offset:
iex> Nx.put_diagonal(Nx.broadcast(0, {4, 4}), Nx.tensor([1, 2, 3]), offset: 1)
#Nx.Tensor<
s64[4][4]
[
[0, 1, 0, 0],
[0, 0, 2, 0],
[0, 0, 0, 3],
[0, 0, 0, 0]
]
>
iex> Nx.put_diagonal(Nx.broadcast(0, {4, 3}), Nx.tensor([1, 2]), offset: 1)
#Nx.Tensor<
s64[4][3]
[
[0, 1, 0],
[0, 0, 2],
[0, 0, 0],
[0, 0, 0]
]
>
Given a 2D tensor and a 1D diagonal with a negative offset:
iex> Nx.put_diagonal(Nx.broadcast(0, {4, 4}), Nx.tensor([1, 2, 3]), offset: -1)
#Nx.Tensor<
s64[4][4]
[
[0, 0, 0, 0],
[1, 0, 0, 0],
[0, 2, 0, 0],
[0, 0, 3, 0]
]
>
iex> Nx.put_diagonal(Nx.broadcast(0, {4, 3}), Nx.tensor([1, 2, 3]), offset: -1)
#Nx.Tensor<
s64[4][3]
[
[0, 0, 0],
[1, 0, 0],
[0, 2, 0],
[0, 0, 3]
]
>
## Options
* `:offset` - offset used for putting the diagonal.
Use offset > 0 for diagonals above the main diagonal,
and offset < 0 for diagonals below the main diagonal.
Defaults to 0.
## Error cases
Given an invalid tensor:
iex> Nx.put_diagonal(Nx.iota({3, 3, 3}), Nx.iota({3}))
** (ArgumentError) put_diagonal/3 expects tensor of rank 2, got tensor of rank: 3
Given invalid diagonals:
iex> Nx.put_diagonal(Nx.iota({3, 3}), Nx.iota({3, 3}))
** (ArgumentError) put_diagonal/3 expects diagonal of rank 1, got tensor of rank: 2
iex> Nx.put_diagonal(Nx.iota({3, 3}), Nx.iota({2}))
** (ArgumentError) expected diagonal tensor of length: 3, got diagonal tensor of length: 2
iex> Nx.put_diagonal(Nx.iota({3, 3}), Nx.iota({3}), offset: 1)
** (ArgumentError) expected diagonal tensor of length: 2, got diagonal tensor of length: 3
Given invalid offsets:
iex> Nx.put_diagonal(Nx.iota({3, 3}), Nx.iota({3}), offset: 4)
** (ArgumentError) offset must be less than length of axis 1 when positive, got: 4
iex> Nx.put_diagonal(Nx.iota({3, 3}), Nx.iota({3}), offset: -3)
** (ArgumentError) absolute value of offset must be less than length of axis 0 when negative, got: -3
"""
@doc type: :creation
def put_diagonal(tensor, diagonal, opts \\ []) do
%{shape: shape} = tensor = to_tensor(tensor)
offset = opts |> keyword!(offset: 0) |> Keyword.fetch!(:offset)
Nx.Shape.put_diagonal(shape, diagonal.shape, offset)
Nx.indexed_put(tensor, diag_indices(shape, offset), diagonal)
end
# Returns the indices of the diagonal of a tensor of the given shape
defp diag_indices(shape, offset) do
{batch_shape, [len, breadth]} = Enum.split(Tuple.to_list(shape), -2)
indices =
case offset do
i when i >= 0 ->
Enum.zip_with(0..(len - 1), i..(breadth - 1), fn x, y -> [x, y] end)
i when i < 0 ->
Enum.zip_with(-i..(len - 1), 0..(breadth - 1), fn x, y -> [x, y] end)
end
case batch_indices(batch_shape) do
[] ->
indices
batch_indices ->
Enum.flat_map(batch_indices, fn batch_index -> Enum.map(indices, &(batch_index ++ &1)) end)
end
|> Nx.tensor()
end
defp batch_indices([]), do: []
defp batch_indices([n]), do: Enum.map(0..(n - 1), &[&1])
defp batch_indices([axis_length | shape]) do
for i <- 0..(axis_length - 1), n <- batch_indices(shape), do: [i | n]
end
@doc """
Creates a one-dimensional tensor from a `binary` with the given `type`.
If the binary size does not match its type, an error is raised.
## Examples
iex> Nx.from_binary(<<1, 2, 3, 4>>, :s8)
#Nx.Tensor<
s8[4]
[1, 2, 3, 4]
>
The atom notation for types is also supported:
iex> Nx.from_binary(<<12.3::float-64-native>>, :f64)
#Nx.Tensor<
f64[1]
[12.3]
>
An error is raised for incompatible sizes:
iex> Nx.from_binary(<<1, 2, 3, 4>>, :f64)
** (ArgumentError) binary does not match the given size
## Options
* `:backend` - the backend to allocate the tensor on. It is either
an atom or a tuple in the shape `{backend, options}`. This option
is ignored inside `defn`
"""
@doc type: :creation
def from_binary(binary, type, opts \\ []) when is_binary(binary) do
opts = keyword!(opts, [:backend])
{_, size} = type = Nx.Type.normalize!(type)
dim = div(bit_size(binary), size)
if binary == "" do
raise ArgumentError, "cannot build an empty tensor"
end
if rem(bit_size(binary), size) != 0 do
raise ArgumentError, "binary does not match the given size"
end
{backend, backend_options} = backend_from_options!(opts) || default_backend()
backend.from_binary(%T{type: type, shape: {dim}, names: [nil]}, binary, backend_options)
end
## Conversions
@doc """
Returns the underlying tensor as a binary.
**Warning**: converting a tensor to a binary can
potentially be a very expensive operation, as it
may copy a GPU tensor fully to the machine memory.
It returns the in-memory binary representation of
the tensor in a row-major fashion. The binary is
in the system endianness, which has to be taken into
account if the binary is meant to be serialized to
other systems.
Note: This function cannot be used in `defn`.
## Options
* `:limit` - limit the number of entries represented in the binary
## Examples
iex> Nx.to_binary(1)
<<1::64-native>>
iex> Nx.to_binary(Nx.tensor([1.0, 2.0, 3.0]))
<<1.0::float-32-native, 2.0::float-32-native, 3.0::float-32-native>>
iex> Nx.to_binary(Nx.tensor([1.0, 2.0, 3.0]), limit: 2)
<<1.0::float-32-native, 2.0::float-32-native>>
### Vectorized tensors
`to_binary/2` disregards the vectorized axes before calculating the data to be returned:
iex> Nx.to_binary(Nx.vectorize(Nx.tensor([[1, 2], [3, 4]]), :x))
<<1::64-native, 2::64-native, 3::64-native, 4::64-native>>
iex> Nx.to_binary(Nx.vectorize(Nx.tensor([1, 2, 3]), :x), limit: 2)
<<1::64-native, 2::64-native>>
"""
@doc type: :conversion
def to_binary(tensor, opts \\ []) do
opts = keyword!(opts, [:limit])
tensor = to_tensor(tensor)
limit =
if limit = opts[:limit] do
Kernel.min(flat_size(tensor), limit)
else
flat_size(tensor)
end
impl!(tensor).to_binary(tensor, limit)
end
@doc """
Converts a data structure into a tensor.
This function only converts types which are automatically
cast to tensors throughout Nx API: numbers, complex numbers,
tensors themselves, and implementations of `Nx.LazyContainer`
(and `Nx.Container`).
If your goal is to create tensors from lists, see `tensor/2`.
If you want to create a tensor from binary, see `from_binary/3`.
If you want to convert a data structure with several tensors at
once into a single one, see `stack/2` or `concatenate/2` instead.
"""
@doc type: :conversion
def to_tensor(%T{} = t),
do: t
def to_tensor(number) when is_number(number) or number in [:infinity, :neg_infinity, :nan] do
{backend, options} = default_backend()
type = Nx.Type.infer(number)
out = %T{shape: {}, type: type, names: []}
backend.constant(out, number, options)
end
def to_tensor(%Complex{re: re, im: im} = number) do
{backend, options} = default_backend()
{_, size} = re |> Nx.Type.infer() |> Nx.Type.merge(Nx.Type.infer(im))
out = %T{shape: {}, type: {:c, size * 2}, names: []}
backend.constant(out, number, options)
end
def to_tensor(container) do
case Nx.LazyContainer.traverse(container, nil, fn _, fun, _ -> {fun.(), nil} end) do
{%T{} = tensor, _} ->
tensor
{_, _} ->
raise ArgumentError,
"cannot convert #{inspect(container)} to tensor because it represents " <>
"a collection of tensors, use Nx.stack/2 or Nx.concatenate/2 instead"
end
end
@doc """
Returns the underlying tensor as a flat list.
Negative infinity (-Inf), infinity (Inf), and "not a number" (NaN)
will be represented by the atoms `:neg_infinity`, `:infinity`, and
`:nan` respectively.
Note: This function cannot be used in `defn`.
## Examples
iex> Nx.to_flat_list(1)
[1]
iex> Nx.to_flat_list(Nx.tensor([1.0, 2.0, 3.0]))
[1.0, 2.0, 3.0]
iex> Nx.to_flat_list(Nx.tensor([1.0, 2.0, 3.0]), limit: 2)
[1.0, 2.0]
Non-finite numbers are returned as atoms:
iex> t = Nx.tensor([:neg_infinity, :nan, :infinity])
iex> Nx.to_flat_list(t)
[:neg_infinity, :nan, :infinity]
### Vectorized tensors
`to_flat_list/2` disregards the vectorized axes before calculating the data to be returned.
Like `to_binary/1`, `:limit` refers to the flattened devectorized data.
iex> t = Nx.vectorize(Nx.tensor([[1], [2], [3], [4]]), :x)
iex> Nx.to_flat_list(t)
[1, 2, 3, 4]
iex> Nx.to_flat_list(t, limit: 2)
[1, 2]
"""
@doc type: :conversion
def to_flat_list(tensor, opts \\ []) do
opts = keyword!(opts, [:limit])
%{type: type} = tensor = to_tensor(tensor)
match_types [type] do
for <<match!(var, 0) <- to_binary(tensor, opts)>> do
read!(var, 0)
end
end
end
@doc """
Converts the tensor into a list reflecting its structure.
Negative infinity (-Inf), infinity (Inf), and "not a number" (NaN)
will be represented by the atoms `:neg_infinity`, `:infinity`, and
`:nan` respectively.
It raises if a scalar tensor is given, use `to_number/1` instead.
Note: This function cannot be used in `defn`.
## Examples
iex> Nx.iota({2, 3}) |> Nx.to_list()
[
[0, 1, 2],
[3, 4, 5]
]
iex> Nx.tensor(123) |> Nx.to_list()
** (ArgumentError) cannot convert a scalar tensor to a list, got: #Nx.Tensor<
s64
123
>
### Vectorized tensors
`to_list/1` disregards the vectorized axes before calculating the data to be returned.
The special case below shows that a vectorized tensor with inner scalar shape will
still be converted to a list accordingly:
iex> %{shape: {}} = t = Nx.vectorize(Nx.tensor([1, 2, 3]), :x)
iex> Nx.to_list(t) # recall that normally, shape == {} would raise!
[1, 2, 3]
"""
@doc type: :conversion
def to_list(tensor) do
%{type: type, shape: shape} = tensor = tensor |> to_tensor() |> devectorize()
if shape == {} do
raise ArgumentError, "cannot convert a scalar tensor to a list, got: #{inspect(tensor)}"
end
binary = to_binary(tensor, [])
dims = Tuple.to_list(shape)
{list, ""} = chunk(dims, binary, type)
list
end
defp chunk([], data, type) do
match_types [type] do
<<match!(head, 0), tail::binary>> = data
{read!(head, 0), tail}
end
end
defp chunk([dim | dims], data, type) do
chunk_each(dim, data, [], dims, type)
end
defp chunk_each(0, data, acc, _dims, _type) do
{Enum.reverse(acc), data}
end
defp chunk_each(dim, data, acc, dims, type) do
{entry, rest} = chunk(dims, data, type)
chunk_each(dim - 1, rest, [entry | acc], dims, type)
end
@doc false
@deprecated "Use to_batched/3 instead"
def to_batched_list(tensor, batch_size, opts \\ []) do
Nx.Shared.raise_vectorization_not_supported(tensor, __ENV__.function)
tensor |> to_batched(batch_size, opts) |> Enum.to_list()
end
@doc """
Converts the underlying tensor to a stream of tensor batches.
The first dimension (axis 0) is divided by `batch_size`.
In case the dimension cannot be evenly divided by
`batch_size`, you may specify what to do with leftover
data using `:leftover`. `:leftover` must be one of `:repeat`
or `:discard`. `:repeat` repeats the first `n` values to
make the last batch match the desired batch size. `:discard`
discards excess elements.
Note: This function cannot be used in `defn`.
## Examples
In the examples below we immediately pipe to `Enum.to_list/1`
for convenience, but in practice you want to lazily traverse
the batches to avoid allocating multiple tensors at once in
certain backends:
iex> [first, second] = Nx.to_batched(Nx.iota({2, 2, 2}), 1) |> Enum.to_list()
iex> first
#Nx.Tensor<
s64[1][2][2]
[
[
[0, 1],
[2, 3]
]
]
>
iex> second
#Nx.Tensor<
s64[1][2][2]
[
[
[4, 5],
[6, 7]
]
]
>
If the batch size would result in uneven batches, you can repeat or discard excess data.
By default, we repeat:
iex> [first, second, third] = Nx.to_batched(Nx.iota({5, 2}, names: [:x, :y]), 2) |> Enum.to_list()
iex> first
#Nx.Tensor<
s64[x: 2][y: 2]
[
[0, 1],
[2, 3]
]
>
iex> second
#Nx.Tensor<
s64[x: 2][y: 2]
[
[4, 5],
[6, 7]
]
>
iex> third
#Nx.Tensor<
s64[x: 2][y: 2]
[
[8, 9],
[0, 1]
]
>
But you can also discard:
iex> [first, second] = Nx.to_batched(Nx.iota({5, 2}, names: [:x, :y]), 2, leftover: :discard) |> Enum.to_list()
iex> first
#Nx.Tensor<
s64[x: 2][y: 2]
[
[0, 1],
[2, 3]
]
>
iex> second
#Nx.Tensor<
s64[x: 2][y: 2]
[
[4, 5],
[6, 7]
]
>
## Vectorized tensors
Similarly to `to_list/1` and `to_binary/1`, `to_batched/2` will
ignore vectorization to perform calculations. Because the output
still contains tensors, however, they will still be vectorized.
iex> t = Nx.iota({2, 2, 2}) |> Nx.vectorize(x: 2)
iex> [first, second] = Nx.to_batched(t, 1) |> Enum.to_list()
iex> first
#Nx.Tensor<
vectorized[x: 1]
s64[2][2]
[
[
[0, 1],
[2, 3]
]
]
>
iex> second
#Nx.Tensor<
vectorized[x: 1]
s64[2][2]
[
[
[4, 5],
[6, 7]
]
]
>
iex> t = Nx.iota({2, 2, 2}) |> Nx.vectorize(x: 2, y: 2)
iex> [first, second] = Nx.to_batched(t, 1) |> Enum.to_list()
iex> first
#Nx.Tensor<
vectorized[x: 1][y: 2]
s64[2]
[
[
[0, 1],
[2, 3]
]
]
>
iex> second
#Nx.Tensor<
vectorized[x: 1][y: 2]
s64[2]
[
[
[4, 5],
[6, 7]
]
]
>
Same rules about uneven batches still apply:
iex> t = Nx.iota({5, 2}, names: [:x, :y]) |> Nx.vectorize(:x)
iex> [first, second, third] = Nx.to_batched(t, 2) |> Enum.to_list()
iex> first
#Nx.Tensor<
vectorized[x: 2]
s64[y: 2]
[
[0, 1],
[2, 3]
]
>
iex> second
#Nx.Tensor<
vectorized[x: 2]
s64[y: 2]
[
[4, 5],
[6, 7]
]
>
iex> third
#Nx.Tensor<
vectorized[x: 2]
s64[y: 2]
[
[8, 9],
[0, 1]
]
>
Because we're dealing with vectorized tensors, a vectorized
scalar tensor can also be batched.
iex> t = Nx.tensor([1, 2, 3]) |> Nx.vectorize(:x)
iex> [first, second] = t |> Nx.to_batched(2) |> Enum.to_list()
iex> first
#Nx.Tensor<
vectorized[x: 2]
s64
[1, 2]
>
iex> second
#Nx.Tensor<
vectorized[x: 2]
s64
[3, 1]
>
"""
@doc type: :conversion
def to_batched(tensor, batch_size, opts \\ [])
when is_integer(batch_size) and batch_size >= 1 do
opts = keyword!(opts, leftover: :repeat)
%T{vectorized_axes: vectorized_axes} = tensor = to_tensor(tensor)
if vectorized_axes == [] and tensor.shape == {} do
raise ArgumentError, "cannot batch non-vectorized scalar tensor #{inspect(tensor)}"
end
tensor = devectorize(tensor, keep_names: false)
if elem(tensor.shape, 0) < batch_size do
raise ArgumentError, "cannot batch beyond original tensor"
end
new_shape = put_elem(tensor.shape, 0, batch_size)
result = impl!(tensor).to_batched(%{tensor | shape: new_shape}, tensor, opts)
case vectorized_axes do
[] ->
result
[{name, _} | remaining_axes] ->
Stream.map(result, &vectorize(&1, [{name, batch_size} | remaining_axes]))
end
end
@doc """
Returns the underlying tensor as a number.
Negative infinity (-Inf), infinity (Inf), and "not a number" (NaN)
will be represented by the atoms `:neg_infinity`, `:infinity`, and
`:nan` respectively.
If the tensor has a dimension or is vectorized, it raises.
Note: This function cannot be used in `defn`.
## Examples
iex> Nx.to_number(1)
1
iex> Nx.to_number(Nx.tensor([1.0, 2.0, 3.0]))
** (ArgumentError) cannot convert tensor of shape {3} to number
iex> Nx.to_number(Nx.vectorize(Nx.tensor([1]), :x))
** (ArgumentError) cannot convert vectorized tensor with axes [x: 1] and shape {} to number
"""
@doc type: :conversion
def to_number(tensor)
def to_number(number) when is_number(number), do: number
def to_number(tensor) do
tensor = to_tensor(tensor)
if tensor.vectorized_axes != [] do
raise ArgumentError,
"cannot convert vectorized tensor with axes #{inspect(tensor.vectorized_axes)} and shape #{inspect(tensor.shape)} to number"
end
if tensor.shape != {} do
raise ArgumentError, "cannot convert tensor of shape #{inspect(tensor.shape)} to number"
end
match_types [tensor.type] do
<<match!(x, 0)>> = to_binary(tensor)
read!(x, 0)
end
end
@doc ~S"""
Returns a heatmap struct with the tensor data.
On terminals, coloring is done via ANSI colors. If ANSI
is not enabled, the tensor is normalized to show numbers
between 0 and 9.
## Terminal coloring
Coloring is enabled by default on most Unix terminals.
It is also available on Windows consoles from Windows
10, although it must be explicitly enabled for the current
user in the registry by running the following command:
reg add HKCU\Console /v VirtualTerminalLevel /t REG_DWORD /d 1
After running the command above, you must restart your current
console.
## Options
* `:ansi_enabled` - forces ansi to be enabled or disabled.
Defaults to `IO.ANSI.enabled?/0`
* `:ansi_whitespace` - which whitespace character to use when
printing. By default it uses `"\u3000"`, which is a full-width
whitespace which often prints more precise shapes
"""
@doc type: :conversion
def to_heatmap(tensor, opts \\ []) when is_list(opts) do
tensor = to_tensor(tensor)
if tensor.shape == {} do
raise ArgumentError, "cannot show heatmap for scalar tensors, got: #{inspect(tensor)}"
end
%Nx.Heatmap{tensor: tensor, opts: opts}
end
## Reflection operations (do not invoke the backend)
@doc """
Changes the type of a tensor.
Note conversion between float and integers truncates the
result. Consider using `round/1`, `floor/1`, or `ceil/1`
before casting from float to integer to guarantee consistent
behavior.
Casting from a higher precision may lead to an overflow
or underflow, which is platform and compiler dependent
behaviour.
Casting of non-finite types to integer types are handled
such as:
* negative infinity becomes the minimum value for said type
* positive infinity becomes the maximum value for said type
* nan becomes zero
## Examples
iex> Nx.as_type(Nx.tensor([0, 1, 2], names: [:data]), :f32)
#Nx.Tensor<
f32[data: 3]
[0.0, 1.0, 2.0]
>
iex> Nx.as_type(Nx.tensor([0.0, 1.0, 2.0], names: [:data]), :bf16)
#Nx.Tensor<
bf16[data: 3]
[0.0, 1.0, 2.0]
>
iex> Nx.as_type(Nx.tensor([0.0, 1.0, 2.0], names: [:data]), :s64)
#Nx.Tensor<
s64[data: 3]
[0, 1, 2]
>
Casting numbers as complex will return the corresponding complex with 0 imaginary component:
iex> Nx.as_type(Nx.tensor([1, -2]), :c64)
#Nx.Tensor<
c64[2]
[1.0+0.0i, -2.0+0.0i]
>
Casting complex numbers will return their real parts as the target type:
iex> Nx.as_type(Nx.tensor([Complex.new(1, 2), Complex.new(0, 3), Complex.new(4, 5)]), :f64)
#Nx.Tensor<
f64[3]
[1.0, 0.0, 4.0]
>
iex> Nx.as_type(Nx.tensor([Complex.new(-1, 2), Complex.new(-2, 3), Complex.new(3, -4)]), :s64)
#Nx.Tensor<
s64[3]
[-1, -2, 3]
>
Casting of non-finite values to integer types convert to pre-determined
integer values:
iex> non_finite = Nx.tensor([:infinity, :nan, :neg_infinity])
iex> Nx.as_type(non_finite, :u8)
#Nx.Tensor<
u8[3]
[255, 0, 0]
>
iex> Nx.as_type(non_finite, :s32)
#Nx.Tensor<
s32[3]
[2147483647, 0, -2147483648]
>
Non-finite values between float types are preserved:
iex> non_finite = Nx.tensor([:infinity, :nan])
iex> Nx.as_type(non_finite, :f64)
#Nx.Tensor<
f64[2]
[Inf, NaN]
>
iex> Nx.as_type(non_finite, :f16)
#Nx.Tensor<
f16[2]
[Inf, NaN]
>
If the input is a numerical constant instead of a tensor, this is an
alias to `Nx.tensor(number, type: type)`. In the example below,
notice how precision is only lost if we pass a type which can't
represent the numerical input:
iex> Nx.as_type(1.0e-128, :f32)
#Nx.Tensor<
f32
0.0
>
iex> Nx.as_type(1.0e-128, :f64)
#Nx.Tensor<
f64
1.0e-128
>
"""
@doc type: :type
def as_type(%T{} = tensor, type) do
tensor = to_tensor(tensor)
new_type = Nx.Type.normalize!(type)
if tensor.type == new_type do
tensor
else
apply_vectorized(tensor, fn tensor ->
impl!(tensor).as_type(%{tensor | type: new_type}, tensor)
end)
end
end
def as_type(number, type) when is_tensor(number), do: tensor(number, type: type)
@doc """
Changes the type of a tensor, using a bitcast.
The width of input tensor's type must match the width
of the output type. `bitcast/1` does not change the
underlying tensor data, but instead changes how
the tensor data is viewed.
Machines with different floating-point representations
will give different results.
For complex numbers, the last axis will change in size
depending on whether you are upcasting or downcasting.
## Examples
iex> t = Nx.bitcast(Nx.tensor([0, 0, 0], names: [:data], type: :s32), :f32)
#Nx.Tensor<
f32[data: 3]
[0.0, 0.0, 0.0]
>
iex> Nx.bitcast(t, :s32)
#Nx.Tensor<
s32[data: 3]
[0, 0, 0]
>
iex> t = Nx.vectorize(Nx.tensor([[0, -1], [1, -2], [2, -3]], type: :s8), :x)
#Nx.Tensor<
vectorized[x: 3]
s8[2]
[
[0, -1],
[1, -2],
[2, -3]
]
>
iex> Nx.bitcast(t, :u8)
#Nx.Tensor<
vectorized[x: 3]
u8[2]
[
[0, 255],
[1, 254],
[2, 253]
]
>
## Error cases
iex> Nx.bitcast(Nx.tensor([0, 1, 2], names: [:data], type: :s16), :f32)
** (ArgumentError) input type width must match new type width, got input type {:s, 16} and output type {:f, 32}
iex> Nx.bitcast(Nx.tensor([0], type: :c64), :s64)
** (ArgumentError) Nx.bitcast/2 does not support complex inputs
iex> Nx.bitcast(Nx.tensor([0], type: :s64), :c64)
** (ArgumentError) Nx.bitcast/2 does not support complex inputs
"""
@doc type: :type
def bitcast(tensor, type) do
apply_vectorized(tensor, fn tensor ->
%T{type: {_, bits} = input_type} = tensor
{_, new_bits} = new_type = Nx.Type.normalize!(type)
Nx.Shared.raise_complex_not_supported(input_type, :bitcast, 2)
Nx.Shared.raise_complex_not_supported(new_type, :bitcast, 2)
unless new_bits == bits do
raise ArgumentError,
"input type width must match new type width," <>
" got input type #{inspect(input_type)} and" <>
" output type #{inspect(new_type)}"
end
impl!(tensor).bitcast(%{tensor | type: new_type}, tensor)
end)
end
@doc """
Changes the shape of a tensor.
The new shape is either a tuple or a tensor which we will
retrieve the current shape from. The shapes must be compatible:
the product of each dimension in the shape must be equal.
You may specify one of the dimensions as `:auto`. Nx will compute
the size of the dimension based on the original shape and new shape.
Reshaping only changes the tensor metadata, it doesn't copy
the underlying structure.
Reshape is a destructive operation with respect to names. You
can optionally provide `:names` for each of the dimensions
in the reshaped tensor. If you do not provide `:names`, they
will be taken from the tensor the shape is taken from or
all of the dimension names will be set to `nil`.
## Examples
iex> t = Nx.tensor([1, 2, 3, 4], names: [:x])
iex> Nx.reshape(t, {2, 2}, names: [:x, :y])
#Nx.Tensor<
s64[x: 2][y: 2]
[
[1, 2],
[3, 4]
]
>
The shape can also be an existing tensor:
iex> shape = Nx.tensor([[0], [0], [0], [0]], names: [:x, :y])
iex> Nx.reshape(Nx.tensor([1, 2, 3, 4]), shape)
#Nx.Tensor<
s64[x: 4][y: 1]
[
[1],
[2],
[3],
[4]
]
>
Even a scalar can be transformed into a 3-dimensional tensor:
iex> t = Nx.tensor(1)
iex> Nx.reshape(t, {1, 1, 1}, names: [:x, :y, :z])
#Nx.Tensor<
s64[x: 1][y: 1][z: 1]
[
[
[1]
]
]
>
You can use `:auto` to infer dimension sizes. This is useful when you
don't know the size some dimension should be ahead of time:
iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]])
iex> Nx.reshape(t, {:auto, 2}, names: [:x, :y])
#Nx.Tensor<
s64[x: 3][y: 2]
[
[1, 2],
[3, 4],
[5, 6]
]
>
## Vectorized tensors
Vectorized tensors have their inner shapes changed, keeping vectors unchanged.
iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]]]) |> Nx.vectorize(:x)
iex> t.shape
{2, 3}
iex> Nx.reshape(t, {3, 2})
#Nx.Tensor<
vectorized[x: 1]
s64[3][2]
[
[
[1, 2],
[3, 4],
[5, 6]
]
]
>
"""
@doc type: :shape
def reshape(tensor, new_shape, opts \\ []) do
%T{shape: old_shape, vectorized_axes: vectorized_axes} = tensor = to_tensor(tensor)
new_names = opts[:names] || names!(new_shape)
new_shape = if is_tuple(new_shape), do: new_shape, else: shape(new_shape)
new_shape = Nx.Shape.reshape(old_shape, new_shape)
names = Nx.Shape.named_axes!(new_names, new_shape)
cond do
old_shape == new_shape ->
%{tensor | names: names}
vectorized_axes == [] ->
impl!(tensor).reshape(%{tensor | shape: new_shape, names: names}, tensor)
true ->
apply_vectorized(tensor, fn tensor, offset ->
new_shape =
tensor.shape
|> Tuple.to_list()
|> Enum.take(offset)
|> Enum.concat(Tuple.to_list(new_shape))
|> List.to_tuple()
impl!(tensor).reshape(
%{tensor | shape: new_shape, names: List.duplicate(nil, offset) ++ names},
tensor
)
end)
end
end
@doc """
Adds (or overrides) the given names to the tensor.
## Examples
iex> Nx.rename(Nx.iota({2, 3}), [:foo, :bar])
#Nx.Tensor<
s64[foo: 2][bar: 3]
[
[0, 1, 2],
[3, 4, 5]
]
>
## Vectorized tensors
Only the inner axis names are renamed. New names must not overlap with
vectorized names.
iex> t = Nx.tensor([[1], [2], [3]], names: [nil, :y]) |> Nx.vectorize(:x)
iex> Nx.rename(t, [:a])
#Nx.Tensor<
vectorized[x: 3]
s64[a: 1]
[
[1],
[2],
[3]
]
>
iex> Nx.rename(t, [:x])
** (ArgumentError) name :x is already a name for a vectorized axis
"""
@doc type: :shape
def rename(tensor, names) do
tensor = to_tensor(tensor)
Enum.each(tensor.vectorized_axes, fn {name, _} ->
if name in names do
raise ArgumentError, "name #{inspect(name)} is already a name for a vectorized axis"
end
end)
%{tensor | names: Nx.Shape.named_axes!(names, tensor.shape)}
end
@doc """
Flattens a n-dimensional tensor to a 1-dimensional tensor.
Flattening only changes the tensor metadata, it doesn't
copy the underlying structure.
Flatten is a destructive operation with respect to names.
## Examples
iex> t = Nx.iota({2, 2, 2, 2})
#Nx.Tensor<
s64[2][2][2][2]
[
[
[
[0, 1],
[2, 3]
],
[
[4, 5],
[6, 7]
]
],
[
[
[8, 9],
[10, 11]
],
[
[12, 13],
[14, 15]
]
]
]
>
iex> Nx.flatten(t)
#Nx.Tensor<
s64[16]
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
>
And if the tensor is already 1-dimensional:
iex> t = Nx.iota({16})
#Nx.Tensor<
s64[16]
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
>
iex> Nx.flatten(t)
#Nx.Tensor<
s64[16]
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
>
You may also pass `:axes` to `Nx.flatten/2`, to specify which consecutive
axes to flatten:
iex> t = Nx.iota({1, 2, 3})
#Nx.Tensor<
s64[1][2][3]
[
[
[0, 1, 2],
[3, 4, 5]
]
]
>
iex> Nx.flatten(t, axes: [1, 2])
#Nx.Tensor<
s64[1][6]
[
[0, 1, 2, 3, 4, 5]
]
>
`:axes` must be consecutive, otherwise it will raise:
iex> t = Nx.iota({1, 2, 3})
#Nx.Tensor<
s64[1][2][3]
[
[
[0, 1, 2],
[3, 4, 5]
]
]
>
iex> Nx.flatten(t, axes: [0, 2])
** (ArgumentError) flatten axes must be consecutive
## Vectorized tensors
Only the inner shape is flattened, leaving vectorized axes untouched.
iex> t = Nx.iota({1, 3, 2, 2}) |> Nx.vectorize(:x) |> Nx.vectorize(:y)
iex> Nx.flatten(t)
#Nx.Tensor<
vectorized[x: 1][y: 3]
s64[4]
[
[
[0, 1, 2, 3],
[4, 5, 6, 7],
[8, 9, 10, 11]
]
]
>
"""
@doc type: :shape
def flatten(tensor, opts \\ []) do
tensor = to_tensor(tensor)
opts = Keyword.validate!(opts, [:axes])
{shape, names} = Nx.Shape.flatten(tensor.shape, tensor.names, opts[:axes])
reshape(tensor, shape, names: names)
end
@doc """
Creates a new tensor by repeating the input tensor
along the given axes.
If the `tensor` has less dimensions than the repetitions given,
the tensor will grow in dimensionality.
If the `tensor` has more dimensions than the repetitions given,
tiling is done from the rightmost dimensions (i.e. if the input
shape is `{1,2,3}` and `repetitions = [2]`, the result is the same
as if `repetitions = [1,1,2]`).
## Examples
iex> a = Nx.tensor([0, 1, 2])
iex> Nx.tile(a, [2])
#Nx.Tensor<
s64[6]
[0, 1, 2, 0, 1, 2]
>
iex> Nx.tile(a, [1, 2])
#Nx.Tensor<
s64[1][6]
[
[0, 1, 2, 0, 1, 2]
]
>
iex> Nx.tile(a, [2, 2])
#Nx.Tensor<
s64[2][6]
[
[0, 1, 2, 0, 1, 2],
[0, 1, 2, 0, 1, 2]
]
>
iex> Nx.tile(a, [2, 1])
#Nx.Tensor<
s64[2][3]
[
[0, 1, 2],
[0, 1, 2]
]
>
iex> Nx.tile(a, [2, 1, 2])
#Nx.Tensor<
s64[2][1][6]
[
[
[0, 1, 2, 0, 1, 2]
],
[
[0, 1, 2, 0, 1, 2]
]
]
>
iex> b = Nx.tensor([[1,2],[3,4]])
iex> Nx.tile(b, [2])
#Nx.Tensor<
s64[2][4]
[
[1, 2, 1, 2],
[3, 4, 3, 4]
]
>
iex> Nx.tile(b, [2, 1])
#Nx.Tensor<
s64[4][2]
[
[1, 2],
[3, 4],
[1, 2],
[3, 4]
]
>
iex> Nx.tile(b, [1, 2])
#Nx.Tensor<
s64[2][4]
[
[1, 2, 1, 2],
[3, 4, 3, 4]
]
>
iex> c = Nx.tensor([1,2,3,4])
iex> Nx.tile(c, [4,1])
#Nx.Tensor<
s64[4][4]
[
[1, 2, 3, 4],
[1, 2, 3, 4],
[1, 2, 3, 4],
[1, 2, 3, 4]
]
>
## Vectorized tensors
Like `reshape/2`, `tile/2` works on the shape, leaving vectors untouched.
iex> t = Nx.vectorize(Nx.tensor([[1, 2, 3], [4, 5, 6]]), :x)
iex> Nx.tile(t, [1, 3, 1])
#Nx.Tensor<
vectorized[x: 2]
s64[1][3][3]
[
[
[
[1, 2, 3],
[1, 2, 3],
[1, 2, 3]
]
],
[
[
[4, 5, 6],
[4, 5, 6],
[4, 5, 6]
]
]
]
>
## Error cases
iex> Nx.tile(Nx.tensor([1,2]), 1.0)
** (ArgumentError) repetitions must be a list of integers, got: 1.0
iex> Nx.tile(Nx.tensor([1,2]), [1, 1.0])
** (ArgumentError) repetitions must be a list of integers, got: [1, 1.0]
iex> Nx.tile(Nx.tensor([1,2]), nil)
** (ArgumentError) repetitions must be a list of integers, got: nil
"""
@doc type: :shape, from_backend: false
def tile(tensor, repetitions) do
unless tile_valid_repetitions?(repetitions) do
raise ArgumentError,
"repetitions must be a list of integers, got: #{inspect(repetitions)}"
end
{tensor_reshape, broadcast_shape, result_shape} = Nx.Shape.tile(tensor, repetitions)
tensor
|> reshape(tensor_reshape)
|> broadcast(broadcast_shape)
|> reshape(result_shape)
end
defp tile_valid_repetitions?(reps) when not is_list(reps), do: false
defp tile_valid_repetitions?(reps) do
Enum.all?(reps, &(is_integer(&1) and &1 >= 1))
end
@doc """
Adds a new `axis` of size 1 with optional `name`.
## Examples
iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]])
iex> Nx.new_axis(t, 0, :new)
#Nx.Tensor<
s64[new: 1][2][3]
[
[
[1, 2, 3],
[4, 5, 6]
]
]
>
iex> Nx.new_axis(t, 1, :new)
#Nx.Tensor<
s64[2][new: 1][3]
[
[
[1, 2, 3]
],
[
[4, 5, 6]
]
]
>
iex> Nx.new_axis(t, 2, :new)
#Nx.Tensor<
s64[2][3][new: 1]
[
[
[1],
[2],
[3]
],
[
[4],
[5],
[6]
]
]
>
Axis can also be negative, which will start from the back:
iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]])
iex> Nx.new_axis(t, -1, :new)
#Nx.Tensor<
s64[2][3][new: 1]
[
[
[1],
[2],
[3]
],
[
[4],
[5],
[6]
]
]
>
## Vectorized tensors
Similarly to `reshape/2`, vectorized tensors will have their
vectors unchanged. The examples below show that the new axes
only affect the tensor shape.
iex> t = Nx.tensor([1]) |> Nx.vectorize(:x)
#Nx.Tensor<
vectorized[x: 1]
s64
[1]
>
iex> t = Nx.new_axis(t, -1, :new)
#Nx.Tensor<
vectorized[x: 1]
s64[new: 1]
[
[1]
]
>
iex> Nx.new_axis(t, 0)
#Nx.Tensor<
vectorized[x: 1]
s64[1][new: 1]
[
[
[1]
]
]
>
"""
@doc type: :shape, from_backend: false
def new_axis(tensor, axis, name \\ nil) when is_integer(axis) do
apply_vectorized(tensor, fn tensor, offset ->
%{shape: shape, names: names} = tensor = to_tensor(tensor)
rank = tuple_size(shape)
norm = if axis < 0, do: axis + rank + 1, else: axis + offset
if norm not in offset..tuple_size(shape) do
raise ArgumentError,
"new axis position for shape #{inspect(shape)} must be " <>
"a number between #{-rank - 1 + offset} and #{rank - offset}, got: #{axis}"
end
new_shape = Tuple.insert_at(shape, norm, 1)
new_names = List.insert_at(names, norm, name)
impl!(tensor).reshape(%{tensor | shape: new_shape, names: new_names}, tensor)
end)
end
@doc """
Squeezes the given size `1` dimensions out of the tensor.
If no axes are given, squeezes all size `1` dimensions
from the tensor.
While this is equivalent to a reshape which eliminates
the size `1` axes, squeeze preserves important information
about which axes were squeezed out which can then be used
later on in transformations.
## Examples
iex> Nx.squeeze(Nx.tensor([[[[[1]]]]]))
#Nx.Tensor<
s64
1
>
iex> Nx.squeeze(Nx.tensor([[[[1]]], [[[2]]]], names: [:x, :y, :z, :i]))
#Nx.Tensor<
s64[x: 2]
[1, 2]
>
iex> Nx.squeeze(Nx.tensor([[1, 2, 3]], names: [:x, :y]), axes: [:x])
#Nx.Tensor<
s64[y: 3]
[1, 2, 3]
>
iex> Nx.squeeze(Nx.tensor([[1], [2]], names: [:x, :y]), axes: [:y])
#Nx.Tensor<
s64[x: 2]
[1, 2]
>
## Vectorized tensors
`squeeze/2` operates on the tensor's shape, leaving vectorized axes untouched.
iex> t = Nx.tensor([[[[[1], [2], [3]]]]]) |> Nx.vectorize(:x)
#Nx.Tensor<
vectorized[x: 1]
s64[1][1][3][1]
[
[
[
[
[1],
[2],
[3]
]
]
]
]
>
iex> Nx.squeeze(t)
#Nx.Tensor<
vectorized[x: 1]
s64[3]
[
[1, 2, 3]
]
>
iex> Nx.squeeze(t, axes: [0, 1])
#Nx.Tensor<
vectorized[x: 1]
s64[3][1]
[
[
[1],
[2],
[3]
]
]
>
## Error cases
iex> Nx.squeeze(Nx.tensor([[1, 2, 3], [4, 5, 6]]), axes: [1])
** (ArgumentError) cannot squeeze dimensions whose sizes are not 1, got 3 for dimension 1
iex> Nx.squeeze(Nx.tensor([[[[[1]]]]]), axes: [0, 0])
** (ArgumentError) axes [0, 0] must be unique integers between 0 and 4
"""
@doc type: :shape
def squeeze(tensor, opts \\ []) do
apply_vectorized(tensor, fn tensor, offset ->
opts = keyword!(opts, [:axes])
%T{shape: old_shape, names: names} = tensor
axes = opts[:axes] || Nx.Shape.squeeze_axes(old_shape, offset)
axes = Nx.Shape.normalize_axes(old_shape, axes, names, offset)
{new_shape, new_names} = Nx.Shape.squeeze(old_shape, axes, names)
if old_shape == new_shape do
tensor
else
impl!(tensor).squeeze(%{tensor | shape: new_shape, names: new_names}, tensor, axes)
end
end)
end
@doc ~S"""
Split a tensor into train and test subsets.
`split` must be defined so that there are no empty result tensors.
This means that `split` must be:
* an integer such that `0 < split` and `split < axis_size`
* a float such that `0.0 < split` and `ceil(axis_size * split) < axis_size`
## Options
* `:axis` - The axis along which to split the tensor. Defaults to `0`.
## Examples
All examples will operate on the same tensor so that it's easier to compare different configurations.
iex> t = Nx.tensor([[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11]])
iex> {left, right} = Nx.split(t, 2, axis: 0)
iex> left
#Nx.Tensor<
s64[2][4]
[
[0, 1, 2, 3],
[4, 5, 6, 7]
]
>
iex> right
#Nx.Tensor<
s64[1][4]
[
[8, 9, 10, 11]
]
>
iex> {left, right} = Nx.split(t, 2, axis: 1)
iex> left
#Nx.Tensor<
s64[3][2]
[
[0, 1],
[4, 5],
[8, 9]
]
>
iex> right
#Nx.Tensor<
s64[3][2]
[
[2, 3],
[6, 7],
[10, 11]
]
>
iex> t = Nx.tensor([[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11]])
iex> {left, right} = Nx.split(t, 0.5, axis: 0)
iex> left
#Nx.Tensor<
s64[2][4]
[
[0, 1, 2, 3],
[4, 5, 6, 7]
]
>
iex> right
#Nx.Tensor<
s64[1][4]
[
[8, 9, 10, 11]
]
>
iex> {left, right} = Nx.split(t, 0.75, axis: 1)
iex> left
#Nx.Tensor<
s64[3][3]
[
[0, 1, 2],
[4, 5, 6],
[8, 9, 10]
]
>
iex> right
#Nx.Tensor<
s64[3][1]
[
[3],
[7],
[11]
]
>
Negative indices are also accepted, in the same fashion as `Enum.split/2`.
iex> t = Nx.tensor([1, 2, 3, 4])
iex> {left, right} = Nx.split(t, -1)
iex> left
#Nx.Tensor<
s64[3]
[1, 2, 3]
>
iex> right
#Nx.Tensor<
s64[1]
[4]
>
"""
@doc type: :indexed
def split(tensor, split, opts \\ [])
def split(tensor, split, opts) do
tensor = to_tensor(tensor)
opts = keyword!(opts, axis: 0)
axis = Keyword.fetch!(opts, :axis)
axis = Nx.Shape.normalize_axis(tensor.shape, axis, tensor.names)
axis_size = axis_size(tensor, axis)
# only used in case the split is a float
float_split_index = Kernel.ceil(split * axis_size)
{split_index, remainder_length} =
cond do
is_integer(split) and split > 0 and split < axis_size ->
{split, axis_size - split}
is_integer(split) and split < 0 and split > -axis_size ->
{axis_size + split, Kernel.abs(split)}
is_integer(split) ->
raise ArgumentError,
"split must be an integer greater than zero and less than the length of the given axis"
is_float(split) and float_split_index > 0 and float_split_index < axis_size ->
{float_split_index, axis_size - float_split_index}
is_float(split) ->
raise ArgumentError,
"split must be a float such that 0 < split and ceil(split * axis_size) < 1"
true ->
raise ArgumentError,
"invalid split received, expected a float or an integer, got: #{inspect(split)}"
end
{
slice_along_axis(tensor, 0, split_index, axis: axis),
slice_along_axis(tensor, split_index, remainder_length, axis: axis)
}
end
@doc """
Broadcasts `tensor` to the given `broadcast_shape`.
The new shape is either a tuple or a tensor which we will
retrieve the current shape from. The broadcast shape must
be of equal or higher rank than the current shape.
An optional `:axes` can be given to customize how broadcasting
happens. `axes` must be a list with the same length as the
tensor shape. Each `axis` in the list maps to the dimension
in the broadcast shape that must match. For example, an axis
of `[1, 2]` says the 0 dimension of the tensor matches to
the 1 dimension of the broadcast shape and the 1 dimension
of the tensor matches the 2 dimension of the broadcast shape.
Each matching dimension must either be 1, for implicit
broadcasting, or match the dimension in the broadcast shape.
Broadcasting is destructive with respect to names. You can
optionally provide new `:names` for the new tensor. If you
pass a tensor with named dimensions, the new tensor will
inherit names from that tensor.
## Examples
### Without axes
## Examples
iex> Nx.broadcast(1, {1, 2, 3})
#Nx.Tensor<
s64[1][2][3]
[
[
[1, 1, 1],
[1, 1, 1]
]
]
>
iex> Nx.broadcast(Nx.tensor([[1], [2]], names: [:x, :y]), Nx.tensor([[10, 20], [30, 40]], names: [:i, :j]))
#Nx.Tensor<
s64[i: 2][j: 2]
[
[1, 1],
[2, 2]
]
>
iex> Nx.broadcast(Nx.tensor([[1, 2]], names: [:x, :y]), Nx.tensor([[10, 20], [30, 40]], names: [:i, :j]))
#Nx.Tensor<
s64[i: 2][j: 2]
[
[1, 2],
[1, 2]
]
>
Note that, even if there is no broadcasting because the
shape is the same, names are discarded if none are given:
iex> Nx.broadcast(Nx.iota({2, 2}, names: [:x, :y]), {2, 2})
#Nx.Tensor<
s64[2][2]
[
[0, 1],
[2, 3]
]
>
iex> Nx.broadcast(Nx.iota({2, 2}, names: [:x, :y]), {2, 2}, names: [:i, :j])
#Nx.Tensor<
s64[i: 2][j: 2]
[
[0, 1],
[2, 3]
]
>
### With axes
Using the default broadcast rules, we cannot broadcast a
tensor of shape (3) to the shape (3, 2), because the lower
dimensions must match. But with `Nx.broadcast/3` we can
configure how the dimensions match:
iex> t = Nx.tensor([1, 2, 3])
iex> Nx.broadcast(t, {3, 2}, axes: [0], names: [:x, :y])
#Nx.Tensor<
s64[x: 3][y: 2]
[
[1, 1],
[2, 2],
[3, 3]
]
>
Or a more complex example:
iex> t = Nx.tensor([1, 2, 3])
iex> Nx.broadcast(t, {2, 3, 2}, axes: [1], names: [:x, :y, :z])
#Nx.Tensor<
s64[x: 2][y: 3][z: 2]
[
[
[1, 1],
[2, 2],
[3, 3]
],
[
[1, 1],
[2, 2],
[3, 3]
]
]
>
## Vectorized tensors
Vectorized axes remain unchanged, and normal broadcast rules apply otherwise.
iex> a = Nx.tensor([[[1, 2, 3]], [[4, 5, 6]]]) |> Nx.vectorize(:x)
iex> Nx.broadcast(a, {2, 3})
#Nx.Tensor<
vectorized[x: 2]
s64[2][3]
[
[
[1, 2, 3],
[1, 2, 3]
],
[
[4, 5, 6],
[4, 5, 6]
]
]
>
For tensors as shapes, the broadcast will only take the shape in consideration.
iex> a = Nx.tensor([[1, 2, 3], [4, 5, 6]]) |> Nx.vectorize(:x)
#Nx.Tensor<
vectorized[x: 2]
s64[3]
[
[1, 2, 3],
[4, 5, 6]
]
>
iex> b = Nx.tensor([[[1, 2, 3], [4, 5, 6]]], names: [nil, nil, :y]) |> Nx.vectorize(:a)
#Nx.Tensor<
vectorized[a: 1]
s64[2][y: 3]
[
[
[1, 2, 3],
[4, 5, 6]
]
]
>
iex> Nx.broadcast(a, b, axes: [1], names: [:i, :j])
#Nx.Tensor<
vectorized[x: 2]
s64[i: 2][j: 3]
[
[
[1, 2, 3],
[1, 2, 3]
],
[
[4, 5, 6],
[4, 5, 6]
]
]
>
"""
@doc type: :shape
def broadcast(tensor, shape, opts \\ []) do
opts = keyword!(opts, [:axes, :names])
apply_vectorized(tensor, fn tensor, offset ->
broadcast_names = opts[:names] || names!(shape)
broadcast_names =
if offset > 0 and is_list(broadcast_names) do
List.duplicate(nil, offset + 1) ++ broadcast_names
else
broadcast_names
end
broadcast_shape_l = shape |> shape() |> Tuple.to_list()
offset_axes =
if offset > 0 do
Enum.map(0..(offset - 1)//1, &elem(tensor.shape, &1)) ++ [1]
else
[]
end
tensor =
if offset > 0 do
new_axis(tensor, offset)
else
tensor
end
broadcast_shape = List.to_tuple(offset_axes ++ broadcast_shape_l)
opts_axes = opts[:axes]
actual_offset = if offset > 0, do: offset + 1, else: 0
axes =
if opts_axes do
axes =
Nx.Shape.normalize_axes(
broadcast_shape,
opts_axes,
tensor.names,
actual_offset
)
if offset > 0 do
Enum.to_list(0..(actual_offset - 1)//1) ++ axes
else
axes
end
else
Nx.Shape.broadcast_axes(tensor.shape, broadcast_shape)
end
broadcast_names = Nx.Shape.named_axes!(broadcast_names, broadcast_shape)
out = %{tensor | names: broadcast_names, shape: broadcast_shape}
out =
if tensor.shape == broadcast_shape and is_nil(opts_axes) do
out
else
_ = Nx.Shape.broadcast!(tensor.shape, broadcast_shape, axes, actual_offset)
impl!(tensor).broadcast(out, tensor, broadcast_shape, axes)
end
if offset > 0 do
squeeze(out, axes: [offset])
else
out
end
end)
end
@doc """
Pads a tensor with a given value.
