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`, and `broadcast/3`. The tensor types can be one of: * unsigned integers (`u2`, `u4`, `u8`, `u16`, `u32`, `u64`) * signed integers (`s2`, `s4`, `s8`, `s16`, `s32`, `s64`) * floats (`f8`, `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< s32[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> ~VEC[1 2 3]f32 #Nx.Tensor< f32[3] [1.0, 2.0, 3.0] > iex> import Nx, only: :sigils iex> ~MAT''' ...> 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< s32[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< s32[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: s32[3] * s64 #=> s32[3] s32[255][255][3] * s32[3] #=> s32[255][255][3] s32[2][1] * s[1][2] #=> s32[2][2] s32[5][1][4][1] * s32[3][4][5] #=> s32[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< s32[2] [1, 2] > iex> t[1] #Nx.Tensor< s32[2] [3, 4] > iex> t[1][1] #Nx.Tensor< s32 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< s32 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. If the tensor is a scalar, it must be a value between 0 and the dimension size, and it behaves the same as an integer. 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< s32 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< s32 1 > A multi-dimensional tensor uses its values to fetch the leading dimension of the tensor, placing them within the shape of the indexing tensor. It is equivalent to `take/3`: iex> t = Nx.tensor([[1, 2], [3, 4]]) iex> t[Nx.tensor([1, 0])] #Nx.Tensor< s32[2][2] [ [3, 4], [1, 2] ] > The example shows how the retrieved indexes are nested with the accessed shape and that you may also access repeated indices: iex> t = Nx.tensor([[1, 2], [3, 4]]) iex> t[Nx.tensor([[1, 0, 1]])] #Nx.Tensor< s32[1][3][2] [ [ [3, 4], [1, 2], [3, 4] ] ] > 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< s32[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< s32[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< s32[3][2] [ [3, 4], [5, 6], [7, 8] ] > iex> t[1..-1//1][1..-1//1] # Drop the first "row" twice #Nx.Tensor< s32[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< s32[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< s32[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< s32[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< s32[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< s32[x: 2][y: 3] [ [4, 5, 6], [7, 8, 9] ] > iex> t[x: 1..2, y: 0..1] #Nx.Tensor< s32[x: 2][y: 2] [ [4, 5], [7, 8] ] > iex> t[x: 1, y: 0..1] #Nx.Tensor< s32[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] import Kernel, except: [bit_size: 1] 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 <> @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< s32 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< s32[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< s32[2][3] [ [1, 2, 3], [4, 5, 6] ] > iex> Nx.tensor([[1, 2], [3, 4], [5, 6]]) #Nx.Tensor< s32[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< s32[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] > Certain backends and compilers support 8-bit floats. The precision iomplementation of 8-bit floats may change per backend, so you must be careful when transferring data across. The binary backend implements F8E5M2: iex> Nx.tensor([1, 2, 3], type: :f8) #Nx.Tensor< f8[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< s32[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< s32[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< s32[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< s32[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, 32} 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< s32[row: 3] [1, 2, 3] > iex> Nx.tensor(Nx.tensor([1, 2, 3], names: [:column])) #Nx.Tensor< s32[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_bitstring()} 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 <- [:u2, :u4, :u8, :u16, :u32, :u64, :s2, :s4, :s8, :s16, :s32, :s64] ++ [:f8, :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< s32[2][3] Nx.TemplateBackend > iex> {int, float} = Nx.to_template({1, 2.0}) iex> int #Nx.Tensor< s32 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 """ 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< s32 0 > iex> Nx.iota({5}) #Nx.Tensor< s32[5] [0, 1, 2, 3, 4] > iex> Nx.iota({3, 2, 3}, names: [:batch, :height, :width]) #Nx.Tensor< s32[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< s32[batch: 3][3] [ [0, 1, 2], [0, 1, 2], [0, 1, 2] ] > iex> Nx.iota({3, 3}, axis: -1) #Nx.Tensor< s32[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< s32[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] s32[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, 32}]) 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< s32[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< s32[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< s32[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] s32[3] [ [ [1, 0, 0], [1, 0, 0] ] ] > iex> Nx.eye({2, 3}, vectorized_axes: [x: 2]) #Nx.Tensor< vectorized[x: 2] s32[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, 32}]) names = Nx.Shape.named_axes!(opts[:names], shape) type = Nx.Type.normalize!(opts[:type]) 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< s32[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< s32[3][3] [ [1, 2, 0], [4, 5, 6], [7, 8, 9] ] > iex> Nx.tril(Nx.iota({2, 3, 4})) #Nx.Tensor< s32[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< s32[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< s32[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< s32[3][3] [ [0, 2, 3], [0, 0, 6], [0, 0, 0] ] > iex> Nx.triu(Nx.iota({2, 3, 4})) #Nx.Tensor< s32[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< s32[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< s32[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< s32[2] [1, 5] > iex> Nx.take_diagonal(Nx.iota({3, 3}), offset: -1) #Nx.Tensor< s32[2] [3, 7] > Given batched matrix: iex> Nx.take_diagonal(Nx.iota({3, 2, 2})) #Nx.Tensor< s32[3][2] [ [0, 3], [4, 7], [8, 11] ] > iex> Nx.take_diagonal(Nx.iota({3, 2, 2}), offset: -1) #Nx.Tensor< s32[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< s32[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< s32[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< s32[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< s32[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< s32[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] s32[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] s32[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< s32[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< s32[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< s32[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< s32[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< s32[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< s32[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< s32[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< s32[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(Kernel.bit_size(binary), size) if binary == "" do raise ArgumentError, "cannot build an empty tensor" end if rem(Kernel.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. 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. This function cannot be used in `defn`. > ### Potentially expensive operation {: .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. > ### Binaries vs bitstrings {: .info} > > If a tensor of type u2/u4/s2/s4 is given to this function, > this function may not return a binary (where the number of bits > is divisible by 8) but rather a bitstring (where the number of > bits may not be divisible by 8). ## Options * `:limit` - limit the number of entries represented in the binary ## Examples iex> Nx.to_binary(1) <<1::32-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::32-native, 2::32-native, 3::32-native, 4::32-native>> iex> Nx.to_binary(Nx.vectorize(Nx.tensor([1, 2, 3]), :x), limit: 2) <<1::32-native, 2::32-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 <> 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< s32 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 <> = 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 """ 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< s32[1][2][2] [ [ [0, 1], [2, 3] ] ] > iex> second #Nx.Tensor< s32[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< s32[x: 2][y: 2] [ [0, 1], [2, 3] ] > iex> second #Nx.Tensor< s32[x: 2][y: 2] [ [4, 5], [6, 7] ] > iex> third #Nx.Tensor< s32[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< s32[x: 2][y: 2] [ [0, 1], [2, 3] ] > iex> second #Nx.Tensor< s32[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] s32[2][2] [ [ [0, 1], [2, 3] ] ] > iex> second #Nx.Tensor< vectorized[x: 1] s32[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] s32[2] [ [ [0, 1], [2, 3] ] ] > iex> second #Nx.Tensor< vectorized[x: 1][y: 2] s32[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] s32[y: 2] [ [0, 1], [2, 3] ] > iex> second #Nx.Tensor< vectorized[x: 2] s32[y: 2] [ [4, 5], [6, 7] ] > iex> third #Nx.Tensor< vectorized[x: 2] s32[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] s32 [1, 2] > iex> second #Nx.Tensor< vectorized[x: 2] s32 [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 <> = 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< s32[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< s32[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< s32[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< s32[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] s32[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< s32[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] s32[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< s32[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< s32[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< s32[16] [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15] > iex> Nx.flatten(t) #Nx.Tensor< s32[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< s32[1][2][3] [ [ [0, 1, 2], [3, 4, 5] ] ] > iex> Nx.flatten(t, axes: [1, 2]) #Nx.Tensor< s32[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< s32[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] s32[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< s32[6] [0, 1, 2, 0, 1, 2] > iex> Nx.tile(a, [1, 2]) #Nx.Tensor< s32[1][6] [ [0, 1, 2, 0, 1, 2] ] > iex> Nx.tile(a, [2, 2]) #Nx.Tensor< s32[2][6] [ [0, 1, 2, 0, 1, 2], [0, 1, 2, 0, 1, 2] ] > iex> Nx.tile(a, [2, 1]) #Nx.Tensor< s32[2][3] [ [0, 1, 2], [0, 1, 2] ] > iex> Nx.tile(a, [2, 1, 2]) #Nx.Tensor< s32[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< s32[2][4] [ [1, 2, 1, 2], [3, 4, 3, 4] ] > iex> Nx.tile(b, [2, 1]) #Nx.Tensor< s32[4][2] [ [1, 2], [3, 4], [1, 2], [3, 4] ] > iex> Nx.tile(b, [1, 2]) #Nx.Tensor< s32[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< s32[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] s32[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< s32[new: 1][2][3] [ [ [1, 2, 3], [4, 5, 6] ] ] > iex> Nx.new_axis(t, 1, :new) #Nx.Tensor< s32[2][new: 1][3] [ [ [1, 2, 3] ], [ [4, 5, 6] ] ] > iex> Nx.new_axis(t, 2, :new) #Nx.Tensor< s32[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< s32[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] s32 [1] > iex> t = Nx.new_axis(t, -1, :new) #Nx.Tensor< vectorized[x: 1] s32[new: 1] [ [1] ] > iex> Nx.new_axis(t, 0) #Nx.Tensor< vectorized[x: 1] s32[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 %{shape: shape, names: names} = tensor, offset -> {shape, names, _axis} = Nx.Shape.new_axis(shape, names, axis, name, 1, offset) impl!(tensor).reshape(%{tensor | shape: shape, names: 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< s32 1 > iex> Nx.squeeze(Nx.tensor([[[[1]]], [[[2]]]], names: [:x, :y, :z, :i])) #Nx.Tensor< s32[x: 2] [1, 2] > iex> Nx.squeeze(Nx.tensor([[1, 2, 3]], names: [:x, :y]), axes: [:x]) #Nx.Tensor< s32[y: 3] [1, 2, 3] > iex> Nx.squeeze(Nx.tensor([[1], [2]], names: [:x, :y]), axes: [:y]) #Nx.Tensor< s32[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] s32[1][1][3][1] [ [ [ [ [1], [2], [3] ] ] ] ] > iex> Nx.squeeze(t) #Nx.Tensor< vectorized[x: 1] s32[3] [ [1, 2, 3] ] > iex> Nx.squeeze(t, axes: [0, 1]) #Nx.Tensor< vectorized[x: 1] s32[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< s32[2][4] [ [0, 1, 2, 3], [4, 5, 6, 7] ] > iex> right #Nx.Tensor< s32[1][4] [ [8, 9, 10, 11] ] > iex> {left, right} = Nx.split(t, 2, axis: 1) iex> left #Nx.Tensor< s32[3][2] [ [0, 1], [4, 5], [8, 9] ] > iex> right #Nx.Tensor< s32[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< s32[2][4] [ [0, 1, 2, 3], [4, 5, 6, 7] ] > iex> right #Nx.Tensor< s32[1][4] [ [8, 9, 10, 11] ] > iex> {left, right} = Nx.split(t, 0.75, axis: 1) iex> left #Nx.Tensor< s32[3][3] [ [0, 1, 2], [4, 5, 6], [8, 9, 10] ] > iex> right #Nx.Tensor< s32[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< s32[3] [1, 2, 3] > iex> right #Nx.Tensor< s32[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 iex> Nx.broadcast(1, {1, 2, 3}) #Nx.Tensor< s32[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< s32[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< s32[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< s32[2][2] [ [0, 1], [2, 3] ] > iex> Nx.broadcast(Nx.iota({2, 2}, names: [:x, :y]), {2, 2}, names: [:i, :j]) #Nx.Tensor< s32[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< s32[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< s32[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] s32[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] s32[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] s32[2][y: 3] [ [ [1, 2, 3], [4, 5, 6] ] ] > iex> Nx.broadcast(a, b, axes: [1], names: [:i, :j]) #Nx.Tensor< vectorized[x: 2] s32[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]) tensor = to_tensor(tensor) input_inner_shape = shape(tensor) 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) ++ broadcast_names else broadcast_names end shape = shape(shape) broadcast_shape_l = Tuple.to_list(shape) offset_axes = if offset > 0 do Enum.map(0..