You must specify a padding configuration. A padding
configuration is a list of tuples consisting of
`{pad_width_low, pad_width_high, pad_width_interior}`
for each dimension in the input tensor. The padding
configuration must be of the same length as the tensor shape.
Padding widths can be negative. If they are negative,
the tensor is clipped on either end according to the
padding width. Interior padding widths cannot be negative.
See also: `reflect/2`
## Examples
iex> Nx.pad(Nx.tensor(1), 0, [])
#Nx.Tensor<
s64
1
>
iex> Nx.pad(Nx.tensor([1, 2, 3], names: [:data]), 0, [{1, 1, 0}])
#Nx.Tensor<
s64[data: 5]
[0, 1, 2, 3, 0]
>
iex> Nx.pad(Nx.tensor([[1, 2, 3], [4, 5, 6]]), 0, [{0, 0, 1}, {0, 0, 1}])
#Nx.Tensor<
s64[3][5]
[
[1, 0, 2, 0, 3],
[0, 0, 0, 0, 0],
[4, 0, 5, 0, 6]
]
>
iex> Nx.pad(Nx.tensor([[1, 2, 3], [4, 5, 6]]), 0, [{1, 1, 0}, {1, 1, 0}])
#Nx.Tensor<
s64[4][5]
[
[0, 0, 0, 0, 0],
[0, 1, 2, 3, 0],
[0, 4, 5, 6, 0],
[0, 0, 0, 0, 0]
]
>
iex> tensor = Nx.tensor([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])
iex> Nx.pad(tensor, 0, [{0, 2, 0}, {1, 1, 0}, {1, 0, 0}])
#Nx.Tensor<
s64[4][4][3]
[
[
[0, 0, 0],
[0, 1, 2],
[0, 3, 4],
[0, 0, 0]
],
[
[0, 0, 0],
[0, 5, 6],
[0, 7, 8],
[0, 0, 0]
],
[
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0]
],
[
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0]
]
]
>
iex> tensor = Nx.tensor([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])
iex> Nx.pad(tensor, 0, [{1, 0, 0}, {1, 1, 0}, {0, 1, 0}])
#Nx.Tensor<
s64[3][4][3]
[
[
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0]
],
[
[0, 0, 0],
[1, 2, 0],
[3, 4, 0],
[0, 0, 0]
],
[
[0, 0, 0],
[5, 6, 0],
[7, 8, 0],
[0, 0, 0]
]
]
>
iex> tensor = Nx.tensor([[[1.0, 2.0], [3.0, 4.0]], [[5.0, 6.0], [7.0, 8.0]]])
iex> Nx.pad(tensor, 0.0, [{1, 2, 0}, {1, 0, 0}, {0, 1, 0}])
#Nx.Tensor<
f32[5][3][3]
[
[
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0]
],
[
[0.0, 0.0, 0.0],
[1.0, 2.0, 0.0],
[3.0, 4.0, 0.0]
],
[
[0.0, 0.0, 0.0],
[5.0, 6.0, 0.0],
[7.0, 8.0, 0.0]
],
[
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0]
],
[
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0]
]
]
>
iex> Nx.pad(Nx.tensor([0, 1, 2, 3, 0]), 0, [{-1, -1, 0}])
#Nx.Tensor<
s64[3]
[1, 2, 3]
>
iex> tensor = Nx.tensor([
...> [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]],
...> [[0, 0, 0], [1, 2, 0], [3, 4, 0], [0, 0, 0]],
...> [[0, 0, 0], [5, 6, 0], [7, 8, 0], [0, 0, 0]]
...> ])
iex> Nx.pad(tensor, 0, [{-1, 0, 0}, {-1, -1, 0}, {0, -1, 0}])
#Nx.Tensor<
s64[2][2][2]
[
[
[1, 2],
[3, 4]
],
[
[5, 6],
[7, 8]
]
]
>
iex> tensor = Nx.tensor([[0, 1, 2, 3], [0, 4, 5, 6]])
iex> Nx.pad(tensor, 0, [{0, 0, 0}, {-1, 1, 0}])
#Nx.Tensor<
s64[2][4]
[
[1, 2, 3, 0],
[4, 5, 6, 0]
]
>
iex> tensor = Nx.tensor([[0, 1, 2], [3, 4, 5]], type: :f32)
iex> Nx.pad(tensor, 0, [{-1, 2, 0}, {1, -1, 0}])
#Nx.Tensor<
f32[3][3]
[
[0.0, 3.0, 4.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0]
]
>
## Vectorized tensors
Like with the non-vectorized case, `pad_value` must be a non-vectorized scalar tensor.
Vectorized axes remain unchanged.
iex> t = Nx.tensor([[1], [2], [3]], names: [nil, :data]) |> Nx.vectorize(:x)
iex> Nx.pad(t, 0, [{1, 1, 0}])
#Nx.Tensor<
vectorized[x: 3]
s64[data: 3]
[
[0, 1, 0],
[0, 2, 0],
[0, 3, 0]
]
>
"""
@doc type: :shape
def pad(tensor, pad_value, padding_config) when is_list(padding_config) do
apply_vectorized(tensor, fn tensor, offset ->
output_type = binary_type(tensor, pad_value)
pad_value = to_tensor(pad_value)
if not (pad_value.shape == {} and pad_value.vectorized_axes == []) do
raise ArgumentError, "padding value must be a scalar and non-vectorized"
end
padding_config = List.duplicate({0, 0, 0}, offset) ++ padding_config
shape = Nx.Shape.pad(tensor.shape, padding_config)
out = %{tensor | type: output_type, shape: shape}
impl!(tensor).pad(out, tensor, pad_value, padding_config)
end)
end
## Reflection
@doc """
Returns the type of the tensor.
See `Nx.Type` for more information.
## Examples
iex> Nx.type(Nx.tensor([1, 2, 3]))
{:s, 64}
iex> Nx.type(Nx.tensor([1, 2, 3], type: :f32))
{:f, 32}
iex> Nx.type(1)
{:s, 64}
iex> Nx.type(1.0)
{:f, 32}
"""
@doc type: :type
def type(tensor) do
%T{type: type} = to_tensor(tensor)
type
end
@doc """
Checks if two tensors have the same shape, type, and compatible names.
The data in the tensor is ignored.
Note: This function cannot be used in `defn`.
## Examples
iex> Nx.compatible?(Nx.iota({3, 2}), Nx.iota({3, 2}))
true
iex> Nx.compatible?(Nx.iota({3, 2}), Nx.iota({3, 2}, names: [:rows, :columns]))
true
iex> Nx.compatible?(
...> Nx.iota({3, 2}, names: [:rows, nil]),
...> Nx.iota({3, 2}, names: [nil, :columns])
...> )
true
iex> Nx.compatible?(
...> Nx.iota({3, 2}, names: [:foo, :bar]),
...> Nx.iota({3, 2}, names: [:rows, :columns])
...> )
false
iex> Nx.compatible?(Nx.iota({3, 2}), Nx.iota({2, 3}))
false
iex> Nx.compatible?(Nx.iota({2, 2}), Nx.iota({2, 2}, type: :f32))
false
Using collections:
iex> Nx.compatible?({Nx.iota({3, 2}), {1, 2}}, {Nx.iota({3, 2}), {3, 4}})
true
iex> Nx.compatible?(%{foo: Nx.iota({3, 2})}, %{foo: Nx.iota({3, 2})})
true
iex> Nx.compatible?(%{foo: Nx.iota({3, 2})}, %{bar: Nx.iota({3, 2})})
false
## Vectorized tensors
Same compatibility criteria applies to vectorized tensors, but there's
the additional requirement that vectorized axes must be the same in both
tensors.
iex> Nx.compatible?(Nx.tensor([1, 2]) |> Nx.vectorize(:x), Nx.tensor([3, 4]) |> Nx.vectorize(:x))
true
iex> Nx.compatible?(Nx.tensor([1, 2, 3]) |> Nx.vectorize(:x), Nx.tensor([1, 2]) |> Nx.vectorize(:x))
false
iex> Nx.compatible?(Nx.tensor([1]) |> Nx.vectorize(:x), Nx.tensor([1, 2]) |> Nx.vectorize(:y))
false
"""
@doc type: :shape
def compatible?(left, right)
def compatible?(
%T{type: type, shape: shape, names: l_names, vectorized_axes: l_axes},
%T{type: type, shape: shape, names: r_names, vectorized_axes: r_axes}
) do
l_axes == r_axes and compatible_names?(l_names, r_names)
end
def compatible?(%T{} = left, %T{} = right) do
%{type: type, shape: shape, names: left_names} = left
case right do
%{type: ^type, shape: ^shape, names: right_names} ->
compatible_names?(left_names, right_names)
%{} ->
false
end
end
def compatible?(left, right),
do: Nx.Defn.Composite.compatible?(left, right, &compatible?(to_tensor(&1), to_tensor(&2)))
defp compatible_names?([name | lnames], [name | rnames]), do: compatible_names?(lnames, rnames)
defp compatible_names?([nil | lnames], [_ | rnames]), do: compatible_names?(lnames, rnames)
defp compatible_names?([_ | lnames], [nil | rnames]), do: compatible_names?(lnames, rnames)
defp compatible_names?([], []), do: true
defp compatible_names?(_, _), do: false
@doc """
Returns the shape of the tensor as a tuple.
The size of this tuple gives the rank of the tensor.
If a shape as a tuple is given, it returns the shape itself.
## Examples
iex> Nx.shape(Nx.tensor(1))
{}
iex> Nx.shape(Nx.tensor([[1, 2, 3], [4, 5, 6]]))
{2, 3}
iex> Nx.shape(1)
{}
iex> Nx.shape({1, 2, 3})
{1, 2, 3}
"""
@doc type: :shape
def shape(%T{shape: shape}), do: shape
def shape(number) when is_number(number), do: {}
def shape(shape) when is_tuple(shape), do: Nx.Shape.validate!(shape, :shape)
def shape(other) do
raise ArgumentError,
"expected a shape. A shape is a n-element tuple with the size of each dimension. " <>
"Alternatively, you can pass a tensor (or a number) and the shape will be retrieved from the tensor. " <>
"Got: #{inspect(other)}"
end
@doc """
Returns the rank of a tensor.
If a tuple is given as a shape, it computes the rank
of the given tuple.
## Examples
iex> Nx.rank(Nx.tensor(1))
0
iex> Nx.rank(Nx.tensor([[1, 2, 3], [4, 5, 6]]))
2
iex> Nx.rank(1)
0
iex> Nx.rank({1, 2, 3})
3
"""
@doc type: :shape
def rank(shape) when is_tuple(shape), do: tuple_size(shape)
def rank(tensor), do: tuple_size(shape(tensor))
@doc """
Returns the size of a given axis of a tensor.
It accepts either an atom as the name or an integer as the axis.
It raises if the axis/name does not exist.
## Examples
iex> Nx.axis_size(Nx.iota({100, 10, 20}), 0)
100
iex> Nx.axis_size(Nx.iota({100, 10, 20}, names: [:batch, :x, :y]), :y)
20
"""
@doc type: :shape
def axis_size(tensor, axis) do
shape = shape(tensor)
index = Nx.Shape.normalize_axis(shape, axis, names(tensor))
elem(shape, index)
end
@doc """
Returns the index of the given axis in the tensor.
## Examples
iex> Nx.axis_index(Nx.iota({100, 10, 20}), 0)
0
iex> Nx.axis_index(Nx.iota({100, 10, 20}), -1)
2
iex> Nx.axis_index(Nx.iota({100, 10, 20}, names: [:batch, :x, :y]), :x)
1
## Error cases
iex> Nx.axis_index(Nx.iota({100, 10, 20}), 3)
** (ArgumentError) given axis (3) invalid for shape with rank 3
iex> Nx.axis_index(Nx.iota({100, 10, 20}, names: [:batch, :x, :y]), :z)
** (ArgumentError) name :z not found in tensor with names [:batch, :x, :y]
"""
@doc type: :shape
def axis_index(tensor, axis) do
shape = shape(tensor)
Nx.Shape.normalize_axis(shape, axis, names(tensor))
end
@doc """
Returns the number of elements in the tensor.
If a tuple is given, it returns the number of elements in a tensor with that shape.
Vectorized tensors will not include vectorized axes sizes. See `flat_size/1`.
## Examples
iex> Nx.size(Nx.tensor([[1, 2, 3], [4, 5, 6]]))
6
iex> Nx.size(1)
1
iex> Nx.size({1, 2, 3, 2})
12
iex> Nx.size(Nx.vectorize(Nx.iota({4, 3, 2}), :x))
6
"""
@doc type: :shape
def size(shape) when is_tuple(shape), do: Tuple.product(shape)
def size(tensor), do: size(shape(tensor))
@doc """
Returns the number of elements in the tensor (including vectorized axes).
See also: `size/1`
## Examples
iex> Nx.flat_size(Nx.tensor([[1, 2, 3], [4, 5, 6]]))
6
iex> Nx.flat_size(10)
1
iex> t = Nx.iota({4, 3, 2})
iex> v1 = Nx.vectorize(t, :x)
iex> Nx.flat_size(v1)
24
iex> Nx.flat_size(Nx.vectorize(v1, :y))
24
"""
@doc type: :shape
def flat_size(%T{vectorized_axes: axes} = tensor) when axes != [] do
base_size = size(tensor)
Enum.reduce(axes, base_size, fn {_, size}, acc -> acc * size end)
end
def flat_size(tensor), do: size(tensor)
@doc """
Returns the byte size of the data in the tensor
computed from its shape and type.
## Examples
iex> Nx.byte_size(Nx.tensor([[1, 2, 3], [4, 5, 6]]))
48
iex> Nx.byte_size(Nx.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]]))
24
iex> Nx.byte_size(Nx.tensor([[1, 2, 3], [4, 5, 6]], type: :u8))
6
iex> Nx.byte_size(1)
8
Vectorized tensors account for all elements
iex> Nx.byte_size(Nx.tensor([[1, 2], [3, 4]]) |> Nx.vectorize(:x))
32
"""
@doc type: :shape
def byte_size(tensor) do
%{type: {_, bit_size}} = tensor = to_tensor(tensor)
flat_size(tensor) * div(bit_size, 8)
end
@doc """
Returns all of the axes in a tensor.
If a shape is given, it returns the axes for the given shape.
## Examples
iex> Nx.axes(Nx.tensor([[1, 2, 3], [4, 5, 6]]))
[0, 1]
iex> Nx.axes(1)
[]
iex> Nx.axes({1, 2, 3})
[0, 1, 2]
"""
@doc type: :shape
def axes(shape), do: count_up(rank(shape), 0)
@doc """
Returns all of the names in a tensor.
## Examples
iex> Nx.names(Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:batch, :data]))
[:batch, :data]
iex> Nx.names(Nx.tensor([1, 2, 3]))
[nil]
iex> Nx.names(5)
[]
"""
@doc type: :shape
def names(%T{names: names}), do: names
def names(a) when is_number(a), do: []
defp count_up(0, _n), do: []
defp count_up(i, n), do: [n | count_up(i - 1, n + 1)]
## Backend API
@doc """
Sets the given `backend` as default in the **current process**.
The default backend is stored only in the process dictionary.
This means if you start a separate process, such as `Task`,
the default backend must be set on the new process too.
Due to this reason, this function is mostly used for scripting
and testing. In your applications, you must prefer to set the
backend in your config files:
config :nx, :default_backend, {EXLA.Backend, device: :cuda}
In your notebooks and on `Mix.install/2`, you might:
Mix.install(
[
{:nx, ">= 0.0.0"}
],
config: [nx: [default_backend: {EXLA.Backend, device: :cuda}]]
)
Or use `Nx.global_default_backend/1` as it changes the
default backend on all processes.
The function returns the value that was previously set as backend.
Note: This function cannot be used in `defn`.
## Examples
Nx.default_backend({EXLA.Backend, device: :cuda})
#=> {Nx.BinaryBackend, []}
"""
@doc type: :backend
def default_backend(backend) do
Process.put(backend_pdict_key(), backend!(backend)) ||
backend!(Application.fetch_env!(:nx, :default_backend))
end
@doc """
Sets the default backend globally.
You must avoid calling this function at runtime. It is mostly
useful during scripts or code notebooks to set a default.
If you need to configure a global default backend in your
applications, it is generally preferred to do so in your
`config/*.exs` files:
config :nx, :default_backend, {EXLA.Backend, []}
In your notebooks and on `Mix.install/2`, you might:
Mix.install(
[
{:nx, ">= 0.0.0"}
],
config: [nx: [default_backend: {EXLA.Backend, device: :cuda}]]
)
The function returns the value that was previously set as global backend.
"""
@doc type: :backend
def global_default_backend(backend) do
current = backend!(Application.fetch_env!(:nx, :default_backend))
Application.put_env(:nx, :default_backend, backend!(backend))
current
end
@doc """
Gets the default backend for the current process.
Note: This function cannot be used in `defn`.
"""
@doc type: :backend
def default_backend() do
Process.get(backend_pdict_key()) || backend!(Application.fetch_env!(:nx, :default_backend))
end
@doc """
Invokes the given function temporarily setting `backend` as the
default backend.
"""
@doc type: :backend
def with_default_backend(backend, fun) do
backend = backend!(backend)
previous_backend = Process.put(backend_pdict_key(), backend)
try do
fun.()
after
if previous_backend do
Process.put(backend_pdict_key(), previous_backend)
else
Process.delete(backend_pdict_key())
end
end
end
@doc """
Copies data to the given backend.
If a backend is not given, `Nx.Tensor` is used, which means
the given tensor backend will pick the most appropriate
backend to copy the data to.
Note this function keeps the data in the original backend.
Therefore, use this function with care, as it may duplicate
large amounts of data across backends. Generally speaking,
you may want to use `backend_transfer/2`, unless you explicitly
want to copy the data.
Note:
* `Nx.default_backend/1` does not affect the behaviour of
this function.
* This function cannot be used in `defn`.
## Examples
iex> Nx.backend_copy(Nx.tensor([[1, 2, 3], [4, 5, 6]]))
#Nx.Tensor<
s64[2][3]
[
[1, 2, 3],
[4, 5, 6]
]
>
"""
@doc type: :backend
def backend_copy(tensor_or_container, backend \\ Nx.BinaryBackend) do
{backend, opts} = backend!(backend)
Nx.Defn.Composite.traverse(tensor_or_container, fn tensor ->
tensor = to_tensor(tensor)
{tensor, axes} = devectorize_with_axes(tensor)
result = impl!(tensor).backend_copy(tensor, backend, opts)
vectorize(result, axes)
end)
end
@doc """
Transfers data to the given backend.
This operation can be seen as an equivalent to `backend_copy/3`
followed by a `backend_deallocate/1` on the initial tensor:
new_tensor = Nx.backend_copy(old_tensor, new_backend)
Nx.backend_deallocate(old_tensor)
If a backend is not given, `Nx.Tensor` is used, which means
the given tensor backend will pick the most appropriate
backend to transfer to.
For Elixir's builtin tensor, transferring to another backend
will call `new_backend.from_binary(tensor, binary, opts)`.
Transferring from a mutable backend, such as GPU memory,
implies the data is copied from the GPU to the Erlang VM
and then deallocated from the device.
Note:
* `Nx.default_backend/1` does not affect the behaviour of this function.
* This function cannot be used in `defn`.
## Examples
Transfer a tensor to an EXLA device backend, stored in the GPU:
device_tensor = Nx.backend_transfer(tensor, {EXLA.Backend, client: :cuda})
Transfer the device tensor back to an Elixir tensor:
tensor = Nx.backend_transfer(device_tensor)
"""
@doc type: :backend
def backend_transfer(tensor_or_container, backend \\ Nx.BinaryBackend) do
{backend, opts} = backend!(backend)
Nx.Defn.Composite.traverse(tensor_or_container, fn tensor ->
tensor = to_tensor(tensor)
{tensor, axes} = devectorize_with_axes(tensor)
result = impl!(tensor).backend_transfer(tensor, backend, opts)
vectorize(result, axes)
end)
end
@doc """
Deallocates data in a device.
It returns either `:ok` or `:already_deallocated`.
Note: This function cannot be used in `defn`.
"""
@doc type: :backend
def backend_deallocate(tensor_or_container) do
Nx.Defn.Composite.reduce(tensor_or_container, :ok, fn
%Nx.Tensor{} = tensor, :ok ->
impl!(tensor).backend_deallocate(tensor)
_, :ok ->
:ok
end)
end
@doc """
Transforms a tensor into a vectorized tensor.
Each vectorization removes the leading axes from the shape and appends them to
the `:vectorized_axes` list for the tensor.
The vectorization specification can be a list of atoms or `{atom, pos_integer}`
pairs. If a single atom is given, it behaves as a single-element list.
The atom names the vectorized axes. If a pair is given, we also verify
that the given size matches the size of the to-be-vectorized axis.
In the examples below, we discuss in more detail how a vectorized tensor works.
## Examples
In this first example, we turn a `{2, 3}`-shaped tensor into a vectorized tensor
with 1 vectorized axes and rank 1 shape, `{3}`, and then into a vectorized tensor
with 2 vectorized axes and rank 0 shape.
iex> t = Nx.iota({2, 3})
iex> vectorized = Nx.vectorize(t, :first)
#Nx.Tensor<
vectorized[first: 2]
s64[3]
[
[0, 1, 2],
[3, 4, 5]
]
>
iex> Nx.vectorize(vectorized, :second)
#Nx.Tensor<
vectorized[first: 2][second: 3]
s64
[
[0, 1, 2],
[3, 4, 5]
]
>
You can also vectorize multiple axes at once by passing a list,
as seen in the examples below. The first example doesn't validate
sizes. The second ensures the second axis has size `3`.
iex> t = Nx.iota({2, 3})
iex> v1 = Nx.vectorize(t, [:first, :second])
#Nx.Tensor<
vectorized[first: 2][second: 3]
s64
[
[0, 1, 2],
[3, 4, 5]
]
>
iex> v2 = Nx.vectorize(t, [:first, second: 3])
iex> v1 == v2
true
A vectorized tensor can be thought of as a tensor that signals
to Nx that any operation applied on it must instead be applied
to each individual entry for the vectorized axis.
Nested vectorizations just apply this idea recursively, ultimately
applying the operation to each non-vectorized entry.
In the following example, notice that you don't need to have the
second argument shaped in a way that can be broadcasted, because
vectorization handles that automatically.
In the example below, shape `{4}` isn't broadcast-compatible with `{2}`:
iex> Nx.add(Nx.tensor([4, 3, 2, 1]), Nx.tensor([0, 1]))
** (ArgumentError) cannot broadcast tensor of dimensions {4} to {2}
If we want to add the two tensors, normally we would need to reshape
to signal which axis are broadcasted together:
iex> left = Nx.tensor([4, 3, 2, 1]) |> Nx.reshape({4, 1})
iex> right = Nx.tensor([0, 1]) |> Nx.reshape({1, 2})
iex> Nx.add(left, right)
#Nx.Tensor<
s64[4][2]
[
[4, 5],
[3, 4],
[2, 3],
[1, 2]
]
>
However, it `vectorize/1` simplifies this process. We can instead
signal that each entry on the `left` tensor will be treated as an
individual tensor, effectively forcing the same broadcast to happen.
In fact, you can think of the following code as a series of
additions between tensors of shapes `{}` and `{2}` respectively.
iex> vectorized = Nx.vectorize(Nx.tensor([4, 3, 2, 1]), :x)
#Nx.Tensor<
vectorized[x: 4]
s64
[4, 3, 2, 1]
>
iex> Nx.add(vectorized, Nx.tensor([0, 1]))
#Nx.Tensor<
vectorized[x: 4]
s64[2]
[
[4, 5],
[3, 4],
[2, 3],
[1, 2]
]
>
## Containers
Containers are also supported:
iex> input = {Nx.tensor([1]), %{a: Nx.tensor([2])}}
iex> {t1, %{a: t2}} = Nx.vectorize(input, x: 1)
iex> t1
#Nx.Tensor<
vectorized[x: 1]
s64
[1]
>
iex> t2
#Nx.Tensor<
vectorized[x: 1]
s64
[2]
>
## Error cases
iex> Nx.vectorize(Nx.tensor(1), :x)
** (ArgumentError) cannot vectorize tensor of rank 0
iex> Nx.vectorize(Nx.tensor([1]), [:x, :y])
** (ArgumentError) number of vectorized axes must not be greater than the shape size
iex> Nx.vectorize(Nx.tensor([1]), [x: 2])
** (ArgumentError) expected vectorized axis :x to have size 2, got 1
iex> Nx.vectorize(Nx.tensor([[1]]), [:x, "y"])
** (ArgumentError) expected vectorized axis specification to be an atom or a tuple of {atom, pos_integer}, got: "y"
iex> Nx.vectorize(Nx.tensor([[1]], names: [:x, :y]), [:y])
** (ArgumentError) cannot use name :y for new vectorized axes because there's already an axis with the same name
iex> t = Nx.vectorize(Nx.tensor([[1]]), :x)
iex> Nx.vectorize(t, :x)
** (ArgumentError) cannot use name :x for new vectorized axes because there's already a vectorized axis with the same name
"""
@doc type: :shape
@spec vectorize(
tensor :: Nx.Tensor.t(),
name_or_axes :: atom() | [atom() | {atom(), pos_integer()}]
) ::
Nx.Tensor.t()
def vectorize(tensor, name_or_axes)
def vectorize(tensor, []) when is_number(tensor) or is_struct(tensor, Complex),
do: to_tensor(tensor)
def vectorize(tensor_or_container, []) when is_struct(tensor_or_container),
do: tensor_or_container
def vectorize(%Nx.Tensor{shape: {}}, _name) do
raise ArgumentError, "cannot vectorize tensor of rank 0"
end
def vectorize(%Nx.Tensor{} = t, name) when is_atom(name), do: vectorize(t, [name])
def vectorize(
%Nx.Tensor{names: names, shape: shape, vectorized_axes: vec_axes} = tensor,
vector_spec
) do
n = length(vector_spec)
if n > tuple_size(shape) do
raise ArgumentError, "number of vectorized axes must not be greater than the shape size"
end
shape_l = Tuple.to_list(shape)
{to_vectorize_shape_l, new_shape_l} = Enum.split(shape_l, n)
new_vectorized_axes =
Enum.zip_with([vector_spec, to_vectorize_shape_l], fn
[name, size] when is_atom(name) ->
{name, size}
[{name, size}, size] when is_atom(name) ->
{name, size}
[{name, other_size}, size] when is_atom(name) and is_integer(other_size) ->
raise ArgumentError,
"expected vectorized axis #{inspect(name)} to have size #{other_size}, got #{size}"
[spec, _] ->
raise ArgumentError,
"expected vectorized axis specification to be an atom or a tuple of {atom, pos_integer}, got: #{inspect(spec)}"
end)
names = Enum.drop(names, n)
for name <- names, {new_axis_name, _} <- new_vectorized_axes, name == new_axis_name do
raise ArgumentError,
"cannot use name #{inspect(name)} for new vectorized axes because there's already an axis with the same name"
end
for {name, _} <- vec_axes, {new_axis_name, _} <- new_vectorized_axes, name == new_axis_name do
raise ArgumentError,
"cannot use name #{inspect(name)} for new vectorized axes because there's already a vectorized axis with the same name"
end
vectorized_axes = vec_axes ++ new_vectorized_axes
%Nx.Tensor{
tensor
| shape: List.to_tuple(new_shape_l),
names: names,
vectorized_axes: vectorized_axes
}
end
def vectorize(container, vectorized_axes) do
{result, nil} =
Nx.LazyContainer.traverse(container, nil, fn _template, fun, _ ->
{vectorize(fun.(), vectorized_axes), nil}
end)
result
end
@doc """
Transforms a vectorized tensor back into a regular tensor.
## Options
* `:keep_names` - a boolean indicating whether
vectorized axes' names should be turned into the new
axes' names. Defaults to `true`.
## Examples
iex> t = Nx.iota({1, 2, 3}) |> Nx.vectorize(:x) |> Nx.vectorize(:y)
#Nx.Tensor<
vectorized[x: 1][y: 2]
s64[3]
[
[
[0, 1, 2],
[3, 4, 5]
]
]
>
iex> Nx.devectorize(t)
#Nx.Tensor<
s64[x: 1][y: 2][3]
[
[
[0, 1, 2],
[3, 4, 5]
]
]
>
iex> Nx.devectorize(t, keep_names: false)
#Nx.Tensor<
s64[1][2][3]
[
[
[0, 1, 2],
[3, 4, 5]
]
]
>
## Containers
Containers are also supported:
iex> input = {1, %{a: Nx.iota({3}, vectorized_axes: [x: 1])}}
iex> {t1, %{a: t2}} = Nx.devectorize(input)
iex> t1
#Nx.Tensor<
s64
1
>
iex> t2
#Nx.Tensor<
s64[x: 1][3]
[
[0, 1, 2]
]
>
"""
@doc type: :shape
def devectorize(tensor_or_container, opts \\ [])
def devectorize(%T{shape: shape, names: names, vectorized_axes: vectorized_axes} = tensor, opts)
when vectorized_axes != [] do
opts = keyword!(opts, keep_names: true)
{vectorized_names, vectorized_sizes} = Enum.unzip(vectorized_axes)
output_shape_l = vectorized_sizes ++ Tuple.to_list(shape)
output_shape = List.to_tuple(output_shape_l)
output_names =
if opts[:keep_names] do
vectorized_names ++ names
else
Enum.reduce(vectorized_names, names, fn _, names -> [nil | names] end)
end
%{tensor | shape: output_shape, names: output_names, vectorized_axes: []}
end
def devectorize(%T{vectorized_axes: []} = tensor, _), do: tensor
def devectorize(number, _)
when is_struct(number, Complex)
when is_number(number),
do: to_tensor(number)
def devectorize(container, opts) do
{result, nil} =
Nx.LazyContainer.traverse(container, nil, fn _template, fun, _ ->
{devectorize(fun.(), opts), nil}
end)
result
end
@doc """
Reshapes input tensors so that they are all vectorized with the same vectors.
For vectors with the same name to be compatible, they need to either
have the same size or one must be of size 1.
## Options
* `:align_ranks` - boolean that indicates whether the inner
shapes should be aligned to the maximum rank of the inputs.
That is, 1-sized leading dimensions are added so
that all tensors have the same rank in the output.
This only applies in case one of the inputs is vectorized.
## Examples
Two vectors of the same name are compatible if they have the same sizes or if either has size 1.
iex> x = Nx.tensor([1, 2, 3]) |> Nx.vectorize(:x)
iex> xy = Nx.tensor([[[5]], [[6]]]) |> Nx.vectorize(:y) |> Nx.vectorize(:x)
iex> [x, xy] = Nx.reshape_vectors([x, xy])
iex> x.vectorized_axes
[x: 3, y: 1]
iex> xy.vectorized_axes
[x: 1, y: 2]
The resulting tensors will all present the combined vectors in the
same order in which each unique vector appears in the input.
The example below shows how this behaves for a pair of tensors.
iex> x = Nx.tensor([1, 2, 3]) |> Nx.vectorize(:x)
iex> y = Nx.tensor([4]) |> Nx.vectorize(:y)
iex> [xv, yv] = Nx.reshape_vectors([x, y])
iex> xv.vectorized_axes
[x: 3, y: 1]
iex> yv.vectorized_axes
[x: 1, y: 1]
iex> [yv, xv] = Nx.reshape_vectors([y, x])
iex> xv.vectorized_axes
[y: 1, x: 3]
iex> yv.vectorized_axes
[y: 1, x: 1]
The `:align_ranks` option controls whether the resulting tensors should end up
with the same rank, which helps with broadcasting in some cases.
iex> x = 1
iex> y = Nx.tensor([[[1], [1]], [[2], [2]], [[3], [3]]]) |> Nx.vectorize(:y)
iex> [xv, yv] = Nx.reshape_vectors([x, y])
iex> xv
#Nx.Tensor<
vectorized[y: 1]
s64
[1]
>
iex> yv
#Nx.Tensor<
vectorized[y: 3]
s64[2][1]
[
[
[1],
[1]
],
[
[2],
[2]
],
[
[3],
[3]
]
]
>
iex> [xv, _yv] = Nx.reshape_vectors([x, y], align_ranks: true)
iex> xv
#Nx.Tensor<
vectorized[y: 1]
s64[1][1]
[
[
[1]
]
]
>
"""
@doc type: :vectorization
def reshape_vectors(tensors_or_containers, opts \\ [])
def reshape_vectors([tensor], _opts), do: [to_tensor(tensor)]
def reshape_vectors(tensors, opts) when is_list(tensors) do
opts = keyword!(opts, align_ranks: false)
{devectorized_tensors, canonical_vectorized_axes, offset} =
do_reshape_vectors(tensors, opts[:align_ranks])
if offset != 0 do
keys = Keyword.keys(canonical_vectorized_axes)
Enum.map(devectorized_tensors, &vectorize(&1, keys))
else
devectorized_tensors
end
end
@doc """
Broadcasts vectorized axes, ensuring they end up with the same final size.
The inner shape is unchanged for each tensor.
The order of the vectorized axes is determined by order of appearance in the input list.
## Options
* `:align_ranks` - boolean that indicates whether the inner
shapes should be aligned to the maximum rank of the inputs.
That is, 1-sized leading dimensions are added so
that all tensors have the same rank in the output.
This only applies in case one of the inputs is vectorized.
## Examples
iex> x = Nx.tensor([1, 2]) |> Nx.vectorize(:x)
#Nx.Tensor<
vectorized[x: 2]
s64
[1, 2]
>
iex> xy = Nx.tensor([[[5]], [[6]]]) |> Nx.vectorize(:y) |> Nx.vectorize(:x)
#Nx.Tensor<
vectorized[y: 2][x: 1]
s64[1]
[
[
[5]
],
[
[6]
]
]
>
iex> [broadcast_x, broadcast_xy] = Nx.broadcast_vectors([x, xy], align_ranks: true)
iex> broadcast_x
#Nx.Tensor<
vectorized[x: 2][y: 2]
s64[1]
[
[
[1],
[1]
],
[
[2],
[2]
]
]
>
iex> broadcast_xy
#Nx.Tensor<
vectorized[x: 2][y: 2]
s64[1]
[
[
[5],
[6]
],
[
[5],
[6]
]
]
>
iex> [broadcast_xy, broadcast_x] = Nx.broadcast_vectors([xy, x])
iex> broadcast_x
#Nx.Tensor<
vectorized[y: 2][x: 2]
s64
[
[1, 2],
[1, 2]
]
>
iex> broadcast_xy
#Nx.Tensor<
vectorized[y: 2][x: 2]
s64[1]
[
[
[5],
[5]
],
[
[6],
[6]
]
]
>
"""
@doc type: :vectorization
def broadcast_vectors(tensors_or_containers, opts \\ [])
def broadcast_vectors([t], _opts), do: [to_tensor(t)]
def broadcast_vectors(tensors, opts) when is_list(tensors) do
opts = keyword!(opts, align_ranks: false)
{devectorized_tensors, target_vectorized_axes, offset} =
do_reshape_vectors(tensors, opts[:align_ranks])
if offset != 0 do
target_vector_shape_l = Keyword.values(target_vectorized_axes)
for t <- devectorized_tensors do
tensor_base_shape_l = t.shape |> Tuple.to_list() |> Enum.drop(offset)
target_shape = List.to_tuple(target_vector_shape_l ++ tensor_base_shape_l)
t
|> broadcast(target_shape, names: t.names)
|> vectorize(target_vectorized_axes)
end
else
devectorized_tensors
end
end
@doc """
Changes the disposition of the vectorized axes of a tensor or `Nx.Container`.
This function is basically a short-hand for:
tensor
|> Nx.devectorize(keep_names: false)
|> Nx.reshape(vectorized_sizes ++ target_shape, names: target_names)
|> Nx.vectorize(vectorized_names)
Accepts the `target_axes` keyword list where the total size must match the current total
size of the vectorized axes.
Between `target_axes` and the `:target_shape` option, there can be at most one `:auto` entry.
### Options
* `:target_shape` - the (non-vectorized) output shape.
* `:target_names` - the names for the output shape.
### Examples
iex> t = Nx.iota({1}, vectorized_axes: [x: 2, y: 3, z: 4])
iex> t2 = Nx.revectorize(t, x: 12, y: :auto)
iex> t2.vectorized_axes
[x: 12, y: 2]
iex> t3 = Nx.revectorize(t, a: :auto)
iex> t3.vectorized_axes
[a: 24]
Also works on containers. Note that the revectorization happens on a per-entry basis.
iex> t1 = Nx.iota({1}, vectorized_axes: [x: 2, y: 3])
iex> t2 = Nx.iota({1}, vectorized_axes: [x: 2, y: 1])
iex> {r1, r2} = Nx.revectorize({t1, t2}, a: :auto)
iex> r1.vectorized_axes
[a: 6]
iex> r2.vectorized_axes
[a: 2]
This function is useful for when you need to introduce a temporary custom axis to ease calculations.
The example below shows how to manipulate your vectorized tensor for that objective.
iex> t = Nx.iota({2, 2, 2}) |> Nx.vectorize(x: 2, y: 2)
#Nx.Tensor<
vectorized[x: 2][y: 2]
s64[2]
[
[
[0, 1],
[2, 3]
],
[
[4, 5],
[6, 7]
]
]
>
iex> Nx.revectorize(t, temp: :auto, x: 2) # Note that if we don't pass `:target_shape`, `:auto` will only act upon the vectorized axes
#Nx.Tensor<
vectorized[temp: 2][x: 2]
s64[2]
[
[
[0, 1],
[2, 3]
],
[
[4, 5],
[6, 7]
]
]
>
iex> revec = Nx.revectorize(t, [temp: :auto, x: 2], target_shape: {})
#Nx.Tensor<
vectorized[temp: 4][x: 2]
s64
[
[0, 1],
[2, 3],
[4, 5],
[6, 7]
]
>
iex> Nx.revectorize(revec, [new_vec: 2], target_shape: {1, 4}, target_names: [:x, :last])
#Nx.Tensor<
vectorized[new_vec: 2]
s64[x: 1][last: 4]
[
[
[0, 1, 2, 3]
],
[
[4, 5, 6, 7]
]
]
>
Note how in the last example the `:x` name could be reused in various positions
(both vectorized and non-vectorized), because `revectorize/2` ensures that the
names are rewritten at each call.
"""
@doc type: :vectorization
def revectorize(tensor, target_axes, opts \\ [])
def revectorize(%T{} = tensor, target_axes, opts) do
opts = keyword!(opts, [:target_shape, :target_names])
{axes_names, axes_sizes} = Enum.unzip(target_axes)
{target_shape, target_names} =
if target_shape = opts[:target_shape] do
target_names = opts[:target_names] || List.duplicate(nil, tuple_size(target_shape))
{target_shape, target_names}
else
{tensor.shape, tensor.names}
end
inner_names = axes_names ++ target_names
inner_shape_l = axes_sizes ++ Tuple.to_list(target_shape)
if Enum.count(inner_shape_l, &(&1 == :auto)) > 1 do
raise ArgumentError,
"cannot have more than one `:auto` occurrence between target_axes and the :target_shape option"
end
inner_shape = List.to_tuple(inner_shape_l)
tensor
|> devectorize(keep_names: false)
|> reshape(inner_shape, names: inner_names)
|> vectorize(axes_names)
end
def revectorize(container, target_axes, opts),
do: Nx.Defn.Composite.traverse(container, &revectorize(&1, target_axes, opts))
defp do_reshape_vectors(tensors, align_ranks) do
# For all tensors to be compatible, each pair also needs to be compatible
# This means that we can do a first pass accumulating axes into
# the first tensor, and then a second pass getting them all into their final shapes.
tensors = Enum.map(tensors, &to_tensor/1)
canonical = calculate_canonical_vectorized_axes(tensors)
n = length(canonical)
devectorized_tensors = do_reshape_vectors_devectorize(tensors, canonical, n, align_ranks)
{devectorized_tensors, canonical, n}
end
defp do_reshape_vectors_devectorize(tensors, [], _n, _align_ranks), do: tensors
defp do_reshape_vectors_devectorize(tensors, canonical_vectorized_axes, n, align_ranks) do
rank =
Enum.reduce(
tl(tensors),
tuple_size(hd(tensors).shape),
&Kernel.max(tuple_size(&1.shape), &2)
)
Enum.map(tensors, fn
%T{names: names, shape: shape, vectorized_axes: current_axes} = t ->
{vectorized_axes, []} =
Enum.map_reduce(canonical_vectorized_axes, current_axes, fn
{k, _}, [] ->
{{k, 1}, []}
{name, _size}, current_axes ->
case List.keytake(current_axes, name, 0) do
{{^name, other_size}, current_axes} ->
{{name, other_size}, current_axes}
_ ->
{{name, 1}, current_axes}
end
end)
size = if align_ranks, do: rank - tuple_size(shape), else: 0
target_shape =
List.to_tuple(
Keyword.values(vectorized_axes) ++
List.duplicate(1, size) ++ Tuple.to_list(shape)
)
target_names = List.duplicate(nil, n + size) ++ names
t
|> devectorize()
|> reshape(target_shape, names: target_names)
end)
end
defp calculate_canonical_vectorized_axes(tensors) do
canonical_axes_reversed =
for %T{vectorized_axes: tensor_axes} <- tensors,
{axis_name, axis_size} <- tensor_axes,
reduce: [] do
canonical_axes ->
case List.keyfind(canonical_axes, axis_name, 0) do
{^axis_name, other_size}
when other_size == axis_size
when other_size == 1
when axis_size == 1 ->
List.keyreplace(
canonical_axes,
axis_name,
0,
{axis_name, Kernel.max(axis_size, other_size)}
)
{^axis_name, other_size} ->
raise ArgumentError,
"expected vectorized axis #{inspect(axis_name)} to have the same size in both tensors or to one of them to have size 1, got #{inspect(axis_size)} and #{inspect(other_size)}"
nil ->
# accumulate in reverse order first, reverse in the end
[{axis_name, axis_size} | canonical_axes]
end
end
Enum.reverse(canonical_axes_reversed)
end
defp devectorize_with_axes(tensor) do
{devectorize(tensor), tensor.vectorized_axes}
end
defp apply_vectorized(tensor, fun) when is_tensor(tensor) do
%T{vectorized_axes: vectorized_axes} = tensor = to_tensor(tensor)
fun =
if is_function(fun, 2) do
&fun.(&1, length(vectorized_axes))
else
fun
end
tensor
|> devectorize()
|> fun.()
|> case do
{t1, t2} -> {vectorize(t1, vectorized_axes), vectorize(t2, vectorized_axes)}
t -> vectorize(t, vectorized_axes)
end
end
defp apply_vectorized([left, right], fun) do
left = to_tensor(left)
right = to_tensor(right)
case do_reshape_vectors([left, right], true) do
{_, [], 0} ->
fun.(left, right)
{[devec_left, devec_right], canonical_vectorized_axes, _offset} ->
devec_left
|> fun.(devec_right)
|> vectorize(canonical_vectorized_axes)
end
end
## Element-wise binary ops
defp non_complex_element_wise_bin_op(left, right, op, fun) do
type = binary_type(left, right) |> fun.()
Nx.Shared.raise_complex_not_supported(type, op, 2)
element_wise_bin_op(left, right, op, fun)
end
defp element_wise_bin_op(left, right, op, fun) do
type = binary_type(left, right) |> fun.()
apply_vectorized([left, right], &devectorized_element_wise_bin_op(type, &1, &2, op))
end
defp devectorized_element_wise_bin_op(type, %T{} = left, %T{} = right, op) do
%T{shape: left_shape, names: left_names} = left
%T{shape: right_shape, names: right_names} = right
{shape, names} = Nx.Shape.binary_broadcast(left_shape, left_names, right_shape, right_names)
apply(impl!(left, right), op, [%{left | type: type, shape: shape, names: names}, left, right])
end
defp non_complex_element_wise_pred_op(left, right, op) do
Nx.Shared.raise_complex_not_supported(type(left), op, 2)
Nx.Shared.raise_complex_not_supported(type(right), op, 2)
element_wise_pred_op(left, right, op)
end
defp element_wise_pred_op(left, right, op) do
apply_vectorized([left, right], &devectorized_element_wise_pred_op(&1, &2, op))
end
defp devectorized_element_wise_pred_op(
%T{shape: left_shape, names: left_names} = left,
%T{shape: right_shape, names: right_names} = right,
op
) do
{shape, names} = Nx.Shape.binary_broadcast(left_shape, left_names, right_shape, right_names)
out = %{left | type: {:u, 8}, shape: shape, names: names}
apply(impl!(left, right), op, [out, left, right])
end
@doc """
Element-wise addition of two tensors.
If a number is given, it is converted to a tensor.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible.
If you're using `Nx.Defn.defn/2`, you can use the `+` operator
in place of this function: `left + right`.
## Examples
### Adding scalars
iex> Nx.add(1, 2)
#Nx.Tensor<
s64
3
>
iex> Nx.add(1, 2.2)
#Nx.Tensor<
f32
3.200000047683716
>
### Adding a scalar to a tensor
iex> Nx.add(Nx.tensor([1, 2, 3], names: [:data]), 1)
#Nx.Tensor<
s64[data: 3]
[2, 3, 4]
>
iex> Nx.add(1, Nx.tensor([1, 2, 3], names: [:data]))
#Nx.Tensor<
s64[data: 3]
[2, 3, 4]
>
Given a float scalar converts the tensor to a float:
iex> Nx.add(Nx.tensor([1, 2, 3], names: [:data]), 1.0)
#Nx.Tensor<
f32[data: 3]
[2.0, 3.0, 4.0]
>
iex> Nx.add(Nx.tensor([1.0, 2.0, 3.0], names: [:data]), 1)
#Nx.Tensor<
f32[data: 3]
[2.0, 3.0, 4.0]
>
iex> Nx.add(Nx.tensor([1.0, 2.0, 3.0], type: :f32, names: [:data]), 1)
#Nx.Tensor<
f32[data: 3]
[2.0, 3.0, 4.0]
>
Unsigned tensors become signed and double their size if a
negative number is given:
iex> Nx.add(Nx.tensor([0, 1, 2], type: :u8, names: [:data]), -1)
#Nx.Tensor<
s16[data: 3]
[-1, 0, 1]
>
### Adding tensors of the same shape
iex> left = Nx.tensor([[1, 2], [3, 4]], names: [:x, :y])
iex> right = Nx.tensor([[10, 20], [30, 40]], names: [nil, :y])
iex> Nx.add(left, right)
#Nx.Tensor<
s64[x: 2][y: 2]
[
[11, 22],
[33, 44]
]
>
### Adding tensors with broadcasting
iex> left = Nx.tensor([[1], [2]], names: [nil, :y])
iex> right = Nx.tensor([[10, 20]], names: [:x, nil])
iex> Nx.add(left, right)
#Nx.Tensor<
s64[x: 2][y: 2]
[
[11, 21],
[12, 22]
]
>
iex> left = Nx.tensor([[10, 20]], names: [:x, nil])
iex> right = Nx.tensor([[1], [2]], names: [nil, :y])
iex> Nx.add(left, right)
#Nx.Tensor<
s64[x: 2][y: 2]
[
[11, 21],
[12, 22]
]
>
iex> left = Nx.tensor([[1], [2]], names: [:x, nil])
iex> right = Nx.tensor([[10, 20], [30, 40]])
iex> Nx.add(left, right)
#Nx.Tensor<
s64[x: 2][2]
[
[11, 21],
[32, 42]
]
>
iex> left = Nx.tensor([[1, 2]])
iex> right = Nx.tensor([[10, 20], [30, 40]])
iex> Nx.add(left, right)
#Nx.Tensor<
s64[2][2]
[
[11, 22],
[31, 42]
]
>
"""
@doc type: :element
def add(left, right), do: element_wise_bin_op(left, right, :add, & &1)
@doc """
Element-wise subtraction of two tensors.