(offset - 1)//1, &elem(tensor.shape, &1)) else [] end num_new_inner_axes = tuple_size(shape) - tuple_size(input_inner_shape) tensor = if offset > 0 do {vector_dims, inner_dims} = Enum.split(Tuple.to_list(tensor.shape), offset) {vector_names, inner_names} = Enum.split(tensor.names, offset) dims = vector_dims ++ List.duplicate(1, num_new_inner_axes) ++ inner_dims names = vector_names ++ List.duplicate(nil, num_new_inner_axes) ++ inner_names reshape(tensor, List.to_tuple(dims), names: names) else tensor end broadcast_shape = List.to_tuple(offset_axes ++ broadcast_shape_l) opts_axes = opts[:axes] axes = if opts_axes do axes = Nx.Shape.normalize_axes( broadcast_shape, opts_axes, tensor.names, offset ) if offset > 0 do Enum.to_list(0..(offset + num_new_inner_axes - 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, 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< s32 1 > iex> Nx.pad(Nx.tensor([1, 2, 3], names: [:data]), 0, [{1, 1, 0}]) #Nx.Tensor< s32[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< s32[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< s32[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< s32[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< s32[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< s32[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< s32[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< s32[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] s32[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_value).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, 32} iex> Nx.type(Nx.tensor([1, 2, 3], type: :f32)) {:f, 32} iex> Nx.type(1) {:s, 32} 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. If the tensor has s2/s4/u2/u4 types, the value will be rounded down. Consider using `bit_size/1` instead. ## Examples iex> Nx.byte_size(Nx.tensor([[1, 2, 3], [4, 5, 6]])) 24 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) 4 Vectorized tensors account for all elements iex> Nx.byte_size(Nx.tensor([[1, 2], [3, 4]]) |> Nx.vectorize(:x)) 16 """ @doc type: :shape def byte_size(tensor), do: div(bit_size(tensor), 8) @doc """ Returns the bit size of the data in the tensor computed from its shape and type. ## Examples iex> Nx.bit_size(Nx.tensor([[1, 2, 3], [4, 5, 6]])) 192 iex> Nx.bit_size(Nx.tensor([[1, 2, 3], [4, 5, 6]], type: :u8)) 48 iex> Nx.bit_size(Nx.tensor([[1, 2, 3], [3, 2, 1]], type: :u2)) 12 iex> Nx.bit_size(1) 32 Vectorized tensors account for all elements iex> Nx.bit_size(Nx.tensor([[1, 2], [3, 4]]) |> Nx.vectorize(:x)) 128 """ @doc type: :shape def bit_size(tensor) do %{type: {_, bit_size}} = tensor = to_tensor(tensor) flat_size(tensor) * bit_size 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< s32[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] s32[3] [ [0, 1, 2], [3, 4, 5] ] > iex> Nx.vectorize(vectorized, :second) #Nx.Tensor< vectorized[first: 2][second: 3] s32 [ [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] s32 [ [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< s32[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] s32 [4, 3, 2, 1] > iex> Nx.add(vectorized, Nx.tensor([0, 1])) #Nx.Tensor< vectorized[x: 4] s32[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] s32 [1] > iex> t2 #Nx.Tensor< vectorized[x: 1] s32 [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: :vectorization @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] s32[3] [ [ [0, 1, 2], [3, 4, 5] ] ] > iex> Nx.devectorize(t) #Nx.Tensor< s32[x: 1][y: 2][3] [ [ [0, 1, 2], [3, 4, 5] ] ] > iex> Nx.devectorize(t, keep_names: false) #Nx.Tensor< s32[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< s32 1 > iex> t2 #Nx.Tensor< s32[x: 1][3] [ [0, 1, 2] ] > """ @doc type: :vectorization 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] s32 [1] > iex> yv #Nx.Tensor< vectorized[y: 3] s32[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] s32[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] s32 [1, 2] > iex> xy = Nx.tensor([[[5]], [[6]]]) |> Nx.vectorize(:y) |> Nx.vectorize(:x) #Nx.Tensor< vectorized[y: 2][x: 1] s32[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] s32[1] [ [ [1], [1] ], [ [2], [2] ] ] > iex> broadcast_xy #Nx.Tensor< vectorized[x: 2][y: 2] s32[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] s32 [ [1, 2], [1, 2] ] > iex> broadcast_xy #Nx.Tensor< vectorized[y: 2][x: 2] s32[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] s32[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] s32[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] s32 [ [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] s32[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} -> leading_names = Keyword.keys(canonical_vectorized_axes) l = %{devec_left | names: leading_names ++ Enum.drop(devec_left.names, offset)} r = %{devec_right | names: leading_names ++ Enum.drop(devec_right.names, offset)} l |> fun.(r) |> 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< s32 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< s32[data: 3] [2, 3, 4] > iex> Nx.add(1, Nx.tensor([1, 2, 3], names: [:data])) #Nx.Tensor< s32[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< s32[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< s32[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< s32[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< s32[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< s32[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< s32 -1 > ### Subtracting tensors and scalars iex> Nx.subtract(Nx.tensor([1, 2, 3], names: [:data]), 1) #Nx.Tensor< s32[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< s32[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< s32 2 > ### Multiplying tensors and scalars iex> Nx.multiply(Nx.tensor([1, 2, 3], names: [:data]), 1) #Nx.Tensor< s32[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< s32[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< s32 16 > ### Power of tensors and scalars iex> Nx.pow(Nx.tensor([1, 2, 3], names: [:data]), 2) #Nx.Tensor< s32[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< s32[x: 2][y: 2] [ [16, 32], [81, 243] ] > """ @doc type: :element def pow(left, right), do: element_wise_bin_op(left, right, :pow, & &1) @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< s32 1 > ### Remainder of tensors and scalars iex> Nx.remainder(Nx.tensor([1, 2, 3], names: [:data]), 2) #Nx.Tensor< s32[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< s32[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< s32 5 > ### Integer dividing tensors and scalars iex> Nx.quotient(Nx.tensor([2, 4, 5], names: [:data]), 2) #Nx.Tensor< s32[data: 3] [1, 2, 2] > iex> Nx.quotient(10, Nx.tensor([1, 2, 3], names: [:data])) #Nx.Tensor< s32[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< s32[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< s32 2 > ### Max between tensors and scalars iex> Nx.max(Nx.tensor([1, 2, 3], names: [:data]), 1) #Nx.Tensor< s32[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< s32[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< s32 1 > ### Min between tensors and scalars iex> Nx.min(Nx.tensor([1, 2, 3], names: [:data]), 1) #Nx.Tensor< s32[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< s32[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`. It does not support short-circuiting. ## Examples ### bitwise and between scalars iex> Nx.bitwise_and(1, 0) #Nx.Tensor< s32 0 > ### bitwise and between tensors and scalars iex> Nx.bitwise_and(Nx.tensor([0, 1, 2], names: [:data]), 