If a number is given, it is converted to a tensor.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible.
If you're using `Nx.Defn.defn/2`, you can use the `-` operator
in place of this function: `left - right`.
## Examples
### Subtracting scalars
iex> Nx.subtract(1, 2)
#Nx.Tensor<
s64
-1
>
### Subtracting tensors and scalars
iex> Nx.subtract(Nx.tensor([1, 2, 3], names: [:data]), 1)
#Nx.Tensor<
s64[data: 3]
[0, 1, 2]
>
iex> Nx.subtract(1, Nx.tensor([1.0, 2.0, 3.0], names: [:data]))
#Nx.Tensor<
f32[data: 3]
[0.0, -1.0, -2.0]
>
### Subtracting tensors
iex> left = Nx.tensor([[1], [2]], names: [:x, :y])
iex> right = Nx.tensor([[10, 20]], names: [:x, :y])
iex> Nx.subtract(left, right)
#Nx.Tensor<
s64[x: 2][y: 2]
[
[-9, -19],
[-8, -18]
]
>
iex> left = Nx.tensor([[1], [2]], type: :s8, names: [:x, nil])
iex> right = Nx.tensor([[10, 20]], type: :s8, names: [nil, :y])
iex> Nx.subtract(left, right)
#Nx.Tensor<
s8[x: 2][y: 2]
[
[-9, -19],
[-8, -18]
]
>
iex> left = Nx.tensor([[1], [2]], type: :f32, names: [nil, :y])
iex> right = Nx.tensor([[10, 20]], type: :f32, names: [:x, nil])
iex> Nx.subtract(left, right)
#Nx.Tensor<
f32[x: 2][y: 2]
[
[-9.0, -19.0],
[-8.0, -18.0]
]
>
"""
@doc type: :element
def subtract(left, right), do: element_wise_bin_op(left, right, :subtract, & &1)
@doc """
Element-wise multiplication of two tensors.
If a number is given, it is converted to a tensor.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible.
If you're using `Nx.Defn.defn/2`, you can use the `*` operator
operator in place of this function as `left * right`.
## Examples
### Multiplying scalars
iex> Nx.multiply(1, 2)
#Nx.Tensor<
s64
2
>
### Multiplying tensors and scalars
iex> Nx.multiply(Nx.tensor([1, 2, 3], names: [:data]), 1)
#Nx.Tensor<
s64[data: 3]
[1, 2, 3]
>
iex> Nx.multiply(1, Nx.tensor([1.0, 2.0, 3.0], names: [:data]))
#Nx.Tensor<
f32[data: 3]
[1.0, 2.0, 3.0]
>
### Multiplying tensors
iex> left = Nx.tensor([[1], [2]], names: [:x, :y])
iex> right = Nx.tensor([[10, 20]], names: [:x, :y])
iex> Nx.multiply(left, right)
#Nx.Tensor<
s64[x: 2][y: 2]
[
[10, 20],
[20, 40]
]
>
iex> left = Nx.tensor([[1], [2]], type: :s8, names: [:x, nil])
iex> right = Nx.tensor([[10, 20]], type: :s8, names: [nil, :y])
iex> Nx.multiply(left, right)
#Nx.Tensor<
s8[x: 2][y: 2]
[
[10, 20],
[20, 40]
]
>
iex> left = Nx.tensor([[1], [2]], type: :f32, names: [nil, :y])
iex> right = Nx.tensor([[10, 20]], type: :f32, names: [:x, nil])
iex> Nx.multiply(left, right)
#Nx.Tensor<
f32[x: 2][y: 2]
[
[10.0, 20.0],
[20.0, 40.0]
]
>
"""
@doc type: :element
def multiply(left, right), do: element_wise_bin_op(left, right, :multiply, & &1)
@doc """
Element-wise power of two tensors.
If a number is given, it is converted to a tensor.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible.
If both tensors are integers and the exponent is
negative, it will raise, but it may trigger undefined
behaviour on some compilers.
## Examples
### Power of scalars
iex> Nx.pow(2, 4)
#Nx.Tensor<
s64
16
>
### Power of tensors and scalars
iex> Nx.pow(Nx.tensor([1, 2, 3], names: [:data]), 2)
#Nx.Tensor<
s64[data: 3]
[1, 4, 9]
>
iex> Nx.pow(2, Nx.tensor([1.0, 2.0, 3.0], names: [:data]))
#Nx.Tensor<
f32[data: 3]
[2.0, 4.0, 8.0]
>
### Power of tensors
iex> Nx.pow(Nx.tensor([[2], [3]], names: [:x, nil]), Nx.tensor([[4, 5]], names: [nil, :y]))
#Nx.Tensor<
s64[x: 2][y: 2]
[
[16, 32],
[81, 243]
]
>
"""
@doc type: :element
def pow(left, right), do: element_wise_bin_op(left, right, :pow, & &1)
@deprecated "Use pow/2 instead"
@doc false
def power(left, right), do: pow(left, right)
@doc """
Element-wise remainder of two tensors.
If a number is given, it is converted to a tensor.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible.
If you're using `Nx.Defn.defn/2`, you can use the `rem/2` function
in place of this function: `rem(left, right)`.
## Examples
### Remainder of scalars
iex> Nx.remainder(1, 2)
#Nx.Tensor<
s64
1
>
### Remainder of tensors and scalars
iex> Nx.remainder(Nx.tensor([1, 2, 3], names: [:data]), 2)
#Nx.Tensor<
s64[data: 3]
[1, 0, 1]
>
iex> Nx.remainder(2, Nx.tensor([1.0, 2.0, 3.0], names: [:data]))
#Nx.Tensor<
f32[data: 3]
[0.0, 0.0, 2.0]
>
### Remainder of tensors
iex> left = Nx.tensor([[10], [20]], names: [:x, :y])
iex> right = Nx.tensor([[3, 4]], names: [nil, :y])
iex> Nx.remainder(left, right)
#Nx.Tensor<
s64[x: 2][y: 2]
[
[1, 2],
[2, 0]
]
>
### Remainder involving negative values
If given a negative value as the right operand, the operation
will return the negative image of the remainder.
For the example below, note that in modulo-10, adding 20 shouldn't
change the result, but in this case it does because the sign changes.
iex> left = Nx.tensor(-11, type: :s8)
iex> right = Nx.tensor(10, type: :u8)
iex> Nx.remainder(left, right)
#Nx.Tensor<
s16
-1
>
iex> Nx.remainder(Nx.add(left, Nx.tensor(20, type: :s8)), right)
#Nx.Tensor<
s16
9
>
iex> positive_left = Nx.tensor(9, type: :u8)
iex> Nx.remainder(positive_left, right)
#Nx.Tensor<
u8
9
>
iex> Nx.remainder(Nx.add(positive_left, Nx.tensor(20, type: :u8)), right)
#Nx.Tensor<
u8
9
>
"""
@doc type: :element
def remainder(left, right), do: non_complex_element_wise_bin_op(left, right, :remainder, & &1)
@doc """
Element-wise division of two tensors.
If a number is given, it is converted to a tensor.
It always returns a float tensor. If any of the input
tensors are not float, they are converted to f32.
Division by zero raises, but it may trigger undefined
behaviour on some compilers.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible.
If you're using `Nx.Defn.defn/2`, you can use the `/` operator
in place of this function: `left / right`.
## Examples
### Dividing scalars
iex> Nx.divide(1, 2)
#Nx.Tensor<
f32
0.5
>
### Dividing tensors and scalars
iex> Nx.divide(Nx.tensor([1, 2, 3], names: [:data]), 1)
#Nx.Tensor<
f32[data: 3]
[1.0, 2.0, 3.0]
>
iex> Nx.divide(1, Nx.tensor([1.0, 2.0, 3.0], names: [:data]))
#Nx.Tensor<
f32[data: 3]
[1.0, 0.5, 0.3333333432674408]
>
### Dividing tensors
iex> left = Nx.tensor([[1], [2]], names: [:x, nil])
iex> right = Nx.tensor([[10, 20]], names: [nil, :y])
iex> Nx.divide(left, right)
#Nx.Tensor<
f32[x: 2][y: 2]
[
[0.10000000149011612, 0.05000000074505806],
[0.20000000298023224, 0.10000000149011612]
]
>
iex> left = Nx.tensor([[1], [2]], type: :s8)
iex> right = Nx.tensor([[10, 20]], type: :s8, names: [:x, :y])
iex> Nx.divide(left, right)
#Nx.Tensor<
f32[x: 2][y: 2]
[
[0.10000000149011612, 0.05000000074505806],
[0.20000000298023224, 0.10000000149011612]
]
>
iex> left = Nx.tensor([[1], [2]], type: :f32, names: [:x, nil])
iex> right = Nx.tensor([[10, 20]], type: :f32, names: [nil, :y])
iex> Nx.divide(left, right)
#Nx.Tensor<
f32[x: 2][y: 2]
[
[0.10000000149011612, 0.05000000074505806],
[0.20000000298023224, 0.10000000149011612]
]
>
"""
@doc type: :element
def divide(left, right), do: element_wise_bin_op(left, right, :divide, &Nx.Type.to_floating/1)
defp assert_quotient_type!(type) do
if Nx.Type.integer?(type) do
type
else
raise ArgumentError,
"quotient expects integer tensors as inputs and outputs an integer tensor, " <>
"got: #{inspect(type)}"
end
end
@doc """
Element-wise integer division of two tensors.
If a number is given, it is converted to a tensor.
It always returns an integer tensor. Input tensors and
numbers must be integer types. Division by zero raises,
but it may trigger undefined behaviour on some compilers.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible.
## Caveat for `grad`
The `grad` operation is not supported for `quotient/2`.
Since integer division is, by definition, a closed operation
for the set of integers and grad involves floating points,
`grad` is undefined.
If you need to support gradients, you might consider using
floor division, but beware of precision errors caused by
floating points:
a |> Nx.divide(b) |> Nx.floor()
## Examples
### Integer dividing scalars
iex> Nx.quotient(11, 2)
#Nx.Tensor<
s64
5
>
### Integer dividing tensors and scalars
iex> Nx.quotient(Nx.tensor([2, 4, 5], names: [:data]), 2)
#Nx.Tensor<
s64[data: 3]
[1, 2, 2]
>
iex> Nx.quotient(10, Nx.tensor([1, 2, 3], names: [:data]))
#Nx.Tensor<
s64[data: 3]
[10, 5, 3]
>
### Dividing tensors
iex> left = Nx.tensor([[10, 20]], names: [nil, :y])
iex> right = Nx.tensor([[1], [2]], names: [:x, nil])
iex> Nx.quotient(left, right)
#Nx.Tensor<
s64[x: 2][y: 2]
[
[10, 20],
[5, 10]
]
>
iex> left = Nx.tensor([[10, 20]], type: :s8, names: [:x, :y])
iex> right = Nx.tensor([[1], [2]], type: :s8)
iex> Nx.quotient(left, right)
#Nx.Tensor<
s8[x: 2][y: 2]
[
[10, 20],
[5, 10]
]
>
iex> left = Nx.tensor([[10, 20]], type: :u8, names: [:x, :y])
iex> right = Nx.tensor([[1], [2]], type: :u32)
iex> Nx.quotient(left, right)
#Nx.Tensor<
u32[x: 2][y: 2]
[
[10, 20],
[5, 10]
]
>
"""
@doc type: :element
def quotient(left, right),
do: element_wise_bin_op(left, right, :quotient, &assert_quotient_type!/1)
@doc """
Element-wise arc tangent of two tensors.
If a number is given, it is converted to a tensor.
It always returns a float tensor. If any of the input
tensors are not float, they are converted to f32.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible.
## Examples
### Arc tangent between scalars
iex> Nx.atan2(1, 2)
#Nx.Tensor<
f32
0.46364760398864746
>
### Arc tangent between tensors and scalars
iex> Nx.atan2(Nx.tensor([1, 2, 3], names: [:data]), 1)
#Nx.Tensor<
f32[data: 3]
[0.7853981852531433, 1.1071487665176392, 1.249045729637146]
>
iex> Nx.atan2(1, Nx.tensor([1.0, 2.0, 3.0], names: [:data]))
#Nx.Tensor<
f32[data: 3]
[0.7853981852531433, 0.46364760398864746, 0.32175055146217346]
>
### Arc tangent between tensors
iex> neg_and_pos_zero_columns = Nx.tensor([[-0.0], [0.0]], type: :f64)
iex> neg_and_pos_zero_rows = Nx.tensor([-0.0, 0.0], type: :f64)
iex> Nx.atan2(neg_and_pos_zero_columns, neg_and_pos_zero_rows)
#Nx.Tensor<
f64[2][2]
[
[-3.141592653589793, -0.0],
[3.141592653589793, 0.0]
]
>
"""
@doc type: :element
def atan2(left, right), do: element_wise_bin_op(left, right, :atan2, &Nx.Type.to_floating/1)
@doc """
Element-wise maximum of two tensors.
If a number is given, it is converted to a tensor.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible.
If you're using `Nx.Defn.defn/2`, you can use the `max/2` function
in place of this function: `max(left, right)`.
## Examples
### Max between scalars
iex> Nx.max(1, 2)
#Nx.Tensor<
s64
2
>
### Max between tensors and scalars
iex> Nx.max(Nx.tensor([1, 2, 3], names: [:data]), 1)
#Nx.Tensor<
s64[data: 3]
[1, 2, 3]
>
iex> Nx.max(1, Nx.tensor([1.0, 2.0, 3.0], names: [:data]))
#Nx.Tensor<
f32[data: 3]
[1.0, 2.0, 3.0]
>
### Max between tensors
iex> left = Nx.tensor([[1], [2]], names: [:x, :y])
iex> right = Nx.tensor([[10, 20]])
iex> Nx.max(left, right)
#Nx.Tensor<
s64[x: 2][y: 2]
[
[10, 20],
[10, 20]
]
>
iex> left = Nx.tensor([[1], [2]], type: :s8, names: [:x, nil])
iex> right = Nx.tensor([[10, 20]], type: :s8)
iex> Nx.max(left, right)
#Nx.Tensor<
s8[x: 2][2]
[
[10, 20],
[10, 20]
]
>
iex> left = Nx.tensor([[1], [2]], type: :f32, names: [:x, nil])
iex> right = Nx.tensor([[10, 20]], type: :f32, names: [nil, :y])
iex> Nx.max(left, right)
#Nx.Tensor<
f32[x: 2][y: 2]
[
[10.0, 20.0],
[10.0, 20.0]
]
>
"""
@doc type: :element
def max(left, right), do: non_complex_element_wise_bin_op(left, right, :max, & &1)
@doc """
Element-wise minimum of two tensors.
If a number is given, it is converted to a tensor.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible.
If you're using `Nx.Defn.defn/2`, you can use the `min/2` function
in place of this function: `min(left, right)`.
## Examples
### Min between scalars
iex> Nx.min(1, 2)
#Nx.Tensor<
s64
1
>
### Min between tensors and scalars
iex> Nx.min(Nx.tensor([1, 2, 3], names: [:data]), 1)
#Nx.Tensor<
s64[data: 3]
[1, 1, 1]
>
iex> Nx.min(1, Nx.tensor([1.0, 2.0, 3.0], names: [:data]))
#Nx.Tensor<
f32[data: 3]
[1.0, 1.0, 1.0]
>
### Min between tensors
iex> left = Nx.tensor([[1], [2]], names: [:x, nil])
iex> right = Nx.tensor([[10, 20]])
iex> Nx.min(left, right)
#Nx.Tensor<
s64[x: 2][2]
[
[1, 1],
[2, 2]
]
>
iex> left = Nx.tensor([[1], [2]], type: :s8, names: [:x, :y])
iex> right = Nx.tensor([[10, 20]], type: :s8)
iex> Nx.min(left, right)
#Nx.Tensor<
s8[x: 2][y: 2]
[
[1, 1],
[2, 2]
]
>
iex> left = Nx.tensor([[1], [2]], type: :f32, names: [:x, nil])
iex> right = Nx.tensor([[10, 20]], type: :f32, names: [nil, :y])
iex> Nx.min(left, right)
#Nx.Tensor<
f32[x: 2][y: 2]
[
[1.0, 1.0],
[2.0, 2.0]
]
>
"""
@doc type: :element
def min(left, right), do: non_complex_element_wise_bin_op(left, right, :min, & &1)
## Bitwise ops
defp assert_bitwise_type!(type) do
if Nx.Type.integer?(type) do
type
else
raise ArgumentError,
"bitwise operators expect integer tensors as inputs and outputs an integer tensor, " <>
"got: #{inspect(type)}"
end
end
@doc """
Element-wise bitwise AND of two tensors.
Only integer tensors are supported. If a float or
complex tensor is given, an error is raised.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible.
If you're using `Nx.Defn.defn/2`, you can use the `&&&` operator
in place of this function: `left &&& right`.
## Examples
### bitwise and between scalars
iex> Nx.bitwise_and(1, 0)
#Nx.Tensor<
s64
0
>
### bitwise and between tensors and scalars
iex> Nx.bitwise_and(Nx.tensor([0, 1, 2], names: [:data]), 1)
#Nx.Tensor<
s64[data: 3]
[0, 1, 0]
>
iex> Nx.bitwise_and(Nx.tensor([0, -1, -2], names: [:data]), -1)
#Nx.Tensor<
s64[data: 3]
[0, -1, -2]
>
### bitwise and between tensors
iex> Nx.bitwise_and(Nx.tensor([0, 0, 1, 1], names: [:data]), Nx.tensor([0, 1, 0, 1]))
#Nx.Tensor<
s64[data: 4]
[0, 0, 0, 1]
>
## Error cases
iex> Nx.bitwise_and(Nx.tensor([0, 0, 1, 1]), 1.0)
** (ArgumentError) bitwise operators expect integer tensors as inputs and outputs an integer tensor, got: {:f, 32}
"""
@doc type: :element
def bitwise_and(left, right),
do: element_wise_bin_op(left, right, :bitwise_and, &assert_bitwise_type!/1)
@doc """
Element-wise bitwise OR of two tensors.
Only integer tensors are supported. If a float or
complex tensor is given, an error is raised.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible.
If you're using `Nx.Defn.defn/2`, you can use the `|||` operator
in place of this function: `left ||| right`.
## Examples
### bitwise or between scalars
iex> Nx.bitwise_or(1, 0)
#Nx.Tensor<
s64
1
>
### bitwise or between tensors and scalars
iex> Nx.bitwise_or(Nx.tensor([0, 1, 2], names: [:data]), 1)
#Nx.Tensor<
s64[data: 3]
[1, 1, 3]
>
iex> Nx.bitwise_or(Nx.tensor([0, -1, -2], names: [:data]), -1)
#Nx.Tensor<
s64[data: 3]
[-1, -1, -1]
>
### bitwise or between tensors
iex> Nx.bitwise_or(Nx.tensor([0, 0, 1, 1], names: [:data]), Nx.tensor([0, 1, 0, 1], names: [:data]))
#Nx.Tensor<
s64[data: 4]
[0, 1, 1, 1]
>
## Error cases
iex> Nx.bitwise_or(Nx.tensor([0, 0, 1, 1]), 1.0)
** (ArgumentError) bitwise operators expect integer tensors as inputs and outputs an integer tensor, got: {:f, 32}
"""
@doc type: :element
def bitwise_or(left, right),
do: element_wise_bin_op(left, right, :bitwise_or, &assert_bitwise_type!/1)
@doc """
Element-wise bitwise XOR of two tensors.
Only integer tensors are supported. If a float or complex
tensor is given, an error is raised.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible.
## Examples
### Bitwise xor between scalars
iex> Nx.bitwise_xor(1, 0)
#Nx.Tensor<
s64
1
>
### Bitwise xor and between tensors and scalars
iex> Nx.bitwise_xor(Nx.tensor([1, 2, 3], names: [:data]), 2)
#Nx.Tensor<
s64[data: 3]
[3, 0, 1]
>
iex> Nx.bitwise_xor(Nx.tensor([-1, -2, -3], names: [:data]), 2)
#Nx.Tensor<
s64[data: 3]
[-3, -4, -1]
>
### Bitwise xor between tensors
iex> Nx.bitwise_xor(Nx.tensor([0, 0, 1, 1]), Nx.tensor([0, 1, 0, 1], names: [:data]))
#Nx.Tensor<
s64[data: 4]
[0, 1, 1, 0]
>
## Error cases
iex> Nx.bitwise_xor(Nx.tensor([0, 0, 1, 1]), 1.0)
** (ArgumentError) bitwise operators expect integer tensors as inputs and outputs an integer tensor, got: {:f, 32}
"""
@doc type: :element
def bitwise_xor(left, right),
do: element_wise_bin_op(left, right, :bitwise_xor, &assert_bitwise_type!/1)
@doc """
Element-wise left shift of two tensors.
Only integer tensors are supported. If a float or complex
tensor is given, an error is raised. If the right side
is negative, it will raise, but it may trigger undefined
behaviour on some compilers.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible. If the number of
shifts are negative, Nx's default backend will raise,
but it may trigger undefined behaviour in other backends.
If you're using `Nx.Defn.defn/2`, you can use the `<<<` operator
in place of this function: `left <<< right`.
## Examples
### Left shift between scalars
iex> Nx.left_shift(1, 0)
#Nx.Tensor<
s64
1
>
### Left shift between tensors and scalars
iex> Nx.left_shift(Nx.tensor([1, 2, 3], names: [:data]), 2)
#Nx.Tensor<
s64[data: 3]
[4, 8, 12]
>
### Left shift between tensors
iex> left = Nx.tensor([1, 1, -1, -1], names: [:data])
iex> right = Nx.tensor([1, 2, 3, 4], names: [:data])
iex> Nx.left_shift(left, right)
#Nx.Tensor<
s64[data: 4]
[2, 4, -8, -16]
>
## Error cases
iex> Nx.left_shift(Nx.tensor([0, 0, 1, 1]), 1.0)
** (ArgumentError) bitwise operators expect integer tensors as inputs and outputs an integer tensor, got: {:f, 32}
"""
@doc type: :element
def left_shift(left, right),
do: element_wise_bin_op(left, right, :left_shift, &assert_bitwise_type!/1)
@doc """
Element-wise right shift of two tensors.
Only integer tensors are supported. If a float or complex
tensor is given, an error is raised. If the right side
is negative, it will raise, but it may trigger undefined
behaviour on some compilers.
It performs an arithmetic shift if the tensor is made of
signed integers, it performs a logical shift otherwise.
In other words, it preserves the sign for signed integers.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible. If the number of
shifts are negative, Nx's default backend will raise,
but it may trigger undefined behaviour in other backends.
If you're using `Nx.Defn.defn/2`, you can use the `>>>` operator
in place of this function: `left >>> right`.
## Examples
### Right shift between scalars
iex> Nx.right_shift(1, 0)
#Nx.Tensor<
s64
1
>
### Right shift between tensors and scalars
iex> Nx.right_shift(Nx.tensor([2, 4, 8], names: [:data]), 2)
#Nx.Tensor<
s64[data: 3]
[0, 1, 2]
>
### Right shift between tensors
iex> left = Nx.tensor([16, 32, -64, -128], names: [:data])
iex> right = Nx.tensor([1, 2, 3, 4])
iex> Nx.right_shift(left, right)
#Nx.Tensor<
s64[data: 4]
[8, 8, -8, -8]
>
## Error cases
iex> Nx.right_shift(Nx.tensor([0, 0, 1, 1]), 1.0)
** (ArgumentError) bitwise operators expect integer tensors as inputs and outputs an integer tensor, got: {:f, 32}
"""
@doc type: :element
def right_shift(left, right),
do: element_wise_bin_op(left, right, :right_shift, &assert_bitwise_type!/1)
@doc """
Element-wise equality comparison of two tensors.
If a number is given, it is converted to a tensor.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible.
If you're using `Nx.Defn.defn/2`, you can use the `==` operator
in place of this function: `left == right`.
## Examples
### Comparison of scalars
iex> Nx.equal(1, 2)
#Nx.Tensor<
u8
0
>
### Comparison of tensors and scalars
iex> Nx.equal(1, Nx.tensor([1, 2, 3], names: [:data]))
#Nx.Tensor<
u8[data: 3]
[1, 0, 0]
>
### Comparison of tensors
iex> left = Nx.tensor([1, 2, 3], names: [:data])
iex> right = Nx.tensor([1, 2, 5])
iex> Nx.equal(left, right)
#Nx.Tensor<
u8[data: 3]
[1, 1, 0]
>
iex> left = Nx.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]], names: [:x, nil])
iex> right = Nx.tensor([1, 2, 3])
iex> Nx.equal(left, right)
#Nx.Tensor<
u8[x: 2][3]
[
[1, 1, 1],
[0, 0, 0]
]
>
"""
@doc type: :element
def equal(left, right), do: element_wise_pred_op(left, right, :equal)
@doc """
Element-wise logical and of two tensors.
Zero is considered false, any other number is considered
true.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible.
If you're using `Nx.Defn.defn/2`, you can use the `and` operator
in place of this function: `left and right`.
## Examples
iex> Nx.logical_and(1, Nx.tensor([-1, 0, 1], names: [:data]))
#Nx.Tensor<
u8[data: 3]
[1, 0, 1]
>
iex> left = Nx.tensor([-1, 0, 1], names: [:data])
iex> right = Nx.tensor([[-1], [0], [1]])
iex> Nx.logical_and(left, right)
#Nx.Tensor<
u8[3][data: 3]
[
[1, 0, 1],
[0, 0, 0],
[1, 0, 1]
]
>
iex> left = Nx.tensor([-1.0, 0.0, 1.0], names: [:data])
iex> right = Nx.tensor([[-1], [0], [1]])
iex> Nx.logical_and(left, right)
#Nx.Tensor<
u8[3][data: 3]
[
[1, 0, 1],
[0, 0, 0],
[1, 0, 1]
]
>
"""
@doc type: :element
def logical_and(left, right), do: element_wise_pred_op(left, right, :logical_and)
@doc """
Element-wise logical or of two tensors.
Zero is considered false, any other number is considered
true.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible.
If you're using `Nx.Defn.defn/2`, you can use the `or` operator
in place of this function: `left or right`.
## Examples
iex> Nx.logical_or(0, Nx.tensor([-1, 0, 1], names: [:data]))
#Nx.Tensor<
u8[data: 3]
[1, 0, 1]
>
iex> left = Nx.tensor([-1, 0, 1], names: [:data])
iex> right = Nx.tensor([[-1], [0], [1]])
iex> Nx.logical_or(left, right)
#Nx.Tensor<
u8[3][data: 3]
[
[1, 1, 1],
[1, 0, 1],
[1, 1, 1]
]
>
iex> left = Nx.tensor([-1.0, 0.0, 1.0], names: [:data])
iex> right = Nx.tensor([[-1], [0], [1]])
iex> Nx.logical_or(left, right)
#Nx.Tensor<
u8[3][data: 3]
[
[1, 1, 1],
[1, 0, 1],
[1, 1, 1]
]
>
"""
@doc type: :element
def logical_or(left, right), do: element_wise_pred_op(left, right, :logical_or)
@doc """
Element-wise logical xor of two tensors.
Zero is considered false, any other number is considered
true.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible.
## Examples
iex> Nx.logical_xor(0, Nx.tensor([-1, 0, 1], names: [:data]))
#Nx.Tensor<
u8[data: 3]
[1, 0, 1]
>
iex> left = Nx.tensor([-1, 0, 1], names: [:data])
iex> right = Nx.tensor([[-1], [0], [1]])
iex> Nx.logical_xor(left, right)
#Nx.Tensor<
u8[3][data: 3]
[
[0, 1, 0],
[1, 0, 1],
[0, 1, 0]
]
>
iex> left = Nx.tensor([-1.0, 0.0, 1.0], names: [:data])
iex> right = Nx.tensor([[-1], [0], [1]])
iex> Nx.logical_xor(left, right)
#Nx.Tensor<
u8[3][data: 3]
[
[0, 1, 0],
[1, 0, 1],
[0, 1, 0]
]
>
"""
@doc type: :element
def logical_xor(left, right), do: element_wise_pred_op(left, right, :logical_xor)
@doc """
Element-wise logical not a tensor.
Zero is considered false, any other number is considered
true.
If you're using `Nx.Defn.defn/2`, you can use the `not` operator
in place of this function: `not tensor`.
## Examples
iex> Nx.logical_not(Nx.tensor([-1, 0, 1], names: [:data]))
#Nx.Tensor<
u8[data: 3]
[0, 1, 0]
>
iex> Nx.logical_not(Nx.tensor([-1.0, 0.0, 1.0], names: [:data]))
#Nx.Tensor<
u8[data: 3]
[0, 1, 0]
>
"""
@doc type: :element
def logical_not(tensor) do
apply_vectorized(tensor, fn tensor ->
output = Nx.template(tensor.shape, {:u, 8}, names: tensor.names)
Nx.Shared.optional(:logical_not, [tensor], output, fn tensor ->
element_wise_pred_op(tensor, 0, :equal)
end)
end)
end
@doc """
Element-wise not-equal comparison of two tensors.
If a number is given, it is converted to a tensor.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible.
If you're using `Nx.Defn.defn/2`, you can use the `!=` operator
in place of this function: `left != right`.
## Examples
### Comparison of scalars
iex> Nx.not_equal(1, 2)
#Nx.Tensor<
u8
1
>
### Comparison of tensor and scalar
iex> Nx.not_equal(Nx.tensor([1, 2, 3], names: [:data]), Nx.tensor(1))
#Nx.Tensor<
u8[data: 3]
[0, 1, 1]
>
### Comparison of tensors
iex> left = Nx.tensor([1, 1, 2])
iex> right = Nx.tensor([1, 2, 3], names: [:data])
iex> Nx.not_equal(left, right)
#Nx.Tensor<
u8[data: 3]
[0, 1, 1]
>
iex> left = Nx.tensor([[1, 4, 2], [4, 5, 6]], names: [:x, :y])
iex> right = Nx.tensor([[1, 3, 2], [4, 2, 1]], names: [:x, :y])
iex> Nx.not_equal(left, right)
#Nx.Tensor<
u8[x: 2][y: 3]
[
[0, 1, 0],
[0, 1, 1]
]
>
"""
@doc type: :element
def not_equal(left, right), do: element_wise_pred_op(left, right, :not_equal)
@doc """
Element-wise greater than comparison of two tensors.
If a number is given, it is converted to a tensor.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible.
If you're using `Nx.Defn.defn/2`, you can use the `>` operator
in place of this function: `left > right`.
## Examples
### Comparison of scalars
iex> Nx.greater(1, 2)
#Nx.Tensor<
u8
0
>
### Comparison of tensors and scalars
iex> Nx.greater(1, Nx.tensor([1, 2, 3], names: [:data]))
#Nx.Tensor<
u8[data: 3]
[0, 0, 0]
>
### Comparison of tensors
iex> left = Nx.tensor([1, 2, 3], names: [:data])
iex> right = Nx.tensor([1, 2, 2])
iex> Nx.greater(left, right)
#Nx.Tensor<
u8[data: 3]
[0, 0, 1]
>
iex> left = Nx.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]], names: [:x, :y])
iex> right = Nx.tensor([1, 2, 3])
iex> Nx.greater(left, right)
#Nx.Tensor<
u8[x: 2][y: 3]
[
[0, 0, 0],
[1, 1, 1]
]
>
"""
@doc type: :element
def greater(left, right), do: non_complex_element_wise_pred_op(left, right, :greater)
@doc """
Element-wise less than comparison of two tensors.
If a number is given, it is converted to a tensor.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible.
If you're using `Nx.Defn.defn/2`, you can use the `<` operator
in place of this function: `left < right`.
## Examples
### Comparison of scalars
iex> Nx.less(1, 2)
#Nx.Tensor<
u8
1
>
### Comparison of tensors and scalars
iex> Nx.less(1, Nx.tensor([1, 2, 3], names: [:data]))
#Nx.Tensor<
u8[data: 3]
[0, 1, 1]
>
### Comparison of tensors
iex> Nx.less(Nx.tensor([1, 2, 1]), Nx.tensor([1, 2, 2], names: [:data]))
#Nx.Tensor<
u8[data: 3]
[0, 0, 1]
>
iex> Nx.less(Nx.tensor([[1.0, 2.0, 3.0], [4.0, 2.0, 1.0]], names: [:x, :y]), Nx.tensor([1, 2, 3]))
#Nx.Tensor<
u8[x: 2][y: 3]
[
[0, 0, 0],
[0, 0, 1]
]
>
"""
@doc type: :element
def less(left, right), do: non_complex_element_wise_pred_op(left, right, :less)
@doc """
Element-wise greater than or equal comparison of two tensors.
If a number is given, it is converted to a tensor.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible.
If you're using `Nx.Defn.defn/2`, you can use the `>=` operator
in place of this function: `left >= right`.
## Examples
### Comparison of scalars
iex> Nx.greater_equal(1, 2)
#Nx.Tensor<
u8
0
>
### Comparison of tensors and scalars
iex> Nx.greater_equal(1, Nx.tensor([1, 2, 3], names: [:data]))
#Nx.Tensor<
u8[data: 3]
[1, 0, 0]
>
### Comparison of tensors
iex> left = Nx.tensor([1, 2, 3], names: [:data])
iex> right = Nx.tensor([1, 2, 2])
iex> Nx.greater_equal(left, right)
#Nx.Tensor<
u8[data: 3]
[1, 1, 1]
>
iex> left = Nx.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]], names: [:x, :y])
iex> right = Nx.tensor([1, 2, 3])
iex> Nx.greater_equal(left, right)
#Nx.Tensor<
u8[x: 2][y: 3]
[
[1, 1, 1],
[1, 1, 1]
]
>
"""
@doc type: :element
def greater_equal(left, right),
do: non_complex_element_wise_pred_op(left, right, :greater_equal)
@doc """
Element-wise less than or equal comparison of two tensors.
If a number is given, it is converted to a tensor.
It will broadcast tensors whenever the dimensions do
not match and broadcasting is possible.
If you're using `Nx.Defn.defn/2`, you can use the `<=` operator
in place of this function: `left <= right`.
## Examples
### Comparison of scalars
iex> Nx.less_equal(1, 2)
#Nx.Tensor<
u8
1
>
### Comparison of tensors and scalars
iex> Nx.less_equal(1, Nx.tensor([1, 2, 3], names: [:data]))
#Nx.Tensor<
u8[data: 3]
[1, 1, 1]
>
### Comparison of tensors
iex> left = Nx.tensor([1, 2, 3], names: [:data])
iex> right = Nx.tensor([1, 2, 2])
iex> Nx.less_equal(left, right)
#Nx.Tensor<
u8[data: 3]
[1, 1, 0]
>
iex> left = Nx.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
iex> right = Nx.tensor([1, 2, 3], names: [:y])
iex> Nx.less_equal(left, right)
#Nx.Tensor<
u8[2][y: 3]
[
[1, 1, 1],
[0, 0, 0]
]
>
"""
@doc type: :element
def less_equal(left, right), do: non_complex_element_wise_pred_op(left, right, :less_equal)
@doc """
Constructs a tensor from two tensors, based on a predicate.
The resulting tensor is built by evaluating each element of
`pred` and returning either the corresponding element from
`on_true` or `on_false`.
`pred` must either be `1` or `0` or a tensor of predicates
with a shape that matches the largest shape between `s1` or `s2`.
If the shape of `on_true` or `on_false` do not match the shape of
`pred`, attempts to broadcast both so they match the shape of `pred`.
## Examples
When the first argument is a scalar:
iex> Nx.select(1, Nx.tensor([1, 2, 3], names: [:x]), Nx.tensor([4, 5, 6], names: [:x]))
#Nx.Tensor<
s64[x: 3]
[1, 2, 3]
>
iex> Nx.select(0, Nx.tensor([1, 2, 3], names: [:y]), Nx.tensor([4, 5, 6], names: [:y]))
#Nx.Tensor<
s64[y: 3]
[4, 5, 6]
>
iex> Nx.select(0, Nx.tensor([[1, 2]], names: [:x, :y]), Nx.tensor([[3], [4]], names: [:x, :y]))
#Nx.Tensor<
s64[x: 2][y: 2]
[
[3, 3],
[4, 4]
]
>
When the first argument is a tensor:
iex> Nx.select(Nx.tensor([0, 1, 0], names: [:x]), Nx.tensor([1, 2, 3], names: [:y]), Nx.tensor([4, 5, 6], names: [:z]))
#Nx.Tensor<
s64[x: 3]
[4, 2, 6]
>
iex> x = Nx.tensor([2, 4, 6], names: [:x])
iex> y = Nx.tensor([3, 2, 1])
iex> Nx.select(Nx.greater(x, y), Nx.tensor([2, 4, 6], names: [:i]), Nx.tensor([1, 3, 5], names: [:j]))
#Nx.Tensor<
s64[x: 3]
[1, 4, 6]
>
iex> x = Nx.tensor([2, 4, 6, 8, 10], names: [:x])
iex> y = Nx.tensor([1, 6, 2, 11, 2], names: [:x])
iex> Nx.select(Nx.greater(x, y), Nx.tensor(2), Nx.tensor([1, 3, 5, 7, 9], names: [:x]))
#Nx.Tensor<
s64[x: 5]
[2, 3, 2, 7, 2]
>
If the tensor has other values, any non-zero value is considered true:
iex> Nx.select(Nx.tensor([0, 1, 2], type: :u8), Nx.tensor([0, 0, 0]), Nx.tensor([1, 1, 1]))
#Nx.Tensor<
s64[3]
[1, 0, 0]
>
iex> Nx.select(Nx.tensor([0, 1, 0]), Nx.tensor([1, 1, 1]), Nx.tensor([2.0, 2.0, 2.0]))
#Nx.Tensor<
f32[3]
[2.0, 1.0, 2.0]
>
## Vectorized tensors
Vectorized and non-vectorized tensors can be mixed-and-matched on all three inputs.
iex> pred = Nx.tensor([[0, 1, 0], [1, 1, 0]]) |> Nx.vectorize(:x)
iex> on_true = 1
iex> on_false = Nx.tensor([2, 3]) |> Nx.vectorize(:y)
iex> Nx.select(pred, on_true, on_false)
#Nx.Tensor<
vectorized[x: 2][y: 2]
s64[3]
[
[
[2, 1, 2],
[3, 1, 3]
],
[
[1, 1, 2],
[1, 1, 3]
]
]
>
In the next example, notice that even though the `pred` input
is scalar, because we're dealing with vectorized inputs, some
broadcasting still occurs.
iex> pred = 1
iex> on_true = Nx.tensor([1, 2, 3]) |> Nx.vectorize(:x)
iex> on_false = Nx.tensor([4, 5]) |> Nx.vectorize(:y)
iex> Nx.select(pred, on_true, on_false)
#Nx.Tensor<
vectorized[x: 3][y: 2]
s64
[
[1, 1],
[2, 2],
[3, 3]
]
>
Finally, broadcasting will also occur if more than one input share
the same vectorized axes, but one of them presents size 1
iex> pred = Nx.tensor([1, 0, 0]) |> Nx.vectorize(:x)
iex> on_true = Nx.tensor([[2]]) |> Nx.vectorize(:x) |> Nx.vectorize(:y)
iex> on_false = Nx.tensor([3, 4]) |> Nx.vectorize(:y)
iex> Nx.select(pred, on_true, on_false)
#Nx.Tensor<
vectorized[x: 3][y: 2]
s64
[
[2, 2],
[3, 4],
[3, 4]
]
>
"""
@doc type: :element
def select(pred, on_true, on_false) do
%T{shape: pred_shape} = pred = to_tensor(pred)
[pred, on_true, on_false] = broadcast_vectors([pred, on_true, on_false], align_ranks: true)
%T{vectorized_axes: vectorized_axes} = pred
pred = devectorize(pred)
on_true = devectorize(on_true)
on_false = devectorize(on_false)
output_type = binary_type(on_true, on_false)
{output_shape, output_names} =
if pred_shape == {} do
Nx.Shape.binary_broadcast(on_true.shape, on_true.names, on_false.shape, on_false.names)
else
{pred.shape, pred.names}
end
_ =
Nx.Shape.broadcast!(
on_true.shape,
output_shape,
Nx.Shape.broadcast_axes(on_true.shape, output_shape)
)
_ =
Nx.Shape.broadcast!(
on_false.shape,
output_shape,
Nx.Shape.broadcast_axes(on_false.shape, output_shape)
)
out = %{pred | shape: output_shape, type: output_type, names: output_names}
if vectorized_axes != [] do
pred =
if pred.shape != output_shape do
broadcast(pred, output_shape)
else
pred
end
result = impl!(pred, on_true, on_false).select(out, pred, on_true, on_false)
vectorize(result, vectorized_axes)
else
impl!(pred, on_true, on_false).select(out, pred, on_true, on_false)
end
end
@doc """
Performs a `window_reduce` to select the maximum index in each
window of the input tensor according to and scatters source tensor
to corresponding maximum indices in the output tensor.
Output tensor is initialized as a full tensor with values
`init_value`. If indices overlap, adds overlapping source values.
The shape of the source tensor must match the valid windows in the
input tensor. This means the shape of the source tensor must match
the shape of the input tensor after a `window_reduce` op with padding
`padding` and strides `strides`.
This function is the gradient of `window_max`.
## Examples
iex> t = Nx.tensor([
...> [7, 2, 5, 3, 10, 2],
...> [3, 8, 9, 3, 4, 2],
...> [1, 5, 7, 5, 6, 1],
...> [0, 6, 2, 7, 2, 8]
...> ])
iex> opts = [strides: [2, 3], padding: :valid]
iex> Nx.window_scatter_max(t, Nx.tensor([[2, 6], [3, 1]]), 0, {2, 3}, opts)
#Nx.Tensor<
s64[4][6]
[
[0, 0, 0, 0, 6, 0],
[0, 0, 2, 0, 0, 0],
[0, 0, 3, 0, 0, 0],
[0, 0, 0, 0, 0, 1]
]
>
iex> t = Nx.tensor([
...> [7, 2, 5, 3, 8],
...> [3, 8, 9, 3, 4],
...> [1, 5, 7, 5, 6],
...> [0, 6, 2, 10, 2]
...> ])
iex> opts = [strides: [2, 2], padding: :valid]
iex> Nx.window_scatter_max(t, Nx.tensor([[2, 6], [3, 1]]), 0, {2, 3}, opts)
#Nx.Tensor<
s64[4][5]
[
[0, 0, 0, 0, 0],
[0, 0, 8, 0, 0],
[0, 0, 3, 0, 0],
[0, 0, 0, 1, 0]
]
>
## Vectorized tensors
The source and target tensors can be vectorized, and will be broadcasted
through `broadcast_vectors/1` for the result calculation. `init_value`
must not be vectorized.
iex> t = Nx.tensor([
...> [
...> [7, 2, 5, 3],
...> [3, 8, 9, 3]
...> ],
...> [
...> [1, 5, 7, 5],
...> [0, 6, 2, 8]
...> ]
...> ]) |> Nx.vectorize(:x)
iex> opts = [strides: [1, 2], padding: :valid]
iex> source = Nx.tensor([[[2, 6]], [[3, 1]]]) |> Nx.vectorize(:y)
iex> Nx.window_scatter_max(t, source, 0, {2, 2}, opts)
#Nx.Tensor<
vectorized[x: 2][y: 2]
s64[2][4]
[
[
[
[0, 0, 0, 0],
[0, 2, 6, 0]
],
[
[0, 0, 0, 0],
[0, 3, 1, 0]
]
],
[
[
[0, 0, 0, 0],
[0, 2, 0, 6]
],
[
[0, 0, 0, 0],
[0, 3, 0, 1]
]
]
]
>
"""
@doc type: :window
def window_scatter_max(tensor, source, init_value, window_dimensions, opts \\ []) do
opts = keyword!(opts, padding: :valid, strides: 1)
Nx.Shape.validate!(window_dimensions, :window_dimensions)
[tensor, source] = broadcast_vectors([tensor, source], align_ranks: true)
%T{shape: input_shape, vectorized_axes: vectorized_axes} = tensor
%T{shape: source_shape, type: source_type} = source
%T{type: value_type, vectorized_axes: value_vectorized_axes} =
init_value = to_tensor(init_value)
if value_vectorized_axes != [] do
raise ArgumentError, "the init_value tensor cannot be vectorized"
end
offset = length(vectorized_axes)
padding = opts[:padding]
strides = opts[:strides]
strides =
if is_integer(strides),
do: List.duplicate(strides, rank(input_shape)),
else: strides
dilations = List.duplicate(1, rank(input_shape))
{output_window_shape, padding_config} =
Nx.Shape.pool(input_shape, window_dimensions, strides, padding, dilations)
unless output_window_shape == source_shape do
raise ArgumentError, "source shape must match valid windows in input tensor"
end
output_type = Nx.Type.merge(source_type, value_type)
Nx.Shared.raise_complex_not_supported(output_type, :window_scatter_max, 5)
padding_config = List.duplicate({0, 0}, offset) ++ padding_config
strides = List.duplicate(1, offset) ++ strides
window_dimensions =
if offset != 0 do
List.to_tuple(List.duplicate(1, offset) ++ Tuple.to_list(window_dimensions))
else
window_dimensions
end
tensor = devectorize(tensor)
source = devectorize(source)
result =
impl!(tensor, source).window_scatter_max(
%{tensor | type: output_type},
tensor,
source,
init_value,
window_dimensions,
padding: padding_config,
strides: strides
)
vectorize(result, vectorized_axes)
end
@doc """
Performs a `window_reduce` to select the minimum index in each
window of the input tensor according to and scatters source tensor
to corresponding minimum indices in the output tensor.
Output tensor is initialized as a full tensor with values
`init_value`. If indices overlap, adds overlapping source values.
The shape of the source tensor must match the valid windows in the
input tensor. This means the shape of the source tensor must match
the shape of the input tensor after a `window_reduce` op with padding
`padding` and strides `strides`.
This function is the gradient of `window_min`.
## Examples
iex> t = Nx.tensor([
...> [7, 2, 5, 3, 10, 2],
...> [3, 8, 9, 3, 4, 2],
...> [1, 5, 7, 5, 6, 1],
...> [0, 6, 2, 7, 2, 8]
...> ])
iex> opts = [strides: [2, 3], padding: :valid]
iex> Nx.window_scatter_min(t, Nx.tensor([[2, 6], [3, 1]]), 0, {2, 3}, opts)
#Nx.Tensor<
s64[4][6]
[
[0, 2, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 6],
[0, 0, 0, 0, 0, 1],
[3, 0, 0, 0, 0, 0]
]
>
iex> t = Nx.tensor([
...> [7, 2, 5, 3, 8],
...> [3, 8, 9, 3, 4],
...> [1, 5, 7, 5, 6],
...> [0, 6, 2, 10, 2]
...> ])
iex> opts = [strides: [2, 2], padding: :valid]
iex> Nx.window_scatter_min(t, Nx.tensor([[2, 6], [3, 1]]), 0, {2, 3}, opts)
#Nx.Tensor<
s64[4][5]
[
[0, 2, 0, 0, 0],
[0, 0, 0, 6, 0],
[0, 0, 0, 0, 0],
[3, 0, 0, 0, 1]
]
>
## Vectorized tensors
The source and target tensors can be vectorized, and will be broadcasted
through `broadcast_vectors/1` for the result calculation. `init_value`
must not be vectorized.
iex> t = Nx.tensor([
...> [
...> [7, 2, 5, 1],
...> [3, 8, 9, 3]
...> ],
...> [
...> [1, 5, 7, 5],
...> [0, 6, 2, 8]
...> ]
...> ]) |> Nx.vectorize(:x)
iex> opts = [strides: [1, 2], padding: :valid]
iex> source = Nx.tensor([[[2, 6]], [[3, 1]]]) |> Nx.vectorize(:y)
iex> Nx.window_scatter_min(t, source, 0, {2, 2}, opts)
#Nx.Tensor<
vectorized[x: 2][y: 2]
s64[2][4]
[
[
[
[0, 2, 0, 6],
[0, 0, 0, 0]
],
[
[0, 3, 0, 1],
[0, 0, 0, 0]
]
],
[
[
[0, 0, 0, 0],
[2, 0, 6, 0]
],
[
[0, 0, 0, 0],
[3, 0, 1, 0]
]
]
]
>
"""
@doc type: :window
def window_scatter_min(tensor, source, init_value, window_dimensions, opts \\ []) do
opts = keyword!(opts, padding: :valid, strides: 1)
[tensor, source] = broadcast_vectors([tensor, source])
%T{shape: input_shape, vectorized_axes: vectorized_axes} = tensor
%T{shape: source_shape, type: source_type} = source
%T{type: value_type, vectorized_axes: value_vectorized_axes} =
init_value = to_tensor(init_value)
if value_vectorized_axes != [] do
raise ArgumentError, "the init_value tensor cannot be vectorized"
end
offset = length(vectorized_axes)
padding = opts[:padding]
strides = opts[:strides]
strides =
if is_integer(strides),
do: List.duplicate(strides, rank(input_shape)),
else: strides
dilations = List.duplicate(1, rank(input_shape))
{output_window_shape, padding_config} =
Nx.Shape.pool(input_shape, window_dimensions, strides, padding, dilations)
unless output_window_shape == source_shape do
raise ArgumentError, "source shape must match valid windows in input tensor"
end
output_type = Nx.Type.merge(source_type, value_type)
Nx.Shared.raise_complex_not_supported(output_type, :window_scatter_min, 5)
padding_config = List.duplicate({0, 0}, offset) ++ padding_config
strides = List.duplicate(1, offset) ++ strides
window_dimensions =
if offset != 0 do
List.to_tuple(List.duplicate(1, offset) ++ Tuple.to_list(window_dimensions))
else
window_dimensions
end
tensor = devectorize(tensor)
source = devectorize(source)
result =
impl!(tensor, source).window_scatter_min(
%{tensor | type: output_type},
tensor,
source,
init_value,
window_dimensions,
padding: padding_config,
strides: strides
)
vectorize(result, vectorized_axes)
end
@doc """
Performs an indexed `add` operation on the `target` tensor,
adding the `updates` into the corresponding `indices` positions.
This operation is the grad for `gather/2` and gather-like operations such as
`take/3` and `take_along_axis/3`.
`indices` must be a fully qualified tensor of shape `{n, Nx.rank(target)}`, with `n`
being an arbitrary number of indices, while `updates` must have a compatible `{n}` shape.
See also: `indexed_add/3`, `gather/2`, `take/3`, `take_along_axis/3`
## Examples
iex> t = Nx.iota({1, 2, 3})
#Nx.Tensor<
s64[1][2][3]
[
[
[0, 1, 2],
[3, 4, 5]
]
]
>
iex> indices = Nx.tensor([[0, 0, 0], [0, 1, 1], [0, 0, 0], [0, 0, 2], [0, 1, 2]])
iex> updates = Nx.tensor([1, 3, 1, -2, 5])
iex> Nx.indexed_add(t, indices, updates)
#Nx.Tensor<
s64[1][2][3]
[
[
[2, 1, 0],
[3, 7, 10]
]
]
>
Type promotions should happen automatically, with the resulting type being the combination
of the `target` type and the `updates` type.
iex> Nx.indexed_add(Nx.tensor([1.0]), Nx.tensor([[0], [0]]), Nx.tensor([1, 1]))
#Nx.Tensor<
f32[1]
[3.0]
>
iex> Nx.indexed_add(Nx.tensor([1]), Nx.tensor([[0], [0]]), Nx.tensor([1.0, 1.0]))
#Nx.Tensor<
f32[1]
[3.0]
>
iex> Nx.indexed_add(Nx.tensor([1], type: :s32), Nx.tensor([[0], [0]]), Nx.tensor([1, 1], type: :s64))
#Nx.Tensor<
s64[1]
[3]
>
As a shorthand notation, rank-1 indices can be used for updating a single entry:
iex> Nx.indexed_add(Nx.tensor([[1], [2]]), Nx.tensor([1, 0]), 8)
#Nx.Tensor<
s64[2][1]
[
[1],
[10]
]
>
## Vectorized tensors
All of the inputs can be vectorized. The function will broadcast along the vectorized axes
before calculating the results.
iex> x = Nx.tensor([[0, 10], [10, 20]]) |> Nx.vectorize(:x)
iex> idx = Nx.tensor([[[0], [0]], [[0], [1]], [[1], [1]]]) |> Nx.vectorize(:y)
iex> Nx.indexed_add(x, idx, Nx.tensor([1, 1]))
#Nx.Tensor<
vectorized[x: 2][y: 3]
s64[2]
[
[
[2, 10],
[1, 11],
[0, 12]
],
[
[12, 20],
[11, 21],
[10, 22]
]
]
>
## Error cases
iex> Nx.indexed_add(Nx.tensor([[1], [2]]), Nx.tensor([[[1, 2, 3]]]), Nx.tensor([0]))
** (ArgumentError) indices must be a rank 1 or 2 tensor, got: 3
iex> Nx.indexed_add(Nx.tensor([[1], [2]]), Nx.tensor([[1, 2]]), Nx.tensor([[0]]))
** (ArgumentError) updates must be a rank 1 tensor, got: 2
iex> Nx.indexed_add(Nx.tensor([[1], [2]]), Nx.tensor([[1, 2, 3]]), Nx.tensor([0]))
** (ArgumentError) expected indices to have shape {*, 2}, got: {1, 3}
iex> Nx.indexed_add(Nx.tensor([[1], [2]]), Nx.tensor([[1, 2]]), Nx.tensor([0, 1]))
** (ArgumentError) expected updates tensor to match the first axis of indices tensor with shape {1, 2}, got {2}
"""
@doc type: :indexed
def indexed_add(target, indices, updates) do
indexed_op(target, indices, updates, :indexed_add)
end
@doc """
Puts individual values from `updates` into the given tensor at the corresponding `indices`.
`indices` must be a fully qualified tensor of shape `{n, Nx.rank(target)}`, with `n`
being an arbitrary number of indices, while `updates` must have a compatible `{n}` shape.
In case of repeating indices, the result is non-determinstic, since the operation happens
in parallel when running on devices such as the GPU.
See also: `indexed_add/3`, `put_slice/3`.
## Examples
iex> Nx.indexed_put(Nx.tensor([0, 0, 0]), Nx.tensor([[1], [2]]), Nx.tensor([2, 4]))
#Nx.Tensor<
s64[3]
[0, 2, 4]
>
iex> Nx.indexed_put(Nx.tensor([0, 0, 0]), Nx.tensor([[1], [2], [1]]), Nx.tensor([3, 4, 2]))
#Nx.Tensor<
s64[3]
[0, 2, 4]
>
iex> t = Nx.iota({1, 2, 3})
#Nx.Tensor<
s64[1][2][3]
[
[
[0, 1, 2],
[3, 4, 5]
]
]
>
iex> indices = Nx.tensor([[0, 0, 0], [0, 1, 1], [0, 0, 2]])
iex> updates = Nx.tensor([1, 3, -2])
iex> Nx.indexed_put(t, indices, updates)
#Nx.Tensor<
s64[1][2][3]
[
[
[1, 1, -2],
[3, 3, 5]
]
]
>
Type promotions should happen automatically, with the resulting type being the combination
of the `target` type and the `updates` type.
iex> Nx.indexed_put(Nx.tensor([1.0]), Nx.tensor([[0]]), Nx.tensor([3]))
#Nx.Tensor<
f32[1]
[3.0]
>
iex> Nx.indexed_put(Nx.tensor([1]), Nx.tensor([[0]]), Nx.tensor([3.0]))
#Nx.Tensor<
f32[1]
[3.0]
>
iex> Nx.indexed_put(Nx.tensor([1], type: :s32), Nx.tensor([[0]]), Nx.tensor([3], type: :s64))
#Nx.Tensor<
s64[1]
[3]
>
As a shorthand notation, rank-1 indices can be used for updating a single entry:
iex> Nx.indexed_put(Nx.tensor([[1], [2]]), Nx.tensor([1, 0]), 10)
#Nx.Tensor<
s64[2][1]
[
[1],
[10]
]
>
## Vectorized tensors
All of the inputs can be vectorized. The function will broadcast along the vectorized axes
before calculating the results.
iex> x = Nx.tensor([[0, 10], [10, 20]]) |> Nx.vectorize(:x)
iex> idx = Nx.tensor([[[0], [0]], [[0], [1]], [[1], [1]]]) |> Nx.vectorize(:y)
iex> Nx.indexed_put(x, idx, Nx.tensor([1, 1]))
#Nx.Tensor<
vectorized[x: 2][y: 3]
s64[2]
[
[
[1, 10],
[1, 1],
[0, 1]
],
[
[1, 20],
[1, 1],
[10, 1]
]
]
>
## Error cases
iex> Nx.indexed_put(Nx.tensor([[1], [2]]), Nx.tensor([[[1, 2, 3]]]), Nx.tensor([0]))
** (ArgumentError) indices must be a rank 1 or 2 tensor, got: 3
iex> Nx.indexed_put(Nx.tensor([[1], [2]]), Nx.tensor([[1, 2]]), Nx.tensor([[0]]))
** (ArgumentError) updates must be a rank 1 tensor, got: 2
iex> Nx.indexed_put(Nx.tensor([[1], [2]]), Nx.tensor([[1, 2, 3]]), Nx.tensor([0]))
** (ArgumentError) expected indices to have shape {*, 2}, got: {1, 3}
iex> Nx.indexed_put(Nx.tensor([[1], [2]]), Nx.tensor([[1, 2]]), Nx.tensor([0, 1]))
** (ArgumentError) expected updates tensor to match the first axis of indices tensor with shape {1, 2}, got {2}
"""
@doc type: :indexed
def indexed_put(target, indices, updates) do
indexed_op(target, indices, updates, :indexed_put)
end
defp indexed_op(target, %Nx.Tensor{shape: {_}} = index, update, op) when is_tensor(update) do
update = to_tensor(update)
Nx.Shape.indexed(target, index, update)
indexed_op(target, Nx.new_axis(index, 0), Nx.new_axis(update, 0), op)
end
defp indexed_op(target, indices, updates, op) do
[%T{vectorized_axes: vectorized_axes} = target, indices, updates] =
broadcast_vectors([target, indices, updates])
idx_type = type(indices)
unless Nx.Type.integer?(idx_type) do
raise ArgumentError, "indices must be an integer tensor, got type: #{inspect(idx_type)}"
end
type = binary_type(target, updates)
Nx.Shape.indexed(target, indices, updates)
target = devectorize(target)
indices = devectorize(indices)
updates = devectorize(updates)
{indices, updates} =
if vectorized_axes != [] do
offset = length(vectorized_axes)
iota_shape = put_elem(indices.shape, tuple_size(indices.shape) - 1, 1)
to_concat =
Enum.reduce((offset - 1)..0//-1, [indices], fn axis, idx ->
[Nx.iota(iota_shape, axis: axis) | idx]
end)
n = elem(indices.shape, tuple_size(indices.shape) - 1)
indices =
to_concat
|> concatenate(axis: -1)
|> reshape({:auto, offset + n})
{indices, flatten(updates)}
else
{indices, updates}
end
out = %{target | type: type}
result = apply(impl!(target, indices, updates), op, [out, target, indices, updates])
vectorize(result, vectorized_axes)
end
## Unary ops
@disallow_complex_type_unary_ops [:erf, :erfc, :erf_inv]
for {name, {desc, code, formula}} <- Nx.Shared.unary_math_funs() do
inputs =
if name in [:acos, :asin, :atan, :atanh, :erf_inv] do
[to_float32(0.1), to_float32(0.5), to_float32(0.9)]
else
[1, 2, 3]
end
outputs =
for input <- inputs do
{res, _} = Code.eval_quoted(code, x: input)
to_float32(res)
end
complex_check_block =
if name in @disallow_complex_type_unary_ops do
quote do
Nx.Shared.raise_complex_not_supported(var!(type), unquote(name), 1)
end
end
@doc """
Calculates the #{desc} of each element in the tensor.
It is equivalent to:
#{formula}
## Examples
iex> Nx.#{name}(#{hd(inputs)})
#Nx.Tensor<
f32
#{hd(outputs)}
>
iex> Nx.#{name}(Nx.tensor(#{inspect(inputs)}, names: [:x]))
#Nx.Tensor<
f32[x: 3]
#{inspect(outputs)}
>
"""
@doc type: :element
def unquote(name)(tensor) do
apply_vectorized(tensor, fn tensor ->
type = Nx.Type.to_floating(tensor.type)
unquote(complex_check_block)
impl!(tensor).unquote(name)(%{tensor | type: type}, tensor)
end)
end
end
@doc """
Determines if each element in `tensor` is a `NaN`.
For complex tensors, if either of the components is `NaN`,
the entry is deemed `NaN` as well.
## Examples
iex> Nx.is_nan(Nx.tensor([:nan, 1, 0]))
#Nx.Tensor<
u8[3]
[1, 0, 0]
>
iex> Nx.is_nan(Nx.tensor([:nan, :infinity, Complex.new(0, :nan)]))
#Nx.Tensor<
u8[3]
[1, 0, 1]
>
iex> Nx.is_nan(Nx.tensor([1, 0]))
#Nx.Tensor<
u8[2]
[0, 0]
>
"""
@doc type: :element
def is_nan(tensor) do
apply_vectorized(tensor, fn tensor ->
impl!(tensor).is_nan(%{tensor | type: {:u, 8}}, tensor)
end)
end
@doc """
Determines if each element in `tensor` is `Inf` or `-Inf`.
For complex tensors, if either of the components is infinity,
the entry is deemed infinity as well.
## Examples
iex> Nx.is_infinity(Nx.tensor([:infinity, :nan, :neg_infinity, 1, 0]))
#Nx.Tensor<
u8[5]
[1, 0, 1, 0, 0]
>
iex> Nx.is_infinity(Nx.tensor([:infinity, 1, Complex.new(0, :infinity), :neg_infinity]))
#Nx.Tensor<
u8[4]
[1, 0, 1, 1]
>
iex> Nx.is_infinity(Nx.tensor([1, 0]))
#Nx.Tensor<
u8[2]
[0, 0]
>
"""
@doc type: :element
def is_infinity(tensor) do
apply_vectorized(tensor, fn tensor ->
impl!(tensor).is_infinity(%{tensor | type: {:u, 8}}, tensor)
end)
end
@doc """
Negates each element in the tensor.
If you're using `Nx.Defn.defn/2`, you can use the `-` unary operator
in place of this function: `-tensor`.
## Examples
iex> Nx.negate(1)
#Nx.Tensor<
s64
-1
>
iex> Nx.negate(Nx.tensor([-1, 0, 1]))
#Nx.Tensor<
s64[3]
[1, 0, -1]
>
iex> Nx.negate(Nx.tensor([1.0, 2.0, 3.0], type: :f32))
#Nx.Tensor<
f32[3]
[-1.0, -2.0, -3.0]
>
If an unsigned tensor is given, it works as `bitwise_not`:
iex> Nx.negate(Nx.tensor([0, 1, 2], type: :u8, names: [:x]))
#Nx.Tensor<
u8[x: 3]
[0, 255, 254]
>
"""
@doc type: :element
def negate(tensor) do
apply_vectorized(tensor, fn tensor ->
impl!(tensor).negate(tensor, tensor)
end)
end
@doc """
Computes the sign of each element in the tensor.
If a number is less than zero, it returns -1.
If a number is more than zero, it returns 1.
Otherwise it returns zero (which may either be
positive or negative for floats).
## Examples
iex> Nx.sign(Nx.tensor([-2, -1, 0, 1, 2], names: [:x]))
#Nx.Tensor<
s64[x: 5]
[-1, -1, 0, 1, 1]
>
"""
@doc type: :element
def sign(tensor) do
apply_vectorized(tensor, fn tensor ->
impl!(tensor).sign(tensor, tensor)
end)
end
@doc """
Computes the absolute value of each element in the tensor.
## Examples
iex> Nx.abs(Nx.tensor([-2, -1, 0, 1, 2], names: [:x]))
#Nx.Tensor<
s64[x: 5]
[2, 1, 0, 1, 2]
>
"""
@doc type: :element
def abs(tensor) do
apply_vectorized(tensor, fn tensor ->
case tensor.type do
{:u, _} -> tensor
{:c, size} -> impl!(tensor).abs(%{tensor | type: {:f, div(size, 2)}}, tensor)
_ -> impl!(tensor).abs(tensor, tensor)
end
end)
end
@doc """
Calculates the complex conjugate of each element in the tensor.
If $$z = a + bi = r e^\\theta$$, $$conjugate(z) = z^* = a - bi = r e^{-\\theta}$$
## Examples
iex> Nx.conjugate(Complex.new(1, 2))
#Nx.Tensor<
c64
1.0-2.0i
>
iex> Nx.conjugate(1)
#Nx.Tensor<
c64
1.0+0.0i
>
iex> Nx.conjugate(Nx.tensor([Complex.new(1, 2), Complex.new(2, -4)]))
#Nx.Tensor<
c64[2]
[1.0-2.0i, 2.0+4.0i]
>
"""
@doc type: :element
def conjugate(tensor) do
apply_vectorized(tensor, fn tensor ->
impl!(tensor).conjugate(%{tensor | type: Nx.Type.to_complex(tensor.type)}, tensor)
end)
end
@doc """
Calculates the complex phase angle of each element in the tensor.
$$phase(z) = atan2(b, a), z = a + bi \\in \\Complex$$
## Examples
iex> Nx.phase(Complex.new(1, 2))
#Nx.Tensor<
f32
1.1071487665176392
>
iex> Nx.phase(1)
#Nx.Tensor<
f32
0.0
>
iex> import Nx, only: [sigil_V: 2]
iex> Nx.phase(~V[1+2i -2+1i])
#Nx.Tensor<
f32[2]
[1.1071487665176392, 2.677945137023926]
>
"""
@doc type: :element
def phase(tensor) do
apply_vectorized(tensor, fn tensor ->
output = %{tensor | type: Nx.Type.to_real(tensor.type)}
Nx.Shared.optional(:phase, [tensor], output, fn tensor ->
tensor
|> imag
|> atan2(real(tensor))
end)
end)
end
@doc """
Returns the real component of each entry in a complex tensor
as a floating point tensor.
## Examples
iex> Nx.real(Complex.new(1, 2))
#Nx.Tensor<
f32
1.0
>
iex> Nx.real(Nx.tensor(1))
#Nx.Tensor<
f32
1.0
>
iex> Nx.real(Nx.tensor(1, type: :bf16))
#Nx.Tensor<
bf16
1.0
>
iex> Nx.real(Nx.tensor([Complex.new(1, 2), Complex.new(2, -4)]))
#Nx.Tensor<
f32[2]
[1.0, 2.0]
>
"""
@doc type: :element
def real(tensor) do
apply_vectorized(tensor, fn %{type: type} = tensor ->
cond do
match?({:c, _}, type) ->
{:c, size} = type
impl!(tensor).real(%{tensor | type: {:f, div(size, 2)}}, tensor)
Nx.Type.float?(type) ->
tensor
tensor ->
as_type(tensor, {:f, 32})
end
end)
end
@doc """
Returns the imaginary component of each entry in a complex tensor
as a floating point tensor.
## Examples
iex> Nx.imag(Complex.new(1, 2))
#Nx.Tensor<
f32
2.0
>
iex> Nx.imag(Nx.tensor(1))
#Nx.Tensor<
f32
0.0
>
iex> Nx.imag(Nx.tensor(1, type: :bf16))
#Nx.Tensor<
bf16
0.0
>
iex> Nx.imag(Nx.tensor([Complex.new(1, 2), Complex.new(2, -4)]))
#Nx.Tensor<
f32[2]
[2.0, -4.0]
>
"""
@doc type: :element
def imag(tensor) do
apply_vectorized(tensor, fn tensor ->
case tensor do
%{type: {:c, size}} = tensor ->
impl!(tensor).imag(%{tensor | type: {:f, div(size, 2)}}, tensor)
tensor ->
floating = Nx.Type.to_floating(tensor.type)
zero = Nx.tensor(0.0, type: floating)
broadcast(zero, tensor)
end
end)
end
@doc """
Constructs a complex tensor from two equally-shaped tensors.
Does not accept complex tensors as inputs.
## Examples
iex> Nx.complex(Nx.tensor(1), Nx.tensor(2))
#Nx.Tensor<
c64
1.0+2.0i
>
iex> Nx.complex(Nx.tensor([1, 2]), Nx.tensor([3, 4]))
#Nx.Tensor<
c64[2]
[1.0+3.0i, 2.0+4.0i]
>
"""
@doc type: :element
def complex(real, imag) do
if elem(type(real), 0) == :c or elem(type(imag), 0) == :c do
Nx.Shared.raise_complex_not_supported("complex", 2)
end
t = type(real) |> Nx.Type.merge(type(imag)) |> Nx.Type.to_complex()
imag
|> multiply(Nx.Constants.i(t))
|> add(real)
end
@doc """
Applies bitwise not to each element in the tensor.
If you're using `Nx.Defn.defn/2`, you can use the `~~~` operator
in place of this function: `~~~tensor`.
## Examples
iex> Nx.bitwise_not(1)
#Nx.Tensor<
s64
-2
>
iex> Nx.bitwise_not(Nx.tensor([-1, 0, 1], type: :s8, names: [:x]))
#Nx.Tensor<
s8[x: 3]
[0, -1, -2]
>
iex> Nx.bitwise_not(Nx.tensor([0, 1, 254, 255], type: :u8, names: [:x]))
#Nx.Tensor<
u8[x: 4]
[255, 254, 1, 0]
>
## Error cases
iex> Nx.bitwise_not(Nx.tensor([0.0, 1.0]))
** (ArgumentError) bitwise operators expect integer tensors as inputs and outputs an integer tensor, got: {:f, 32}
"""
@doc type: :element
def bitwise_not(tensor) do
apply_vectorized(tensor, fn tensor ->
assert_bitwise_type!(tensor.type)
impl!(tensor).bitwise_not(tensor, tensor)
end)
end
@doc """
Computes the bitwise population count of each element in the tensor.
## Examples
iex> Nx.population_count(1)
#Nx.Tensor<
s64
1
>
iex> Nx.population_count(-128)
#Nx.Tensor<
s64
57
>
iex> Nx.population_count(Nx.tensor([0, 1, 254, 255], names: [:x]))
#Nx.Tensor<
s64[x: 4]
[0, 1, 7, 8]
>
iex> Nx.population_count(Nx.tensor([0, 1, 126, 127, -1, -127, -128], type: :s8, names: [:x]))
#Nx.Tensor<
s8[x: 7]
[0, 1, 6, 7, 8, 2, 1]
>
## Error cases
iex> Nx.population_count(Nx.tensor([0.0, 1.0]))
** (ArgumentError) bitwise operators expect integer tensors as inputs and outputs an integer tensor, got: {:f, 32}
"""
@doc type: :element
def population_count(tensor) do
apply_vectorized(tensor, fn tensor ->
assert_bitwise_type!(tensor.type)
impl!(tensor).population_count(tensor, tensor)
end)
end
@doc """
Counts the number of leading zeros of each element in the tensor.
## Examples
iex> Nx.count_leading_zeros(1)
#Nx.Tensor<
s64
63
>
iex> Nx.count_leading_zeros(-1)
#Nx.Tensor<
s64
0
>
iex> Nx.count_leading_zeros(Nx.tensor([0, 0xF, 0xFF, 0xFFFF], names: [:x]))
#Nx.Tensor<
s64[x: 4]
[64, 60, 56, 48]
>
iex> Nx.count_leading_zeros(Nx.tensor([0xF000000000000000, 0x0F00000000000000], names: [:x]))
#Nx.Tensor<
s64[x: 2]
[0, 4]
>
iex> Nx.count_leading_zeros(Nx.tensor([0, 0xF, 0xFF, 0xFFFF], type: :s32, names: [:x]))
#Nx.Tensor<
s32[x: 4]
[32, 28, 24, 16]
>
iex> Nx.count_leading_zeros(Nx.tensor([0, 0xF, 0xFF, 0xFFFF], type: :s16, names: [:x]))
#Nx.Tensor<
s16[x: 4]
[16, 12, 8, 0]
>
iex> Nx.count_leading_zeros(Nx.tensor([0, 1, 2, 4, 8, 16, 32, 64, -1, -128], type: :s8, names: [:x]))
#Nx.Tensor<
s8[x: 10]
[8, 7, 6, 5, 4, 3, 2, 1, 0, 0]
>
iex> Nx.count_leading_zeros(Nx.tensor([0, 1, 2, 4, 8, 16, 32, 64, 128], type: :u8, names: [:x]))
#Nx.Tensor<
u8[x: 9]
[8, 7, 6, 5, 4, 3, 2, 1, 0]
>
## Error cases
iex> Nx.count_leading_zeros(Nx.tensor([0.0, 1.0]))
** (ArgumentError) bitwise operators expect integer tensors as inputs and outputs an integer tensor, got: {:f, 32}
"""
@doc type: :element
def count_leading_zeros(tensor) do
apply_vectorized(tensor, fn tensor ->
assert_bitwise_type!(tensor.type)
impl!(tensor).count_leading_zeros(tensor, tensor)
end)
end
for {name, desc} <- [floor: "floor", ceil: "ceil", round: "round (away from zero)"] do
[res1, res2, res3, res4] = Enum.map([-1.5, -0.5, 0.5, 1.5], &apply(:erlang, name, [&1]))
@doc """
Calculates the #{desc} of each element in the tensor.
If a non-floating tensor is given, it is returned as is.
If a floating tensor is given, then we apply the operation,
but keep its type.
## Examples
iex> Nx.#{name}(Nx.tensor([-1, 0, 1], names: [:x]))
#Nx.Tensor<
s64[x: 3]
[-1, 0, 1]
>
iex> Nx.#{name}(Nx.tensor([-1.5, -0.5, 0.5, 1.5], names: [:x]))
#Nx.Tensor<
f32[x: 4]
[#{res1}.0, #{res2}.0, #{res3}.0, #{res4}.0]
>
"""
@doc type: :element
def unquote(name)(tensor) do
apply_vectorized(tensor, fn tensor ->
case tensor do
%T{type: {type, _}} = tensor when type in [:s, :u] -> tensor
%T{type: {:c, _}} -> Nx.Shared.raise_complex_not_supported(unquote(name), 1)
%T{} = tensor -> impl!(tensor).unquote(name)(tensor, tensor)
end
end)
end
end
## Aggregate ops
@doc """
Returns a scalar tensor of value 1 if all of the
tensor values are not zero. Otherwise the value is 0.
If the `:axes` option is given, it aggregates over
the given dimensions, effectively removing them.
`axes: [0]` implies aggregating over the highest order
dimension and so forth. If the axis is negative, then
counts the axis from the back. For example, `axes: [-1]`
will always aggregate all rows.
You may optionally set `:keep_axes` to true, which will
retain the rank of the input tensor by setting the reduced
axes to size 1.
## Examples
iex> Nx.all(Nx.tensor([0, 1, 2]))
#Nx.Tensor<
u8
0
>
iex> Nx.all(Nx.tensor([[-1, 0, 1], [2, 3, 4]], names: [:x, :y]), axes: [:x])
#Nx.Tensor<
u8[y: 3]
[1, 0, 1]
>
iex> Nx.all(Nx.tensor([[-1, 0, 1], [2, 3, 4]], names: [:x, :y]), axes: [:y])
#Nx.Tensor<
u8[x: 2]
[0, 1]
>
### Keeping axes
iex> Nx.all(Nx.tensor([[-1, 0, 1], [2, 3, 4]], names: [:x, :y]), axes: [:y], keep_axes: true)
#Nx.Tensor<
u8[x: 2][y: 1]
[
[0],
[1]
]
>
### Vectorized tensors
iex> t = Nx.vectorize(Nx.tensor([[0, 1], [1, 1]]), :x)
iex> Nx.all(t, axes: [0], keep_axes: true)
#Nx.Tensor<
vectorized[x: 2]
u8[1]
[
[0],
[1]
]
>
iex> t = Nx.vectorize(Nx.tensor([1, 0]), :x)
iex> Nx.all(t)
#Nx.Tensor<
vectorized[x: 2]
u8
[1, 0]
>
"""
@doc type: :aggregation
def all(tensor, opts \\ []) do
aggregate_axes_op(to_tensor(tensor), :all, {:u, 8}, opts)
end
@doc """
Returns a scalar tensor of value 1 if any of the
tensor values are not zero. Otherwise the value is 0.
If the `:axes` option is given, it aggregates over
the given dimensions, effectively removing them.
`axes: [0]` implies aggregating over the highest order
dimension and so forth. If the axis is negative, then
counts the axis from the back. For example, `axes: [-1]`
will always aggregate all rows.
You may optionally set `:keep_axes` to true, which will
retain the rank of the input tensor by setting the reduced
axes to size 1.
## Examples
iex> Nx.any(Nx.tensor([0, 1, 2]))
#Nx.Tensor<
u8
1
>
iex> Nx.any(Nx.tensor([[0, 1, 0], [0, 1, 2]], names: [:x, :y]), axes: [:x])
#Nx.Tensor<
u8[y: 3]
[0, 1, 1]
>
iex> Nx.any(Nx.tensor([[0, 1, 0], [0, 1, 2]], names: [:x, :y]), axes: [:y])
#Nx.Tensor<
u8[x: 2]
[1, 1]
>
### Keeping axes
iex> Nx.any(Nx.tensor([[0, 1, 0], [0, 1, 2]], names: [:x, :y]), axes: [:y], keep_axes: true)
#Nx.Tensor<
u8[x: 2][y: 1]
[
[1],
[1]
]
>
### Vectorized tensors
iex> t = Nx.vectorize(Nx.tensor([[0, 1], [0, 0]]), :x)
iex> Nx.any(t, axes: [0], keep_axes: true)
#Nx.Tensor<
vectorized[x: 2]
u8[1]
[
[1],
[0]
]
>
"""
@doc type: :aggregation
def any(tensor, opts \\ []) do
aggregate_axes_op(to_tensor(tensor), :any, {:u, 8}, opts)
end
@doc """
Returns a scalar tensor of value 1 if all element-wise values
are within tolerance of b. Otherwise returns value 0.
You may set the absolute tolerance, `:atol` and relative tolerance
`:rtol`. Given tolerances, this functions returns 1 if
absolute(a - b) <= (atol + rtol * absolute(b))
is true for all elements of a and b.
## Options
* `:rtol` - relative tolerance between numbers, as described above. Defaults to 1.0e-5
* `:atol` - absolute tolerance between numbers, as described above. Defaults to 1.0e-8
* `:equal_nan` - if `false`, NaN will always compare as false.
Otherwise `NaN` will only equal `NaN`. Defaults to `false`
## Examples
iex> Nx.all_close(Nx.tensor([1.0e10, 1.0e-7]), Nx.tensor([1.00001e10, 1.0e-8]))
#Nx.Tensor<
u8
0
>
iex> Nx.all_close(Nx.tensor([1.0e-8, 1.0e-8]), Nx.tensor([1.0e-8, 1.0e-9]))
#Nx.Tensor<
u8
1
>
Although `NaN` by definition isn't equal to itself, so this implementation
also considers all `NaN`s different from each other by default:
iex> Nx.all_close(Nx.tensor(:nan), Nx.tensor(:nan))
#Nx.Tensor<
u8
0
>
iex> Nx.all_close(Nx.tensor(:nan), Nx.tensor(0))
#Nx.Tensor<
u8
0
>
We can change this behavior with the `:equal_nan` option:
iex> t = Nx.tensor([:nan, 1])
iex> Nx.all_close(t, t, equal_nan: true) # nan == nan -> true
#Nx.Tensor<
u8
1
>
iex> Nx.all_close(t, t, equal_nan: false) # nan == nan -> false, default behavior
#Nx.Tensor<
u8
0
>
Infinities behave as expected, being "close" to themselves but not
to other numbers:
iex> Nx.all_close(Nx.tensor(:infinity), Nx.tensor(:infinity))
#Nx.Tensor<
u8
1
>
iex> Nx.all_close(Nx.tensor(:infinity), Nx.tensor(:neg_infinity))
#Nx.Tensor<
u8
0
>
iex> Nx.all_close(Nx.tensor(1.0e30), Nx.tensor(:infinity))
#Nx.Tensor<
u8
0
>
## Vectorized tensors
Vectorized inputs have their vectorized axes broadcast together
before calculations are performed.
iex> x = Nx.tensor([0, 1]) |> Nx.vectorize(:x)
iex> Nx.all_close(x, x)
#Nx.Tensor<
vectorized[x: 2]
u8
[1, 1]
>
iex> x = Nx.tensor([0, 1, 2]) |> Nx.vectorize(:x)
iex> y = Nx.tensor([0, 1]) |> Nx.vectorize(:y)
iex> Nx.all_close(x, y)
#Nx.Tensor<
vectorized[x: 3][y: 2]
u8
[
[1, 0],
[0, 1],
[0, 0]
]
>
"""
@doc type: :aggregation
def all_close(a, b, opts \\ []) do
opts = keyword!(opts, equal_nan: false, rtol: 1.0e-5, atol: 1.0e-8)
[%T{vectorized_axes: vectorized_axes} = a, b] = broadcast_vectors([a, b], align_ranks: true)
if vectorized_axes != [] do
vectorized_all_close(a, b, opts)
else
Nx.Shared.optional(
:all_close,
[a, b, opts],
%{a | names: [], shape: {}, type: {:u, 8}},
&vectorized_all_close/3
)
end
end
defp vectorized_all_close(a, b, opts) do
atol = opts[:atol]
rtol = opts[:rtol]
finite_entries = less_equal(Nx.abs(subtract(a, b)), add(atol, multiply(rtol, Nx.abs(b))))
if Nx.Type.integer?(a.type) and Nx.Type.integer?(b.type) do
all(finite_entries)
else
# inf - inf is a nan, however, they are equal,
# so we explicitly check for equal entries.
inf_a = is_infinity(a)
inf_b = is_infinity(b)
inf_entries = select(logical_or(inf_a, inf_b), equal(a, b), finite_entries)
if opts[:equal_nan] do
nan_a = is_nan(a)
nan_b = is_nan(b)
nan_entries = logical_and(nan_a, nan_b)
all(select(nan_entries, 1, inf_entries))
else
all(inf_entries)
end
end
end
@doc """
Returns the sum for the tensor.
If the `:axes` option is given, it aggregates over
the given dimensions, effectively removing them.
`axes: [0]` implies aggregating over the highest order
dimension and so forth. If the axis is negative, then
counts the axis from the back. For example, `axes: [-1]`
will always aggregate all rows.
You may optionally set `:keep_axes` to true, which will
retain the rank of the input tensor by setting the summed
axes to size 1.
## Examples
By default the sum always returns a scalar:
iex> Nx.sum(Nx.tensor(42))
#Nx.Tensor<
s64
42
>
iex> Nx.sum(Nx.tensor([1, 2, 3]))
#Nx.Tensor<
s64
6
>
iex> Nx.sum(Nx.tensor([[1.0, 2.0], [3.0, 4.0]]))
#Nx.Tensor<
f32
10.0
>
Giving a tensor with low precision casts it to a higher
precision to make sure the sum does not overflow:
iex> Nx.sum(Nx.tensor([[101, 102], [103, 104]], type: :s8))
#Nx.Tensor<
s64
410
>
iex> Nx.sum(Nx.tensor([[101, 102], [103, 104]], type: :s16))
#Nx.Tensor<
s64
410
>
### Aggregating over an axis
iex> Nx.sum(Nx.tensor([1, 2, 3]), axes: [0])
#Nx.Tensor<
s64
6
>
Same tensor over different axes combinations:
iex> t = Nx.iota({2, 2, 3}, names: [:x, :y, :z])
iex> Nx.sum(t, axes: [:x])
#Nx.Tensor<
s64[y: 2][z: 3]
[
[6, 8, 10],
[12, 14, 16]
]
>
iex> Nx.sum(t, axes: [:y])
#Nx.Tensor<
s64[x: 2][z: 3]
[
[3, 5, 7],
[15, 17, 19]
]
>
iex> Nx.sum(t, axes: [:z])
#Nx.Tensor<
s64[x: 2][y: 2]
[
[3, 12],
[21, 30]
]
>
iex> Nx.sum(t, axes: [:x, :z])
#Nx.Tensor<
s64[y: 2]
[24, 42]
>
iex> Nx.sum(t, axes: [-3])
#Nx.Tensor<
s64[y: 2][z: 3]
[
[6, 8, 10],
[12, 14, 16]
]
>
### Keeping axes
iex> t = Nx.tensor([[1, 2], [3, 4]], names: [:x, :y])
iex> Nx.sum(t, axes: [:x], keep_axes: true)
#Nx.Tensor<
s64[x: 1][y: 2]
[
[4, 6]
]
>
### Vectorized tensors
iex> t = Nx.tensor([[[[1, 2]], [[3, 4]]], [[[5, 6]], [[7, 8]]]]) |> Nx.vectorize(:x) |> Nx.vectorize(:y)
#Nx.Tensor<
vectorized[x: 2][y: 2]
s64[1][2]
[
[
[
[1, 2]
],
[
[3, 4]
]
],
[
[
[5, 6]
],
[
[7, 8]
]
]
]
>
iex> Nx.sum(t)
#Nx.Tensor<
vectorized[x: 2][y: 2]
s64
[
[3, 7],
[11, 15]
]
>
iex> Nx.sum(t, axes: [0])
#Nx.Tensor<
vectorized[x: 2][y: 2]
s64[2]
[
[
[1, 2],
[3, 4]
],
[
[5, 6],
[7, 8]
]
]
>
### Errors
iex> Nx.sum(Nx.tensor([[1, 2]]), axes: [2])
** (ArgumentError) given axis (2) invalid for shape with rank 2
"""
@doc type: :aggregation
def sum(tensor, opts \\ []) do
tensor = to_tensor(tensor)
type = Nx.Type.to_aggregate(tensor.type)
aggregate_axes_op(tensor, :sum, type, opts)
end
@doc """
Returns the mean for the tensor.
If the `:axes` option is given, it aggregates over
that dimension, effectively removing it. `axes: [0]`
implies aggregating over the highest order dimension
and so forth. If the axis is negative, then counts
the axis from the back. For example, `axes: [-1]` will
always aggregate all rows.
You may optionally set `:keep_axes` to true, which will
retain the rank of the input tensor by setting the averaged
axes to size 1.
## Examples
iex> Nx.mean(Nx.tensor(42))
#Nx.Tensor<
f32
42.0
>
iex> Nx.mean(Nx.tensor([1, 2, 3]))
#Nx.Tensor<
f32
2.0
>
### Aggregating over an axis
iex> Nx.mean(Nx.tensor([1, 2, 3]), axes: [0])
#Nx.Tensor<
f32
2.0
>
iex> Nx.mean(Nx.tensor([1, 2, 3], type: :u8, names: [:x]), axes: [:x])
#Nx.Tensor<
f32
2.0
>
iex> t = Nx.tensor(Nx.iota({2, 2, 3}), names: [:x, :y, :z])
iex> Nx.mean(t, axes: [:x])
#Nx.Tensor<
f32[y: 2][z: 3]
[
[3.0, 4.0, 5.0],
[6.0, 7.0, 8.0]
]
>
iex> t = Nx.tensor(Nx.iota({2, 2, 3}), names: [:x, :y, :z])
iex> Nx.mean(t, axes: [:x, :z])
#Nx.Tensor<
f32[y: 2]
[4.0, 7.0]
>
iex> t = Nx.tensor(Nx.iota({2, 2, 3}), names: [:x, :y, :z])
iex> Nx.mean(t, axes: [-1])
#Nx.Tensor<
f32[x: 2][y: 2]
[
[1.0, 4.0],
[7.0, 10.0]
]
>
### Keeping axes
iex> t = Nx.tensor(Nx.iota({2, 2, 3}), names: [:x, :y, :z])
iex> Nx.mean(t, axes: [-1], keep_axes: true)
#Nx.Tensor<
f32[x: 2][y: 2][z: 1]
[
[
[1.0],
[4.0]
],
[
[7.0],
[10.0]
]
]
>
## Vectorized tensors
iex> t = Nx.iota({2, 5}, vectorized_axes: [x: 2])
iex> Nx.mean(t)
#Nx.Tensor<
vectorized[x: 2]
f32
[4.5, 4.5]
>
iex> Nx.mean(t, axes: [0])
#Nx.Tensor<
vectorized[x: 2]
f32[5]
[
[2.5, 3.5, 4.5, 5.5, 6.5],
[2.5, 3.5, 4.5, 5.5, 6.5]
]
>
iex> Nx.mean(t, axes: [1])
#Nx.Tensor<
vectorized[x: 2]
f32[2]
[
[2.0, 7.0],
[2.0, 7.0]
]
>
"""
@doc type: :aggregation, from_backend: false
def mean(tensor, opts \\ []) do
%T{shape: shape, names: names} = tensor = to_tensor(tensor)
mean_den =
if axes = opts[:axes] do
mean_den(shape, Nx.Shape.normalize_axes(shape, axes, names))
else
size(shape)
end
divide(sum(tensor, opts), mean_den)
end
defp mean_den(_shape, []), do: 1
defp mean_den(shape, [axis | axes]) when axis >= 0,
do: elem(shape, axis) * mean_den(shape, axes)
@doc """
Returns the weighted mean for the tensor and the weights.
If the `:axes` option is given, it aggregates over
those dimensions, effectively removing them. `axes: [0]`
implies aggregating over the highest order dimension
and so forth. If the axes are negative, then the axes will
be counted from the back. For example, `axes: [-1]` will
always aggregate over the last dimension.
You may optionally set `:keep_axes` to true, which will
retain the rank of the input tensor by setting the averaged
axes to size 1.
## Examples
iex> Nx.weighted_mean(Nx.tensor(42), Nx.tensor(2))
#Nx.Tensor<
f32
42.0
>
iex> Nx.weighted_mean(Nx.tensor([1, 2, 3]), Nx.tensor([3, 2, 1]))
#Nx.Tensor<
f32
1.6666666269302368
>
### Aggregating over axes
iex> Nx.weighted_mean(Nx.tensor([1, 2, 3], names: [:x]), Nx.tensor([4, 5, 6]), axes: [0])
#Nx.Tensor<
f32
2.133333444595337
>
iex> Nx.weighted_mean(Nx.tensor([1, 2, 3], type: :u8, names: [:x]), Nx.tensor([1, 3, 5]), axes: [:x])
#Nx.Tensor<
f32
2.444444417953491
>
iex> t = Nx.iota({3, 4})
iex> weights = Nx.tensor([1, 2, 3, 4])
iex> Nx.weighted_mean(t, weights, axes: [1])
#Nx.Tensor<
f32[3]
[2.0, 6.0, 10.0]
>
iex> t = Nx.iota({2, 4, 4, 1})
iex> weights = Nx.broadcast(2, {4, 4})
iex> Nx.weighted_mean(t, weights, axes: [1, 2])
#Nx.Tensor<
f32[2][1]
[
[7.5],
[23.5]
]
>
### Keeping axes
iex> t = Nx.tensor(Nx.iota({2, 2, 3}), names: [:x, :y, :z])
iex> weights = Nx.tensor([[[0, 1, 2], [1, 1, 0]], [[-1, 1, -1], [1, 1, -1]]])
iex> Nx.weighted_mean(t, weights, axes: [-1], keep_axes: true)
#Nx.Tensor<
f32[x: 2][y: 2][z: 1]
[
[
[1.6666666269302368],
[3.5]
],
[
[7.0],
[8.0]
]
]
>
### Vectorized tensors
iex> t = Nx.tensor([[1, 2, 3], [1, 1, 1]]) |> Nx.vectorize(:x)
#Nx.Tensor<
vectorized[x: 2]
s64[3]
[
[1, 2, 3],
[1, 1, 1]
]
>
iex> w = Nx.tensor([[1, 1, 1], [0, 0, 1]]) |> Nx.vectorize(:y)
#Nx.Tensor<
vectorized[y: 2]
s64[3]
[
[1, 1, 1],
[0, 0, 1]
]
>
iex> Nx.weighted_mean(t, w)
#Nx.Tensor<
vectorized[x: 2][y: 2]
f32
[
[2.0, 3.0],
[1.0, 1.0]
]
>
"""
@doc type: :aggregation, from_backend: false
def weighted_mean(tensor, weights, opts \\ []) do
opts = keyword!(opts, [:axes, keep_axes: false])
%T{shape: shape, names: names} = tensor = to_tensor(tensor)
%T{shape: weights_shape} = weights = to_tensor(weights)
axes =
if opts[:axes] do
Nx.Shape.normalize_axes(shape, opts[:axes], names)
end
weights =
if shape != weights_shape do
cond do
axes == nil ->
raise ArgumentError, "axes must be specified when shapes of input and weights differ"
tuple_size(weights_shape) != length(axes) ->
raise ArgumentError,
"weights tensor must have rank equal to the number of aggregation axes when input shapes differ"
true ->
nil
end
dims_to_reshape =
List.duplicate(1, tuple_size(shape) - length(axes)) ++ Tuple.to_list(weights_shape)
dims_to_reshape = List.to_tuple(dims_to_reshape)
weights = reshape(weights, dims_to_reshape)
dims_to_swap = for i <- 0..(tuple_size(dims_to_reshape) - 1), do: i
checked_axes = if is_list(axes), do: Enum.at(axes, 0), else: axes
dims_to_swap = swap_last(dims_to_swap, checked_axes)
transpose(weights, axes: dims_to_swap)
else
weights
end
weights_sum = sum(weights, axes: axes, keep_axes: opts[:keep_axes])
tensor
|> multiply(weights)
|> sum(axes: axes, keep_axes: opts[:keep_axes])
|> divide(weights_sum)
end
defp swap_last(a, i) do
e1 = Enum.fetch!(a, i)
e2 = Enum.fetch!(a, -1)
a
|> List.replace_at(i, e2)
|> List.replace_at(-1, e1)
end
@doc """
Returns the median for the tensor.
The median is the value in the middle of a data set.
If the `:axis` option is given, it aggregates over
that dimension, effectively removing it. `axis: 0`
implies aggregating over the highest order dimension
and so forth. If the axis is negative, then the axis will
be counted from the back. For example, `axis: -1` will
always aggregate over the last dimension.
You may optionally set `:keep_axis` to true, which will
retain the rank of the input tensor by setting the reduced
axis to size 1.
## Examples
iex> Nx.median(Nx.tensor(42))
#Nx.Tensor<
s64
42
>
iex> Nx.median(Nx.tensor([1, 2, 3]))
#Nx.Tensor<
s64
2
>
iex> Nx.median(Nx.tensor([1, 2]))
#Nx.Tensor<
f32
1.5
>
iex> Nx.median(Nx.iota({2, 3, 3}))
#Nx.Tensor<
f32
8.5
>
### Aggregating over an axis
iex> Nx.median(Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:x, :y]), axis: 0)
#Nx.Tensor<
f32[y: 3]
[2.5, 3.5, 4.5]
>
iex> Nx.median(Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:x, :y]), axis: :y)
#Nx.Tensor<
s64[x: 2]
[2, 5]
>
iex> t = Nx.tensor(Nx.iota({2, 2, 3}), names: [:x, :y, :z])
iex> Nx.median(t, axis: :x)
#Nx.Tensor<
f32[y: 2][z: 3]
[
[3.0, 4.0, 5.0],
[6.0, 7.0, 8.0]
]
>
iex> t = Nx.tensor([[[1, 2, 2], [3, 4, 2]], [[4, 5, 2], [7, 9, 2]]])
iex> Nx.median(t, axis: -1)
#Nx.Tensor<
s64[2][2]
[
[2, 3],
[4, 7]
]
>
### Keeping axis
iex> t = Nx.tensor([[[1, 2, 2], [3, 4, 2]], [[4, 5, 2], [7, 9, 2]]])
iex> Nx.median(t, axis: -1, keep_axis: true)
#Nx.Tensor<
s64[2][2][1]
[
[
[2],
[3]
],
[
[4],
[7]
]
]
>
### Vectorized tensors
For vectorized inputs, `:axis` refers to the
non-vectorized shape:
iex> Nx.median(Nx.tensor([[1, 2, 3], [4, 5, 6]]) |> Nx.vectorize(:x), axis: 0)
#Nx.Tensor<
vectorized[x: 2]
s64
[2, 5]
>
"""
@doc type: :aggregation, from_backend: false
def median(tensor, opts \\ []) do
opts = keyword!(opts, axis: nil, keep_axis: false)
%T{shape: shape, names: names} = tensor = to_tensor(tensor)
axis =
if axis_opt = opts[:axis] do
Nx.Shape.normalize_axis(shape, axis_opt, names)
end
t =
if axis do
sort(tensor, axis: axis)
else
tensor |> flatten() |> sort()
end
axis_size =
if axis do
axis_size(tensor, axis)
else
size(tensor)
end
half_idx = div(axis_size, 2)
axis_size_is_odd = rem(axis_size, 2) == 1
cond do
axis != nil and axis_size_is_odd ->
res = slice_along_axis(t, half_idx, 1, axis: axis)
if opts[:keep_axis], do: res, else: squeeze(res, axes: [axis])
axis != nil ->
two_elems = slice_along_axis(t, half_idx - 1, 2, axis: axis)
mean(two_elems, axes: [axis], keep_axes: opts[:keep_axis])
axis == nil and axis_size_is_odd ->
t[[half_idx]]
:otherwise ->
t[[half_idx - 1]]
|> add(t[[half_idx]])
|> divide(2)
end
end
@doc """
Returns the mode of a tensor.