1) #Nx.Tensor< s32[data: 3] [0, 1, 0] > iex> Nx.bitwise_and(Nx.tensor([0, -1, -2], names: [:data]), -1) #Nx.Tensor< s32[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< s32[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`. It does not support short-circuiting. ## Examples ### bitwise or between scalars iex> Nx.bitwise_or(1, 0) #Nx.Tensor< s32 1 > ### bitwise or between tensors and scalars iex> Nx.bitwise_or(Nx.tensor([0, 1, 2], names: [:data]), 1) #Nx.Tensor< s32[data: 3] [1, 1, 3] > iex> Nx.bitwise_or(Nx.tensor([0, -1, -2], names: [:data]), -1) #Nx.Tensor< s32[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< s32[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< s32 1 > ### Bitwise xor and between tensors and scalars iex> Nx.bitwise_xor(Nx.tensor([1, 2, 3], names: [:data]), 2) #Nx.Tensor< s32[data: 3] [3, 0, 1] > iex> Nx.bitwise_xor(Nx.tensor([-1, -2, -3], names: [:data]), 2) #Nx.Tensor< s32[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< s32[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< s32 1 > ### Left shift between tensors and scalars iex> Nx.left_shift(Nx.tensor([1, 2, 3], names: [:data]), 2) #Nx.Tensor< s32[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< s32[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< s32 1 > ### Right shift between tensors and scalars iex> Nx.right_shift(Nx.tensor([2, 4, 8], names: [:data]), 2) #Nx.Tensor< s32[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< s32[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< s32[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< s32[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< s32[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< s32[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< s32[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< s32[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< s32[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] s32[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] s32 [ [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] s32 [ [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< s32[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< s32[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] s32[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< s32[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< s32[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] s32[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` ## Options * `:axes` - controls which dimensions the indexes apply to. It must be a sorted list of axes and be of the same size as the second (last) dimension of the indexes tensor. It defaults to the leading axes of the tensor. ## Examples ### Adding a single entry as a scalar 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< s32[2][1] [ [1], [10] ] > ### Adding multiple scalar entries iex> t = Nx.iota({1, 2, 3}) #Nx.Tensor< s32[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< s32[1][2][3] [ [ [2, 1, 0], [3, 7, 10] ] ] > ### Type promotions 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] > ## 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] s32[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, 1])) ** (ArgumentError) expected the leading axis of indices ({1, 2}) and leading axis of updates ({2}) to match iex> Nx.indexed_add(Nx.tensor([[1, 2, 3]]), Nx.tensor([[0]]), Nx.tensor([[1, 2, 3, 4, 5]])) ** (ArgumentError) axis (1) of updates ({1, 5}) must be less than or equal to the axis (1) of {1, 3}) """ @doc type: :indexed def indexed_add(target, indices, updates, opts \\ []) do indexed_op(target, indices, updates, opts, :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, i}`, with `n` being an arbitrary number of indices, while `updates` must have a compatible `{n, ...j}` shape, such that `i + j = rank(tensor)`. 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`. ## Options * `:axes` - controls which dimensions the indexes apply to. It must be a sorted list of axes and be of the same size as the second (last) dimension of the indexes tensor. It defaults to the leading axes of the tensor. ## Examples ### Storing a single entry as a scalar 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< s32[2][1] [ [1], [10] ] > ### Storing multiple scalar entries scalars iex> Nx.indexed_put(Nx.tensor([0, 0, 0]), Nx.tensor([[1], [2]]), Nx.tensor([2, 4])) #Nx.Tensor< s32[3] [0, 2, 4] > iex> Nx.indexed_put(Nx.tensor([0, 0, 0]), Nx.tensor([[1], [2]]), Nx.tensor([3, 4])) #Nx.Tensor< s32[3] [0, 3, 4] > iex> t = Nx.iota({1, 2, 3}) #Nx.Tensor< s32[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< s32[1][2][3] [ [ [1, 1, -2], [3, 3, 5] ] ] > ### Storing non-scalars on a given dimension iex> t = Nx.iota({1, 3, 2}) #Nx.Tensor< s32[1][3][2] [ [ [0, 1], [2, 3], [4, 5] ] ] > iex> indices = Nx.tensor([[0, 0], [0, 2]]) iex> updates = Nx.tensor([[0, 10], [40, 50]]) iex> Nx.indexed_put(t, indices, updates) #Nx.Tensor< s32[1][3][2] [ [ [0, 10], [2, 3], [40, 50] ] ] > The `:axes` option controls which dimensions the indexes apply to. It must be a sorted list of axes. All non-listed axes are taken as the update dimensions: iex> t = Nx.iota({1, 2, 3}) #Nx.Tensor< s32[1][2][3] [ [ [0, 1, 2], [3, 4, 5] ] ] > iex> indices = Nx.tensor([[0, 0], [0, 2]]) iex> updates = Nx.tensor([[0, 30], [20, 50]]) iex> Nx.indexed_put(t, indices, updates, axes: [0, 2]) #Nx.Tensor< s32[1][2][3] [ [ [0, 1, 20], [30, 4, 50] ] ] > ### Type promotions 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] > ## 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] s32[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, 1])) ** (ArgumentError) expected the leading axis of indices ({1, 2}) and leading axis of updates ({2}) to match iex> Nx.indexed_put(Nx.iota({1, 2, 3}), Nx.tensor([[0, 1, 2]]), 10, axes: [1, 0, 2]) ** (ArgumentError) :axes must be an ordered list """ @doc type: :indexed def indexed_put(target, indices, updates, opts \\ []) do indexed_op(target, indices, updates, opts, :indexed_put) end defp indexed_op(target, %Nx.Tensor{shape: {_}} = index, update, opts, op) when is_tensor(update) do update = to_tensor(update) Nx.Shape.indexed_scalar(target.shape, index.shape, update.shape) indexed_op(target, Nx.new_axis(index, 0), Nx.new_axis(update, 0), opts, op) end defp indexed_op(target, indices, updates, opts, op) do opts = keyword!(opts, [:axes]) [%T{vectorized_axes: vectorized_axes} = target, indices, updates] = broadcast_vectors([target, indices, updates]) unless Nx.Type.integer?(indices.type) do raise ArgumentError, "indices must be an integer tensor, got type: #{inspect(indices.type)}" end axes = indexed_axes(target, indices, opts) Nx.Shape.indexed(target.shape, indices.shape, updates.shape, axes) type = binary_type(target, updates) target = devectorize(target) indices = devectorize(indices) updates = devectorize(updates) {indices, updates, axes} = 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}) axes = Enum.to_list(0..(offset - 1)) ++ Enum.map(axes, &(&1 + offset)) {indices, flatten(updates), axes} else {indices, updates, axes} end impl!(target, indices, updates) |> apply(op, [%{target | type: type}, target, indices, updates, [axes: axes]]) |> vectorize(vectorized_axes) end defp indexed_axes(tensor, indices, opts) do n = elem(indices.shape, tuple_size(indices.shape) - 1) if axes = opts[:axes] do axes = Nx.Shape.normalize_axes(tensor.shape, axes, tensor.names) Enum.reduce(axes, fn next, prev when prev < next -> next _, _ -> raise ArgumentError, ":axes must be an ordered list" end) if length(axes) != n do raise ArgumentError, ":axes must have the same number of elements as the last dimension of indices" end axes else Enum.to_list(0..(n - 1)) end 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< s32 -1 > iex> Nx.negate(Nx.tensor([-1, 0, 1])) #Nx.Tensor< s32[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< s32[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< s32[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_VEC: 2] iex> Nx.phase(~VEC[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< s32 -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< s32 1 > iex> Nx.population_count(-128) #Nx.Tensor< s32 25 > iex> Nx.population_count(Nx.tensor([0, 1, 254, 255], names: [:x])) #Nx.Tensor< s32[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< s32 31 > iex> Nx.count_leading_zeros(-1) #Nx.Tensor< s32 0 > iex> Nx.count_leading_zeros(Nx.tensor([0, 0xF, 0xFF, 0xFFFF], names: [:x])) #Nx.Tensor< s32[x: 4] [32, 28, 24, 16] > iex> Nx.count_leading_zeros(Nx.tensor([0xF0000000, 0x0F000000], names: [:x])) #Nx.Tensor< s32[x: 2] [0, 4] > iex> Nx.count_leading_zeros(Nx.tensor([0, 0xF, 0xFF, 0xFFFF], type: :s64, names: [:x])) #Nx.Tensor< s64[x: 4] [64, 60, 56, 48] > 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, fun}} <- [ floor: {"floor", &:math.floor/1}, ceil: {"ceil", &:math.ceil/1}, round: {"round (away from zero)", &:erlang.round/1} ] do [res1, res2, res3, res4] = Enum.map([-1.5, -0.5, 0.5, 1.5], fn x -> fun.(x) * 1.0 end) @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< s32[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}, #{res2}, #{res3}, #{res4}] > """ @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< s32 42 > iex> Nx.sum(Nx.tensor([1, 2, 3])) #Nx.Tensor< s32 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< s32 410 > iex> Nx.sum(Nx.tensor([[101, 102], [103, 104]], type: :s16)) #Nx.Tensor< s32 410 > ### Aggregating over an axis iex> Nx.sum(Nx.tensor([1, 2, 3]), axes: [0]) #Nx.Tensor< s32 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< s32[y: 2][z: 3] [ [6, 8, 10], [12, 14, 16] ] > iex> Nx.sum(t, axes: [:y]) #Nx.Tensor< s32[x: 2][z: 3] [ [3, 5, 7], [15, 17, 19] ] > iex> Nx.sum(t, axes: [:z]) #Nx.Tensor< s32[x: 2][y: 2] [ [3, 12], [21, 30] ] > iex> Nx.sum(t, axes: [:x, :z]) #Nx.Tensor< s32[y: 2] [24, 42] > iex> Nx.sum(t, axes: [-3]) #Nx.Tensor< s32[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< s32[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] s32[1][2] [ [ [ [1, 2] ], [ [3, 4] ] ], [ [ [5, 6] ], [ [7, 8] ] ] ] > iex> Nx.sum(t) #Nx.Tensor< vectorized[x: 2][y: 2] s32 [ [3, 7], [11, 15] ] > iex> Nx.sum(t, axes: [0]) #Nx.Tensor< vectorized[x: 2][y: 2] s32[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] s32[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] s32[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 axes = opts[:axes] do Nx.Shape.normalize_axes(shape, 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< s32 42 > iex> Nx.median(Nx.tensor([1, 2, 3])) #Nx.Tensor< s32 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< s32[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< s32[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< s32[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] s32 [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< s32 42 > iex> Nx.mode(Nx.tensor([[1]])) #Nx.Tensor< s32 1 > iex> Nx.mode(Nx.tensor([1, 2, 2, 3, 5])) #Nx.Tensor< s32 2 > iex> Nx.mode(Nx.tensor([[1, 2, 2, 3, 5], [1, 1, 76, 8, 1]])) #Nx.Tensor< s32 1 > ### Aggregating over an axis iex> Nx.mode(Nx.tensor([[1, 2, 2, 3, 5], [1, 1, 76, 8, 1]]), axis: 0) #Nx.Tensor< s32[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< s32[2] [2, 1] > iex> Nx.mode(Nx.tensor([[[1]]]), axis: 1) #Nx.Tensor< s32[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< s32[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] s32[5] [ [1, 1, 2, 3, 1], [1, 2, 2, 2, 1] ] > iex> Nx.mode(t, axis: 1) #Nx.Tensor< vectorized[x: 2] s32[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< s32 42 > iex> Nx.product(Nx.tensor([1, 2, 3])) #Nx.Tensor< s32 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< u32 240000 > iex> Nx.product(Nx.tensor([[10, 20], [30, 40]], type: :s8, names: [:x, :y])) #Nx.Tensor< s32 240000 > ### Aggregating over an axis iex> Nx.product(Nx.tensor([1, 2, 3]), axes: [0]) #Nx.Tensor< s32 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< s32[y: 2][z: 3] [ [0, 7, 16], [27, 40, 55] ] > iex> Nx.product(t, axes: [:y]) #Nx.Tensor< s32[x: 2][z: 3] [ [0, 4, 10], [54, 70, 88] ] > iex> Nx.product(t, axes: [:x, :z]) #Nx.Tensor< s32[y: 2] [0, 59400] > iex> Nx.product(t, axes: [:z]) #Nx.Tensor< s32[x: 2][y: 2] [ [0, 60], [336, 990] ] > iex> Nx.product(t, axes: [-3]) #Nx.Tensor< s32[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< s32[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] s32[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< s32 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< s32 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< s32[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< s32[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< s32[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< s32[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] s32[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< s32 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< s32 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< s32[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< s32[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< s32[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< s32[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] s32[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. * `:type` - The type of the resulting tensor. Defaults to `:s32`. ## Examples iex> Nx.argmax(4) #Nx.Tensor< s32 0 > iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]]) iex> Nx.argmax(t) #Nx.Tensor< s32 10 > If a tensor of floats is given, it still returns integers: iex> Nx.argmax(Nx.tensor([2.0, 4.0])) #Nx.Tensor< s32 1 > If the tensor includes any NaNs, returns the index of any of them (NaNs are not equal, hence tie-break does not apply): iex> Nx.argmax(Nx.tensor([2.0, :nan, 4.0])) #Nx.Tensor< s32 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< s32[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< s32[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< s32[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< s32[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, type: :u32) #Nx.Tensor< u32[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< s32[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] s32 [2, 0] > iex> Nx.argmax(v, axis: 0) #Nx.Tensor< vectorized[x: 2] s32 [2, 0] > iex> Nx.argmax(v, keep_axis: true) #Nx.Tensor< vectorized[x: 2] s32[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. * `:type` - The