The mode is the value that appears most often.
If the `:axis` option is given, it aggregates over
that dimension, effectively removing it. `axis: 0`
implies aggregating over the highest order dimension
and so forth. If the axis is negative, then the axis will
be counted from the back. For example, `axis: -1` will
always aggregate over the last dimension.
You may optionally set `:keep_axis` to true, which will
retain the rank of the input tensor by setting the reduced
axis to size 1.
## Examples
iex> Nx.mode(Nx.tensor(42))
#Nx.Tensor<
s64
42
>
iex> Nx.mode(Nx.tensor([[1]]))
#Nx.Tensor<
s64
1
>
iex> Nx.mode(Nx.tensor([1, 2, 2, 3, 5]))
#Nx.Tensor<
s64
2
>
iex> Nx.mode(Nx.tensor([[1, 2, 2, 3, 5], [1, 1, 76, 8, 1]]))
#Nx.Tensor<
s64
1
>
### Aggregating over an axis
iex> Nx.mode(Nx.tensor([[1, 2, 2, 3, 5], [1, 1, 76, 8, 1]]), axis: 0)
#Nx.Tensor<
s64[5]
[1, 1, 2, 3, 1]
>
iex> Nx.mode(Nx.tensor([[1, 2, 2, 3, 5], [1, 1, 76, 8, 1]]), axis: 1)
#Nx.Tensor<
s64[2]
[2, 1]
>
iex> Nx.mode(Nx.tensor([[[1]]]), axis: 1)
#Nx.Tensor<
s64[1][1]
[
[1]
]
>
### Keeping axis
iex> Nx.mode(Nx.tensor([[1, 2, 2, 3, 5], [1, 1, 76, 8, 1]]), axis: 1, keep_axis: true)
#Nx.Tensor<
s64[2][1]
[
[2],
[1]
]
>
### Vectorized tensors
For vectorized tensors, `:axis` refers to the non-vectorized shape:
iex> t = Nx.tensor([[[1, 2, 2, 3, 5], [1, 1, 76, 8, 1]], [[1, 2, 2, 2, 5], [5, 2, 2, 2, 1]]]) |> Nx.vectorize(:x)
iex> Nx.mode(t, axis: 0)
#Nx.Tensor<
vectorized[x: 2]
s64[5]
[
[1, 1, 2, 3, 1],
[1, 2, 2, 2, 1]
]
>
iex> Nx.mode(t, axis: 1)
#Nx.Tensor<
vectorized[x: 2]
s64[2]
[
[2, 1],
[2, 2]
]
>
"""
@doc type: :aggregation, from_backend: false
def mode(tensor, opts \\ []) do
opts = keyword!(opts, axis: nil, keep_axis: false)
%T{shape: shape, names: names} = tensor = to_tensor(tensor)
axis =
if opts[:axis] != nil,
do: Nx.Shape.normalize_axis(shape, opts[:axis], names),
else: opts[:axis]
tensor_rank = rank(tensor)
tensor_size = size(tensor)
cond do
tensor_rank == 0 ->
if opts[:keep_axis], do: new_axis(tensor, -1), else: tensor
tensor_size == 1 and axis == nil ->
if opts[:keep_axis], do: tensor, else: squeeze(tensor)
axis != nil and (tensor_size == 1 or Nx.axis_size(tensor, axis) == 1) ->
if opts[:keep_axis], do: tensor, else: squeeze(tensor, axes: [axis])
axis == nil ->
tensor = flatten(tensor)
res = mode_general(tensor, axis: 0)
if opts[:keep_axis], do: reshape(res, Tuple.duplicate(1, tensor_rank)), else: res
true ->
mode_general(tensor, axis: axis, keep_axis: opts[:keep_axis])
end
end
defp mode_general(tensor, opts) do
tensor_shape = shape(tensor)
axis = opts[:axis]
sorted = sort(tensor, axis: axis)
size_to_broadcast = tensor_shape |> put_elem(axis, 1)
group_indices =
concatenate(
[
broadcast(0, size_to_broadcast),
not_equal(
slice_along_axis(sorted, 0, axis_size(sorted, axis) - 1, axis: axis),
slice_along_axis(sorted, 1, axis_size(sorted, axis) - 1, axis: axis)
)
],
axis: axis
)
|> cumulative_sum(axis: axis)
num_elements = Tuple.product(tensor_shape)
counting_indices =
0..(rank(group_indices) - 1)//1
|> Enum.map(fn
^axis ->
reshape(group_indices, {num_elements, 1})
axis ->
shape(group_indices)
|> iota(axis: axis)
|> reshape({num_elements, 1})
end)
|> concatenate(axis: 1)
largest_group_indices =
broadcast(0, sorted)
|> indexed_add(counting_indices, broadcast(1, {num_elements}))
|> argmax(axis: axis, keep_axis: true)
indices =
largest_group_indices
|> broadcast(shape(group_indices))
|> equal(group_indices)
|> argmax(axis: axis, keep_axis: true)
res = take_along_axis(sorted, indices, axis: axis)
if opts[:keep_axis], do: res, else: squeeze(res, axes: [axis])
end
@doc """
Returns the product for the tensor.
If the `:axes` option is given, it aggregates over
the given dimensions, effectively removing them.
`axes: [0]` implies aggregating over the highest order
dimension and so forth. If the axis is negative, then
counts the axis from the back. For example, `axes: [-1]`
will always aggregate all rows.
You may optionally set `:keep_axes` to true, which will
retain the rank of the input tensor by setting the multiplied
axes to size 1.
## Examples
By default the product always returns a scalar:
iex> Nx.product(Nx.tensor(42))
#Nx.Tensor<
s64
42
>
iex> Nx.product(Nx.tensor([1, 2, 3]))
#Nx.Tensor<
s64
6
>
iex> Nx.product(Nx.tensor([[1.0, 2.0], [3.0, 4.0]]))
#Nx.Tensor<
f32
24.0
>
Giving a tensor with low precision casts it to a higher
precision to make sure the sum does not overflow:
iex> Nx.product(Nx.tensor([[10, 20], [30, 40]], type: :u8, names: [:x, :y]))
#Nx.Tensor<
u64
240000
>
iex> Nx.product(Nx.tensor([[10, 20], [30, 40]], type: :s8, names: [:x, :y]))
#Nx.Tensor<
s64
240000
>
### Aggregating over an axis
iex> Nx.product(Nx.tensor([1, 2, 3]), axes: [0])
#Nx.Tensor<
s64
6
>
Same tensor over different axes combinations:
iex> t = Nx.iota({2, 2, 3}, names: [:x, :y, :z])
iex> Nx.product(t, axes: [:x])
#Nx.Tensor<
s64[y: 2][z: 3]
[
[0, 7, 16],
[27, 40, 55]
]
>
iex> Nx.product(t, axes: [:y])
#Nx.Tensor<
s64[x: 2][z: 3]
[
[0, 4, 10],
[54, 70, 88]
]
>
iex> Nx.product(t, axes: [:x, :z])
#Nx.Tensor<
s64[y: 2]
[0, 59400]
>
iex> Nx.product(t, axes: [:z])
#Nx.Tensor<
s64[x: 2][y: 2]
[
[0, 60],
[336, 990]
]
>
iex> Nx.product(t, axes: [-3])
#Nx.Tensor<
s64[y: 2][z: 3]
[
[0, 7, 16],
[27, 40, 55]
]
>
### Keeping axes
iex> t = Nx.iota({2, 2, 3}, names: [:x, :y, :z])
iex> Nx.product(t, axes: [:z], keep_axes: true)
#Nx.Tensor<
s64[x: 2][y: 2][z: 1]
[
[
[0],
[60]
],
[
[336],
[990]
]
]
>
### Vectorized tensors
iex> t = Nx.vectorize(Nx.tensor([[1, 2], [3, 4]]), :x)
iex> Nx.product(t, axes: [0], keep_axes: true)
#Nx.Tensor<
vectorized[x: 2]
s64[1]
[
[2],
[12]
]
>
### Errors
iex> Nx.product(Nx.tensor([[1, 2]]), axes: [2])
** (ArgumentError) given axis (2) invalid for shape with rank 2
"""
@doc type: :aggregation
def product(tensor, opts \\ []) do
tensor = to_tensor(tensor)
type = Nx.Type.to_aggregate(tensor.type)
aggregate_axes_op(tensor, :product, type, opts)
end
@doc """
Returns the maximum values of the tensor.
If the `:axes` option is given, it aggregates over
the given dimensions, effectively removing them.
`axes: [0]` implies aggregating over the highest order
dimension and so forth. If the axis is negative, then
counts the axis from the back. For example, `axes: [-1]`
will always aggregate all rows.
You may optionally set `:keep_axes` to true, which will
retain the rank of the input tensor by setting the reduced
axes to size 1.
## Examples
iex> Nx.reduce_max(Nx.tensor(42))
#Nx.Tensor<
s64
42
>
iex> Nx.reduce_max(Nx.tensor(42.0))
#Nx.Tensor<
f32
42.0
>
iex> Nx.reduce_max(Nx.tensor([1, 2, 3]))
#Nx.Tensor<
s64
3
>
### Aggregating over an axis
iex> t = Nx.tensor([[3, 1, 4], [2, 1, 1]], names: [:x, :y])
iex> Nx.reduce_max(t, axes: [:x])
#Nx.Tensor<
s64[y: 3]
[3, 1, 4]
>
iex> t = Nx.tensor([[3, 1, 4], [2, 1, 1]], names: [:x, :y])
iex> Nx.reduce_max(t, axes: [:y])
#Nx.Tensor<
s64[x: 2]
[4, 2]
>
iex> t = Nx.tensor([[[1, 2], [4, 5]], [[2, 4], [3, 8]]], names: [:x, :y, :z])
iex> Nx.reduce_max(t, axes: [:x, :z])
#Nx.Tensor<
s64[y: 2]
[4, 8]
>
### Keeping axes
iex> t = Nx.tensor([[[1, 2], [4, 5]], [[2, 4], [3, 8]]], names: [:x, :y, :z])
iex> Nx.reduce_max(t, axes: [:x, :z], keep_axes: true)
#Nx.Tensor<
s64[x: 1][y: 2][z: 1]
[
[
[4],
[8]
]
]
>
### Vectorized tensors
iex> t = Nx.vectorize(Nx.tensor([[1, 2], [3, 4]]), :x)
iex> Nx.reduce_max(t, axes: [0], keep_axes: true)
#Nx.Tensor<
vectorized[x: 2]
s64[1]
[
[2],
[4]
]
>
"""
@doc type: :aggregation
def reduce_max(tensor, opts \\ []) do
%{type: type} = tensor = to_tensor(tensor)
Nx.Shared.raise_complex_not_supported(type, :reduce_max, 2)
aggregate_axes_op(tensor, :reduce_max, type, opts)
end
@doc """
Returns the minimum values of the tensor.
If the `:axes` option is given, it aggregates over
the given dimensions, effectively removing them.
`axes: [0]` implies aggregating over the highest order
dimension and so forth. If the axis is negative, then
counts the axis from the back. For example, `axes: [-1]`
will always aggregate all rows.
You may optionally set `:keep_axes` to true, which will
retain the rank of the input tensor by setting the reduced
axes to size 1.
## Examples
iex> Nx.reduce_min(Nx.tensor(42))
#Nx.Tensor<
s64
42
>
iex> Nx.reduce_min(Nx.tensor(42.0))
#Nx.Tensor<
f32
42.0
>
iex> Nx.reduce_min(Nx.tensor([1, 2, 3]))
#Nx.Tensor<
s64
1
>
### Aggregating over an axis
iex> t = Nx.tensor([[3, 1, 4], [2, 1, 1]], names: [:x, :y])
iex> Nx.reduce_min(t, axes: [:x])
#Nx.Tensor<
s64[y: 3]
[2, 1, 1]
>
iex> t = Nx.tensor([[3, 1, 4], [2, 1, 1]], names: [:x, :y])
iex> Nx.reduce_min(t, axes: [:y])
#Nx.Tensor<
s64[x: 2]
[1, 1]
>
iex> t = Nx.tensor([[[1, 2], [4, 5]], [[2, 4], [3, 8]]], names: [:x, :y, :z])
iex> Nx.reduce_min(t, axes: [:x, :z])
#Nx.Tensor<
s64[y: 2]
[1, 3]
>
### Keeping axes
iex> t = Nx.tensor([[[1, 2], [4, 5]], [[2, 4], [3, 8]]], names: [:x, :y, :z])
iex> Nx.reduce_min(t, axes: [:x, :z], keep_axes: true)
#Nx.Tensor<
s64[x: 1][y: 2][z: 1]
[
[
[1],
[3]
]
]
>
### Vectorized tensors
iex> t = Nx.vectorize(Nx.tensor([[1, 2], [3, 4]]), :x)
iex> Nx.reduce_min(t, axes: [0], keep_axes: true)
#Nx.Tensor<
vectorized[x: 2]
s64[1]
[
[1],
[3]
]
>
"""
@doc type: :aggregation
def reduce_min(tensor, opts \\ []) do
%{type: type} = tensor = to_tensor(tensor)
Nx.Shared.raise_complex_not_supported(type, :reduce_min, 2)
aggregate_axes_op(tensor, :reduce_min, type, opts)
end
defp aggregate_axes_op(tensor, op, type, opts) do
apply_vectorized(tensor, fn tensor, offset ->
%T{shape: shape, names: names} = tensor
opts = keyword!(opts, [:axes, keep_axes: false])
keep_axes = opts[:keep_axes]
axes = opts[:axes]
{shape, names, axes} =
cond do
not is_nil(axes) ->
axes = Nx.Shape.normalize_axes(shape, axes, names, offset)
{new_shape, new_names} = Nx.Shape.contract(shape, axes, names, keep_axes)
{new_shape, new_names, axes}
keep_axes ->
output_shape =
shape
|> Tuple.to_list()
|> Enum.with_index(fn axis_size, axis ->
if axis < offset do
axis_size
else
1
end
end)
|> List.to_tuple()
{output_shape, names, count_up(tuple_size(shape) - offset, offset)}
true ->
output_shape =
shape
|> Tuple.to_list()
|> Enum.take(offset)
|> List.to_tuple()
axes =
if offset != 0 do
count_up(tuple_size(shape) - offset, offset)
end
{output_shape, List.duplicate(nil, offset), axes}
end
if axes == [] do
Nx.as_type(tensor, type)
else
apply(impl!(tensor), op, [
%{tensor | type: type, shape: shape, names: names},
tensor,
[axes: axes, keep_axes: keep_axes]
])
end
end)
end
@doc """
Returns the indices of the maximum values.
## Options
* `:axis` - the axis to aggregate on. If no axis is given,
returns the index of the absolute maximum value in the tensor.
* `:keep_axis` - whether or not to keep the reduced axis with
a size of 1. Defaults to `false`.
* `:tie_break` - how to break ties. one of `:high`, or `:low`.
default behavior is to always return the lower index.
## Examples
iex> Nx.argmax(4)
#Nx.Tensor<
s64
0
>
iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]])
iex> Nx.argmax(t)
#Nx.Tensor<
s64
10
>
If a tensor of floats is given, it still returns integers:
iex> Nx.argmax(Nx.tensor([2.0, 4.0]))
#Nx.Tensor<
s64
1
>
### Aggregating over an axis
iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]])
iex> Nx.argmax(t, axis: 0)
#Nx.Tensor<
s64[2][3]
[
[1, 0, 0],
[1, 1, 0]
]
>
iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]], names: [:x, :y, :z])
iex> Nx.argmax(t, axis: :y)
#Nx.Tensor<
s64[x: 2][z: 3]
[
[0, 0, 0],
[0, 1, 0]
]
>
iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]], names: [:x, :y, :z])
iex> Nx.argmax(t, axis: :z)
#Nx.Tensor<
s64[x: 2][y: 2]
[
[0, 2],
[0, 1]
]
>
### Tie breaks
iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]], names: [:x, :y, :z])
iex> Nx.argmax(t, tie_break: :low, axis: :y)
#Nx.Tensor<
s64[x: 2][z: 3]
[
[0, 0, 0],
[0, 1, 0]
]
>
iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]], names: [:x, :y, :z])
iex> Nx.argmax(t, tie_break: :high, axis: :y)
#Nx.Tensor<
s64[x: 2][z: 3]
[
[0, 0, 1],
[0, 1, 1]
]
>
### Keep axis
iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]], names: [:x, :y, :z])
iex> Nx.argmax(t, axis: :y, keep_axis: true)
#Nx.Tensor<
s64[x: 2][y: 1][z: 3]
[
[
[0, 0, 0]
],
[
[0, 1, 0]
]
]
>
### Vectorized tensors
iex> v = Nx.tensor([[1, 2, 3], [6, 5, 4]]) |> Nx.vectorize(:x)
iex> Nx.argmax(v)
#Nx.Tensor<
vectorized[x: 2]
s64
[2, 0]
>
iex> Nx.argmax(v, axis: 0)
#Nx.Tensor<
vectorized[x: 2]
s64
[2, 0]
>
iex> Nx.argmax(v, keep_axis: true)
#Nx.Tensor<
vectorized[x: 2]
s64[1]
[
[2],
[0]
]
>
"""
@doc type: :aggregation
def argmax(tensor, opts \\ []) do
argmin_or_max(tensor, :argmax, opts)
end
@doc """
Returns the indices of the minimum values.
## Options
* `:axis` - the axis to aggregate on. If no axis is given,
returns the index of the absolute minimum value in the tensor.
* `:keep_axis` - whether or not to keep the reduced axis with
a size of 1. Defaults to `false`.
* `:tie_break` - how to break ties. one of `:high`, or `:low`.
Default behavior is to always return the lower index.
## Examples
iex> Nx.argmin(4)
#Nx.Tensor<
s64
0
>
iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]])
iex> Nx.argmin(t)
#Nx.Tensor<
s64
4
>
If a tensor of floats is given, it still returns integers:
iex> Nx.argmin(Nx.tensor([2.0, 4.0]))
#Nx.Tensor<
s64
0
>
### Aggregating over an axis
iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]])
iex> Nx.argmin(t, axis: 0)
#Nx.Tensor<
s64[2][3]
[
[0, 0, 0],
[0, 0, 0]
]
>
iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]], names: [:x, :y, :z])
iex> Nx.argmin(t, axis: 1)
#Nx.Tensor<
s64[x: 2][z: 3]
[
[1, 1, 0],
[1, 0, 0]
]
>
iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]], names: [:x, :y, :z])
iex> Nx.argmin(t, axis: :z)
#Nx.Tensor<
s64[x: 2][y: 2]
[
[1, 1],
[1, 2]
]
>
### Tie breaks
iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]], names: [:x, :y, :z])
iex> Nx.argmin(t, tie_break: :low, axis: :y)
#Nx.Tensor<
s64[x: 2][z: 3]
[
[1, 1, 0],
[1, 0, 0]
]
>
iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]], names: [:x, :y, :z])
iex> Nx.argmin(t, tie_break: :high, axis: :y)
#Nx.Tensor<
s64[x: 2][z: 3]
[
[1, 1, 1],
[1, 0, 1]
]
>
### Keep axis
iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]], names: [:x, :y, :z])
iex> Nx.argmin(t, axis: :y, keep_axis: true)
#Nx.Tensor<
s64[x: 2][y: 1][z: 3]
[
[
[1, 1, 0]
],
[
[1, 0, 0]
]
]
>
### Vectorized tensors
iex> v = Nx.tensor([[1, 2, 3], [6, 5, 4]]) |> Nx.vectorize(:x)
iex> Nx.argmin(v)
#Nx.Tensor<
vectorized[x: 2]
s64
[0, 2]
>
iex> Nx.argmin(v, axis: 0)
#Nx.Tensor<
vectorized[x: 2]
s64
[0, 2]
>
iex> Nx.argmin(v, keep_axis: true)
#Nx.Tensor<
vectorized[x: 2]
s64[1]
[
[0],
[2]
]
>
"""
@doc type: :aggregation
def argmin(tensor, opts \\ []) do
argmin_or_max(tensor, :argmin, opts)
end
defp argmin_or_max(tensor, op, opts) do
apply_vectorized(tensor, fn tensor, offset ->
opts = keyword!(opts, [:axis, tie_break: :low, keep_axis: false])
tie_break =
case opts[:tie_break] do
:high ->
:high
:low ->
:low
other ->
raise ArgumentError,
"unknown value for :tie_break, expected :high or :low, got: #{inspect(other)}"
end
%{shape: shape, names: names, type: type} = tensor
Nx.Shared.raise_complex_not_supported(type, op, 2)
{tensor, shape, names, axis} =
cond do
axis = opts[:axis] ->
axis = Nx.Shape.normalize_axis(shape, axis, names, offset)
{new_shape, new_names} = Nx.Shape.contract(shape, [axis], names, opts[:keep_axis])
{tensor, new_shape, new_names, axis}
offset == 0 ->
# unvectorized case, so we can reduce all
{tensor, {}, [], nil}
true ->
{new_shape, new_names} =
Nx.Shape.contract(
shape,
count_up(tuple_size(shape) - offset, offset),
names,
opts[:keep_axis]
)
flattened_shape =
if opts[:keep_axis] do
new_shape
|> Tuple.delete_at(tuple_size(new_shape) - 1)
|> Tuple.append(:auto)
else
Tuple.append(new_shape, :auto)
end
reshaped_tensor = reshape(tensor, flattened_shape)
{reshaped_tensor, new_shape, new_names, offset}
end
out = %{tensor | type: {:s, 64}, shape: shape, names: names}
opts = [tie_break: tie_break, axis: axis, keep_axis: opts[:keep_axis]]
apply(impl!(tensor), op, [out, tensor, opts])
end)
end
defp aggregate_window_op(tensor, window_dimensions, opts, op) when is_list(opts) do
apply_vectorized(tensor, fn tensor, offset ->
opts = keyword!(opts, [:window_dilations, padding: :valid, strides: 1])
Nx.Shape.validate!(window_dimensions, :window_dimensions)
%{shape: shape} = tensor
strides = opts[:strides]
padding = opts[:padding]
offset_ones = List.duplicate(1, offset)
dilations =
case opts[:window_dilations] do
nil ->
List.duplicate(1, rank(shape))
dilations when is_integer(dilations) ->
offset_ones ++ List.duplicate(dilations, rank(shape) - offset)
dilations ->
offset_ones ++ dilations
end
strides =
cond do
strides == 1 ->
List.duplicate(1, rank(shape))
is_integer(strides) ->
offset_ones ++ List.duplicate(strides, rank(shape) - offset)
true ->
offset_ones ++ strides
end
window_dimensions = List.to_tuple(offset_ones ++ Tuple.to_list(window_dimensions))
{output_shape, padding_config} =
Nx.Shape.pool(shape, window_dimensions, strides, padding, dilations)
out = %{tensor | shape: output_shape}
opts = [padding: padding_config, strides: strides, window_dilations: dilations]
apply(impl!(tensor), op, [out, tensor, window_dimensions, opts])
end)
end
@doc """
Sums over each window of size `window_dimensions` in the
given tensor, producing a tensor that contains the same
number of elements as valid positions of the window.
You may optionally specify `:strides` which is a tuple
of non-zero steps to take along each axis between
each window.
You may also optionally specify `:padding` which is either
one of `:valid` (no padding) or `:same` (pad so output shape
is the same as input shape) or a general padding configuration
for each dimension in the input tensor. Your padding configuration
cannot include any negative pad values. You may only specify
padding for the high and low edges of the given dimension. Pads
with `0`.
## Examples
iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]]])
iex> Nx.window_sum(t, {1, 2, 1})
#Nx.Tensor<
s64[2][1][3]
[
[
[5, 7, 9]
],
[
[5, 7, 9]
]
]
>
iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]]])
iex> Nx.window_sum(t, {2, 2, 1}, strides: [1, 2, 3], padding: [{0, 1}, {2, 0}, {1, 1}])
#Nx.Tensor<
s64[2][2][2]
[
[
[0, 0],
[0, 18]
],
[
[0, 0],
[0, 9]
]
]
>
iex> t = Nx.tensor([[[4.0, 2.0, 3.0], [2.0, 5.0, 6.5]], [[1.2, 2.2, 3.2], [4.0, 5.0, 6.2]]])
iex> Nx.window_sum(t, {2, 1, 1}, strides: [2, 1, 1], padding: [{1, 1}, {0, 0}, {1, 1}])
#Nx.Tensor<
f32[2][2][5]
[
[
[0.0, 4.0, 2.0, 3.0, 0.0],
[0.0, 2.0, 5.0, 6.5, 0.0]
],
[
[0.0, 1.2000000476837158, 2.200000047683716, 3.200000047683716, 0.0],
[0.0, 4.0, 5.0, 6.199999809265137, 0.0]
]
]
>
iex> t = Nx.tensor([[[4, 2, 1, 3], [4, 2, 1, 7]], [[1, 2, 5, 7], [1, 8, 9, 2]]])
iex> opts = [strides: [2, 1, 1], padding: :valid, window_dilations: [1, 2, 1]]
iex> Nx.window_sum(t, {1, 1, 2}, opts)
#Nx.Tensor<
s64[1][2][3]
[
[
[6, 3, 4],
[6, 3, 8]
]
]
>
iex> t = Nx.tensor([[[4, 2, 1, 3], [4, 2, 1, 7]], [[1, 2, 5, 7], [1, 8, 9, 2]]])
iex> opts = [strides: [2, 1, 1], padding: :valid, window_dilations: [1, 2, 2]]
iex> Nx.window_sum(t, {1, 1, 2}, opts)
#Nx.Tensor<
s64[1][2][2]
[
[
[5, 5],
[5, 9]
]
]
>
iex> t = Nx.tensor([[[4, 2, 1, 3], [4, 2, 1, 7]], [[1, 2, 5, 7], [1, 8, 9, 2]]])
iex> opts = [strides: [2, 1, 1], padding: [{2, 1}, {3, 1}, {1, 0}], window_dilations: [1, 2, 2]]
iex> Nx.window_sum(t, {2, 1, 2}, opts)
#Nx.Tensor<
s64[2][6][3]
[
[
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0]
],
[
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[4, 11, 14],
[10, 15, 19],
[0, 0, 0]
]
]
>
## Vectorized tensors
For vectorized tensors, the windows will slide throughout all vectorized axes,
and all options refer to the inner shape only.
iex> t = Nx.iota({2, 1, 2, 5}) |> Nx.vectorize(:x) |> Nx.vectorize(:y)
#Nx.Tensor<
vectorized[x: 2][y: 1]
s64[2][5]
[
[
[
[0, 1, 2, 3, 4],
[5, 6, 7, 8, 9]
]
],
[
[
[10, 11, 12, 13, 14],
[15, 16, 17, 18, 19]
]
]
]
>
iex> Nx.window_sum(t, {2, 2}, strides: [1, 2], window_dilations: [1, 2])
#Nx.Tensor<
vectorized[x: 2][y: 1]
s64[1][2]
[
[
[
[14, 22]
]
],
[
[
[54, 62]
]
]
]
>
"""
@doc type: :window
def window_sum(tensor, window_dimensions, opts \\ []),
do: aggregate_window_op(tensor, window_dimensions, opts, :window_sum)
@doc """
Averages over each window of size `window_dimensions` in the
given tensor, producing a tensor that contains the same
number of elements as valid positions of the window.
You may optionally specify `:strides` which is a tuple
of non-zero steps to take along each axis between
each window.
You may also optionally specify `:padding` which is either
one of `:valid` (no padding) or `:same` (pad so output shape
is the same as input shape) or a general padding configuration
for each dimension in the input tensor. Your padding configuration
cannot include any negative pad values. You may only specify
padding for the high and low edges of the given dimension. Pads
with `0`.
## Examples
iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]]])
iex> Nx.window_mean(t, {1, 2, 1})
#Nx.Tensor<
f32[2][1][3]
[
[
[2.5, 3.5, 4.5]
],
[
[2.5, 3.5, 4.5]
]
]
>
iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]]])
iex> Nx.window_mean(t, {2, 2, 1}, strides: [1, 2, 3], padding: [{0, 1}, {2, 0}, {1, 1}])
#Nx.Tensor<
f32[2][2][2]
[
[
[0.0, 0.0],
[0.0, 4.5]
],
[
[0.0, 0.0],
[0.0, 2.25]
]
]
>
iex> t = Nx.tensor([[[4.0, 2.0, 3.0], [2.0, 5.0, 6.5]], [[1.2, 2.2, 3.2], [4.0, 5.0, 6.2]]])
iex> Nx.window_mean(t, {2, 1, 1}, strides: [2, 1, 1], padding: [{1, 1}, {0, 0}, {1, 1}])
#Nx.Tensor<
f32[2][2][5]
[
[
[0.0, 2.0, 1.0, 1.5, 0.0],
[0.0, 1.0, 2.5, 3.25, 0.0]
],
[
[0.0, 0.6000000238418579, 1.100000023841858, 1.600000023841858, 0.0],
[0.0, 2.0, 2.5, 3.0999999046325684, 0.0]
]
]
>
iex> t = Nx.tensor([[[4, 2, 1, 3], [4, 2, 1, 7]], [[1, 2, 5, 7], [1, 8, 9, 2]]])
iex> opts = [strides: [2, 1, 1], padding: :valid, window_dilations: [1, 2, 1]]
iex> Nx.window_mean(t, {1, 1, 2}, opts)
#Nx.Tensor<
f32[1][2][3]
[
[
[3.0, 1.5, 2.0],
[3.0, 1.5, 4.0]
]
]
>
iex> t = Nx.tensor([[[4, 2, 1, 3], [4, 2, 1, 7]], [[1, 2, 5, 7], [1, 8, 9, 2]]])
iex> opts = [strides: [2, 1, 1], padding: :valid, window_dilations: [1, 2, 2]]
iex> Nx.window_mean(t, {1, 1, 2}, opts)
#Nx.Tensor<
f32[1][2][2]
[
[
[2.5, 2.5],
[2.5, 4.5]
]
]
>
## Vectorized tensors
For vectorized tensors, the windows will slide throughout all vectorized axes,
and all options refer to the inner shape only.
iex> t = Nx.iota({2, 1, 2, 5}) |> Nx.vectorize(:x) |> Nx.vectorize(:y)
#Nx.Tensor<
vectorized[x: 2][y: 1]
s64[2][5]
[
[
[
[0, 1, 2, 3, 4],
[5, 6, 7, 8, 9]
]
],
[
[
[10, 11, 12, 13, 14],
[15, 16, 17, 18, 19]
]
]
]
>
iex> Nx.window_mean(t, {2, 2}, strides: [1, 2], window_dilations: [1, 2])
#Nx.Tensor<
vectorized[x: 2][y: 1]
f32[1][2]
[
[
[
[3.5, 5.5]
]
],
[
[
[13.5, 15.5]
]
]
]
>
"""
@doc type: :window
def window_mean(tensor, window_dimensions, opts \\ []) do
divide(window_sum(tensor, window_dimensions, opts), size(window_dimensions))
end
@doc """
Returns the maximum over each window of size `window_dimensions`
in the given tensor, producing a tensor that contains the same
number of elements as valid positions of the window.
You may optionally specify `:strides` which is a tuple
of non-zero steps to take along each axis between
each window.
You may also optionally specify `:padding` which is either
one of `:valid` (no padding) or `:same` (pad so output shape
is the same as input shape) or a general padding configuration
for each dimension in the input tensor. Your padding configuration
cannot include any negative pad values. You may only specify
padding for the high and low edges of the given dimension. Pads
with the minimum value for the type of the given tensor.
## Examples
iex> Nx.window_max(Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]]]), {1, 2, 1})
#Nx.Tensor<
s64[2][1][3]
[
[
[4, 5, 6]
],
[
[4, 5, 6]
]
]
>
iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]]])
iex> Nx.window_max(t, {2, 2, 1}, strides: [1, 2, 3], padding: [{0, 1}, {2, 0}, {1, 1}])
#Nx.Tensor<
s64[2][2][2]
[
[
[-9223372036854775808, -9223372036854775808],
[-9223372036854775808, 6]
],
[
[-9223372036854775808, -9223372036854775808],
[-9223372036854775808, 6]
]
]
>
iex> t = Nx.tensor([[[4.0, 2.0, 3.0], [2.0, 5.0, 6.5]], [[1.2, 2.2, 3.2], [4.0, 5.0, 6.2]]])
iex> Nx.window_max(t, {2, 1, 1}, strides: [2, 1, 1], padding: [{1, 1}, {0, 0}, {1, 1}])
#Nx.Tensor<
f32[2][2][5]
[
[
[-Inf, 4.0, 2.0, 3.0, -Inf],
[-Inf, 2.0, 5.0, 6.5, -Inf]
],
[
[-Inf, 1.2000000476837158, 2.200000047683716, 3.200000047683716, -Inf],
[-Inf, 4.0, 5.0, 6.199999809265137, -Inf]
]
]
>
iex> t = Nx.tensor([[[4, 2, 1, 3], [4, 2, 1, 7]], [[1, 2, 5, 7], [1, 8, 9, 2]]])
iex> opts = [strides: [2, 1, 1], padding: :valid, window_dilations: [1, 2, 2]]
iex> Nx.window_max(t, {1, 1, 2}, opts)
#Nx.Tensor<
s64[1][2][2]
[
[
[4, 3],
[4, 7]
]
]
>
## Vectorized tensors
For vectorized tensors, the windows will slide throughout all vectorized axes,
and all options refer to the inner shape only.
iex> t = Nx.iota({2, 1, 2, 5}) |> Nx.vectorize(:x) |> Nx.vectorize(:y)
#Nx.Tensor<
vectorized[x: 2][y: 1]
s64[2][5]
[
[
[
[0, 1, 2, 3, 4],
[5, 6, 7, 8, 9]
]
],
[
[
[10, 11, 12, 13, 14],
[15, 16, 17, 18, 19]
]
]
]
>
iex> Nx.window_max(t, {2, 2}, strides: [1, 2], window_dilations: [1, 2])
#Nx.Tensor<
vectorized[x: 2][y: 1]
s64[1][2]
[
[
[
[7, 9]
]
],
[
[
[17, 19]
]
]
]
>
"""
@doc type: :window
def window_max(tensor, window_dimensions, opts \\ []) do
tensor = to_tensor(tensor)
Nx.Shared.raise_complex_not_supported(tensor.type, :window_max, 3)
aggregate_window_op(tensor, window_dimensions, opts, :window_max)
end
@doc """
Returns the minimum over each window of size `window_dimensions`
in the given tensor, producing a tensor that contains the same
number of elements as valid positions of the window.
You may optionally specify `:strides` which is a tuple
of non-zero steps to take along each axis between
each window.
You may also optionally specify `:padding` which is either
one of `:valid` (no padding) or `:same` (pad so output shape
is the same as input shape) or a general padding configuration
for each dimension in the input tensor. Your padding configuration
cannot include any negative pad values. You may only specify
padding for the high and low edges of the given dimension. Pads
with the maximum value for the type of the given tensor.
## Examples
iex> Nx.window_min(Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]]]), {1, 2, 1})
#Nx.Tensor<
s64[2][1][3]
[
[
[1, 2, 3]
],
[
[1, 2, 3]
]
]
>
iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]]])
iex> Nx.window_min(t, {2, 2, 1}, strides: [1, 2, 3], padding: [{0, 1}, {2, 0}, {1, 1}])
#Nx.Tensor<
s64[2][2][2]
[
[
[9223372036854775807, 9223372036854775807],
[9223372036854775807, 3]
],
[
[9223372036854775807, 9223372036854775807],
[9223372036854775807, 3]
]
]
>
iex> t = Nx.tensor([[[4.0, 2.0, 3.0], [2.0, 5.0, 6.5]], [[1.2, 2.2, 3.2], [4.0, 5.0, 6.2]]])
iex> Nx.window_min(t, {2, 1, 1}, strides: [2, 1, 1], padding: [{1, 1}, {0, 0}, {1, 1}])
#Nx.Tensor<
f32[2][2][5]
[
[
[Inf, 4.0, 2.0, 3.0, Inf],
[Inf, 2.0, 5.0, 6.5, Inf]
],
[
[Inf, 1.2000000476837158, 2.200000047683716, 3.200000047683716, Inf],
[Inf, 4.0, 5.0, 6.199999809265137, Inf]
]
]
>
iex> t = Nx.tensor([[[4, 2, 1, 3], [4, 2, 1, 7]], [[1, 2, 5, 7], [1, 8, 9, 2]]])
iex> opts = [strides: [2, 1, 1], padding: :valid, window_dilations: [1, 2, 2]]
iex> Nx.window_min(t, {1, 1, 2}, opts)
#Nx.Tensor<
s64[1][2][2]
[
[
[1, 2],
[1, 2]
]
]
>
## Vectorized tensors
For vectorized tensors, the windows will slide throughout all vectorized axes,
and all options refer to the inner shape only.
iex> t = Nx.iota({2, 1, 2, 5}) |> Nx.vectorize(:x) |> Nx.vectorize(:y)
#Nx.Tensor<
vectorized[x: 2][y: 1]
s64[2][5]
[
[
[
[0, 1, 2, 3, 4],
[5, 6, 7, 8, 9]
]
],
[
[
[10, 11, 12, 13, 14],
[15, 16, 17, 18, 19]
]
]
]
>
iex> Nx.window_min(t, {2, 2}, strides: [1, 2], window_dilations: [1, 2])
#Nx.Tensor<
vectorized[x: 2][y: 1]
s64[1][2]
[
[
[
[0, 2]
]
],
[
[
[10, 12]
]
]
]
>
"""
@doc type: :window
def window_min(tensor, window_dimensions, opts \\ []) do
tensor = to_tensor(tensor)
Nx.Shared.raise_complex_not_supported(tensor.type, :window_min, 3)
aggregate_window_op(tensor, window_dimensions, opts, :window_min)
end
@doc """
Returns the product over each window of size `window_dimensions`
in the given tensor, producing a tensor that contains the same
number of elements as valid positions of the window.
The rank of the input tensor and the window dimensions must
match.
You may optionally specify `:strides` which is a tuple
of non-zero steps to take along each axis between
each window.
You may also optionally specify `:padding` which is either
one of `:valid` (no padding) or `:same` (pad so output shape
is the same as input shape) or a general padding configuration
for each dimension in the input tensor. Your padding configuration
cannot include any negative pad values. You may only specify
padding for the high and low edges of the given dimension. Pads
with 1.
## Examples
iex> Nx.window_product(Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]]]), {1, 2, 1})
#Nx.Tensor<
s64[2][1][3]
[
[
[4, 10, 18]
],
[
[4, 10, 18]
]
]
>
iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]]])
iex> Nx.window_product(t, {2, 2, 1}, strides: [1, 2, 3], padding: [{0, 1}, {2, 0}, {1, 1}])
#Nx.Tensor<
s64[2][2][2]
[
[
[1, 1],
[1, 324]
],
[
[1, 1],
[1, 18]
]
]
>
iex> t = Nx.tensor([[[4.0, 2.0, 3.0], [2.0, 5.0, 6.5]], [[1.2, 2.2, 3.2], [4.0, 5.0, 6.2]]])
iex> Nx.window_product(t, {2, 1, 1}, strides: [2, 1, 1], padding: [{1, 1}, {0, 0}, {1, 1}])
#Nx.Tensor<
f32[2][2][5]
[
[
[1.0, 4.0, 2.0, 3.0, 1.0],
[1.0, 2.0, 5.0, 6.5, 1.0]
],
[
[1.0, 1.2000000476837158, 2.200000047683716, 3.200000047683716, 1.0],
[1.0, 4.0, 5.0, 6.199999809265137, 1.0]
]
]
>
iex> t = Nx.tensor([[[4, 2, 1, 3], [4, 2, 1, 7]], [[1, 2, 5, 7], [1, 8, 9, 2]]])
iex> opts = [strides: [2, 1, 1], padding: :valid, window_dilations: [1, 2, 2]]
iex> Nx.window_product(t, {1, 1, 2}, opts)
#Nx.Tensor<
s64[1][2][2]
[
[
[4, 6],
[4, 14]
]
]
>
## Vectorized tensors
For vectorized tensors, the windows will slide throughout all vectorized axes,
and all options refer to the inner shape only.
iex> t = Nx.iota({2, 1, 2, 5}) |> Nx.vectorize(:x) |> Nx.vectorize(:y)
#Nx.Tensor<
vectorized[x: 2][y: 1]
s64[2][5]
[
[
[
[0, 1, 2, 3, 4],
[5, 6, 7, 8, 9]
]
],
[
[
[10, 11, 12, 13, 14],
[15, 16, 17, 18, 19]
]
]
]
>
iex> Nx.window_product(t, {2, 2}, strides: [1, 2], window_dilations: [1, 2])
#Nx.Tensor<
vectorized[x: 2][y: 1]
s64[1][2]
[
[
[
[0, 504]
]
],
[
[
[30600, 54264]
]
]
]
>
"""
@doc type: :window
def window_product(tensor, window_dimensions, opts \\ []),
do: aggregate_window_op(tensor, window_dimensions, opts, :window_product)
@doc """
Returns the cumulative sum of elements along an axis.
## Options
* `:axis` - the axis to sum elements along. Defaults to `0`
* `:reverse` - whether to perform accumulation in the opposite direction. Defaults to `false`
## Examples
iex> Nx.cumulative_sum(Nx.tensor([1, 2, 3, 4]))
#Nx.Tensor<
s64[4]
[1, 3, 6, 10]
>
iex> Nx.cumulative_sum(Nx.iota({3, 3}), axis: 0)
#Nx.Tensor<
s64[3][3]
[
[0, 1, 2],
[3, 5, 7],
[9, 12, 15]
]
>
iex> Nx.cumulative_sum(Nx.iota({3, 3}), axis: 1)
#Nx.Tensor<
s64[3][3]
[
[0, 1, 3],
[3, 7, 12],
[6, 13, 21]
]
>
iex> Nx.cumulative_sum(Nx.iota({3, 3}), axis: 0, reverse: true)
#Nx.Tensor<
s64[3][3]
[
[9, 12, 15],
[9, 11, 13],
[6, 7, 8]
]
>
iex> Nx.cumulative_sum(Nx.iota({3, 3}), axis: 1, reverse: true)
#Nx.Tensor<
s64[3][3]
[
[3, 3, 2],
[12, 9, 5],
[21, 15, 8]
]
>
## Vectorized axes
Works the same as if the accumulation was to happen over a list of tensors.
`:axis` refers to the non-vectorized shape.
iex> Nx.cumulative_sum(Nx.tensor([[2, 3, 1], [1, 3, 2], [2, 1, 3]]) |> Nx.vectorize(:x), axis: 0)
#Nx.Tensor<
vectorized[x: 3]
s64[3]
[
[2, 5, 6],
[1, 4, 6],
[2, 3, 6]
]
>
"""
@doc type: :cumulative
def cumulative_sum(tensor, opts \\ []),
do: cumulative_op(tensor, opts, :cumulative_sum, &Nx.add/2)
@doc """
Returns the cumulative product of elements along an axis.
## Options
* `:axis` - the axis to multiply elements along. Defaults to `0`
* `:reverse` - whether to perform accumulation in the opposite direction. Defaults to `false`
## Examples
iex> Nx.cumulative_product(Nx.tensor([1, 2, 3, 4]))
#Nx.Tensor<
s64[4]
[1, 2, 6, 24]
>
iex> Nx.cumulative_product(Nx.iota({3, 3}), axis: 0)
#Nx.Tensor<
s64[3][3]
[
[0, 1, 2],
[0, 4, 10],
[0, 28, 80]
]
>
iex> Nx.cumulative_product(Nx.iota({3, 3}), axis: 1)
#Nx.Tensor<
s64[3][3]
[
[0, 0, 0],
[3, 12, 60],
[6, 42, 336]
]
>
iex> Nx.cumulative_product(Nx.iota({3, 3}), axis: 0, reverse: true)
#Nx.Tensor<
s64[3][3]
[
[0, 28, 80],
[18, 28, 40],
[6, 7, 8]
]
>
iex> Nx.cumulative_product(Nx.iota({3, 3}), axis: 1, reverse: true)
#Nx.Tensor<
s64[3][3]
[
[0, 2, 2],
[60, 20, 5],
[336, 56, 8]
]
>
## Vectorized axes
Works the same as if the accumulation was to happen over a list of tensors.
`:axis` refers to the non-vectorized shape.
iex> Nx.cumulative_product(Nx.tensor([[2, 3, 0], [1, 3, 2], [2, 1, 3]]) |> Nx.vectorize(:x), axis: 0)
#Nx.Tensor<
vectorized[x: 3]
s64[3]
[
[2, 6, 0],
[1, 3, 6],
[2, 2, 6]
]
>
"""
@doc type: :cumulative
def cumulative_product(tensor, opts \\ []),
do: cumulative_op(tensor, opts, :cumulative_product, &Nx.multiply/2)
@doc """
Returns the cumulative minimum of elements along an axis.
## Options
* `:axis` - the axis to compare elements along. Defaults to `0`
* `:reverse` - whether to perform accumulation in the opposite direction. Defaults to `false`
## Examples
iex> Nx.cumulative_min(Nx.tensor([3, 4, 2, 1]))
#Nx.Tensor<
s64[4]
[3, 3, 2, 1]
>
iex> Nx.cumulative_min(Nx.tensor([[2, 3, 1], [1, 3, 2], [2, 1, 3]]), axis: 0)
#Nx.Tensor<
s64[3][3]
[
[2, 3, 1],
[1, 3, 1],
[1, 1, 1]
]
>
iex> Nx.cumulative_min(Nx.tensor([[2, 3, 1], [1, 3, 2], [2, 1, 3]]), axis: 1)
#Nx.Tensor<
s64[3][3]
[
[2, 2, 1],
[1, 1, 1],
[2, 1, 1]
]
>
iex> Nx.cumulative_min(Nx.tensor([[2, 3, 1], [1, 3, 2], [2, 1, 3]]), axis: 0, reverse: true)
#Nx.Tensor<
s64[3][3]
[
[1, 1, 1],
[1, 1, 2],
[2, 1, 3]
]
>
iex> Nx.cumulative_min(Nx.tensor([[2, 3, 1], [1, 3, 2], [2, 1, 3]]), axis: 1, reverse: true)
#Nx.Tensor<
s64[3][3]
[
[1, 1, 1],
[1, 2, 2],
[1, 1, 3]
]
>
## Vectorized axes
Works the same as if the accumulation was to happen over a list of tensors.
`:axis` refers to the non-vectorized shape.
iex> Nx.cumulative_min(Nx.tensor([[2, 3, 1], [1, 3, 2], [2, 1, 3]]) |> Nx.vectorize(:x), axis: 0)
#Nx.Tensor<
vectorized[x: 3]
s64[3]
[
[2, 2, 1],
[1, 1, 1],
[2, 1, 1]
]
>
"""
@doc type: :cumulative
def cumulative_min(tensor, opts \\ []),
do: cumulative_op(tensor, opts, :cumulative_min, &Nx.min/2)
@doc """
Returns the cumulative maximum of elements along an axis.
## Options
* `:axis` - the axis to compare elements along. Defaults to `0`
* `:reverse` - whether to perform accumulation in the opposite direction. Defaults to `false`
## Examples
iex> Nx.cumulative_max(Nx.tensor([3, 4, 2, 1]))
#Nx.Tensor<
s64[4]
[3, 4, 4, 4]
>
iex> Nx.cumulative_max(Nx.tensor([[2, 3, 1], [1, 3, 2], [2, 1, 3]]), axis: 0)
#Nx.Tensor<
s64[3][3]
[
[2, 3, 1],
[2, 3, 2],
[2, 3, 3]
]
>
iex> Nx.cumulative_max(Nx.tensor([[2, 3, 1], [1, 3, 2], [2, 1, 3]]), axis: 1)
#Nx.Tensor<
s64[3][3]
[
[2, 3, 3],
[1, 3, 3],
[2, 2, 3]
]
>
iex> Nx.cumulative_max(Nx.tensor([[2, 3, 1], [1, 3, 2], [2, 1, 3]]), axis: 0, reverse: true)
#Nx.Tensor<
s64[3][3]
[
[2, 3, 3],
[2, 3, 3],
[2, 1, 3]
]
>
iex> Nx.cumulative_max(Nx.tensor([[2, 3, 1], [1, 3, 2], [2, 1, 3]]), axis: 1, reverse: true)
#Nx.Tensor<
s64[3][3]
[
[3, 3, 1],
[3, 3, 2],
[3, 3, 3]
]
>
## Vectorized axes
Works the same as if the accumulation was to happen over a list of tensors.