type of the resulting tensor. Defaults to `:s32`. ## Examples iex> Nx.argmin(4) #Nx.Tensor< s32 0 > iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]]) iex> Nx.argmin(t) #Nx.Tensor< s32 4 > If a tensor of floats is given, it still returns integers: iex> Nx.argmin(Nx.tensor([2.0, 4.0])) #Nx.Tensor< s32 0 > If the tensor includes any NaNs, returns the index of any of them (NaNs are not equal, hence tie-break does not apply): iex> Nx.argmin(Nx.tensor([2.0, :nan, 4.0])) #Nx.Tensor< s32 1 > ### 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< s32[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< s32[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< s32[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< s32[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, type: :u32) #Nx.Tensor< u32[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< s32[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] s32 [0, 2] > iex> Nx.argmin(v, axis: 0) #Nx.Tensor< vectorized[x: 2] s32 [0, 2] > iex> Nx.argmin(v, keep_axis: true) #Nx.Tensor< vectorized[x: 2] s32[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, type: {:s, 32}]) 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: Nx.Type.normalize!(opts[:type]), 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< s32[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< s32[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< s32[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< s32[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< s32[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] s32[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] s32[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] s32[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< s32[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< s32[2][2][2] [ [ [-2147483648, -2147483648], [-2147483648, 6] ], [ [-2147483648, -2147483648], [-2147483648, 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< s32[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] s32[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] s32[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< s32[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< s32[2][2][2] [ [ [2147483647, 2147483647], [2147483647, 3] ], [ [2147483647, 2147483647], [2147483647, 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< s32[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] s32[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] s32[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< s32[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< s32[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< s32[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] s32[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] s32[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< s32[4] [1, 3, 6, 10] > iex> Nx.cumulative_sum(Nx.iota({3, 3}), axis: 0) #Nx.Tensor< s32[3][3] [ [0, 1, 2], [3, 5, 7], [9, 12, 15] ] > iex> Nx.cumulative_sum(Nx.iota({3, 3}), axis: 1) #Nx.Tensor< s32[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< s32[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< s32[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] s32[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< s32[4] [1, 2, 6, 24] > iex> Nx.cumulative_product(Nx.iota({3, 3}), axis: 0) #Nx.Tensor< s32[3][3] [ [0, 1, 2], [0, 4, 10], [0, 28, 80] ] > iex> Nx.cumulative_product(Nx.iota({3, 3}), axis: 1) #Nx.Tensor< s32[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< s32[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< s32[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] s32[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< s32[4] [3, 3, 2, 1] > iex> Nx.cumulative_min(Nx.tensor([[2, 3, 1], [1, 3, 2], [2, 1, 3]]), axis: 0) #Nx.Tensor< s32[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< s32[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< s32[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< s32[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] s32[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< s32[4] [3, 4, 4, 4] > iex> Nx.cumulative_max(Nx.tensor([[2, 3, 1], [1, 3, 2], [2, 1, 3]]), axis: 0) #Nx.Tensor< s32[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< s32[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< s32[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< s32[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] s32[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< s32[4] [1, 2, 3, -7] > iex> Nx.diff(Nx.tensor([1, 2, 4, 7, 0]), order: 2) #Nx.Tensor< s32[3] [1, 1, -10] > iex> Nx.diff(Nx.tensor([[1, 3, 6, 10], [0, 5, 6, 8]])) #Nx.Tensor< s32[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< s32[1][4] [ [-1, 2, 0, -2] ] > iex> Nx.diff(Nx.tensor([1, 2, 4, 7, 0]), order: 0) #Nx.Tensor< s32[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< # s32[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< # s32[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< # s32[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< s32 42 > iex> Nx.reduce(Nx.tensor([1, 2, 3]), 0, fn x, y -> Nx.add(x, y) end) #Nx.Tensor< s32 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< s32 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< s32[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< s32[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< s32[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< s32[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< s32[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< s32[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] s32[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(:s32) 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< s32[3][3] [ [5, 6, 7], [8, 9, 10], [12, 13, 14] ] > iex> init_value = Nx.Constants.min_finite(:s32) 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< s32[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< s32[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< s32[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] s32[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 ## 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< s32 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< s32 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< s32[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< s32[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< s32[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< s32[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] s32 [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] s32[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< s32[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] s32[2][2] [ [ [7, 10], [7, 10] ], [ [4, 6], [4, 6] ] ] > iex> Nx.dot(t1, [1], t2, [0]) #Nx.Tensor< vectorized[x: 2] s32[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< s32[y: 2][width: 2] [ [100, 140], [140, 200] ] > iex> Nx.dot(t1, [0], [], t2, [1], []) #Nx.Tensor< s32[y: 2][height: 2] [ [70, 150], [100, 220] ] > iex> Nx.dot(t1, [1], [], t2, [0], []) #Nx.Tensor< s32[x: 2][width: 2] [ [70, 100], [150, 220] ] > iex> Nx.dot(t1, [1], [], t2, [1], []) #Nx.Tensor< s32[x: 2][height: 2] [ [50, 110], [110, 250] ] > iex> Nx.dot(t1, [0, 1], [], t2, [0, 1], []) #Nx.Tensor< s32 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< s32[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< s32[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< s32[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] s32[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< s32[x: 3][1] [ [100], [200], [300] ] > iex> Nx.outer(Nx.tensor([1, 2, 3], names: [:x]), Nx.tensor([10, 20], names: [:y])) #Nx.Tensor< s32[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< s32[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] s32[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 out_type = binary_type(t1, t2) lhs = reshape(t1, {size(t1), 1}) rhs = if Nx.Type.complex?(out_type) do reshape(conjugate(t2), {1, size(t2)}) else reshape(t2, {1, size(t2)}) end %{multiply(lhs, rhs) | 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< s32 1 > iex> Nx.transpose(Nx.iota({2, 3, 4}, names: [:x, :y, :z])) #Nx.Tensor< s32[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< s32 1 > iex> Nx.transpose(Nx.iota({2, 3, 4}, names: [:batch, :x, :y]), axes: [2, 1, :batch]) #Nx.Tensor< s32[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] ] ] > ### 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] s32[2][3] [ [ [0, 1, 2], [3, 4, 5] ] ] > iex> Nx.transpose(v) #Nx.Tensor< vectorized[x: 1] s32[3][2] [ [ [0, 3], [1, 4], [2, 5] ] ] > iex> Nx.transpose(v, axes: [1, 0]) #Nx.Tensor< vectorized[x: 1] s32[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< s32[3] [3, 2, 1] > iex> Nx.reverse(Nx.tensor([[1, 2, 3], [4, 5, 6]])) #Nx.Tensor< s32[2][3] [ [6, 5, 4], [3, 2, 1] ] > iex> Nx.reverse(Nx.tensor([1, 2, 3], names: [:x]), axes: [:x]) #Nx.Tensor< s32[x: 3] [3, 2, 1] > iex> Nx.reverse(Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:x, :y]), axes: [:x]) #Nx.Tensor< s32[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< s32[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] s32[2][3] [ [ [0, 1, 2], [3, 4, 5] ] ] > iex> Nx.reverse(v) #Nx.Tensor< vectorized[x: 1] s32[2][3] [ [ [5, 4, 3], [2, 1, 0] ] ] > iex> Nx.reverse(v, axes: [1]) #Nx.Tensor< vectorized[x: 1] s32[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({1, 1, 3, 3}) iex> right = Nx.iota({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({1, 1, 3, 3}) iex> right = Nx.iota({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< s32[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< s32[3] [1, 2, 3] > iex> Nx.slice(Nx.tensor([1, 2, 3, 4, 5, 6]), [0], [6], strides: [2]) #Nx.Tensor< s32[3] [1, 3, 5] > iex> Nx.slice(Nx.tensor([[1, 2], [3, 4], [5, 6]]), [0, 0], [3, 2], strides: [2, 1]) #Nx.Tensor< s32[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< s32[2][1] [ [1], [5] ] > A more complex example: iex> t = Nx.iota({2, 15, 30}) iex> Nx.slice(t, [0, 4, 11], [2, 3, 9], strides: [2, 1, 3]) #Nx.Tensor< s32[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< s32[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< s32[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< s32[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< s32[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] s32[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] s32[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< s32[2][2] [ [2, 3], [4, 5] ] > iex> Nx.slice_along_axis(Nx.iota({2, 5}), 1, 2, axis: 1) #Nx.Tensor< s32[2][2] [ [1, 2], [6, 7] ] > iex> Nx.slice_along_axis(Nx.iota({2, 5}, names: [:x, :y]), 0, 1, axis: :x) #Nx.Tensor< s32[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< s32[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< s32[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] s32[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 """ 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`, `indexed_put/3`. ## Examples iex> t = Nx.tensor([0, 1, 2, 3, 4]) iex> Nx.put_slice(t, [2], Nx.tensor([5, 6])) #Nx.Tensor< s32[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< s32[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< s32[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] s32[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< s32[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< s32[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< s32[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< s32[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< s32[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< s32[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] s32[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] s32[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] s32 [ [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] s32[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) out = %{tensor | shape: inner_shape, names: inner_names} Nx.Shared.optional(:take, [tensor, indices, [axis: axis]], out, fn tensor, indices, _opts -> gather_indices = new_axis(indices, rank(indices)) {indices_axes, tensor_axes} = Enum.split(axes(inner_shape), rank(indices)) {leading, trailing} = Enum.split(tensor_axes, axis) transpose_axes = leading ++ indices_axes ++ trailing tensor |> gather(gather_indices, axes: [axis]) |> transpose(axes: transpose_axes) |> rename(inner_names) end) 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< s32[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< s32[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< s32[1][3][2] [ [ [1, 2], [3, 4], [5, 6] ] ] > iex> idx1 = Nx.argsort(tensor, axis: 1, direction: :desc) #Nx.Tensor< s32[1][3][2] [ [ [2, 2], [1, 1], [0, 0] ] ] > iex> Nx.take_along_axis(tensor, idx1, axis: 1) #Nx.Tensor< s32[1][3][2] [ [ [5, 6], [3, 4], [1, 2] ] ] > iex> idx2 = Nx.argsort(tensor, axis: 2, direction: :desc) #Nx.Tensor< s32[1][3][2] [ [ [1, 0], [1, 0], [1, 0] ] ] > iex> Nx.take_along_axis(tensor, idx2, axis: 2) #Nx.Tensor< s32[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] s32[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] s32[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) out = %{tensor | shape: shape} result = Nx.Shared.optional(:take_along_axis, [tensor, indices, [axis: axis]], out, fn tensor, indices, _opts -> axes_range = axes(indices) new_axis_shape = Tuple.append(shape(indices), 1) full_indices = axes_range |> Enum.map(fn ^axis -> reshape(indices, new_axis_shape) axis -> iota(new_axis_shape, axis: axis) end) |> concatenate(axis: rank(indices)) tensor |> gather(full_indices) |> rename(tensor.names) end) vectorize(result, vectorized_axes) end @doc """ Builds a new tensor by taking individual values from the original tensor at the given indices. Indices must be a tensor where the last dimension is usually of the same size as the `tensor` rank. Each entry in `indices` will be part of the results. If the last dimension of indices is less than the `tensor` rank, then a multidimensional tensor is gathered and spliced into the result. ## Options * `:axes` - controls to which dimensions of `tensor` each element in the last dimension of `indexes` applies to. It defaults so the first element in indexes apply to the first axis, the second to the second, and