`:axis` refers to the non-vectorized shape.
iex> Nx.cumulative_max(Nx.tensor([[2, 3, 1], [1, 3, 2], [2, 1, 3]]) |> Nx.vectorize(:x), axis: 0)
#Nx.Tensor<
vectorized[x: 3]
s64[3]
[
[2, 3, 3],
[1, 3, 3],
[2, 2, 3]
]
>
"""
@doc type: :cumulative
def cumulative_max(tensor, opts \\ []),
do: cumulative_op(tensor, opts, :cumulative_max, &Nx.max/2)
defp cumulative_op(tensor, opts, op, reduce_fun) do
apply_vectorized(tensor, fn tensor, offset ->
opts = keyword!(opts, axis: 0, reverse: false)
reverse = opts[:reverse]
axis = Nx.Shape.normalize_axis(tensor.shape, opts[:axis], tensor.names, offset)
Nx.Shared.optional(op, [tensor, [axis: axis, reverse: reverse]], tensor, fn tensor, opts ->
associative_scan(tensor, reduce_fun, opts)
end)
end)
end
@doc """
Calculate the n-th discrete difference along the given axis.
The first difference is given by $out_i = a_{i+1} - a_i$ along the given axis,
higher differences are calculated by using `diff` recursively.
## Options
* `:order` - the number of times to perform the difference. Defaults to `1`
* `:axis` - the axis to perform the difference along. Defaults to `-1`
## Examples
iex> Nx.diff(Nx.tensor([1, 2, 4, 7, 0]))
#Nx.Tensor<
s64[4]
[1, 2, 3, -7]
>
iex> Nx.diff(Nx.tensor([1, 2, 4, 7, 0]), order: 2)
#Nx.Tensor<
s64[3]
[1, 1, -10]
>
iex> Nx.diff(Nx.tensor([[1, 3, 6, 10], [0, 5, 6, 8]]))
#Nx.Tensor<
s64[2][3]
[
[2, 3, 4],
[5, 1, 2]
]
>
iex> Nx.diff(Nx.tensor([[1, 3, 6, 10], [0, 5, 6, 8]]), axis: 0)
#Nx.Tensor<
s64[1][4]
[
[-1, 2, 0, -2]
]
>
iex> Nx.diff(Nx.tensor([1, 2, 4, 7, 0]), order: 0)
#Nx.Tensor<
s64[5]
[1, 2, 4, 7, 0]
>
iex> Nx.diff(Nx.tensor([1, 2, 4, 7, 0]), order: -1)
** (ArgumentError) order must be non-negative but got: -1
"""
@doc type: :ndim
def diff(tensor, opts \\ []) do
opts = keyword!(opts, order: 1, axis: -1)
%T{shape: shape, names: names} = tensor = to_tensor(tensor)
n = opts[:order]
axis = Nx.Shape.normalize_axis(shape, opts[:axis], names)
if rank(tensor) == 0 do
raise ArgumentError, "cannot compute diff of a scalar"
end
if n < 0 do
raise ArgumentError, "order must be non-negative but got: #{inspect(n)}"
end
axis_size = Nx.axis_size(tensor, axis)
Enum.reduce(0..(n - 1)//1, tensor, fn x, acc ->
subtract(
slice_along_axis(acc, 1, axis_size - x - 1, axis: axis),
slice_along_axis(acc, 0, axis_size - x - 1, axis: axis)
)
end)
end
# Scans the given tensor using an associative binary operator.
#
# The scanning function must be associative and perform an element-wise
# operation over the `:axis` dimension.
#
# ## Options
#
# * `:axis` - the axis to scan along. Defaults to `0`
#
# * `:reverse` - whether to scan in the opposite direction. Defaults to `false`
#
# ## Examples
#
# A cumulative sum of numbers can be expressed as:
#
# iex> Nx.associative_scan(Nx.tensor([1, 2, 3, 4]), &Nx.add/2)
# #Nx.Tensor<
# s64[4]
# [1, 3, 6, 10]
# >
#
# Or a reversed one:
#
# iex> Nx.associative_scan(Nx.tensor([1, 2, 3, 4]), &Nx.add/2, reverse: true)
# #Nx.Tensor<
# s64[4]
# [10, 9, 7, 4]
# >
#
# A cumulative product of a sequence of matrices:
#
# iex> matrices = Nx.tensor([[2, 0], [0, 2]]) |> Nx.tile([3, 1, 1])
# iex> Nx.associative_scan(matrices, &Nx.dot(&1, [2], [0], &2, [1], [0]))
# #Nx.Tensor<
# s64[3][2][2]
# [
# [
# [2, 0],
# [0, 2]
# ],
# [
# [4, 0],
# [0, 4]
# ],
# [
# [8, 0],
# [0, 8]
# ]
# ]
# >
#
defp associative_scan(tensor, fun, opts) do
opts = keyword!(opts, axis: 0, reverse: false)
tensor
|> maybe_reverse(opts[:reverse])
|> do_associative_scan(fun, axis: opts[:axis])
|> maybe_reverse(opts[:reverse])
|> rename(tensor.names)
end
defp maybe_reverse(tensor, true), do: Nx.reverse(tensor)
defp maybe_reverse(tensor, false), do: tensor
# Let's assume addition as the reduction function. The algorithm is based
# on two observations:
#
# 1. Elements at odd indices in the final result can be computed by first
# summing consecutive pairs of elements and performing a scan on that
# half-sized tensor (recursively).
#
# 2. Elements at even indices in the final result can be computed from those
# at odd indices (from 1.) by adding a corresponding even element from the
# original tensor.
#
# Also see https://en.wikipedia.org/wiki/Prefix_sum#Algorithm_2:_Work-efficient.
defp do_associative_scan(tensor, fun, opts) do
axis = opts[:axis]
axis_size = Nx.axis_size(tensor, axis)
if axis_size < 2 do
tensor
else
even = Nx.slice_along_axis(tensor, 0, axis_size - 1, axis: axis, strides: 2)
odd = Nx.slice_along_axis(tensor, 1, axis_size - 1, axis: axis, strides: 2)
reduced_pairs = fun.(odd, even)
scanned_odd = do_associative_scan(reduced_pairs, fun, opts)
cond do
axis_size == 2 ->
Nx.concatenate([even, reduced_pairs], axis: axis)
rem(axis_size, 2) == 0 ->
scanned_even =
fun.(
Nx.slice_along_axis(scanned_odd, 0, div(axis_size, 2) - 1, axis: axis),
Nx.slice_along_axis(even, 1, div(axis_size, 2) - 1, axis: axis)
)
scanned_even =
Nx.concatenate(
[Nx.slice_along_axis(even, 0, 1, axis: axis), scanned_even],
axis: axis
)
interleave(scanned_even, scanned_odd, axis: axis)
true ->
scanned_even =
fun.(
scanned_odd,
Nx.slice_along_axis(tensor, 2, axis_size - 2, axis: axis, strides: 2)
)
Nx.concatenate(
[
Nx.slice_along_axis(tensor, 0, 1, axis: axis),
interleave(scanned_odd, scanned_even, axis: axis)
],
axis: axis
)
end
end
end
# Interleaves elements from same-shaped tensors along an axis
defp interleave(left, right, opts) do
opts = keyword!(opts, axis: 0)
axis = opts[:axis]
interleave_axis = axis + 1
Nx.concatenate(
[
Nx.new_axis(left, interleave_axis),
Nx.new_axis(right, interleave_axis)
],
axis: interleave_axis
)
|> flatten_axis(interleave_axis)
end
# Merges the given axis with the preceding one
defp flatten_axis(tensor, axis) do
shape = Nx.shape(tensor)
new_shape = shape |> Tuple.delete_at(axis) |> put_elem(axis - 1, :auto)
Nx.reshape(tensor, new_shape)
end
@doc """
Reduces over a tensor with the given accumulator.
The given `fun` will receive two tensors and it must
return the reduced value.
The tensor may be reduced in parallel and the reducer
function can be called with arguments in any order, the
initial accumulator may be given multiples, and it may
be non-deterministic. Therefore, the reduction function
should be associative (or as close as possible to
associativity considered floats themselves are not
strictly associative).
By default, it reduces all dimensions of the tensor and
return a scalar. If the `:axes` option is given, it
aggregates over multiple dimensions, effectively removing
them. `axes: [0]` implies aggregating over the highest
order dimension and so forth. If the axis is negative,
then counts the axis from the back. For example,
`axes: [-1]` will always aggregate all rows.
The type of the returned tensor will be computed based on
the given tensor and the initial value. For example,
a tensor of integers with a float accumulator will be
cast to float, as done by most binary operators. You can
also pass a `:type` option to change this behaviour.
You may optionally set `:keep_axes` to true, which will
retain the rank of the input tensor by setting the reduced
axes to size 1.
## Limitations
Given this function relies on anonymous functions, it
may not be available or efficient on all Nx backends.
Therefore, you should avoid using `reduce/4` whenever
possible. Instead, use functions `sum/2`, `reduce_max/2`,
`all/1`, and so forth.
Inside `defn`, consider using `Nx.Defn.Kernel.while/4` instead.
## Examples
iex> Nx.reduce(Nx.tensor(42), 0, fn x, y -> Nx.add(x, y) end)
#Nx.Tensor<
s64
42
>
iex> Nx.reduce(Nx.tensor([1, 2, 3]), 0, fn x, y -> Nx.add(x, y) end)
#Nx.Tensor<
s64
6
>
iex> Nx.reduce(Nx.tensor([[1.0, 2.0], [3.0, 4.0]]), 0, fn x, y -> Nx.add(x, y) end)
#Nx.Tensor<
f32
10.0
>
### Aggregating over axes
iex> t = Nx.tensor([1, 2, 3], names: [:x])
iex> Nx.reduce(t, 0, [axes: [:x]], fn x, y -> Nx.add(x, y) end)
#Nx.Tensor<
s64
6
>
iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]], names: [:x, :y, :z])
iex> Nx.reduce(t, 0, [axes: [:x]], fn x, y -> Nx.add(x, y) end)
#Nx.Tensor<
s64[y: 2][z: 3]
[
[8, 10, 12],
[14, 16, 18]
]
>
iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]], names: [:x, :y, :z])
iex> Nx.reduce(t, 0, [axes: [:y]], fn x, y -> Nx.add(x, y) end)
#Nx.Tensor<
s64[x: 2][z: 3]
[
[5, 7, 9],
[17, 19, 21]
]
>
iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]], names: [:x, :y, :z])
iex> Nx.reduce(t, 0, [axes: [:x, 2]], fn x, y -> Nx.add(x, y) end)
#Nx.Tensor<
s64[y: 2]
[30, 48]
>
iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]], names: [:x, :y, :z])
iex> Nx.reduce(t, 0, [axes: [-1]], fn x, y -> Nx.add(x, y) end)
#Nx.Tensor<
s64[x: 2][y: 2]
[
[6, 15],
[24, 33]
]
>
iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]], names: [:x, :y, :z])
iex> Nx.reduce(t, 0, [axes: [:x]], fn x, y -> Nx.add(x, y) end)
#Nx.Tensor<
s64[y: 2][z: 3]
[
[8, 10, 12],
[14, 16, 18]
]
>
iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]], names: [:x, :y, :z])
iex> Nx.reduce(t, 0, [axes: [:x], keep_axes: true], fn x, y -> Nx.add(x, y) end)
#Nx.Tensor<
s64[x: 1][y: 2][z: 3]
[
[
[8, 10, 12],
[14, 16, 18]
]
]
>
## Vectorized tensors
Only `tensor` can be vectorized. Normal behavior of `reduce/4`
is applied to each corresponding entry. `:axes` refers to the
non-vectorized shape.
iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[10, 20, 30], [40, 50, 60]]]) |> Nx.vectorize(:x)
iex> Nx.reduce(t, 10, [axes: [1]], &Nx.add/2)
#Nx.Tensor<
vectorized[x: 2]
s64[2]
[
[16, 25],
[70, 160]
]
>
"""
@doc type: :aggregation
def reduce(tensor, acc, opts \\ [], fun) when is_function(fun, 2) do
opts = keyword!(opts, [:axes, :type, keep_axes: false])
type = Nx.Type.normalize!(opts[:type] || binary_type(tensor, acc))
keep_axes = opts[:keep_axes]
%T{vectorized_axes: vectorized_axes} = to_tensor(tensor)
acc = to_tensor(acc)
if not (acc.shape == {} and acc.vectorized_axes == []) do
raise ArgumentError, "the accumulator must be a non-vectorized scalar, got: #{inspect(acc)}"
end
%T{shape: shape, names: names} = tensor = devectorize(tensor, keep_names: false)
offset = length(vectorized_axes)
axes = opts[:axes]
{shape, names, axes} =
cond do
not is_nil(axes) ->
axes = Nx.Shape.normalize_axes(shape, axes, names, offset)
{new_shape, new_names} = Nx.Shape.contract(shape, axes, names, keep_axes)
{new_shape, new_names, axes}
keep_axes ->
shape =
List.to_tuple(
Keyword.values(vectorized_axes) ++ List.duplicate(1, tuple_size(shape) - offset)
)
axes = count_up(tuple_size(shape) - offset, offset)
{shape, names, axes}
offset != 0 ->
axes = count_up(tuple_size(shape) - offset, offset)
shape = vectorized_axes |> Keyword.values() |> List.to_tuple()
names = List.duplicate(nil, offset)
{shape, names, axes}
true ->
{{}, [], nil}
end
output =
if offset == 0 and axes == [] do
tensor
else
out = %{tensor | type: type, shape: shape, names: names}
impl!(tensor).reduce(out, tensor, acc, [axes: axes, keep_axes: keep_axes], fun)
end
vectorize(output, vectorized_axes)
end
@doc """
Reduces over each window of size `dimensions`
in the given tensor, producing a tensor that contains the same
number of elements as valid positions of the window.
The rank of the input tensor and the window dimensions must
match.
You may optionally specify `:strides` which is a tuple
of non-zero steps to take along each axis between
each window.
You may also optionally specify `:padding` which is either
one of `:valid` (no padding) or `:same` (pad so output shape
is the same as input shape) or a general padding configuration
for each dimension in the input tensor. Your padding configuration
cannot include any negative pad values. You may only specify
padding for the high and low edges of the given dimension. The
padding value is equal to the initial value passed to `acc`.
The initial value must be a number or a scalar shaped tensor.
## Examples
iex> init_value = Nx.Constants.min_finite(:s64)
iex> t = Nx.tensor([[1, 2, 3, 4], [4, 5, 6, 7], [7, 8, 9, 10], [11, 12, 13, 14]])
iex> Nx.window_reduce(t, init_value, {2, 2}, fn x, acc -> Nx.max(x, acc) end)
#Nx.Tensor<
s64[3][3]
[
[5, 6, 7],
[8, 9, 10],
[12, 13, 14]
]
>
iex> init_value = Nx.Constants.min_finite(:s64)
iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
iex> opts = [padding: :same, strides: [1, 1]]
iex> Nx.window_reduce(t, init_value, {2, 2}, opts, fn x, acc -> Nx.max(x, acc) end)
#Nx.Tensor<
s64[3][3]
[
[5, 6, 6],
[8, 9, 9],
[8, 9, 9]
]
>
iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]])
iex> opts = [padding: :same, strides: [1, 1]]
iex> Nx.window_reduce(t, 0, {1, 2}, opts, fn x, acc -> Nx.add(x, acc) end)
#Nx.Tensor<
s64[2][3]
[
[3, 5, 3],
[9, 11, 6]
]
>
iex> t = Nx.tensor([[[4, 2, 1, 3], [4, 2, 1, 7]], [[1, 2, 5, 7], [1, 8, 9, 2]]])
iex> opts = [padding: :valid, strides: [2, 1, 1], window_dilations: [1, 1, 2]]
iex> Nx.window_reduce(t, 0, {1, 1, 2}, opts, fn x, acc -> Nx.add(x, acc) end)
#Nx.Tensor<
s64[1][2][2]
[
[
[5, 5],
[5, 9]
]
]
>
## Vectorized tensors
The accumulator must not be vectorized. Aside from that, `window_reduce` will apply the reduction
over each non-vectorized entry, as follows:
iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[0, -1, -2], [-3, -4, -5]]]) |> Nx.vectorize(x: 2)
iex> opts = [padding: [{0, 0}, {0, 1}], strides: [1, 1]]
iex> Nx.window_reduce(t, 0, {2, 2}, opts, fn x, acc -> Nx.add(x, acc) end)
#Nx.Tensor<
vectorized[x: 2]
s64[1][3]
[
[
[12, 16, 9]
],
[
[-8, -12, -7]
]
]
>
"""
@doc type: :window
def window_reduce(tensor, acc, window_dimensions, opts \\ [], fun)
when is_tuple(window_dimensions) do
opts = keyword!(opts, [:window_dilations, :strides, padding: :valid])
tensor = to_tensor(tensor)
acc = to_tensor(acc)
if acc.vectorized_axes != [] do
raise ArgumentError, "accumulator for window_reduce/4 cannot be vectorized"
end
padding = opts[:padding]
strides = opts[:strides] || List.duplicate(1, rank(tensor.shape))
dilations = opts[:window_dilations] || List.duplicate(1, rank(tensor.shape))
dilations =
if is_integer(dilations),
do: List.duplicate(dilations, rank(tensor.shape)),
else: dilations
strides =
if is_integer(strides),
do: List.duplicate(strides, rank(tensor.shape)),
else: strides
apply_vectorized(tensor, fn tensor, offset ->
ones = List.duplicate(1, offset)
strides = ones ++ strides
window_dimensions = List.to_tuple(ones ++ Tuple.to_list(window_dimensions))
dilations = ones ++ dilations
padding = if is_list(padding), do: List.duplicate({0, 0}, offset) ++ padding, else: padding
{output_shape, padding_config} =
Nx.Shape.pool(tensor.shape, window_dimensions, strides, padding, dilations)
out = %{tensor | shape: output_shape}
opts = [padding: padding_config, strides: strides, window_dilations: dilations]
impl!(tensor).window_reduce(out, tensor, acc, window_dimensions, opts, fun)
end)
end
@doc """
Maps the given scalar function over the entire
tensor.
The type of the returned tensor will be of the same type
as the input tensor, unless the `:type` option is given.
Therefore, you may need to explicitly cast the tensor to
avoid errors. For example, if you have an integer tensor
and you convert it to a float, as below, it will fail:
tensor = Nx.tensor([[1, 2, 3], [4, 5, 6]]),
Nx.map(tensor, fn x -> Nx.multiply(x, 1.0) end)
You need to explicitly pass the output type in such cases:
iex> tensor = Nx.tensor([[1, 2, 3], [4, 5, 6]])
iex> Nx.map(tensor, [type: :f32], fn x -> Nx.multiply(x, 1.0) end)
#Nx.Tensor<
f32[2][3]
[
[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0]
]
>
## Limitations
Given this function relies on anonymous functions, it
may not be available or efficient on all Nx backends.
Therefore, you should avoid using `map/2` whenever possible
and use other functions in the `Nx` module to achieve the
desired result.
Inside `defn`, consider using `Nx.Defn.Kernel.while/4` instead.
## Examples
iex> Nx.map(Nx.tensor([[1, 2, 3], [4, 5, 6]]), fn x -> Nx.add(x, 1) end)
#Nx.Tensor<
s64[2][3]
[
[2, 3, 4],
[5, 6, 7]
]
>
iex> Nx.map(Nx.tensor(1), fn x -> Nx.add(x, 1) end)
#Nx.Tensor<
s64
2
>
iex> Nx.map(Nx.tensor([[1, 2, 3], [4, 5, 6]]), [type: :f64], fn x -> Nx.add(x, 1) end)
#Nx.Tensor<
f64[2][3]
[
[2.0, 3.0, 4.0],
[5.0, 6.0, 7.0]
]
>
## Vectorized tensors
`map/3` behaves the same as with non-vectorized tensors, applying
`fun` in an element-wise fashion.
iex> Nx.map(Nx.tensor([[1, 2, 3], [4, 5, 6]]) |> Nx.vectorize(:x), [type: :f64], &Nx.add(&1, 1))
#Nx.Tensor<
vectorized[x: 2]
f64[3]
[
[2.0, 3.0, 4.0],
[5.0, 6.0, 7.0]
]
>
"""
@doc type: :element
def map(tensor, opts \\ [], fun) do
apply_vectorized(tensor, fn tensor ->
%T{type: type} = tensor
opts = keyword!(opts, type: type)
output_type = Nx.Type.normalize!(opts[:type])
out = %{tensor | type: output_type}
impl!(tensor).map(out, tensor, opts, fun)
end)
end
## Matrix ops
@doc """
Returns the dot product of two tensors.
Given `a` and `b`, computes the dot product according to
the following rules:
* If both `a` and `b` are scalars, it is equivalent to `a * b`.
* If `a` is a scalar and `b` is a tensor, it is equivalent to `Nx.multiply(a, b)`.
* If `a` is a tensor and `b` is a scalar, it is equivalent to `Nx.multiply(a, b)`.
* If both `a` and `b` are 1-D tensors (vectors), it is the sum of the element-wise
product between `a` and `b`. The lengths of `a` and `b` must be equal.
* If both `a` and `b` are 2-D tensors (matrices), it is equivalent to matrix-multiplication.
* If either `a` or `b` is a 1-D tensor, and the other is an n-D tensor, it is the
sum of the element-wise product along the last axis of `a` or `b`. The length of the
1-D tensor must match the last dimension of the n-D tensor.
* If `a` is an n-D tensor and `b` is an m-D tensor, it is the sum of the element-wise
product along the last axis of `a` and the second-to-last axis of `b`. The last dimension
of `a` must match the second-to-last dimension of `b`.
For a more general `dot` function where you control which axes contract,
see `dot/4`.
## Examples
### Dot product of scalars
iex> Nx.dot(5, 5)
#Nx.Tensor<
s64
25
>
iex> Nx.dot(-2.0, 5.0)
#Nx.Tensor<
f32
-10.0
>
iex> Nx.dot(2, 2.0)
#Nx.Tensor<
f32
4.0
>
### Dot product of vectors
iex> Nx.dot(Nx.tensor([1, 2, 3]), Nx.tensor([4, 5, 6]))
#Nx.Tensor<
s64
32
>
iex> Nx.dot(Nx.tensor([2.0, 4.0, 3.0, 5.0]), Nx.tensor([1.0, 2.0, 3.0, 4.0]))
#Nx.Tensor<
f32
39.0
>
iex> Nx.dot(Nx.tensor([1.0, 2.0, 3.0]), Nx.tensor([1, 2, 3]))
#Nx.Tensor<
f32
14.0
>
### Dot product of matrices
iex> left = Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:i, :j])
iex> right = Nx.tensor([[7, 8], [9, 10], [11, 12]], names: [:x, :y])
iex> Nx.dot(left, right)
#Nx.Tensor<
s64[i: 2][y: 2]
[
[58, 64],
[139, 154]
]
>
iex> left = Nx.tensor([[10.0, 13.0, 14.0, 15.0], [59.0, 20.0, 10.0, 30.0]], names: [:i, :j])
iex> right = Nx.tensor([[2.0, 4.0], [5.0, 1.0], [6.0, 8.0], [9.0, 10.0]], names: [:x, :y])
iex> Nx.dot(left, right)
#Nx.Tensor<
f32[i: 2][y: 2]
[
[304.0, 315.0],
[548.0, 636.0]
]
>
iex> left = Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:i, :j])
iex> right = Nx.tensor([[7.0, 8.0], [9.0, 10.0], [11.0, 12.0]], names: [:x, :y])
iex> Nx.dot(left, right)
#Nx.Tensor<
f32[i: 2][y: 2]
[
[58.0, 64.0],
[139.0, 154.0]
]
>
### Dot product of vector and n-d tensor
iex> left = Nx.tensor([[[1, 2], [3, 4]], [[5, 6], [7, 8]]], names: [:i, :j, :k])
iex> right = Nx.tensor([5, 10], names: [:x])
iex> Nx.dot(left, right)
#Nx.Tensor<
s64[i: 2][j: 2]
[
[25, 55],
[85, 115]
]
>
iex> left = Nx.tensor([5, 10], names: [:x])
iex> right = Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:i, :j])
iex> Nx.dot(left, right)
#Nx.Tensor<
s64[j: 3]
[45, 60, 75]
>
iex> left = Nx.tensor([[[[[1.0, 2.0], [3.0, 4.0]], [[5.0, 6.0], [7.0, 8.0]]]]], names: [:shard, :batch, :x, :y, :z])
iex> right = Nx.tensor([2.0, 2.0], names: [:data])
iex> Nx.dot(left, right)
#Nx.Tensor<
f32[shard: 1][batch: 1][x: 2][y: 2]
[
[
[
[6.0, 14.0],
[22.0, 30.0]
]
]
]
>
### Dot product of n-D and m-D tensor
iex> left = Nx.tensor([[[1, 2, 3], [4, 5, 6], [7, 8, 9]], [[1, 2, 3], [4, 5, 6], [7, 8, 9]]], names: [:x, :y, :z])
iex> right = Nx.tensor([[[1, 2, 3], [3, 4, 5], [5, 6, 7]]], names: [:i, :j, :k])
iex> Nx.dot(left, right)
#Nx.Tensor<
s64[x: 2][y: 3][i: 1][k: 3]
[
[
[
[22, 28, 34]
],
[
[49, 64, 79]
],
[
[76, 100, 124]
]
],
[
[
[22, 28, 34]
],
[
[49, 64, 79]
],
[
[76, 100, 124]
]
]
]
>
## Vectorized tensors
Vectorized axes are treated as batched axes, much like
`dot/6` behaves with non-vectorized tensors.
iex> t1 = Nx.tensor([[1, 2], [3, 4]]) |> Nx.vectorize(:x)
iex> t2 = Nx.tensor([[10, 20], [30, 40]]) |> Nx.vectorize(:x)
iex> Nx.dot(t1, t2)
#Nx.Tensor<
vectorized[x: 2]
s64
[50, 250]
>
iex> t1 = Nx.tensor([1, 2]) |> Nx.vectorize(:x)
iex> t2 = Nx.tensor([[10, 20]]) |> Nx.vectorize(:y)
iex> Nx.dot(t1, t2)
#Nx.Tensor<
vectorized[x: 2][y: 1]
s64[2]
[
[
[10, 20]
],
[
[20, 40]
]
]
>
## Error cases
iex> Nx.dot(Nx.tensor([1, 2, 3]), Nx.tensor([1, 2]))
** (ArgumentError) dot/zip expects shapes to be compatible, dimension 0 of left-side (3) does not equal dimension 0 of right-side (2)
"""
@doc type: :ndim
def dot(t1, t2) do
%T{shape: s1} = t1 = to_tensor(t1)
%T{shape: s2} = t2 = to_tensor(t2)
case {tuple_size(s1), tuple_size(s2)} do
{0, _} -> multiply(t1, t2)
{_, 0} -> multiply(t1, t2)
{n, 1} -> dot(t1, [n - 1], [], t2, [0], [])
{1, m} -> dot(t1, [0], [], t2, [m - 2], [])
{n, m} when n >= 2 and m >= 2 -> dot(t1, [n - 1], [], t2, [m - 2], [])
end
end
@doc """
Computes the generalized dot product between two tensors, given
the contracting axes.
This is equivalent to calling `Nx.dot/6` with no batching dimensions:
Nx.dot(t1, contract_axes1, [], t2, contract_axes2, [])
## Examples
iex> t1 = Nx.tensor([[1, 2], [3, 4]], names: [:x, :y])
iex> t2 = Nx.tensor([[10, 20], [30, 40]], names: [:height, :width])
iex> Nx.dot(t1, [0], t2, [0])
#Nx.Tensor<
s64[y: 2][width: 2]
[
[100, 140],
[140, 200]
]
>
iex> t1 = Nx.tensor([[0.0, 1.0, 2.0], [3.0, 4.0, 5.0]])
iex> t2 = Nx.tensor([[0.0, 1.0], [2.0, 3.0], [4.0, 5.0]])
iex> Nx.dot(t1, [0, 1], t2, [1, 0])
#Nx.Tensor<
f32
50.0
>
## Vectorized tensors
The contracting axes refer to the tensors' shapes
and do not apply to the vectorized axes:
iex> t1 = Nx.tensor([[[1, 1], [2, 2]], [[1, 1], [1, 1]]]) |> Nx.vectorize(:x)
iex> t2 = Nx.tensor([[1, 2], [3, 4]])
iex> Nx.dot(t1, [0], t2, [0])
#Nx.Tensor<
vectorized[x: 2]
s64[2][2]
[
[
[7, 10],
[7, 10]
],
[
[4, 6],
[4, 6]
]
]
>
iex> Nx.dot(t1, [1], t2, [0])
#Nx.Tensor<
vectorized[x: 2]
s64[2][2]
[
[
[4, 6],
[8, 12]
],
[
[4, 6],
[4, 6]
]
]
>
"""
@doc type: :ndim
def dot(t1, contract_axes1, t2, contract_axes2) do
dot(t1, contract_axes1, [], t2, contract_axes2, [])
end
@doc """
Computes the generalized dot product between two tensors, given
the contracting and batch axes.
The dot product is computed by multiplying the values from `t1`
given by `contract_axes1` against the values from `t2` given by
`contract_axes2`, considering batch axes of `batch_axes1` and
`batch_axes2`. For instance, the first axis in `contract_axes1`
will be matched against the first axis in `contract_axes2` and
so on. The axes given by `contract_axes1` and `contract_axes2`
are effectively removed from the final tensor, which is why they
are often called the contraction axes.
If no contracting axes are given, the final product works like
`Nx.outer/2`.
Specifying batch axes will compute a vectorized dot product
along the given batch dimensions. The length of `batch_axes1`
and `batch_axes2` must match. Additionally, `batch_axes1` and
`batch_axes2` must be a list of successive dimension numbers,
where each batch axis matches the dimension of the corresponding
batch axis in the other input.
The contracting axes must be dot-product compatible and the
batch dimensions must always have the same number of elements.
## Examples
### Contracting along axes
iex> t1 = Nx.tensor([[1, 2], [3, 4]], names: [:x, :y])
iex> t2 = Nx.tensor([[10, 20], [30, 40]], names: [:height, :width])
iex> Nx.dot(t1, [0], [], t2, [0], [])
#Nx.Tensor<
s64[y: 2][width: 2]
[
[100, 140],
[140, 200]
]
>
iex> Nx.dot(t1, [0], [], t2, [1], [])
#Nx.Tensor<
s64[y: 2][height: 2]
[
[70, 150],
[100, 220]
]
>
iex> Nx.dot(t1, [1], [], t2, [0], [])
#Nx.Tensor<
s64[x: 2][width: 2]
[
[70, 100],
[150, 220]
]
>
iex> Nx.dot(t1, [1], [], t2, [1], [])
#Nx.Tensor<
s64[x: 2][height: 2]
[
[50, 110],
[110, 250]
]
>
iex> Nx.dot(t1, [0, 1], [], t2, [0, 1], [])
#Nx.Tensor<
s64
300
>
If no axes are given, it works like `outer/2`:
iex> t1 = Nx.tensor([[1, 2], [3, 4]])
iex> t2 = Nx.tensor([[10, 20], [30, 40]])
iex> Nx.dot(t1, [], [], t2, [], [])
#Nx.Tensor<
s64[2][2][2][2]
[
[
[
[10, 20],
[30, 40]
],
[
[20, 40],
[60, 80]
]
],
[
[
[30, 60],
[90, 120]
],
[
[40, 80],
[120, 160]
]
]
]
>
### Dot product between two batched tensors
iex> u = Nx.tensor([[[1]], [[2]]])
iex> v = Nx.tensor([[[3]], [[4]]])
iex> Nx.dot(u, [2], [0], v, [2], [0])
#Nx.Tensor<
s64[2][1][1]
[
[
[3]
],
[
[8]
]
]
>
iex> u = Nx.tensor([[[1, 1]], [[2, 2]]])
iex> v = Nx.tensor([[[3], [3]], [[4], [4]]])
iex> Nx.dot(u, [2], [0], v, [1], [0])
#Nx.Tensor<
s64[2][1][1]
[
[
[6]
],
[
[16]
]
]
>
## Vectorized tensors
If you already have vectorized axes, they will be automatically
added to the batched axes of `dot/6`. Input axes must refer to
the tensor shape, and offsets due to vectorized axes are
handled internally.
Rewriting the previous example with vectorization:
iex> u = Nx.tensor([[[1, 1]], [[2, 2]]]) |> Nx.vectorize(:x)
iex> v = Nx.tensor([[[3], [3]], [[4], [4]]]) |> Nx.vectorize(:x)
iex> Nx.dot(u, [1], [], v, [0], []) # note that axes refer to the inner shapes
#Nx.Tensor<
vectorized[x: 2]
s64[1][1]
[
[
[6]
],
[
[16]
]
]
>
Because the batch axes are now empty, we can use `dot/4` to be more concise.
Nx.dot(u, [1], v, [0])
However, we can go even further. Since we are contracting the last axis of
`u` with the first axis of `v`, we can rely on `dot/2` to achieve the same
result.
Nx.dot(u, v)
## Error cases
iex> u = Nx.tensor([[[1, 1]], [[2, 2]]])
iex> v = Nx.tensor([[[3], [3]], [[4], [4]]])
iex> Nx.dot(u, [2], [0], v, [1], [])
** (ArgumentError) right tensor must be batched if left tensor is batched
iex> u = Nx.tensor([[[1, 1]], [[2, 2]]])
iex> v = Nx.tensor([[[3], [3]], [[4], [4]]])
iex> Nx.dot(u, [2], [], v, [1], [0])
** (ArgumentError) left tensor must be batched if right tensor is batched
iex> u = Nx.tensor([[[1, 1]], [[2, 2]]])
iex> v = Nx.tensor([[[3], [3]], [[4], [4]]])
iex> Nx.dot(u, [2], [1], v, [1], [0])
** (ArgumentError) invalid dot batch axis for the left tensor, batch axes must be successive dimensions starting from 0, got [1]
iex> u = Nx.tensor([[[1, 1]], [[2, 2]]])
iex> v = Nx.tensor([[[3], [3]], [[4], [4]]])
iex> Nx.dot(u, [2], [0], v, [1], [1])
** (ArgumentError) invalid dot batch axis for the right tensor, batch axes must be successive dimensions starting from 0, got [1]
iex> u = Nx.tensor([[[1, 1]], [[2, 2]]])
iex> v = Nx.tensor([[[3], [3]], [[4], [4]]])
iex> Nx.dot(u, [0], [0], v, [1], [0])
** (ArgumentError) dot batch axes for left tensor ([0]) cannot be in contract axes ([0])
iex> u = Nx.tensor([[[1, 1]], [[2, 2]]])
iex> v = Nx.tensor([[[3], [3]], [[4], [4]]])
iex> Nx.dot(u, [2], [0], v, [0], [0])
** (ArgumentError) dot batch axes for right tensor ([0]) cannot be in contract axes ([0])
"""
@doc type: :ndim
def dot(t1_in, contract_axes1, batch_axes1, t2_in, contract_axes2, batch_axes2) do
[t1, t2] = broadcast_vectors([t1_in, t2_in])
%{vectorized_axes: vectorized_axes} = t1
%{shape: s1, names: names1} = t1
%{shape: s2, names: names2} = t2
output_type = binary_type(t1, t2)
offset = length(vectorized_axes)
# Axes normalization
c1 = Nx.Shape.normalize_axes(s1, contract_axes1, names1)
c2 = Nx.Shape.normalize_axes(s2, contract_axes2, names2)
b1 = Nx.Shape.normalize_axes(s1, batch_axes1, names1)
b2 = Nx.Shape.normalize_axes(s2, batch_axes2, names2)
{output_shape, output_names} = Nx.Shape.dot(s1, c1, names1, b1, s2, c2, names2, b2)
out = %{t1 | type: output_type, names: output_names, shape: output_shape}
if offset != 0 do
offset_axes = count_up(offset, 0)
t1 = devectorize(t1)
t2 = devectorize(t2)
out = devectorize(out)
c1 = Enum.map(c1, &(&1 + offset))
c2 = Enum.map(c2, &(&1 + offset))
b1 = offset_axes ++ Enum.map(b1, &(&1 + offset))
b2 = offset_axes ++ Enum.map(b2, &(&1 + offset))
res = impl!(t1, t2).dot(out, t1, c1, b1, t2, c2, b2)
vectorize(res, vectorized_axes)
else
impl!(t1, t2).dot(out, t1, c1, b1, t2, c2, b2)
end
end
@doc """
Computes the outer product of two tensors.
The output is always a two-dimensional tensor.
## Examples
iex> Nx.outer(Nx.tensor([1, 2, 3], names: [:x]), 100)
#Nx.Tensor<
s64[x: 3][1]
[
[100],
[200],
[300]
]
>
iex> Nx.outer(Nx.tensor([1, 2, 3], names: [:x]), Nx.tensor([10, 20], names: [:y]))
#Nx.Tensor<
s64[x: 3][y: 2]
[
[10, 20],
[20, 40],
[30, 60]
]
>
iex> Nx.outer(Nx.tensor([[1, 2], [3, 4]], names: [:x, :y]), Nx.tensor([10, 20, 30], names: [:z]))
#Nx.Tensor<
s64[x: 4][z: 3]
[
[10, 20, 30],
[20, 40, 60],
[30, 60, 90],
[40, 80, 120]
]
>
## Vectorized tensors
Because `outer/2` is built on top of other
iex> x = Nx.tensor([[1, 2, 3], [0, -1, -2]], names: [nil, :a]) |> Nx.vectorize(:x)
iex> y = Nx.tensor([[10, 20], [-10, -20]], names: [nil, :b]) |> Nx.vectorize(:y)
iex> Nx.outer(x, y)
#Nx.Tensor<
vectorized[x: 2][y: 2]
s64[a: 3][b: 2]
[
[
[
[10, 20],
[20, 40],
[30, 60]
],
[
[-10, -20],
[-20, -40],
[-30, -60]
]
],
[
[
[0, 0],
[-10, -20],
[-20, -40]
],
[
[0, 0],
[10, 20],
[20, 40]
]
]
]
>
"""
@doc type: :ndim
def outer(t1, t2) do
%T{names: n1} = t1 = to_tensor(t1)
%T{names: n2} = t2 = to_tensor(t2)
names =
case {n1, n2} do
{[], rhs} -> [nil, List.last(rhs)]
{lhs, rhs} -> [hd(lhs), List.last(rhs)]
end
%{multiply(reshape(t1, {size(t1), 1}), reshape(t2, {1, size(t2)})) | names: names}
end
@doc """
Transposes a tensor to the given `axes`.
If no axes are given, the default behavior is to
reverse the order of the original tensor's axes.
The axes is a list of integers or dimension names
containing how the new dimensions must be ordered.
The highest dimension is zero.
## Examples
iex> Nx.transpose(Nx.tensor(1))
#Nx.Tensor<
s64
1
>
iex> Nx.transpose(Nx.iota({2, 3, 4}, names: [:x, :y, :z]))
#Nx.Tensor<
s64[z: 4][y: 3][x: 2]
[
[
[0, 12],
[4, 16],
[8, 20]
],
[
[1, 13],
[5, 17],
[9, 21]
],
[
[2, 14],
[6, 18],
[10, 22]
],
[
[3, 15],
[7, 19],
[11, 23]
]
]
>
iex> Nx.transpose(Nx.tensor(1), axes: [])
#Nx.Tensor<
s64
1
>
iex> Nx.transpose(Nx.iota({2, 3, 4}, names: [:batch, :x, :y]), axes: [2, 1, :batch])
#Nx.Tensor<
s64[y: 4][x: 3][batch: 2]
[
[
[0, 12],
[4, 16],
[8, 20]
],
[
[1, 13],
[5, 17],
[9, 21]
],
[
[2, 14],
[6, 18],
[10, 22]
],
[
[3, 15],
[7, 19],
[11, 23]
]
]
>
iex> Nx.transpose(Nx.iota({2, 3, 4}, names: [:batch, :x, :y]), axes: [:y, :batch, :x])
#Nx.Tensor<
s64[y: 4][batch: 2][x: 3]
[
[
[0, 4, 8],
[12, 16, 20]
],
[
[1, 5, 9],
[13, 17, 21]
],
[
[2, 6, 10],
[14, 18, 22]
],
[
[3, 7, 11],
[15, 19, 23]
]
]
>
iex> Nx.transpose(Nx.iota({2, 3, 4}, names: [:batch, :x, :y]), axes: [:batch, :y, :x])
#Nx.Tensor<
s64[batch: 2][y: 4][x: 3]
[
[
[0, 4, 8],
[1, 5, 9],
[2, 6, 10],
[3, 7, 11]
],
[
[12, 16, 20],
[13, 17, 21],
[14, 18, 22],
[15, 19, 23]
]
]
>
### Vectorized tensors
For vectorized tensors, transpose will manipulate the inner shape only,
keeping the order of vectorized axes the same.
iex> v = Nx.vectorize(Nx.iota({1, 2, 3}), :x)
#Nx.Tensor<
vectorized[x: 1]
s64[2][3]
[
[
[0, 1, 2],
[3, 4, 5]
]
]
>
iex> Nx.transpose(v)
#Nx.Tensor<
vectorized[x: 1]
s64[3][2]
[
[
[0, 3],
[1, 4],
[2, 5]
]
]
>
iex> Nx.transpose(v, axes: [1, 0])
#Nx.Tensor<
vectorized[x: 1]
s64[3][2]
[
[
[0, 3],
[1, 4],
[2, 5]
]
]
>
### Errors
iex> Nx.transpose(Nx.iota({2, 2}, names: [:batch, :x]), axes: [:batch])
** (ArgumentError) expected length of permutation (1) to match rank of shape (2)
iex> Nx.transpose(Nx.iota({2, 2}), axes: [1, 2])
** (ArgumentError) given axis (2) invalid for shape with rank 2
"""
@doc type: :shape
def transpose(tensor, opts \\ []) do
base_shape = shape(tensor)
apply_vectorized(tensor, fn tensor, offset ->
opts = keyword!(opts, [:axes])
%{shape: shape, names: names} = tensor
offset_axes = count_up(offset, 0)
axes =
case opts[:axes] do
nil ->
offset_axes ++ Nx.Shape.transpose_axes(base_shape, offset)
axes ->
offset_axes ++ Nx.Shape.normalize_axes(shape, axes, names, offset)
end
if axes == Nx.axes(shape) do
tensor
else
{shape, names} = Nx.Shape.transpose(shape, axes, names)
impl!(tensor).transpose(%{tensor | shape: shape, names: names}, tensor, axes)
end
end)
end
@doc """
Reverses the tensor in the given dimensions.
If no axes are provided, reverses every axis.
You can pass either names or numbers for the reverse
dimensions. Dimensions must be unique, but they do not
have to be successive.
## Examples
iex> Nx.reverse(Nx.tensor([1, 2, 3]))
#Nx.Tensor<
s64[3]
[3, 2, 1]
>
iex> Nx.reverse(Nx.tensor([[1, 2, 3], [4, 5, 6]]))
#Nx.Tensor<
s64[2][3]
[
[6, 5, 4],
[3, 2, 1]
]
>
iex> Nx.reverse(Nx.tensor([1, 2, 3], names: [:x]), axes: [:x])
#Nx.Tensor<
s64[x: 3]
[3, 2, 1]
>
iex> Nx.reverse(Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:x, :y]), axes: [:x])
#Nx.Tensor<
s64[x: 2][y: 3]
[
[4, 5, 6],
[1, 2, 3]
]
>
iex> Nx.reverse(Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:x, :y]), axes: [:y])
#Nx.Tensor<
s64[x: 2][y: 3]
[
[3, 2, 1],
[6, 5, 4]
]
>
iex> Nx.reverse(Nx.iota({2, 2, 2}, type: :f32, names: [:x, :y, :z]), axes: [:x, :z])
#Nx.Tensor<
f32[x: 2][y: 2][z: 2]
[
[
[5.0, 4.0],
[7.0, 6.0]
],
[
[1.0, 0.0],
[3.0, 2.0]
]
]
>
### Vectorized tensors
For vectorized tensors, the `:axes` refer to the non-vectorized part.
Vectorized axes will always remain unchanged.
iex> v = Nx.vectorize(Nx.iota({1, 2, 3}), :x)
#Nx.Tensor<
vectorized[x: 1]
s64[2][3]
[
[
[0, 1, 2],
[3, 4, 5]
]
]
>
iex> Nx.reverse(v)
#Nx.Tensor<
vectorized[x: 1]
s64[2][3]
[
[
[5, 4, 3],
[2, 1, 0]
]
]
>
iex> Nx.reverse(v, axes: [1])
#Nx.Tensor<
vectorized[x: 1]
s64[2][3]
[
[
[2, 1, 0],
[5, 4, 3]
]
]
>
"""
@doc type: :ndim
def reverse(tensor, opts \\ []) do
base_shape = shape(tensor)
apply_vectorized(tensor, fn tensor, offset ->
opts = keyword!(opts, [:axes])
%{shape: shape, names: names} = tensor
axes = opts[:axes] || axes(base_shape)
case Nx.Shape.normalize_axes(shape, axes, names, offset) do
[] ->
tensor
axes ->
impl!(tensor).reverse(tensor, tensor, Enum.sort(axes))
end
end)
end
## Conv
@doc """
Computes an n-D convolution (where `n >= 3`) as used in neural networks.
This function can be thought of as sliding an n-D
kernel across the input, producing a new tensor that
has the same number of elements as the number of valid
windows in the input tensor. Each element is the result
of summing the element-wise products in the window across
each input channel.
The ranks of both `input` and `kernel` must match. By
default, both `input` and `kernel` are expected to have shapes
of the following form:
* `input` - `{batch_size, input_channels, input_d0, ..., input_dn}`
* `kernel` - `{output_channels, input_channels, kernel_d0, ..., kernel_dn}`
Where `input_d0...input_dn` and `kernel_d0...kernel_dn` represent
an arbitrary number of spatial dimensions. You can alter this configuration
using one of the `*_permutation` configuration options. Permutations
are input, kernel, and output specifications for the layout of the
convolution. For example, if your input tensor is configured with
"channels last", you can specify the input permutation with:
Nx.conv(img, kernel, input_permutation: [0, 3, 1, 2])
Permutations expect configurations that specify the location of
dimensions in the following orders:
* `input_permutation` - `[batch_dim, input_channel_dim, ...spatial_dims...]`
* `kernel_permutation` - `[output_channel_dim, input_channel_dim, ...spatial_dims...]`
* `output_permutation` - `[batch_dim, output_channel_dim, ...spatial_dims...]`
Using named tensors, it's a bit easier to see how permutations
help you configure the convolution. Given input tensor with names
`[:batch, :height, :width, :channels]` (channels last) and kernel
tensor with names `[:input, :output, :height, :width]`, you can
configure the convolution with the following permutations:
Nx.conv(img, kernel,
input_permutation: [:batch, :channels, :height, :width],
kernel_permutation: [:output, :input, :height, :width],
output_permutation: [:batch, :channels, :height, :width]
)
Notice that `output_permutation` is normalized with respect to
the input permutation names. We cannot guarantee that every
permutation is supported in every backend or compiler.
To configure how the window slides along the input tensor, you
can specify `:strides`. `:strides` must be a positive integer
or tuple of positive integers for each spatial dimension
in the input and kernel. For each spatial dimension, the
window will slide by the configuration specified in `:strides`.
As an example, for a 2-D convolution with `strides: [2, 1]`,
the window will slide 2 positions along the first spatial
dimension until it reaches the end of the dimension and then
1 position along the second spatial dimension.
You may specify a padding configuration using `:padding`,
which will zero-pad the input tensor. Acceptable padding
configurations are:
* `:valid` - no padding
* `:same` - pad input spatial dimensions such that they
will remain unchanged in the output tensor
* `[{d0_hi, d0_lo}, ..., {dn_hi, dn_lo}]` - a general padding
configuration of edge high and edge low padding values. You
may only specify padding for the edges of spatial dimensions
of the input tensor. Padding values may be negative.
You can dilate convolutions by setting `:input_dilation` or
`:kernel_dilation`. Both `:input_dilation` and `:kernel_dilation`
must either be positive integers or tuples of positive integers
for each spatial dimension in the input and kernel tensors. Dilations
can be thought of as applying `dilation - 1` interior padding to the
input or kernel tensor.
You can split both the input and kernel tensor into feature groups
using `:feature_group_size`. This will split both the input and kernel
tensor channels and compute a grouped convolution. The size of the
kernel input feature channels times the size of the feature group must
match the size of the input tensor feature channels. Additionally,
the size of the kernel output feature channels must be evenly divisible
by the group size.
You can also split the input tensor along the batch dimension by
specifying `:batch_group_size`. This will compute a grouped convolution
in the same way as with `:feature_group_size`, however, the input
tensor will be split into groups along the batch dimension.
## Examples
iex> left = Nx.iota({9})
iex> left = Nx.reshape(left, {1, 1, 3, 3})
iex> right = Nx.iota({4})
iex> right = Nx.reshape(right, {4, 1, 1, 1})
iex> Nx.conv(left, right, strides: [1, 1])
#Nx.Tensor<
f32[1][4][3][3]
[
[
[
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0]
],
[
[0.0, 1.0, 2.0],
[3.0, 4.0, 5.0],
[6.0, 7.0, 8.0]
],
[
[0.0, 2.0, 4.0],
[6.0, 8.0, 10.0],
[12.0, 14.0, 16.0]
],
[
[0.0, 3.0, 6.0],
[9.0, 12.0, 15.0],
[18.0, 21.0, 24.0]
]
]
]
>
iex> left = Nx.iota({9})
iex> left = Nx.reshape(left, {1, 1, 3, 3})
iex> right = Nx.iota({8})
iex> right = Nx.reshape(right, {4, 1, 2, 1})
iex> Nx.conv(left, right, strides: 2, padding: :same, kernel_dilation: [2, 1])
#Nx.Tensor<
f32[1][4][2][2]
[
[
[
[3.0, 5.0],
[0.0, 0.0]
],
[
[9.0, 15.0],
[6.0, 10.0]
],
[
[15.0, 25.0],
[12.0, 20.0]
],
[
[21.0, 35.0],
[18.0, 30.0]
]
]
]
>
Complex tensors are also supported:
iex> left = Nx.tensor([[[Complex.new(1, 1), 2, Complex.new(3, -3)]]])
iex> right = Nx.tensor([[[1, Complex.new(0, 2), Complex.new(0, 3)]]])
iex> Nx.conv(left, right, padding: [{2, 2}])
#Nx.Tensor<
c64[1][1][5]
[
[
[-3.0+3.0i, -2.0+8.0i, 10.0+14.0i, 8.0+6.0i, 3.0-3.0i]
]
]
>
"""
@doc type: :ndim
def conv(tensor, kernel, opts \\ []) when is_list(opts) do
opts =
keyword!(opts, [
:input_permutation,
:kernel_permutation,
:output_permutation,
padding: :valid,
strides: 1,
input_dilation: 1,
kernel_dilation: 1,
feature_group_size: 1,
batch_group_size: 1
])
type = binary_type(tensor, kernel) |> Nx.Type.to_floating()
padding = opts[:padding]
strides = opts[:strides]
input_dilation = opts[:input_dilation]
kernel_dilation = opts[:kernel_dilation]
feature_group_count = opts[:feature_group_size]
batch_group_count = opts[:batch_group_size]
[tensor, kernel] = broadcast_vectors([tensor, kernel])
Nx.Shape.validate_conv!(tensor.shape, kernel.shape)
vectorized_axes = tensor.vectorized_axes
offset = length(vectorized_axes)
%{shape: input_shape, names: input_names} =
tensor = conv_collapse_into_batch_axes(tensor, offset)
%{shape: kernel_shape, names: kernel_names} =
kernel = conv_collapse_into_batch_axes(kernel, offset)
input_permutation = opts[:input_permutation] || axes(input_shape)
input_permutation = Nx.Shape.normalize_axes(input_shape, input_permutation, input_names)
kernel_permutation = opts[:kernel_permutation] || axes(kernel_shape)
kernel_permutation = Nx.Shape.normalize_axes(kernel_shape, kernel_permutation, kernel_names)
output_permutation = opts[:output_permutation] || axes(input_shape)
output_permutation = Nx.Shape.normalize_axes(input_shape, output_permutation, input_names)
strides =
if is_integer(strides),
do: List.duplicate(strides, Nx.rank(input_shape) - 2),
else: strides
cond do
!is_integer(input_dilation) and !is_list(input_dilation) ->
raise ArgumentError,
"input dilation must be a positive integer or list of positive integers, got " <>
inspect(input_dilation)
!is_integer(kernel_dilation) and !is_list(kernel_dilation) ->
raise ArgumentError,
"kernel dilation must be a positive integer or list of positive integers, got " <>
inspect(kernel_dilation)
true ->
:ok
end
input_dilation =
if is_list(input_dilation),
do: input_dilation,
else: for(_ <- 1..(Nx.rank(input_shape) - 2), do: input_dilation)
kernel_dilation =
if is_list(kernel_dilation),
do: kernel_dilation,
else: for(_ <- 1..(Nx.rank(kernel_shape) - 2), do: kernel_dilation)
vectorized_size = Enum.reduce(vectorized_axes, 1, fn {_, s}, acc -> s * acc end)
batch_group_size = batch_group_count * vectorized_size
{shape, names, padding_config} =
Nx.Shape.conv(
input_shape,
input_names,
kernel_shape,
kernel_names,
strides,
padding,
feature_group_count,
batch_group_size,
input_dilation,
kernel_dilation,
input_permutation,
kernel_permutation,
output_permutation
)
out = %{tensor | type: type, shape: shape, names: names}
result =
impl!(tensor).conv(
out,
tensor,
kernel,
strides: strides,
padding: padding_config,
input_dilation: input_dilation,
kernel_dilation: kernel_dilation,
feature_group_size: feature_group_count,
batch_group_size: batch_group_size,
input_permutation: input_permutation,
kernel_permutation: kernel_permutation,
output_permutation: output_permutation
)
if vectorized_axes != [] do
[output_axis, batch | features] = Tuple.to_list(shape)
unwrapped_shape =
List.to_tuple(
Keyword.values(vectorized_axes) ++ [output_axis, div(batch, vectorized_size) | features]
)
unwrapped_names = List.duplicate(nil, offset) ++ names
result
|> reshape(unwrapped_shape, names: unwrapped_names)
|> vectorize(vectorized_axes)
else
result
end
end
defp conv_collapse_into_batch_axes(t, 0), do: t
defp conv_collapse_into_batch_axes(t, offset) do
t = devectorize(t)
{batch_axes, other_axes} = t.shape |> Tuple.to_list() |> Enum.split(offset + 1)
{_, names} = Enum.split(t.names, offset)
reshape(t, List.to_tuple([Enum.product(batch_axes) | other_axes]), names: names)
end
@doc """
Clips the values of the tensor on the closed
interval `[min, max]`.
You can pass a tensor to `min` or `max` as long
as the tensor has a scalar shape.
## Examples
iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:x, :y])
iex> Nx.clip(t, 2, 4)
#Nx.Tensor<
s64[x: 2][y: 3]
[
[2, 2, 3],
[4, 4, 4]
]
>
iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:x, :y])
iex> Nx.clip(t, 2.0, 3)
#Nx.Tensor<
f32[x: 2][y: 3]
[
[2.0, 2.0, 3.0],
[3.0, 3.0, 3.0]
]
>
iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:x, :y])
iex> Nx.clip(t, Nx.tensor(2.0), Nx.max(1.0, 3.0))
#Nx.Tensor<
f32[x: 2][y: 3]
[
[2.0, 2.0, 3.0],
[3.0, 3.0, 3.0]
]
>
iex> t = Nx.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]], names: [:x, :y])
iex> Nx.clip(t, 2, 6.0)
#Nx.Tensor<
f32[x: 2][y: 3]
[
[2.0, 2.0, 3.0],
[4.0, 5.0, 6.0]
]
>
iex> t = Nx.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]], type: :f32, names: [:x, :y])
iex> Nx.clip(t, 1, 4)
#Nx.Tensor<
f32[x: 2][y: 3]
[
[1.0, 2.0, 3.0],
[4.0, 4.0, 4.0]
]
>
## Vectorized tensors
Only the main input tensor is allowed to be vectorized. `min` and `max` threshold tensors
must be unvectorized scalar tensors.
iex> t = Nx.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]], type: :f32, names: [nil, :y]) |> Nx.vectorize(:x)
iex> Nx.clip(t, 1, 4)
#Nx.Tensor<
vectorized[x: 2]
f32[y: 3]
[
[1.0, 2.0, 3.0],
[4.0, 4.0, 4.0]
]
>
"""
@doc type: :element
def clip(tensor, min, max) do
apply_vectorized(tensor, fn tensor ->
%T{type: type} = tensor
%T{type: min_type, shape: min_shape, vectorized_axes: min_vectorized_axes} =
min = to_tensor(min)
%T{type: max_type, shape: max_shape, vectorized_axes: max_vectorized_axes} =
max = to_tensor(max)
if not (min_shape == {} and min_vectorized_axes == []) do
raise ArgumentError,
"min value must be a non-vectorized scalar shape, got shape #{inspect(min_shape)} and vectorized axes #{inspect(min_vectorized_axes)}"
end
if not (max_shape == {} and max_vectorized_axes == []) do
raise ArgumentError,
"max value must be a non-vectorized scalar shape, got shape #{inspect(max_shape)} and vectorized axes #{inspect(max_vectorized_axes)}"
end
output_type = Nx.Type.merge(type, Nx.Type.merge(min_type, max_type))
Nx.Shared.raise_complex_not_supported(output_type, :clip, 2)
impl!(tensor).clip(%{tensor | type: output_type}, tensor, min, max)
end)
end
@doc """
Slices a tensor from `start_indices` with `lengths`.
You can optionally provide a `stride` to specify the amount
of stride in each dimension.
Both start indices and lengths must match the rank of the
input tensor shape. All start indexes must be greater than
or equal to zero. All lengths must be strictly greater than
zero. If `start_index + length` exceeds the tensor dimension,
the `start_index` will be clipped in order to guarantee the
`length` is the requested one. See the "Clipping" section below.
It is possible for `start_indices` to be a list of tensors.
However, `lengths` must always be a list of integers. If you
want to specify a tensor as the list of indices, see `take/3`.
If the `:strides` is given, it must be strictly greater than zero.
The resulting tensor will have the shape of `length` unless
`:strides` are given.
It is not possible to slice in reverse. See `gather/2`,
`slice_along_axis/4`, `take/3`, and `take_along_axis/3` for other ways
to retrieve values from a tensor.
## Examples
iex> Nx.slice(Nx.tensor([1, 2, 3, 4, 5, 6]), [0], [3])
#Nx.Tensor<
s64[3]
[1, 2, 3]
>
iex> Nx.slice(Nx.tensor([1, 2, 3, 4, 5, 6]), [0], [6], strides: [2])
#Nx.Tensor<
s64[3]
[1, 3, 5]
>
iex> Nx.slice(Nx.tensor([[1, 2], [3, 4], [5, 6]]), [0, 0], [3, 2], strides: [2, 1])
#Nx.Tensor<
s64[2][2]
[
[1, 2],
[5, 6]
]
>
Strides can also be a number that applies to all dimensions:
iex> t = Nx.tensor([[1, 2], [3, 4], [5, 6]])
iex> Nx.slice(t, [0, 0], [3, 2], strides: 2)
#Nx.Tensor<
s64[2][1]
[
[1],
[5]
]
>
A more complex example:
iex> t = Nx.iota({900})
iex> t = Nx.reshape(t, {2, 15, 30})
iex> Nx.slice(t, [0, 4, 11], [2, 3, 9], strides: [2, 1, 3])
#Nx.Tensor<
s64[1][3][3]
[
[
[131, 134, 137],
[161, 164, 167],
[191, 194, 197]
]
]
>
## Tensors as `start_indices`
The `start_indices` list can be made of scalar tensors:
iex> Nx.slice(Nx.tensor([[1, 2, 3], [4, 5, 6]]), [Nx.tensor(1), Nx.tensor(2)], [1, 1])
#Nx.Tensor<
s64[1][1]
[
[6]
]
>
iex> t = Nx.tensor([
...> [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
...> [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
...> [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],
...> [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],
...> [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],
...> [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]
...> ])
iex> Nx.slice(t, [Nx.tensor(0), Nx.tensor(0)], [6, 7], strides: [5, 3])
#Nx.Tensor<
f32[2][3]
[
[0.0, 0.0, 0.0],
[1.0, 1.0, 1.0]
]
>
## Clipping
`slice/3` will always guarantee the return tensor has the
given `lengths`. See the following example:
iex> Nx.slice(Nx.iota({3, 3}), [2, 2], [1, 1])
#Nx.Tensor<
s64[1][1]
[
[8]
]
>
In the example above, `start_index + length <= dimension`,
so there is no clipping. However, if the `start_index + length`
is to exceed the dimension, the index will be clipped in order
to guarantee the given lengths:
iex> Nx.slice(Nx.iota({3, 3}), [2, 2], [2, 2])
#Nx.Tensor<
s64[2][2]
[
[4, 5],
[7, 8]
]
>
This also applies when the start index is given by tensors:
iex> Nx.slice(Nx.iota({3, 3}), [Nx.tensor(2), Nx.tensor(2)], [2, 2])
#Nx.Tensor<
s64[2][2]
[
[4, 5],
[7, 8]
]
>
## Vectorized tensors
Both the tensor to be sliced and the indices can be vectorized.
iex> Nx.slice(Nx.iota({3, 3}, vectorized_axes: [x: 2]), [0, Nx.tensor(1)], [2, 2])
#Nx.Tensor<
vectorized[x: 2]
s64[2][2]
[
[
[1, 2],
[4, 5]
],
[
[1, 2],
[4, 5]
]
]
>
iex> idx = Nx.tensor([0, 1, 10]) |> Nx.vectorize(:i)
iex> Nx.slice(Nx.iota({3, 3}), [0, idx], [2, 2])
#Nx.Tensor<
vectorized[i: 3]
s64[2][2]
[
[
[0, 1],
[3, 4]
],
[
[1, 2],
[4, 5]
],
[
[1, 2],
[4, 5]
]
]
>
## Error cases
iex> Nx.slice(Nx.tensor([[1, 2, 3], [4, 5, 6]]), [Nx.tensor([1, 2]), Nx.tensor(1)], [1, 1])
** (ArgumentError) index must be scalar, got shape {2} for axis 0
iex> Nx.slice(Nx.tensor([[1, 2, 3], [4, 5, 6]]), [Nx.tensor(1.0), Nx.tensor(0)], [1, 1])
** (ArgumentError) index must be integer type, got {:f, 32} for axis 0
"""
@doc type: :indexed
def slice(tensor, start_indices, lengths, opts \\ [])
when is_list(start_indices) and is_list(lengths) and is_list(opts) do
opts = keyword!(opts, strides: 1)
%T{vectorized_axes: vectorized_axes, shape: shape} = tensor = to_tensor(tensor)
if Enum.any?(start_indices, &(is_struct(&1, T) and &1.vectorized_axes != [])) do
# if any of the indices is vectorized, we instead treat this slice as a gather
[%{vectorized_axes: [{first_axis, _} | _] = vectorized_axes} | _] =
start_indices = Nx.broadcast_vectors(start_indices)
n = tuple_size(shape)
idx =
Enum.zip_with([start_indices, lengths, 0..(n - 1)], fn [s, l, i] ->
s = to_tensor(s)
if s.shape != {} do
raise "start index must be a scalar, got shape: #{inspect(s.shape)}"
end
# The indexed vec_axes are added so that we can easily get the cartesian
# product of the constructed-along-axis indices.
# Because we want to ensure that the name is different than the other,
# we build the new axis name based on the first_axis's name.
vec_axis = :"#{first_axis}_#{i}"
max_idx = add(s, l)
max_valid = axis_size(tensor, i) - 1
offset =
select(greater(max_idx, max_valid), subtract(max_idx, max_valid) |> subtract(1), 0)
offset = Nx.max(offset, 0)
{l}
|> iota(vectorized_axes: vectorized_axes)
|> revectorize([{first_axis, :auto}, {vec_axis, l}], target_shape: {})
|> add(s)
|> subtract(offset)
end)
|> Nx.stack()
|> Nx.revectorize(vectorized_axes,
target_shape: Tuple.append(List.to_tuple(lengths), :auto)
)
Nx.gather(tensor, idx)
else
strides = opts[:strides]
start_indices = to_indices(start_indices)
strides =
if is_integer(strides),
do: List.duplicate(strides, rank(shape)),
else: strides
{start_indices, output_shape} = Nx.Shape.slice(shape, start_indices, lengths, strides)
offset = length(vectorized_axes)
start_indices = List.duplicate(0, offset) ++ start_indices
offset_shape = Keyword.values(vectorized_axes)
lengths = offset_shape ++ lengths
tensor = devectorize(tensor)
output_shape_devec =
if offset != 0 do
List.to_tuple(offset_shape ++ Tuple.to_list(output_shape))
else
output_shape
end
out = %{tensor | shape: output_shape_devec}
strides = List.duplicate(1, offset) ++ strides
result = impl!(tensor).slice(out, tensor, start_indices, lengths, strides)
vectorize(result, vectorized_axes)
end
end
@doc """
Slices a tensor along the given axis.
You can optionally provide a `stride` to specify the amount
of stride in along the given dimension.
Start index must be greater than or equal to zero. It can be an
integer or a scalar tensor. Length must be strictly greater than
zero. `start_index + length` must not exceed the respective tensor
dimension.
The axis will be normalized with the dimensions and names of the
given tensor.
If the `:strides` is given, it must be strictly greater than zero.
It is not possible to slice in reverse. See `gather/2`, `slice/3`,
`take/3`, and `take_along_axis/3` for other ways to retrieve values
from a tensor.
## Options
* `:axis` - The axis along which to take the values from. Defaults to `0`.
* `:strides` - The stride to slice the axis along of. Defaults to `1`.
## Examples
iex> Nx.slice_along_axis(Nx.iota({5, 2}), 1, 2, axis: 0)
#Nx.Tensor<
s64[2][2]
[
[2, 3],
[4, 5]
]
>
iex> Nx.slice_along_axis(Nx.iota({2, 5}), 1, 2, axis: 1)
#Nx.Tensor<
s64[2][2]
[
[1, 2],
[6, 7]
]
>
iex> Nx.slice_along_axis(Nx.iota({2, 5}, names: [:x, :y]), 0, 1, axis: :x)
#Nx.Tensor<
s64[x: 1][y: 5]
[
[0, 1, 2, 3, 4]
]
>
iex> Nx.slice_along_axis(Nx.iota({2, 5}, names: [:x, :y]), Nx.tensor(0), 1, axis: :x)
#Nx.Tensor<
s64[x: 1][y: 5]
[
[0, 1, 2, 3, 4]
]
>
iex> Nx.slice_along_axis(Nx.iota({2, 5}), 0, 3, axis: -1, strides: 2)
#Nx.Tensor<
s64[2][2]
[
[0, 2],
[5, 7]
]
>
## Vectorized tensors
Slices are taken over each vectorized entry.
The `start_index` cannot be vectorized.
iex> t = Nx.iota({2, 5}, vectorized_axes: [x: 2])
iex> Nx.slice_along_axis(t, 0, 3, axis: 1, strides: 2)
#Nx.Tensor<
vectorized[x: 2]
s64[2][2]
[
[
[0, 2],
[5, 7]
],
[
[0, 2],
[5, 7]
]
]
>
"""
@doc type: :indexed, from_backend: false
def slice_along_axis(tensor, start_index, len, opts \\ []) when is_integer(len) do
opts = keyword!(opts, strides: 1, axis: 0)
axis = Keyword.fetch!(opts, :axis)
strides = Keyword.fetch!(opts, :strides)
%T{shape: shape, names: names} = tensor = to_tensor(tensor)
axis = Nx.Shape.normalize_axis(shape, axis, names)
if start_index == 0 and strides == 1 and elem(shape, axis) == len do
tensor
else
rank = rank(shape)
start_indices = List.duplicate(0, rank) |> List.replace_at(axis, start_index)
lengths = shape |> put_elem(axis, len) |> Tuple.to_list()
strides = List.duplicate(1, rank) |> List.replace_at(axis, strides)
slice(tensor, start_indices, lengths, strides: strides)
end
end
@doc false
@deprecated "Use slice_along_axis/4 instead"
def slice_axis(tensor, start_index, len, axis, opts \\ []) when is_integer(len) do
slice_along_axis(tensor, start_index, len, [axis: axis] ++ opts)
end
@doc false
@deprecated "Use sigmoid/1 instead"
def logistic(tensor) do
sigmoid(tensor)
end
@doc """
Puts the given `slice` into the given `tensor` at the given
`start_indices`.
The given slice must be of the same rank as tensor. Each axis
must be less than or equal to the size to the equivalent axis
in the tensor.
The number of elements in `start_indices` should match the
rank of the tensor.
See also: `indexed_add/3`, `put_slice/3`.
## Examples
iex> t = Nx.tensor([0, 1, 2, 3, 4])
iex> Nx.put_slice(t, [2], Nx.tensor([5, 6]))
#Nx.Tensor<
s64[5]
[0, 1, 5, 6, 4]
>
iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]])
iex> Nx.put_slice(t, [0, 1], Nx.tensor([[7, 8], [9, 10]]))
#Nx.Tensor<
s64[2][3]
[
[1, 7, 8],
[4, 9, 10]
]
>
Similar to `slice/3`, dynamic start indexes are also supported:
iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]])
iex> Nx.put_slice(t, [Nx.tensor(0), Nx.tensor(1)], Nx.tensor([[10.0, 11.0]]))
#Nx.Tensor<
f32[2][3]
[
[1.0, 10.0, 11.0],
[4.0, 5.0, 6.0]
]
>
Also similar to `slice/3`, if `start_index + slice_dimension > dimension`,
the start index will be clipped in order to put the whole slice:
iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]])
iex> Nx.put_slice(t, [1, 1], Nx.tensor([[7, 8], [9, 10]]))
#Nx.Tensor<
s64[2][3]
[
[1, 7, 8],
[4, 9, 10]
]
>
## Vectorized tensors
The both tensor to be sliced and the slices can be vectorized,
but indices must be non-vectorized.
iex> t = Nx.tensor([[1, 2, 3, 4], [5, 6, 7, 8]]) |> Nx.vectorize(:x)
iex> slice = Nx.tensor([[10, 20], [30, 40]]) |> Nx.vectorize(:y)
iex> Nx.put_slice(t, [2], slice)
#Nx.Tensor<
vectorized[x: 2][y: 2]
s64[4]
[
[
[1, 2, 10, 20],
[1, 2, 30, 40]
],
[
[5, 6, 10, 20],
[5, 6, 30, 40]
]
]
>
"""
@doc type: :indexed
def put_slice(tensor, start_indices, slice) when is_list(start_indices) do
[tensor, slice] = broadcast_vectors([tensor, slice], align_ranks: true)
%T{vectorized_axes: vectorized_axes, shape: shape, names: names, type: type} = tensor
%T{shape: slice_shape, names: slice_names, type: slice_type} = slice
output_type = binary_type(type, slice_type)
start_indices = to_indices(start_indices)
{output_shape, output_names} =
Nx.Shape.put_slice(shape, names, slice_shape, slice_names, start_indices)
offset = length(vectorized_axes)
start_indices = List.duplicate(0, offset) ++ start_indices
offset_shape = Keyword.values(vectorized_axes)
tensor = devectorize(tensor)
slice = devectorize(slice)
output_shape_devec =
if offset != 0 do
List.to_tuple(offset_shape ++ Tuple.to_list(output_shape))
else
output_shape
end
output_names = List.duplicate(nil, offset) ++ output_names
result =
impl!(tensor).put_slice(
%{tensor | shape: output_shape_devec, names: output_names, type: output_type},
tensor,
start_indices,
slice
)
vectorize(result, vectorized_axes)
end
@doc """
Takes and concatenates slices along an axis.
Intuitively speaking, `take/3` reorders tensor slices along
the given axis based on the given indices, possibly duplicating
and removing slices.
Passing a multi-dimensional indices tensor only affects the
resulting shape. Specifically, the given axis in the input shape
gets replaced with the indices shape.
See `gather/2`, `slice/3`, `slice_along_axis/4`, and `take_along_axis/3`
for other ways to retrieve values from a tensor.
## Options
* `:axis` - an axis to take tensor slices over. Defaults to 0.
## Examples
iex> t = Nx.tensor([[1, 2], [3, 4]])
iex> Nx.take(t, Nx.tensor([1, 0, 1]))
#Nx.Tensor<
s64[3][2]
[
[3, 4],
[1, 2],
[3, 4]
]
>
iex> t = Nx.tensor([[1, 2], [3, 4]])
iex> Nx.take(t, Nx.tensor([1, 0, 1]), axis: 1)
#Nx.Tensor<
s64[2][3]
[
[2, 1, 2],
[4, 3, 4]
]
>
iex> t = Nx.tensor([[1, 2], [3, 4]], names: [:x, :y])
iex> Nx.take(t, Nx.tensor([1, 0, 1]), axis: :y)
#Nx.Tensor<
s64[x: 2][y: 3]
[
[2, 1, 2],
[4, 3, 4]
]
>
iex> t = Nx.tensor([[[1, 2], [11, 12]], [[101, 102], [111, 112]]])
iex> Nx.take(t, Nx.tensor([1, 0, 1]), axis: 1)
#Nx.Tensor<
s64[2][3][2]
[
[
[11, 12],
[1, 2],
[11, 12]
],
[
[111, 112],
[101, 102],
[111, 112]
]
]
>
Multi-dimensional indices tensor:
iex> t = Nx.tensor([[1, 2], [11, 12]])
iex> Nx.take(t, Nx.tensor([[0, 0], [1, 1], [0, 0]]), axis: 1)
#Nx.Tensor<
s64[2][3][2]
[
[
[1, 1],
[2, 2],
[1, 1]
],
[
[11, 11],
[12, 12],
[11, 11]
]
]
>
iex> t = Nx.tensor([[[1, 2], [11, 12]], [[101, 102], [111, 112]]])
iex> Nx.take(t, Nx.tensor([[0, 0, 0], [1, 1, 1], [0, 0, 0]]), axis: 1)
#Nx.Tensor<
s64[2][3][3][2]
[
[
[
[1, 2],
[1, 2],
[1, 2]
],
[
[11, 12],
[11, 12],
[11, 12]
],
[
[1, 2],
[1, 2],
[1, 2]
]
],
[
[
[101, 102],
[101, 102],
[101, 102]
],
[
[111, 112],
[111, 112],
[111, 112]
],
[
[101, 102],
[101, 102],
[101, 102]
]
]
]
>
## Vectorized tensors
`tensor` and `indices` have their vectorized axes broadcast together,
and then the operation takes place normally, with `:axis` and `indices`
having their values in reference to the input shape.
iex> t = Nx.tensor([[1, 2], [11, 12]])
iex> idx = Nx.tensor([0, 1, 0]) |> Nx.vectorize(:x)
iex> Nx.take(t, idx)
#Nx.Tensor<
vectorized[x: 3]
s64[2]
[
[1, 2],
[11, 12],
[1, 2]
]
>
iex> t = Nx.tensor([[[1, 2]], [[11, 12]]]) |> Nx.vectorize(:x)
iex> idx = Nx.tensor([0, 1])
iex> Nx.take(t, idx, axis: 1)
#Nx.Tensor<
vectorized[x: 2]
s64[1][2]
[
[
[1, 2]
],
[
[11, 12]
]
]
>
In case both inputs are vectorized, they will be broadcasted
together before calculations are performed:
iex> t = Nx.tensor([[1, 2], [11, 12]]) |> Nx.vectorize(:x)
iex> idx = Nx.tensor([0, 1, 0]) |> Nx.vectorize(:y)
iex> Nx.take(t, idx)
#Nx.Tensor<
vectorized[x: 2][y: 3]
s64
[
[1, 2, 1],
[11, 12, 11]
]
>
iex> t = Nx.tensor([[1, 2], [11, 12]]) |> Nx.vectorize(:x)
iex> idx = Nx.tensor([[0, 1, 0], [0, 1, 1]]) |> Nx.vectorize(:x)
iex> Nx.take(t, idx)
#Nx.Tensor<
vectorized[x: 2]
s64[3]
[
[1, 2, 1],
[11, 12, 12]
]
>
## Error cases
iex> Nx.take(Nx.tensor([[1, 2], [3, 4]]), Nx.tensor([1, 0, 1], type: :f32))
** (ArgumentError) indices must be an integer tensor, got {:f, 32}
"""
@doc type: :indexed
def take(tensor, indices, opts \\ []) when is_list(opts) do
unless Nx.Type.integer?(type(indices)) do
raise ArgumentError, "indices must be an integer tensor, got #{inspect(type(indices))}"
end
opts = keyword!(opts, axis: 0)
tensor = to_tensor(tensor)
indices = to_tensor(indices)
axis =
Nx.Shape.normalize_axis(
tensor.shape,
opts[:axis],
tensor.names
)
{inner_shape, inner_names} =
Nx.Shape.take(
tensor.shape,
tensor.names,
indices.shape,
indices.names,
axis
)
if tensor.vectorized_axes != [] or indices.vectorized_axes != [] do
axes_range = axes(tensor)
indices_shape =
axes_range
|> Enum.map(fn
^axis -> Tuple.product(indices.shape)
_ -> 1
end)
|> List.to_tuple()
idx_tiling =
tensor.shape
|> Tuple.to_list()
|> Enum.with_index(fn
_x, ^axis ->
1
x, _ ->
x
end)
indices_for_axis =
indices
|> reshape(indices_shape)
|> tile(idx_tiling)
indices =
axes_range
|> Enum.map(fn
^axis ->
reshape(indices_for_axis, {:auto, 1})
current ->
indices_for_axis
|> shape()
|> iota(axis: current, vectorized_axes: indices.vectorized_axes)
|> reshape({:auto, 1})
end)
|> concatenate(axis: 1)
tensor
|> gather(indices)
|> reshape(inner_shape, names: inner_names)
else
tensor = devectorize(tensor, keep_names: false)
indices = devectorize(indices, keep_names: false)
impl!(tensor).take(
%{tensor | shape: inner_shape, names: inner_names},
tensor,
indices,
axis
)
end
end
@doc """
Takes the values from a tensor given an `indices` tensor, along the specified axis.
The `indices` shape must be the same as the `tensor`'s shape, with the exception for
the `axis` dimension, which can have arbitrary size. The returned tensor will have the
same shape as the `indices` tensor.
See `gather/2`, `slice/3`, `slice_along_axis/4`, and `take/3` for other ways to retrieve
values from a tensor.
## Options
* `:axis` - The axis along which to take the values from. Defaults to `0`.
## Examples
iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]])
iex> Nx.take_along_axis(t, Nx.tensor([[0, 0, 2, 2, 1, 1], [2, 2, 1, 1, 0, 0]]), axis: 1)
#Nx.Tensor<
s64[2][6]
[
[1, 1, 3, 3, 2, 2],
[6, 6, 5, 5, 4, 4]
]
>
iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]])
iex> Nx.take_along_axis(t, Nx.tensor([[0, 1, 1], [1, 0, 0], [0, 1, 0]]), axis: 0)
#Nx.Tensor<
s64[3][3]
[
[1, 5, 6],
[4, 2, 3],
[1, 5, 3]
]
>
The indices returned from `Nx.argsort/2` can be used with `Nx.take_along_axis/3` to
produce the sorted tensor (or to sort more tensors according to the same criteria).
iex> tensor = Nx.tensor([[[1, 2], [3, 4], [5, 6]]])
#Nx.Tensor<
s64[1][3][2]
[
[
[1, 2],
[3, 4],
[5, 6]
]
]
>
iex> idx1 = Nx.argsort(tensor, axis: 1, direction: :desc)
#Nx.Tensor<
s64[1][3][2]
[
[
[2, 2],
[1, 1],
[0, 0]
]
]
>
iex> Nx.take_along_axis(tensor, idx1, axis: 1)
#Nx.Tensor<
s64[1][3][2]
[
[
[5, 6],
[3, 4],
[1, 2]
]
]
>
iex> idx2 = Nx.argsort(tensor, axis: 2, direction: :desc)
#Nx.Tensor<
s64[1][3][2]
[
[
[1, 0],
[1, 0],
[1, 0]
]
]
>
iex> Nx.take_along_axis(tensor, idx2, axis: 2)
#Nx.Tensor<
s64[1][3][2]
[
[
[2, 1],
[4, 3],
[6, 5]
]
]
>
## Vectorized tensors
`tensor` and `indices` have their vectorized axes broadcast together,
and then the operation takes place normally, with `:axis` and `indices`
having their values in reference to the input shape.
iex> t = Nx.tensor([[[1, 2, 3]], [[4, 5, 6]]]) |> Nx.vectorize(:x)
iex> idx = Nx.tensor([[[0, 0, 2, 1]], [[2, 1, 0, 0]]]) |> Nx.vectorize(:x)
iex> Nx.take_along_axis(t, idx, axis: 1)
#Nx.Tensor<
vectorized[x: 2]
s64[1][4]
[
[
[1, 1, 3, 2]
],
[
[6, 5, 4, 4]
]
]
>
In the example below, we have broadcasting throughout the vectorized axes
iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]]) |> Nx.vectorize(:x)
iex> idx = Nx.tensor([[0, 0, 2, 1], [2, 1, 0, 0]]) |> Nx.vectorize(:y)
iex> Nx.take_along_axis(t, idx, axis: 0)
#Nx.Tensor<
vectorized[x: 2][y: 2]
s64[4]
[
[
[1, 1, 3, 2],
[3, 2, 1, 1]
],
[
[4, 4, 6, 5],
[6, 5, 4, 4]
]
]
>
## Error cases
iex> tensor = Nx.iota({3, 3})
iex> idx = Nx.tensor([[2.0], [1.0], [2.0]], type: :f32)
iex> Nx.take_along_axis(tensor, idx, axis: 1)
** (ArgumentError) indices must be an integer tensor, got {:f, 32}
"""
@doc type: :indexed
def take_along_axis(tensor, indices, opts \\ []) when is_list(opts) do
[%T{vectorized_axes: vectorized_axes} = tensor, indices] =
broadcast_vectors([tensor, indices], align_ranks: true)
unless Nx.Type.integer?(indices.type) do
raise ArgumentError, "indices must be an integer tensor, got #{inspect(indices.type)}"
end
opts = keyword!(opts, axis: 0)
tensor = devectorize(tensor, keep_names: false)
indices = devectorize(indices, keep_names: false)
offset = length(vectorized_axes)
axis = Nx.Shape.normalize_axis(tensor.shape, opts[:axis], tensor.names, offset)
shape = Nx.Shape.take_along_axis(tensor.shape, indices.shape, axis)
result = impl!(tensor).take_along_axis(%{tensor | shape: shape}, tensor, indices, axis)
vectorize(result, vectorized_axes)
end
@doc """
Builds a new tensor by taking individual values from the original
tensor at the given indices.
The last dimension in indices must have the same size as the tensor
rank, think of it as one value per axis.
## Examples
iex> t = Nx.tensor([[1, 2], [3, 4]])
iex> Nx.gather(t, Nx.tensor([[1, 1], [0, 1], [1, 0]]))
#Nx.Tensor<
s64[3]
[4, 2, 3]
>
iex> t = Nx.tensor([[1, 2], [3, 4]])
iex> Nx.gather(t, Nx.tensor([[[1, 1], [0, 0]], [[1, 0], [0, 1]]]))
#Nx.Tensor<
s64[2][2]
[
[4, 1],
[3, 2]
]
>
iex> t = Nx.tensor([[[1, 2], [11, 12]], [[101, 102], [111, 112]]])
iex> Nx.gather(t, Nx.tensor([[0, 0, 0], [0, 1, 1], [1, 1, 1]]))
#Nx.Tensor<
s64[3]
[1, 12, 112]
>
## Vectorized tensors
`tensor` and `indices` have their vectorized axes broadcast together,
and then the operation takes place normally, with `:axis` and `indices`
having their values in reference to the input shape.
iex> t = Nx.tensor([[[1, 2], [11, 12]], [[101, 102], [111, 112]]]) |> Nx.vectorize(:x)
iex> idx = Nx.tensor([[[0, 0], [0, 1]], [[1, 0], [1, 1]]]) |> Nx.vectorize(:x)
iex> Nx.gather(t, idx)
#Nx.Tensor<
vectorized[x: 2]
s64[2]
[
[1, 2],
[111, 112]
]
>
And with vectorized broadcasting:
iex> t = Nx.tensor([[[1, 2], [11, 12]], [[101, 102], [111, 112]]]) |> Nx.vectorize(:x)
iex> idx = Nx.tensor([[[0, 0], [0, 1]], [[1, 0], [1, 1]]]) |> Nx.vectorize(:y)
iex> Nx.gather(t, idx)
#Nx.Tensor<
vectorized[x: 2][y: 2]
s64[2]
[
[
[1, 2],
[11, 12]
],
[
[101, 102],
[111, 112]
]
]
>
## Error cases
iex> Nx.gather(Nx.tensor([[1, 2], [3, 4]]), Nx.tensor([[0, 0]], type: :f32))
** (ArgumentError) indices must be an integer tensor, got {:f, 32}
"""
@doc type: :indexed
def gather(tensor, indices) do
[%T{vectorized_axes: vectorized_axes} = tensor, indices] =
broadcast_vectors([tensor, indices], align_ranks: false)
unless Nx.Type.integer?(indices.type) do
raise ArgumentError, "indices must be an integer tensor, got #{inspect(indices.type)}"
end
offset = length(vectorized_axes)
{tensor, indices} =
if offset != 0 do
tensor = devectorize(tensor, keep_names: false)
indices = devectorize(indices, keep_names: false)
iota_shape =
indices.shape |> Tuple.delete_at(tuple_size(indices.shape) - 1) |> Tuple.append(1)
offset_axes = (offset - 1)..0//-1
indices =
offset_axes
|> Enum.reduce([indices], &[Nx.iota(iota_shape, axis: &1) | &2])
|> concatenate(axis: -1)
{tensor, indices}
else
{tensor, indices}
end
{shape, names} = Nx.Shape.gather(tensor.shape, indices.shape)
result = impl!(tensor).gather(%{tensor | shape: shape, names: names}, tensor, indices)
vectorize(result, vectorized_axes)
end
@doc """
Concatenates tensors along the given axis.
Tensors can be a tuple or any `Nx.Container` or `Nx.LazyContainer`.
This means you can easily concatenate all columns in a dataframe
and other data structures. For convenience, this function also allows
a list of tensors to be given, which may be common outside of `defn`.
If no axis is provided, defaults to 0. All tensors must have the same
rank and all of their axis except the concatenated one must match.
If tensors with mixed types are given, the types will
be merged to a higher type and all of the tensors will
be cast to the higher type before concatenating.
If tensors are named, the names must match.
## Examples
Giving a single tensor is a no-op:
iex> Nx.concatenate([Nx.tensor([1, 2, 3])])
#Nx.Tensor<
s64[3]
[1, 2, 3]
>
Multiple tensors are concatented:
iex> Nx.concatenate([Nx.tensor([1, 2, 3]), Nx.tensor([4, 5, 6])])
#Nx.Tensor<
s64[6]
[1, 2, 3, 4, 5, 6]
>
Types are merged and names must match:
iex> t1 = Nx.iota({2, 2, 2}, names: [:x, :y, :z], type: :f32)
iex> t2 = Nx.iota({1, 2, 2}, names: [:x, :y, :z], type: :u8)
iex> t3 = Nx.iota({1, 2, 2}, names: [:x, :y, :z], type: :s64)
iex> Nx.concatenate([t1, t2, t3], axis: :x)
#Nx.Tensor<
f32[x: 4][y: 2][z: 2]
[
[
[0.0, 1.0],
[2.0, 3.0]
],
[
[4.0, 5.0],
[6.0, 7.0]
],
[
[0.0, 1.0],
[2.0, 3.0]
],
[
[0.0, 1.0],
[2.0, 3.0]
]
]
>
And you can pick a different axis:
iex> t1 = Nx.iota({1, 3, 2}, names: [:x, :y, :z])
iex> t2 = Nx.iota({1, 1, 2}, names: [:x, :y, :z])
iex> t3 = Nx.iota({1, 2, 2}, names: [:x, :y, :z])
iex> Nx.concatenate([t1, t2, t3], axis: :y)
#Nx.Tensor<
s64[x: 1][y: 6][z: 2]
[
[
[0, 1],
[2, 3],
[4, 5],
[0, 1],
[0, 1],
[2, 3]
]
]
>
You can also pass any container (or lazy container) as first argument
and they are recursively traversed:
iex> Nx.concatenate({Nx.tensor([1, 2]), {Nx.tensor([3, 4]), Nx.tensor([5, 6])}})
#Nx.Tensor<
s64[6]
[1, 2, 3, 4, 5, 6]
>
## Vectorized tensors
If vectorized tensors are given, they are all broadcasted throughout the
vectorized axes before concatenation. Normal concatenation rules still apply
to the inner shapes.
iex> x = Nx.tensor([[1, 2]]) |> Nx.vectorize(:x)
iex> y = Nx.tensor([[3, 4], [5, 6]]) |> Nx.vectorize(:y)
iex> z = Nx.tensor([[10], [11]]) |> Nx.vectorize(:x)
iex> Nx.concatenate({x, y, z})
#Nx.Tensor<
vectorized[x: 2][y: 2]
s64[5]
[
[
[1, 2, 3, 4, 10],
[1, 2, 5, 6, 10]
],
[
[1, 2, 3, 4, 11],
[1, 2, 5, 6, 11]
]
]
>
## Error cases
Shapes must have the same rank and match on the non-concatenating axis.
For example, the tensors below work if we concatenate on axis 1, but not on axis 0:
iex> t1 = Nx.iota({1, 2, 3})
iex> t2 = Nx.iota({1, 1, 3})
iex> result = Nx.concatenate([t1, t2], axis: 1)
iex> Nx.shape(result)
{1, 3, 3}
iex> Nx.concatenate([t1, t2], axis: 0)
** (ArgumentError) expected all shapes to match {*, 2, 3}, got unmatching shape: {1, 1, 3}
If the ranks are different, it doesn't work, regardless of the axis choice:
iex> t1 = Nx.iota({1, 2, 3})
iex> t2 = Nx.iota({1, 1})
iex> Nx.concatenate([t1, t2])
** (ArgumentError) expected all shapes to match {*, 2, 3}, got unmatching shape: {1, 1}
"""
@doc type: :ndim
def concatenate(tensors, opts \\ []) do
opts = keyword!(opts, axis: 0)
axis = opts[:axis]
case flatten_list_or_container(tensors) do
[] ->
raise ArgumentError, "no tensors were given to concatenate"
[t] ->
t
[_ | _] = tensors ->
[%T{vectorized_axes: vectorized_axes} | _] =
tensors = broadcast_vectors(tensors, align_ranks: true)
offset = length(vectorized_axes)
tensors = if vectorized_axes != [], do: Enum.map(tensors, &devectorize/1), else: tensors
{types, [s1 | _] = shapes, [n1 | _] = names} =
Enum.reduce(tensors, {[], [], []}, fn
%T{type: t, shape: s, names: n}, {types, shapes, names} ->
{[t | types], [s | shapes], [n | names]}
end)
axis = Nx.Shape.normalize_axis(s1, axis, n1, offset)
output_type = Enum.reduce(types, fn t1, t2 -> Nx.Type.merge(t1, t2) end)
{output_shape, output_names} =
Nx.Shape.concatenate(Enum.reverse(shapes), Enum.reverse(names), axis)
out = %{hd(tensors) | type: output_type, shape: output_shape, names: output_names}
result = list_impl!(tensors).concatenate(out, tensors, axis)
vectorize(result, vectorized_axes)
end
end
defp flatten_list_or_container(list) when is_list(list) do
list
|> Enum.reduce([], &flatten_container/2)
|> Enum.reverse()
end
defp flatten_list_or_container(container) do
container
|> flatten_container([])
|> Enum.reverse()
end
defp flatten_container(container, acc) do
if match?(%{}, container) and not match?(%_{}, container) do
IO.warn(
"a map has been given to stack/concatenate. Maps do not have a predefined order " <>
"and therefore there is no guarantee over of the stack/concatenated tensors"
)
end
container
|> Nx.LazyContainer.traverse(acc, fn template, fun, acc -> {template, [fun.() | acc]} end)
|> elem(1)
end
@doc """
Stacks a list of tensors with the same shape along a new axis.
Tensors can be a tuple or any `Nx.Container` or `Nx.LazyContainer`.
This means you can easily concatenate all columns in a dataframe
and other data structures. For convenience, this function also allows
a list of tensors to be given, which may be common outside of `defn`.
If no axis is provided, defaults to 0. All tensors must have the same
shape.
If tensors with mixed types are given, the types will
be merged to a higher type and all of the tensors will
be cast to the higher type before concatenating.
If tensors are named, the names must match.
### Options
* `:axis` - optional index of the axis along which the tensors are stacked. Defaults to 0.
* `:name` - optional name for the added dimension. Defaults to an unnamed axis.
## Examples
Stacking always creates a new dimension:
iex> Nx.stack([1, 2, 3])
#Nx.Tensor<
s64[3]
[1, 2, 3]
>
iex> Nx.stack([Nx.tensor([1, 2, 3]), Nx.tensor([4, 5, 6])])
#Nx.Tensor<
s64[2][3]
[
[1, 2, 3],
[4, 5, 6]
]
>
The axis option can be given:
iex> t1 = Nx.iota({2, 1, 4})
iex> t2 = Nx.iota({2, 1, 4})
iex> t3 = Nx.iota({2, 1, 4})
iex> Nx.stack([t1, t2, t3], axis: -1)
#Nx.Tensor<
s64[2][1][4][3]
[
[
[
[0, 0, 0],
[1, 1, 1],
[2, 2, 2],
[3, 3, 3]
]
],
[
[
[4, 4, 4],
[5, 5, 5],
[6, 6, 6],
[7, 7, 7]
]
]
]
>
And a name can be given for the new dimension:
iex> Nx.stack([Nx.tensor(1), Nx.tensor(2)], name: :x)
#Nx.Tensor<
s64[x: 2]
[1, 2]
>
You can also pass any container (or lazy container) as first argument
and they are recursively traversed:
iex> Nx.stack({Nx.tensor([1, 2]), {Nx.tensor([3, 4]), Nx.tensor([5, 6])}})
#Nx.Tensor<
s64[3][2]
[
[1, 2],
[3, 4],
[5, 6]
]
>
"""
@doc type: :ndim, from_backend: false
def stack(tensors, opts \\ []) do
opts = keyword!(opts, axis: 0, name: nil)
axis = opts[:axis]
name = opts[:name]
tensors
|> flatten_list_or_container()
|> Enum.map(&Nx.new_axis(&1, axis, name))
|> Nx.concatenate(axis: axis)
end
@doc """
Sorts the tensor along the given axis according
to the given direction.
If no axis is given, defaults to `0`.
### Options
* `:axis` - The name or number of the corresponding axis on which the sort
should be applied
* `:direction` - Can be `:asc` or `:desc`. Defaults to `:asc`
## Examples
iex> Nx.sort(Nx.tensor([16, 23, 42, 4, 8, 15]))
#Nx.Tensor<
s64[6]
[4, 8, 15, 16, 23, 42]
>
iex> t = Nx.tensor([[3, 1, 7], [2, 5, 4]], names: [:x, :y])
iex> Nx.sort(t, axis: :x)
#Nx.Tensor<
s64[x: 2][y: 3]
[
[2, 1, 4],
[3, 5, 7]
]
>
iex> t = Nx.tensor([[3, 1, 7], [2, 5, 4]], names: [:x, :y])
iex> Nx.sort(t, axis: :y)
#Nx.Tensor<
s64[x: 2][y: 3]
[
[1, 3, 7],
[2, 4, 5]
]
>
iex> t = Nx.tensor([[3, 1, 7], [2, 5, 4]], names: [:x, :y])
iex> Nx.sort(t, axis: :y, direction: :asc)
#Nx.Tensor<
s64[x: 2][y: 3]
[
[1, 3, 7],
[2, 4, 5]
]
>
iex> t = Nx.tensor(
...> [
...> [[4, 5], [2, 5], [5, 0]],
...> [[1, 9], [2, 1], [2, 1]],
...> [[0, -1], [-1, 0], [0, -1]],
...> [[-1, 0], [0, -1], [-1, 0]]
...> ],
...> names: [:x, :y, :z]
...> )
iex> Nx.sort(t, axis: :x)
#Nx.Tensor<
s64[x: 4][y: 3][z: 2]
[
[
[-1, -1],
[-1, -1],
[-1, -1]
],
[
[0, 0],
[0, 0],
[0, 0]
],
[
[1, 5],
[2, 1],
[2, 0]
],
[
[4, 9],
[2, 5],
[5, 1]
]
]
>
Same tensor sorted over different axes:
iex> t = Nx.tensor(
...> [
...> [
...> [4, 5, 2],
...> [2, 5, 3],
...> [5, 0, 2]
...> ],
...> [
...> [1, 9, 8],
...> [2, 1, 3],
...> [2, 1, 4]
...> ]
...> ],
...> names: [:x, :y, :z]
...> )
iex> Nx.sort(t, axis: :x)
#Nx.Tensor<
s64[x: 2][y: 3][z: 3]
[
[
[1, 5, 2],
[2, 1, 3],
[2, 0, 2]
],
[
[4, 9, 8],
[2, 5, 3],
[5, 1, 4]
]
]
>
iex> Nx.sort(t, axis: :y)
#Nx.Tensor<
s64[x: 2][y: 3][z: 3]
[
[
[2, 0, 2],
[4, 5, 2],
[5, 5, 3]
],
[
[1, 1, 3],
[2, 1, 4],
[2, 9, 8]
]
]
>
iex> Nx.sort(t, axis: :z)
#Nx.Tensor<
s64[x: 2][y: 3][z: 3]
[
[
[2, 4, 5],
[2, 3, 5],
[0, 2, 5]
],
[
[1, 8, 9],
[1, 2, 3],
[1, 2, 4]
]
]
>
"""
@doc type: :ndim
def sort(tensor, opts \\ []) do
opts = keyword!(opts, axis: 0, direction: :asc)
apply_vectorized(tensor, fn tensor, offset ->
direction =
case opts[:direction] do
:asc ->
:asc
:desc ->
:desc
other ->
raise ArgumentError,
"unknown value for :direction, expected :asc or :desc, got: #{inspect(other)}"
end
%T{shape: shape, names: names, type: type} = tensor
Nx.Shared.raise_complex_not_supported(type, :sort, 2)
axis = Nx.Shape.normalize_axis(shape, opts[:axis], names, offset)
impl!(tensor).sort(
tensor,
tensor,
axis: axis,
direction: direction
)
end)
end
@doc """
Returns a tuple of `{values, indices}` for the top `k`
values in last dimension of the tensor.
`:k` is an option and must be at least 1, and less than
or equal to the size of the last dimension of the tensor.
It defaults to `1`.
## Examples
iex> a = Nx.tensor([1, 2, 3, 4, 5])
iex> {values, indices} = Nx.top_k(a, k: 2)
iex> values
#Nx.Tensor<
s64[2]
[5, 4]
>
iex> indices
#Nx.Tensor<
s64[2]
[4, 3]
>
`:k` defaults to 1:
iex> a = Nx.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
iex> {values, indices} = Nx.top_k(a)
iex> values
#Nx.Tensor<
f32[2][1]
[
[3.0],
[6.0]
]
>
iex> indices
#Nx.Tensor<
s64[2][1]
[
[2],
[2]
]
>
## Error cases
iex> a = Nx.tensor([1, 2, 3, 4, 5])
iex> Nx.top_k(a, k: 6)
** (ArgumentError) top_k input last axis size must be greater than or equal to k, got size=5 and k=6
iex> a = Nx.tensor(1)
iex> Nx.top_k(a, k: 1)
** (ArgumentError) top_k input must have at least rank 1
"""
@doc type: :ndim
def top_k(tensor, opts \\ []) do
apply_vectorized(tensor, fn tensor ->
opts = Keyword.validate!(opts, k: 1)
%T{shape: shape, names: names} = tensor
{output_shape, output_names} = Nx.Shape.top_k(shape, names, opts[:k])
out_values = %{tensor | shape: output_shape, names: output_names}
out_indices = %{tensor | shape: output_shape, names: output_names, type: {:s, 64}}
Nx.Shared.optional(:top_k, [tensor, opts], {out_values, out_indices}, fn tensor, opts ->
k = Keyword.fetch!(opts, :k)
rank = rank(tensor)
indices = argsort(tensor, axis: rank - 1, direction: :desc)
values = Nx.take_along_axis(tensor, indices, axis: rank - 1)
{slice_along_axis(values, 0, k, axis: rank - 1),
slice_along_axis(indices, 0, k, axis: rank - 1)}
end)
end)
end
@doc """
Sorts the tensor along the given axis according
to the given direction and returns the corresponding indices
of the original tensor in the new sorted positions.
If no axis is given, defaults to `0`.
See `take_along_axis/3` for examples on how to apply the
resulting indices from this function.
## Options
* `:axis` - The name or number of the corresponding axis on which the sort
should be applied
* `:direction` - Can be `:asc` or `:desc`. Defaults to `:asc`
## Examples
iex> Nx.argsort(Nx.tensor([16, 23, 42, 4, 8, 15]))
#Nx.Tensor<
s64[6]
[3, 4, 5, 0, 1, 2]
>
iex> t = Nx.tensor([[3, 1, 7], [2, 5, 4]], names: [:x, :y])
iex> Nx.argsort(t, axis: :x)
#Nx.Tensor<
s64[x: 2][y: 3]
[
[1, 0, 1],
[0, 1, 0]
]
>
iex> t = Nx.tensor([[3, 1, 7], [2, 5, 4]], names: [:x, :y])
iex> Nx.argsort(t, axis: :y)
#Nx.Tensor<
s64[x: 2][y: 3]
[
[1, 0, 2],
[0, 2, 1]
]
>
iex> t = Nx.tensor([[3, 1, 7], [2, 5, 4]], names: [:x, :y])
iex> Nx.argsort(t, axis: :y, direction: :asc)
#Nx.Tensor<
s64[x: 2][y: 3]
[
[1, 0, 2],
[0, 2, 1]
]
>
Same tensor sorted over different axes:
iex> t = Nx.tensor(
...> [
...> [
...> [4, 5, 2],
...> [2, 5, 3],
...> [5, 0, 2]
...> ],
...> [
...> [1, 9, 8],
...> [2, 1, 3],
...> [2, 1, 4]
...> ]
...> ],
...> names: [:x, :y, :z]
...> )
iex> Nx.argsort(t, axis: :x)
#Nx.Tensor<
s64[x: 2][y: 3][z: 3]
[
[
[1, 0, 0],
[0, 1, 0],
[1, 0, 0]
],
[
[0, 1, 1],
[1, 0, 1],
[0, 1, 1]
]
]
>
iex> Nx.argsort(t, axis: :y)
#Nx.Tensor<
s64[x: 2][y: 3][z: 3]
[
[
[1, 2, 0],
[0, 0, 2],
[2, 1, 1]
],
[
[0, 1, 1],
[1, 2, 2],
[2, 0, 0]
]
]
>
iex> Nx.argsort(t, axis: :z)
#Nx.Tensor<
s64[x: 2][y: 3][z: 3]
[
[
[2, 0, 1],
[0, 2, 1],
[1, 2, 0]
],
[
[0, 2, 1],
[1, 0, 2],
[1, 0, 2]
]
]
>
"""
@doc type: :ndim
def argsort(tensor, opts \\ []) do
opts = keyword!(opts, axis: 0, direction: :asc)
apply_vectorized(tensor, fn tensor, offset ->
direction =
case opts[:direction] do
:asc ->
:asc
:desc ->
:desc
other ->
raise ArgumentError,
"unknown value for :direction, expected :asc or :desc, got: #{inspect(other)}"
end
%T{type: type, shape: shape, names: names} = tensor
axis = Nx.Shape.normalize_axis(shape, opts[:axis], names, offset)
Nx.Shared.raise_complex_not_supported(type, :argsort, 2)
impl!(tensor).argsort(
%{tensor | type: {:s, 64}},
tensor,
axis: axis,
direction: direction
)
end)
end
## Utilities
@doc """
Serializes the given tensor or container of tensors to iodata.
You may pass any tensor or `Nx.Container` to serialization.
Opposite to other functions in this module, `Nx.LazyContainer`
cannot be serialized and they must be explicitly converted
to tensors before (that's because lazy containers do not preserve
their shape).
`opts` controls the serialization options. For example, you can choose
to compress the given tensor or container of tensors by passing a
compression level:
Nx.serialize(tensor, compressed: 9)
Compression level corresponds to compression options in `:erlang.term_to_iovec/2`.
`iodata` is a list of binaries that can be written to any io device,
such as a file or a socket. You can ensure the result is a binary by
calling `IO.iodata_to_binary/1`.
Note: This function cannot be used in `defn`.
## Examples
iex> a = Nx.tensor([1, 2, 3])
iex> serialized_a = Nx.serialize(a)
iex> Nx.deserialize(serialized_a)
#Nx.Tensor<
s64[3]
[1, 2, 3]
>
iex> container = {Nx.tensor([1, 2, 3]), %{b: Nx.tensor([4, 5, 6])}}
iex> serialized_container = Nx.serialize(container)
iex> {a, %{b: b}} = Nx.deserialize(serialized_container)
iex> a
#Nx.Tensor<
s64[3]
[1, 2, 3]
>
iex> b
#Nx.Tensor<
s64[3]
[4, 5, 6]
>
"""
@doc type: :conversion
def serialize(tensor_or_container, opts \\ []) do
{term, {binaries, _offsets}} = to_term(tensor_or_container, {[], 0})
data = :erlang.term_to_iovec(term, opts)
endianness = endianness_to_byte(System.endianness())
[<<@file_prefix, @file_version, endianness, IO.iodata_length(data)::64>> | data] ++
Enum.reverse(binaries)
end
defp to_term(tensor_or_container, {binaries, offset}) do
case tensor_or_container do
number when is_number(number) when is_struct(number, Complex) ->
type = Nx.Type.infer(number)
binary = number_to_binary(number, type)
size = Kernel.byte_size(binary)
acc = {[binary | binaries], offset + size}
{{:t, {}, type, [], [], offset, size}, acc}
%T{vectorized_axes: vectorized_axes} = tensor ->
%{shape: shape, names: names} = devectorize(tensor)
type = type(tensor)
binary = to_binary(tensor)
size = Kernel.byte_size(binary)
acc = {[binary | binaries], offset + size}
{{:t, shape, type, names, vectorized_axes, offset, size}, acc}
other ->
{module, pairs, meta} = Nx.Container.serialize(other)
{pairs, acc} =
Enum.map_reduce(pairs, {binaries, offset}, fn {k, v}, acc ->
{v, acc} = to_term(v, acc)
{{k, v}, acc}
end)
{{module, pairs, meta}, acc}
end
end
defp endianness_to_byte(:little), do: 0
defp endianness_to_byte(:big), do: 1
defp byte_to_endianness(0), do: :little
defp byte_to_endianness(1), do: :big
@doc """
Deserializes a serialized representation of a tensor or a container
with the given options.
It is the opposite of `Nx.serialize/2`.
Note: This function cannot be used in `defn`.
## Examples
iex> a = Nx.tensor([1, 2, 3])
iex> serialized_a = Nx.serialize(a)
iex> Nx.deserialize(serialized_a)
#Nx.Tensor<
s64[3]
[1, 2, 3]
>
iex> container = {Nx.vectorize(Nx.tensor([1, 2, 3]), :x), %{b: Nx.tensor([4, 5, 6])}}
iex> serialized_container = Nx.serialize(container)
iex> {a, %{b: b}} = Nx.deserialize(serialized_container)
iex> a
#Nx.Tensor<
vectorized[x: 3]
s64
[1, 2, 3]
>
iex> b
#Nx.Tensor<
s64[3]
[4, 5, 6]
>
"""
@doc type: :conversion
def deserialize(data, opts \\ []) do
data
|> IO.iodata_to_binary()
|> deserialize_binary(opts)
end
defp deserialize_binary(
<<@file_prefix, @file_version, endianness, size::64, data::binary-size(size),
buffers::binary>>,
opts
) do
term = :erlang.binary_to_term(data, opts)
from_buffers(term, byte_to_endianness(endianness), buffers)
end
defp deserialize_binary(<<@file_prefix, version, _::binary>>, _opts) do
raise ArgumentError, "cannot deserialize Nx format v#{version}"
end
# TODO: Remove me in future releases (format for Nx v0.5 and earlier).
defp deserialize_binary(binary, opts) do
{1, endianness, term} = :erlang.binary_to_term(binary, opts)
from_term(term, endianness)
end
defp from_buffers(term, endianness, buffers) do
case term do
{:t, flat_shape, {_, type_size} = type, names, vectorized_axes, offset, size} ->
buffers
|> binary_part(offset, size)
|> new_byte_order(type_size, endianness)
|> from_binary(type)
|> reshape(flat_shape, names: names)
|> vectorize(vectorized_axes)
{module, pairs, metadata} ->
pairs = Enum.map(pairs, fn {k, v} -> {k, from_buffers(v, endianness, buffers)} end)
module.deserialize(pairs, metadata)
_ ->
raise ArgumentError, "unable to deserialize term to tensor: #{inspect(term)}"
end
end
defp from_term(term, endianness) do
case term do
{:tensor, shape, {_, size} = type, names, binary} ->
binary
|> new_byte_order(size, endianness)
|> from_binary(type)
|> reshape(shape, names: names)
{:container, container} ->
{deserialized, :ok} =
Nx.Container.traverse(container, :ok, fn container_elem, :ok ->
{from_term(container_elem, endianness), :ok}
end)
deserialized
{module, pairs, metadata} ->
pairs = Enum.map(pairs, fn {k, v} -> {k, from_term(v, endianness)} end)
module.deserialize(pairs, metadata)
_ ->
raise ArgumentError, "unable to deserialize binary term to tensor"
end
end
@doc """
Loads a `.npy` file into a tensor.
An `.npy` file stores a single array created from Python's
NumPy library. This function can be useful for loading data
originally created or intended to be loaded from NumPy into
Elixir.
This function will raise if the archive or any of its contents
are invalid.
Note: This function cannot be used in `defn`.
## Examples
"array.npy"
|> File.read!()
|> Nx.load_numpy!()
#=>
#Nx.Tensor<
s64[3]
[1, 2, 3]
>
"""
@doc type: :conversion
@spec load_numpy!(data :: binary) :: Nx.Tensor.t()
def load_numpy!(data)
def load_numpy!(<<"\x93NUMPY"::binary, major::size(8), minor::size(8), rest::binary>>) do
load_numpy!(rest, major, minor)
end
def load_numpy!(_) do
raise ArgumentError,
"unable to parse NumPy file, it may be corrupted" <>
" or invalid"
end
defp load_numpy!(<<header_size::size(16)-little-unsigned, rest::binary>>, 1, 0) do
do_numpy_to_tensor(rest, header_size)
end
defp load_numpy!(<<header_size::size(32)-little-unsigned, rest::binary>>, _, _) do
do_numpy_to_tensor(rest, header_size)
end
defp do_numpy_to_tensor(rest, header_size) when is_binary(rest) do
<<header::size(header_size)-binary, array::binary>> = rest
{byte_order, {_, size} = type, shape, fortran_order?} = parse_header(header)
byte_size_of_array = div(size, 8) * Nx.size(shape)
<<data::size(byte_size_of_array)-binary>> = array
data
|> new_byte_order(size, byte_order)
|> Nx.from_binary(type)
|> reshape_with_order(shape, fortran_order?)
end
defp parse_header(header) do
case header do
"{'descr': " <> <<dtype::size(5)-binary>> <> ", 'fortran_order': False, 'shape': " <> shape ->
{byte_order, type} = parse_type(dtype)
{byte_order, type, parse_shape(shape), false}
"{'descr': " <> <<dtype::size(5)-binary>> <> ", 'fortran_order': True, 'shape': " <> shape ->
{byte_order, type} = parse_type(dtype)
{byte_order, type, parse_shape(shape), true}
end
end
defp parse_type(<<?', ?|, type, ?1, ?'>>) do
type =
case type do
?u -> :u
?i -> :s
?f -> :f
_ -> raise "unsupported numpy type: #{type}"
end
{System.endianness(), {type, 8}}
end
defp parse_type(<<?', byte_order, type, size, ?'>>) do
byte_order =
case byte_order do
?> ->
:big
?< ->
:little
# We can't just infer native endianness matches our native endianness
endianness ->
raise ArgumentError, "unsupported numpy endianness: #{endianness}"
end
type =
case type do
?u -> :u
?i -> :s
?f -> :f
_ -> raise "unsupported numpy type: #{type}"
end
size = (size - ?0) * 8
{byte_order, {type, size}}
end
defp parse_shape("(" <> shape) do
shape
|> String.split(")", parts: 2)
|> hd()
|> String.split(",", trim: true)
|> Enum.map(&(String.trim(&1) |> String.to_integer()))
|> List.to_tuple()
end
defp new_byte_order(binary, size, endianness) do
if System.endianness() == endianness do
binary
else
data =
for <<data::size(size)-binary <- binary>> do
data
|> :binary.decode_unsigned()
|> :binary.encode_unsigned(endianness)
end
IO.iodata_to_binary(data)
end
end
defp reshape_with_order(tensor, shape, false), do: Nx.reshape(tensor, shape)
defp reshape_with_order(tensor, shape, true) do
shape = shape |> Tuple.to_list() |> Enum.reverse() |> List.to_tuple()
Nx.reshape(tensor, shape) |> Nx.transpose()
end
@doc """
Loads a `.npz` archive into a list of tensors.
An `.npz` file is a zipped, possibly compressed
archive containing multiple `.npy` files.
It returns a list of two elements tuples, where
the tensor name is first and the serialized tensor
is second. The list is returned in the same order
as in the archive. Use `Map.new/1` afterwards if
you want to access the list elements by name.
It will raise if the archive or any of its contents
are invalid.
Note: This function cannot be used in `defn`.
## Examples
"archive.npz"
|> File.read!()
|> Nx.load_numpy_archive!()
#=>
[
{"foo",
#Nx.Tensor<
s64[3]
[1, 2, 3]
>},
{"bar",
#Nx.Tensor<
f64[5]
[-1.0, -0.5, 0.0, 0.5, 1.0]
>}
]
"""
@doc type: :conversion
@spec load_numpy_archive!(data :: binary) :: [{name :: binary, Nx.Tensor.t()}]
def load_numpy_archive!(archive) do
case :zip.unzip(archive, [:memory]) do
{:ok, files} ->
Enum.map(files, fn {name, data} ->
name = to_string(name)
name =
if String.ends_with?(name, ".npy") do
binary_part(name, 0, Kernel.byte_size(name) - 4)
else
name
end
{name, load_numpy!(data)}
end)
_ ->
raise ArgumentError,
"unable to parse NumPy archive, it may be corrupted" <>
" or invalid"
end
end
@doc """
Finds the variance of a tensor.
The variance is the average of the squared deviations from the mean.
The mean is typically calculated as `sum(tensor) / n`, where `n` is the total
of elements. If, however, `:ddof` (delta degrees of freedom) is specified, the
divisor `n - ddof` is used instead.
## Examples
iex> Nx.variance(Nx.tensor([[1, 2], [3, 4]]))
#Nx.Tensor<
f32
1.25
>
iex> Nx.variance(Nx.tensor([[1, 2], [3, 4]]), ddof: 1)
#Nx.Tensor<
f32
1.6666666269302368
>
iex> Nx.variance(Nx.tensor([[1, 2], [3, 4]]), axes: [0])
#Nx.Tensor<
f32[2]
[1.0, 1.0]
>
iex> Nx.variance(Nx.tensor([[1, 2], [3, 4]]), axes: [1])
#Nx.Tensor<
f32[2]
[0.25, 0.25]
>
iex> Nx.variance(Nx.tensor([[1, 2], [3, 4]]), axes: [0], ddof: 1)
#Nx.Tensor<
f32[2]
[2.0, 2.0]
>
iex> Nx.variance(Nx.tensor([[1, 2], [3, 4]]), axes: [1], ddof: 1)
#Nx.Tensor<
f32[2]
[0.5, 0.5]
>
### Keeping axes
iex> Nx.variance(Nx.tensor([[1, 2], [3, 4]]), axes: [1], keep_axes: true)
#Nx.Tensor<
f32[2][1]
[
[0.25],
[0.25]
]
>
### Vectorized tensors
iex> Nx.variance(Nx.tensor([[1, 2], [0, 4]]) |> Nx.vectorize(:x))
#Nx.Tensor<
vectorized[x: 2]
f32
[0.25, 4.0]
>
"""
@doc type: :aggregation
@spec variance(tensor :: Nx.Tensor.t(), opts :: Keyword.t()) :: Nx.Tensor.t()
def variance(tensor, opts \\ []) do
%T{shape: shape, names: names} = tensor = to_tensor(tensor)
opts = keyword!(opts, [:axes, ddof: 0, keep_axes: false])
axes = opts[:axes]
{ddof, opts} = Keyword.pop!(opts, :ddof)
total =
if axes do
mean_den(shape, Nx.Shape.normalize_axes(shape, axes, names))
else
size(shape)
end
mean = mean(tensor, Keyword.put(opts, :keep_axes, true))
tensor
|> subtract(mean)
|> pow(2)
|> sum(opts)
|> divide(total - ddof)
end
@doc """
Finds the standard deviation of a tensor.
The standard deviation is taken as the square root of the variance.
If the `:ddof` (delta degrees of freedom) option is given, the divisor
`n - ddof` is used to calculate the variance. See `variance/2`.
## Examples
iex> Nx.standard_deviation(Nx.tensor([[1, 2], [3, 4]]))
#Nx.Tensor<
f32
1.1180340051651
>
iex> Nx.standard_deviation(Nx.tensor([[1, 2], [3, 4]]), ddof: 1)
#Nx.Tensor<
f32
1.29099440574646
>
iex> Nx.standard_deviation(Nx.tensor([[1, 2], [10, 20]]), axes: [0])
#Nx.Tensor<
f32[2]
[4.5, 9.0]
>
iex> Nx.standard_deviation(Nx.tensor([[1, 2], [10, 20]]), axes: [1])
#Nx.Tensor<
f32[2]
[0.5, 5.0]
>
iex> Nx.standard_deviation(Nx.tensor([[1, 2], [10, 20]]), axes: [0], ddof: 1)
#Nx.Tensor<
f32[2]
[6.363961219787598, 12.727922439575195]
>
iex> Nx.standard_deviation(Nx.tensor([[1, 2], [10, 20]]), axes: [1], ddof: 1)
#Nx.Tensor<
f32[2]
[0.7071067690849304, 7.071067810058594]
>
### Keeping axes
iex> Nx.standard_deviation(Nx.tensor([[1, 2], [10, 20]]), keep_axes: true)
#Nx.Tensor<
f32[1][1]
[
[7.628073215484619]
]
>
### Vectorized tensors
iex> Nx.standard_deviation(Nx.tensor([[1, 2], [0, 4]]) |> Nx.vectorize(:x))
#Nx.Tensor<
vectorized[x: 2]
f32
[0.5, 2.0]
>
"""
@doc type: :aggregation
@spec standard_deviation(tensor :: Nx.Tensor.t(), opts :: Keyword.t()) :: Nx.Tensor.t()
def standard_deviation(tensor, opts \\ []) do
sqrt(variance(tensor, opts))
end
@doc """
Calculates the DFT of the given tensor.
## Options
* `:eps` - Threshold which backends can use for cleaning-up results. Defaults to `1.0e-10`.
* `:length` - Either a positive integer or `:power_of_two`. Will pad or slice the tensor
accordingly. `:power_of_two` will automatically pad to the next power of two.
## Examples
iex> Nx.fft(Nx.tensor([1, 1, 0, 0]))
#Nx.Tensor<
c64[4]
[2.0+0.0i, 1.0-1.0i, 0.0+0.0i, 1.0+1.0i]
>
iex> Nx.fft(Nx.tensor([1, 1, 1, 0, 1, 1]))
#Nx.Tensor<
c64[6]
[5.0+0.0i, 1.0+0.0i, -1.0+0.0i, 1.0+0.0i, -1.0+0.0i, 1.0+0.0i]
>
Padding and slicing can be introduced through `:length`:
iex> Nx.fft(Nx.tensor([1, 1]), length: 4)
#Nx.Tensor<
c64[4]
[2.0+0.0i, 1.0-1.0i, 0.0+0.0i, 1.0+1.0i]
>
iex> Nx.fft(Nx.tensor([1, 1, 0]), length: :power_of_two)
#Nx.Tensor<
c64[4]
[2.0+0.0i, 1.0-1.0i, 0.0+0.0i, 1.0+1.0i]
>
iex> Nx.fft(Nx.tensor([1, 1, 0, 0, 2, 3]), length: 4)
#Nx.Tensor<
c64[4]
[2.0+0.0i, 1.0-1.0i, 0.0+0.0i, 1.0+1.0i]
>
If an N-dimensional tensor is passed, the DFT is applied to its last axis:
iex> Nx.fft(Nx.tensor([[1, 1, 0, 0, 2, 3], [1, 0, 0, 0, 2, 3]]), length: 4)
#Nx.Tensor<
c64[2][4]
[
[2.0+0.0i, 1.0-1.0i, 0.0+0.0i, 1.0+1.0i],
[1.0+0.0i, 1.0+0.0i, 1.0+0.0i, 1.0+0.0i]
]
>
## Vectorized tensors
Vectorized tensors work the same as N-dimensional tensors
iex> tensor = Nx.tensor([[1, 1, 0, 0, 2, 3], [1, 0, 0, 0, 2, 3]]) |> Nx.vectorize(:x)
iex> Nx.fft(tensor, length: 4)
#Nx.Tensor<
vectorized[x: 2]
c64[4]
[
[2.0+0.0i, 1.0-1.0i, 0.0+0.0i, 1.0+1.0i],
[1.0+0.0i, 1.0+0.0i, 1.0+0.0i, 1.0+0.0i]
]
>
## Error Cases
iex> Nx.fft(Nx.tensor([1, 1]), length: :invalid)
** (RuntimeError) expected an integer or :power_of_two as length, got: :invalid
"""
@doc type: :ndim
def fft(tensor, opts \\ []), do: call_fft(tensor, opts, :fft)
@doc """
Calculates the Inverse DFT of the given tensor.
## Options
* `:eps` - Threshold which backends can use for cleaning-up results. Defaults to `1.0e-10`.
* `:length` - Either a positive integer or `:power_of_two`. Will pad or slice the tensor
accordingly. `:power_of_two` will automatically pad to the next power of two.
## Examples
iex> Nx.ifft(Nx.tensor([2, Complex.new(1, -1), 0, Complex.new(1, 1)]))
#Nx.Tensor<
c64[4]
[1.0+0.0i, 1.0+0.0i, 0.0+0.0i, 0.0+0.0i]
>
iex> Nx.ifft(Nx.tensor([5, 1, -1, 1, -1, 1]))
#Nx.Tensor<
c64[6]
[1.0+0.0i, 1.0+0.0i, 1.0+0.0i, 0.0+0.0i, 1.0+0.0i, 1.0+0.0i]
>
Padding and slicing can be introduced through `:length`:
iex> Nx.ifft(Nx.tensor([1, 1]), length: 4)
#Nx.Tensor<
c64[4]
[0.5+0.0i, 0.25+0.25i, 0.0+0.0i, 0.25-0.25i]
>
iex> Nx.ifft(Nx.tensor([1, 1, 0]), length: :power_of_two)
#Nx.Tensor<
c64[4]
[0.5+0.0i, 0.25+0.25i, 0.0+0.0i, 0.25-0.25i]
>
iex> Nx.ifft(Nx.tensor([1, 1, 0, 0, 2, 3]), length: 4)
#Nx.Tensor<
c64[4]
[0.5+0.0i, 0.25+0.25i, 0.0+0.0i, 0.25-0.25i]
>
If an N-dimensional tensor is passed, the Inverse DFT is applied to its last axis:
iex> Nx.ifft(Nx.tensor([[1, 1, 0, 0, 2, 3], [1, 0, 0, 0, 2, 3]]), length: 4)
#Nx.Tensor<
c64[2][4]
[
[0.5+0.0i, 0.25+0.25i, 0.0+0.0i, 0.25-0.25i],
[0.25+0.0i, 0.25+0.0i, 0.25+0.0i, 0.25+0.0i]
]
>
## Vectorized tensors
Vectorized tensors work the same as N-dimensional tensors
iex> tensor = Nx.tensor([[1, 1, 0, 0, 2, 3], [1, 0, 0, 0, 2, 3]]) |> Nx.vectorize(:x)
iex> Nx.ifft(tensor, length: 4)
#Nx.Tensor<
vectorized[x: 2]
c64[4]
[
[0.5+0.0i, 0.25+0.25i, 0.0+0.0i, 0.25-0.25i],
[0.25+0.0i, 0.25+0.0i, 0.25+0.0i, 0.25+0.0i]
]
>
## Error Cases
iex> Nx.ifft(Nx.tensor([1, 1]), length: :invalid)
** (RuntimeError) expected an integer or :power_of_two as length, got: :invalid
"""
@doc type: :ndim
def ifft(tensor, opts \\ []), do: call_fft(tensor, opts, :ifft)
defp call_fft(tensor, opts, kind) do
apply_vectorized(tensor, fn tensor ->
shape = Nx.Shape.fft(tensor.shape)
n = elem(shape, tuple_size(shape) - 1)
opts = Keyword.validate!(opts, length: n, eps: 1.0e-10)
length =
case opts[:length] do
:power_of_two ->
2 ** Kernel.ceil(:math.log2(n))
n when is_integer(n) and n > 0 ->
n
length ->
raise "expected an integer or :power_of_two as length, got: #{inspect(length)}"
end
opts = Keyword.put(opts, :length, length)
output_shape =
shape
|> Tuple.insert_at(tuple_size(shape) - 1, length)
|> Tuple.delete_at(tuple_size(shape))
out = to_template(%{tensor | shape: output_shape, type: Nx.Type.to_complex(tensor.type)})
apply(impl!(tensor), kind, [out, tensor, opts])
end)
end
@doc """
Creates a tensor of shape `{n}` with linearly spaced samples between `start` and `stop`.
## Options
* `:n` - The number of samples in the tensor.
* `:name` - Optional name for the output axis.
* `:type` - Optional type for the output. Defaults to `{:f, 32}`
* `:endpoint` - Boolean that indicates whether to include `stop`
as the last point in the output. Defaults to `true`
## Examples
iex> Nx.linspace(5, 8, n: 5)
#Nx.Tensor<
f32[5]
[5.0, 5.75, 6.5, 7.25, 8.0]
>
iex> Nx.linspace(0, 10, n: 5, endpoint: false, name: :x)
#Nx.Tensor<
f32[x: 5]
[0.0, 2.0, 4.0, 6.0, 8.0]
>
For integer types, the results might not be what's expected.
When `endpoint: true` (the default), the step is given by
`step = (stop - start) / (n - 1)`, which means that instead
of a step of `3` in the example below, we get a step close to
`3.42`. The results are calculated first and only cast in the
end, so that the `:endpoint` condition is respected.
iex> Nx.linspace(0, 24, n: 8, type: {:u, 8}, endpoint: true)
#Nx.Tensor<
u8[8]
[0, 3, 6, 10, 13, 17, 20, 24]
>
iex> Nx.linspace(0, 24, n: 8, type: {:s, 64}, endpoint: false)
#Nx.Tensor<
s64[8]
[0, 3, 6, 9, 12, 15, 18, 21]
>
One can also pass two higher order tensors with the same shape `{j, k, ...}`, in which case
the output will be of shape `{j, k, ..., n}`.
iex> Nx.linspace(Nx.tensor([[[0, 10]]]), Nx.tensor([[[10, 100]]]), n: 10, name: :samples, type: {:u, 8})
#Nx.Tensor<
u8[1][1][2][samples: 10]
[
[
[
[0, 1, 2, 3, 4, 5, 6, 7, 8, 10],
[10, 20, 30, 40, 50, 60, 70, 80, 90, 100]
]
]
]
>
## Vectorized tensors
iex> Nx.linspace(0, Nx.vectorize(Nx.tensor([10, 20]), :x), n: 5)
#Nx.Tensor<
vectorized[x: 2]
f32[5]
[
[0.0, 2.5, 5.0, 7.5, 10.0],
[0.0, 5.0, 10.0, 15.0, 20.0]
]
>
iex> start = Nx.vectorize(Nx.tensor([0, 1]), :x)
iex> stop = Nx.vectorize(Nx.tensor([10, 20]), :y)
iex> Nx.linspace(start, stop, n: 5)
#Nx.Tensor<
vectorized[x: 2][y: 2]
f32[5]
[
[
[0.0, 2.5, 5.0, 7.5, 10.0],
[0.0, 5.0, 10.0, 15.0, 20.0]
],
[
[1.0, 3.25, 5.5, 7.75, 10.0],
[1.0, 5.75, 10.5, 15.25, 20.0]
]
]
>
iex> start = Nx.vectorize(Nx.tensor([0, 1]), :x)
iex> stop = Nx.vectorize(Nx.tensor([10, 10]), :x)
iex> Nx.linspace(start, stop, n: 5)
#Nx.Tensor<
vectorized[x: 2]
f32[5]
[
[0.0, 2.5, 5.0, 7.5, 10.0],
[1.0, 3.25, 5.5, 7.75, 10.0]
]
>
## Error cases
iex> Nx.linspace(0, 24, n: 1.0)
** (ArgumentError) expected n to be a non-negative integer, got: 1.0
iex> Nx.linspace(Nx.tensor([[0, 1]]), Nx.tensor([1, 2, 3]), n: 2)
** (ArgumentError) expected start and stop to have the same shape. Got shapes {1, 2} and {3}
"""
@doc type: :creation
def linspace(start, stop, opts \\ []) do
opts = keyword!(opts, [:n, :name, type: {:f, 32}, endpoint: true])
[%{vectorized_axes: vectorized_axes} = start, stop] =
reshape_vectors([start, stop], align_ranks: true)
start = Nx.as_type(start, opts[:type])
stop = Nx.as_type(stop, opts[:type])
n = opts[:n]
unless is_integer(n) and n > 0 do
raise ArgumentError, "expected n to be a non-negative integer, got: #{inspect(n)}"
end
{iota_shape, start, stop} =
case {start.shape, stop.shape} do
{shape, shape} ->
iota_shape = Tuple.insert_at(shape, tuple_size(shape), n)
{iota_shape, new_axis(start, -1, opts[:name]), new_axis(stop, -1, opts[:name])}
{start_shape, stop_shape} ->
raise ArgumentError,
"expected start and stop to have the same shape. Got shapes #{inspect(start_shape)} and #{inspect(stop_shape)}"
end
iota = iota(iota_shape, axis: -1, type: opts[:type], vectorized_axes: vectorized_axes)
divisor =
if opts[:endpoint] do
n - 1
else
n
end
step = Nx.subtract(stop, start) |> Nx.divide(divisor)
iota
|> multiply(step)
|> add(start)
|> as_type(opts[:type])
end
@doc """
Pads a tensor of rank 1 or greater along the given axes through periodic reflections.
## Options
* `:padding_config` - A list of tuples in the format `{pre, post}`,
which specify the length (0 or greater) of the reflection before and
after the tensor along a each axis.
See also: `pad/3`
## Examples
iex> Nx.reflect(Nx.tensor([0, 1, 2]), padding_config: [{3, 1}])
#Nx.Tensor<
s64[7]
[1, 2, 1, 0, 1, 2, 1]
>
iex> Nx.reflect(Nx.tensor([[0, 1, 2], [3, 4, 5]], names: [:x, :y]), padding_config: [{2, 0}, {2, 1}])
#Nx.Tensor<
s64[x: 4][y: 6]
[
[2, 1, 0, 1, 2, 1],
[5, 4, 3, 4, 5, 4],
[2, 1, 0, 1, 2, 1],
[5, 4, 3, 4, 5, 4]
]
>
"""
@doc type: :shape
def reflect(tensor, opts \\ []) do
opts = keyword!(opts, [:padding_config])
apply_vectorized(tensor, fn tensor, offset ->
padding_config = opts[:padding_config]
unless padding_config do
raise ArgumentError, "missing mandatory option :padding_config"
end
padding_config = List.duplicate({0, 0}, offset) ++ padding_config
rank = Nx.rank(tensor)
unless rank > 0 do
raise ArgumentError, "expected tensor to have rank greater than 0"
end
axes = axes(tensor)
if rank != length(padding_config) do
raise ArgumentError, "expected to have one padding_config entry each tensor axis"
end
Enum.zip_reduce(
padding_config,
axes,
tensor,
fn
{left_padding, right_padding}, axis, tensor
when left_padding >= 0 and right_padding >= 0 ->
n = Nx.axis_size(tensor, axis)
left_padding =
if(left_padding > 0) do
idx_period = left_reflect_index_period(n)
repetitions = div(left_padding, n) + 1
idx =
Nx.tile(idx_period, [repetitions])
|> Nx.take(Nx.iota({left_padding}))
|> Nx.reverse()
Nx.take(tensor, idx, axis: axis)
end
right_padding =
if(right_padding > 0) do
idx_period = right_reflect_index_period(n)
repetitions = div(right_padding, n) + 1
idx = idx_period |> Nx.tile([repetitions]) |> Nx.take(Nx.iota({right_padding}))
Nx.take(tensor, idx, axis: axis)
end
case({left_padding, right_padding}) do
{nil, nil} ->
tensor
{nil, right} ->
Nx.concatenate([tensor, right], axis: axis)
{left, nil} ->
Nx.concatenate([left, tensor], axis: axis)
{left, right} ->
Nx.concatenate([left, tensor, right], axis: axis)
end
padding, axis, _ ->
raise ArgumentError,
"expected padding config for axis #{axis} to be of the format {left, right}, with left and right as non-negative integers, got: #{inspect(padding)}"
end
)
end)
end
defp left_reflect_index_period(1), do: Nx.tensor([0])
defp left_reflect_index_period(n) do
# Generates the indices for pre-reflecting on the axis
left = Nx.iota({n - 1}) |> Nx.add(1)
right = Nx.subtract(n - 2, Nx.iota({n - 1}))
Nx.concatenate([left, right])
end
defp right_reflect_index_period(1), do: Nx.tensor([0])
defp right_reflect_index_period(n) do
# Generates the indices for post-reflecting on the axis
left = Nx.subtract(n - 2, Nx.iota({n - 1}))
right = Nx.iota({n - 1}) |> Nx.add(1)
Nx.concatenate([left, right])
end
@doc """
Calculates the element-wise logarithm of a tensor with base 2.
## Examples
iex> Nx.log2(2)
#Nx.Tensor<
f32
1.0
>
iex> Nx.log2(Nx.tensor([1, 2, 4, 8]))
#Nx.Tensor<
f32[4]
[0.0, 1.0, 2.0, 3.0]
>
"""
@doc type: :element
def log2(tensor) do
divide(log(tensor), log(2))
end
@doc """
Calculates the element-wise logarithm of a tensor with base 10.
## Examples
iex> Nx.log10(10)
#Nx.Tensor<
f32
1.0
>
iex> Nx.log10(Nx.tensor([1, 10, 100, 1000]))
#Nx.Tensor<
f32[4]
[0.0, 1.0, 2.0, 3.0]
>
"""
@doc type: :element
def log10(tensor) do
divide(log(tensor), log(10))
end
@doc """
Calculates the element-wise logarithm of a tensor with given `base`.
## Examples
iex> Nx.log(2, 2)
#Nx.Tensor<
f32
1.0
>
iex> Nx.log(Nx.tensor([3, 9, 27, 81]), 3)
#Nx.Tensor<
f32[4]
[1.0, 2.0, 3.0, 4.0]
>
"""
@doc type: :element
def log(tensor, base) do
if is_number(base) and (base <= 0 or base == 1) do
raise ArgumentError,
"expected base to be greater than 0 and different than 1, got: #{inspect(base)}"
end
divide(log(tensor), log(base))
end
## Sigils
@doc """
A convenient `~M` sigil for building matrices (two-dimensional tensors).
## Examples
Before using sigils, you must first import them:
import Nx, only: :sigils
Then you use the sigil to create matrices. The sigil:
~M<
-1 0 0 1
0 2 0 0
0 0 3 0
0 0 0 4
>
Is equivalent to:
Nx.tensor([
[-1, 0, 0, 1],
[0, 2, 0, 0],
[0, 0, 3, 0],
[0, 0, 0, 4]
])
If the tensor has any complex type, it defaults to c64.
If the tensor has any float type, it defaults to f32.
Otherwise, it is s64. You can specify the tensor type
as a sigil modifier:
iex> import Nx, only: :sigils
iex> ~M[0.1 0.2 0.3 0.4]f16
#Nx.Tensor<
f16[1][4]
[
[0.0999755859375, 0.199951171875, 0.300048828125, 0.39990234375]
]
>
iex> ~M[1+1i 2-2.0i -3]
#Nx.Tensor<
c64[1][3]
[
[1.0+1.0i, 2.0-2.0i, -3.0+0.0i]
]
>
iex> ~M[1 Inf NaN]
#Nx.Tensor<
f32[1][3]
[
[1.0, Inf, NaN]
]
>
iex> ~M[1i Inf NaN]
#Nx.Tensor<
c64[1][3]
[
[0.0+1.0i, Inf+0.0i, NaN+0.0i]
]
>
iex> ~M[1i Inf+2i NaN-Infi]
#Nx.Tensor<
c64[1][3]
[
[0.0+1.0i, Inf+2.0i, NaN-Infi]
]
>
"""
@doc type: :creation
defmacro sigil_M({:<<>>, _meta, [string]}, modifiers) do
{numbers, type} = string |> String.trim() |> binary_to_numbers()
numbers_to_tensor(numbers, type, modifiers)
end
@doc """
A convenient `~V` sigil for building vectors (one-dimensional tensors).
## Examples
Before using sigils, you must first import them:
import Nx, only: :sigils
Then you use the sigil to create vectors. The sigil:
~V[-1 0 0 1]
Is equivalent to:
Nx.tensor([-1, 0, 0, 1])
If the tensor has any complex type, it defaults to c64.
If the tensor has any float type, it defaults to f32.
Otherwise, it is s64. You can specify the tensor type
as a sigil modifier:
iex> import Nx, only: :sigils
iex> ~V[0.1 0.2 0.3 0.4]f16
#Nx.Tensor<
f16[4]
[0.0999755859375, 0.199951171875, 0.300048828125, 0.39990234375]
>
iex> ~V[1+1i 2-2.0i -3]
#Nx.Tensor<
c64[3]
[1.0+1.0i, 2.0-2.0i, -3.0+0.0i]
>
iex> ~V[1 Inf NaN]
#Nx.Tensor<
f32[3]
[1.0, Inf, NaN]
>
iex> ~V[1i Inf NaN]
#Nx.Tensor<
c64[3]
[0.0+1.0i, Inf+0.0i, NaN+0.0i]
>
iex> ~V[1i Inf+2i NaN-Infi]
#Nx.Tensor<
c64[3]
[0.0+1.0i, Inf+2.0i, NaN-Infi]
>
"""
@doc type: :creation
defmacro sigil_V({:<<>>, _meta, [string]}, modifiers) do
string
|> String.trim()
|> binary_to_numbers()
|> case do
{[numbers], type} ->
numbers_to_tensor(numbers, type, modifiers)
_ ->
raise ArgumentError, "must be one-dimensional"
end
end
defp numbers_to_tensor(numbers, type, modifiers) do
type =
case modifiers do
[unit | size] ->
Nx.Type.normalize!({List.to_atom([unit]), List.to_integer(size)})
[] ->
type
end
{shape, binary} = flatten_list(numbers, type)
quote do
unquote(binary)
|> Nx.from_binary(unquote(type))
|> Nx.reshape(unquote(Macro.escape(shape)))
end
end
defp binary_to_numbers(string) do
string
|> String.split(["\n", "\r\n"], trim: true)
|> Enum.map_reduce({:s, 64}, fn row, type ->
row
|> String.split(" ", trim: true)
|> Enum.map_reduce(type, fn str, type ->
{module, type} =
cond do
elem(type, 0) == :c -> {Complex, type}
String.contains?(str, ["Inf", "NaN"]) -> {Complex, type}
String.contains?(str, "i") -> {Complex, {:c, 64}}
String.contains?(str, ".") -> {Float, {:f, 32}}
true -> {Integer, type}
end
parse_string_to_number(module, str, type)
end)
end)
end
defp parse_string_to_number(Complex, str, {type_class, _} = type) do
apply_parse = fn fun ->
case apply(fun, [str]) do
:error -> false
val -> val
end
end
result = Enum.find_value([&Complex.parse/1, &Float.parse/1, &Integer.parse/1], apply_parse)
case result do
{%Complex{re: re, im: im}, ""}
when re in [:nan, :neg_infinity, :infinity] and im == 0 and type_class != :c ->
{re, Nx.Type.merge(type, {:f, 32})}
{%Complex{} = num, ""} ->
{num, Nx.Type.merge(type, {:c, 64})}
{num, ""} ->
{Complex.new(num), Nx.Type.merge(type, {:c, 64})}
_ ->
raise ArgumentError, "expected a numerical value for tensor, got #{str}"
end
end
defp parse_string_to_number(module, str, type) do
case module.parse(str) do
{number, ""} ->
{number, type}
_ ->
raise ArgumentError, "expected a numerical value for tensor, got #{str}"
end
end
## Helpers
defp backend!(backend) when is_atom(backend) do
backend!({backend, []})
end
defp backend!({backend, options}) when is_atom(backend) and is_list(options) do
{backend, backend.init(options)}
end
defp backend!(other) do
raise ArgumentError,
"backend must be an atom or a tuple {backend, options}, got: #{inspect(other)}"
end
defp number_to_binary(number, type), do: match_types([type], do: <<write!(number, 0)>>)
defp names!(%T{names: names}), do: names
defp names!(_), do: nil
defp to_indices(start_indices) do
all_static? = Enum.all?(start_indices, &is_integer/1)
if all_static? do
start_indices
else
Enum.with_index(start_indices, fn index, i ->
%T{shape: idx_shape, type: idx_type} = t = to_tensor(index)
if t.vectorized_axes != [] do
raise ArgumentError, "index for axis #{i} must be non-vectorized"
end
unless idx_shape == {} do
raise ArgumentError,
"index must be scalar, got shape #{inspect(idx_shape)}" <>
" for axis #{i}"
end
unless Nx.Type.integer?(idx_type) do
raise ArgumentError,
"index must be integer type, got #{inspect(idx_type)} for axis #{i}"
end
t
end)
end
end
@doc """
Returns the logarithm of the sum of the exponentials of tensor elements.
If the `:axes` option is given, it aggregates over
the given dimensions, effectively removing them.
`axes: [0]` implies aggregating over the highest order
dimension and so forth. If the axis is negative, then
counts the axis from the back. For example, `axes: [-1]`
will always aggregate all rows.
You may optionally set `:keep_axes` to true, which will
retain the rank of the input tensor by setting the reduced
axes to size 1.
Exponentials can be scaled before summation by multiplying
them with `:exp_scaling_factor` option. It must be of the same shape
as the input tensor or broadcastable to it.
## Examples
iex> Nx.logsumexp(Nx.tensor([1, 2, 3, 4, 5, 6]))
#Nx.Tensor<
f32
6.456193447113037
>
iex> Nx.logsumexp(Nx.tensor([1, 2, 3, 4, 5, 6]), exp_scaling_factor: 0.5)
#Nx.Tensor<
f32
5.7630462646484375
>
iex> t = Nx.tensor([1, 2, 3, 4, 5, 6])
iex> a = Nx.tensor([-1, -1, -1, 1, 1, 1])
iex> Nx.logsumexp(t, exp_scaling_factor: a)
#Nx.Tensor<
f32
6.356536865234375
>
iex> Nx.logsumexp(Nx.tensor([[1, 2], [3, 4], [5, 6]]))
#Nx.Tensor<
f32
6.456193447113037
>
### Aggregating over an axis
iex> t = Nx.tensor([[1, 2], [3, 4], [5, 6]], names: [:x, :y])
iex> Nx.logsumexp(t, axes: [:x])
#Nx.Tensor<
f32[y: 2]
[5.1429314613342285, 6.1429314613342285]
>
iex> t = Nx.tensor([[1, 2], [3, 4], [5, 6]], names: [:x, :y])
iex> Nx.logsumexp(t, axes: [:y])
#Nx.Tensor<
f32[x: 3]
[2.3132617473602295, 4.31326150894165, 6.31326150894165]
>
iex> t = Nx.tensor([[[1, 2], [3, 4]], [[5, 6], [7, 8]]], names: [:x, :y, :z])
iex> Nx.logsumexp(t, axes: [:x, :z])
#Nx.Tensor<
f32[y: 2]
[6.331411361694336, 8.331411361694336]
>
### Keeping axes
iex> t = Nx.tensor([[[1, 2], [3, 4]], [[5, 6], [7, 8]]], names: [:x, :y, :z])
iex> Nx.logsumexp(t, axes: [:x, :z], keep_axes: true)
#Nx.Tensor<
f32[x: 1][y: 2][z: 1]
[
[
[6.331411361694336],
[8.331411361694336]
]
]
>
### Vectorized tensors
iex> t = Nx.vectorize(Nx.tensor([[1, 2], [3, 4], [5, 6]]), :x)
iex> Nx.logsumexp(t, axes: [0], keep_axes: true)
#Nx.Tensor<
vectorized[x: 3]
f32[1]
[
[2.3132617473602295],
[4.31326150894165],
[6.31326150894165]
]
>
"""
@doc type: :aggregation
def logsumexp(tensor, opts \\ []) do
type = type(tensor)
opts = keyword!(opts, [:axes, :exp_scaling_factor, :keep_axes])
axes = opts[:axes]
keep_axes = opts[:keep_axes]
max = reduce_max(tensor, axes: axes, keep_axes: true)
infinity_mask = is_infinity(max)
max = select(infinity_mask, Nx.tensor(0, type: type), max)
exponentials = tensor |> subtract(max) |> exp()
exponentials =
if exp_scaling_factor = opts[:exp_scaling_factor] do
multiply(exp_scaling_factor, exponentials)
else
exponentials
end
max = if keep_axes, do: max, else: squeeze(max, axes: axes)
exponentials
|> sum(axes: axes, keep_axes: keep_axes)
|> log()
|> add(max)
end
end