so on. It must be a sorted list of axes and be of the same size as the last dimension of the indexes tensor. ## Examples ### Gathering scalars iex> t = Nx.tensor([[1, 2], [3, 4]]) iex> Nx.gather(t, Nx.tensor([[1, 1], [0, 1], [1, 0]])) #Nx.Tensor< s32[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< s32[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< s32[3] [1, 12, 112] > ### Gathering subsets iex> t = Nx.tensor([[1, 2, 3], [3, 4, 5]]) iex> Nx.gather(t, Nx.tensor([[1], [0]])) #Nx.Tensor< s32[2][3] [ [3, 4, 5], [1, 2, 3] ] > The `:axes` option controls which dimensions the indexes point to, this can be useful, for example, to access columns instead of rows. Note can also access the same index several times: iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]]) iex> Nx.gather(t, Nx.tensor([[1], [0], [2], [1]]), axes: [1]) #Nx.Tensor< s32[4][2] [ [2, 5], [1, 4], [3, 6], [2, 5] ] > The overall output shape will have the format of the indices shape (except the last element) followed by all non-indexed dimensions of the tensor. Here is a more complex example: iex> t = Nx.iota({2, 1, 3}) iex> Nx.gather(t, Nx.tensor([[[1], [0], [2]]]), axes: [2]) #Nx.Tensor< s32[1][3][2][1] [ [ [ [1], [4] ], [ [0], [3] ], [ [2], [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], [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] s32[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] s32[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, opts \\ []) do opts = keyword!(opts, [:axes]) [%T{vectorized_axes: vectorized_axes} = tensor, indices] = broadcast_vectors([tensor, indices], align_ranks: false) axes = indexed_axes(tensor, indices, opts) 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, axes} = 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) axes = Enum.to_list(0..(offset - 1)) ++ Enum.map(axes, &(&1 + offset)) {tensor, indices, axes} else {tensor, indices, axes} end {shape, names} = Nx.Shape.gather(tensor.shape, indices.shape, axes) out = %{tensor | shape: shape, names: names} result = impl!(tensor).gather(out, tensor, indices, axes: axes) 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< s32[3] [1, 2, 3] > Multiple tensors are concatented: iex> Nx.concatenate([Nx.tensor([1, 2, 3]), Nx.tensor([4, 5, 6])]) #Nx.Tensor< s32[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< s32[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< s32[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] s32[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 -> concatenate_or_stack( tensors, fn shapes, names, offset -> Nx.Shape.concatenate(shapes, names, axis, offset) end, fn out, tensors, axis -> list_impl!(tensors).concatenate(out, tensors, axis) end ) end end defp concatenate_or_stack(tensors, shape_and_name, callback) do [%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, shapes, names} = Enum.reduce(tensors, {[], [], []}, fn %T{type: t, shape: s, names: n}, {types, shapes, names} -> {[t | types], [s | shapes], [n | names]} end) output_type = Enum.reduce(types, &Nx.Type.merge/2) {output_shape, output_names, axis} = shape_and_name.(Enum.reverse(shapes), Enum.reverse(names), offset) out = %{hd(tensors) | type: output_type, shape: output_shape, names: output_names} result = callback.(out, tensors, axis) vectorize(result, vectorized_axes) 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< s32[3] [1, 2, 3] > iex> Nx.stack([Nx.tensor([1, 2, 3]), Nx.tensor([4, 5, 6])]) #Nx.Tensor< s32[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< s32[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< s32[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< s32[3][2] [ [1, 2], [3, 4], [5, 6] ] > """ @doc type: :ndim def stack(tensors, opts \\ []) do opts = keyword!(opts, axis: 0, name: nil) axis = opts[:axis] name = opts[:name] case flatten_list_or_container(tensors) do [] -> raise ArgumentError, "no tensors were given to stack" [t] -> Nx.new_axis(t, axis, name) [_ | _] = tensors -> concatenate_or_stack( tensors, fn shapes, names, offset -> Nx.Shape.stack(shapes, names, axis, name, offset) end, fn out, tensors, axis -> list_impl!(tensors).stack(out, tensors, axis) end ) end 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` * `:stable` - If the sorting is stable. Defaults to `false` ## Examples iex> Nx.sort(Nx.tensor([16, 23, 42, 4, 8, 15])) #Nx.Tensor< s32[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< s32[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< s32[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< s32[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< s32[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< s32[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< s32[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< s32[x: 2][y: 3][z: 3] [ [ [2, 4, 5], [2, 3, 5], [0, 2, 5] ], [ [1, 8, 9], [1, 2, 3], [1, 2, 4] ] ] > When it comes to NaN and infinities, NaN always sorts higher than everything else: iex> t = Nx.tensor([:nan, :neg_infinity, 0.0, :infinity]) iex> Nx.sort(t) #Nx.Tensor< f32[4] [-Inf, 0.0, Inf, NaN] > iex> Nx.sort(t, direction: :desc) #Nx.Tensor< f32[4] [NaN, Inf, 0.0, -Inf] > """ @doc type: :ndim def sort(tensor, opts \\ []) do opts = keyword!(opts, axis: 0, direction: :asc, stable: false) 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, stable: opts[:stable] ) 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< s32[2] [5, 4] > iex> indices #Nx.Tensor< s32[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< s32[2][1] [ [2], [2] ] > When it comes to NaN and infinities, NaN always sorts higher than everything else: iex> t = Nx.tensor([:nan, :neg_infinity, :infinity, 0.0]) iex> {values, indices} = Nx.top_k(t, k: 3) iex> values #Nx.Tensor< f32[3] [NaN, Inf, 0.0] > iex> indices #Nx.Tensor< s32[3] [0, 2, 3] > ## 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, 32}} 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` * `:stable` - If the sorting is stable. Defaults to `false` * `:type` - The type of the resulting tensor. Defaults to `:s32`. ## Examples iex> Nx.argsort(Nx.tensor([16, 23, 42, 4, 8, 15])) #Nx.Tensor< s32[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< s32[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< s32[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, type: :u32) #Nx.Tensor< u32[x: 2][y: 3] [ [1, 0, 2], [0, 2, 1] ] > Same tensor sorted over different axes. In this case, we pass the stable option to preserve the order in case of duplicate elements: 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, stable: true) #Nx.Tensor< s32[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, stable: true) #Nx.Tensor< s32[x: 2][y: 3][z: 3] [ [ [1, 2, 0], [0, 0, 2], [2, 1, 1] ], [ [0, 1, 1], [1, 2, 2], [2, 0, 0] ] ] > When it comes to NaN and infinities, NaN always sorts higher than everything else: iex> t = Nx.tensor([:nan, :neg_infinity, :infinity, 0.0]) iex> Nx.argsort(t) #Nx.Tensor< s32[4] [1, 3, 2, 0] > iex> Nx.argsort(t, direction: :desc) #Nx.Tensor< s32[4] [0, 2, 3, 1] > """ @doc type: :ndim def argsort(tensor, opts \\ []) do opts = keyword!(opts, axis: 0, direction: :asc, stable: false, type: {:s, 32}) 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: Nx.Type.normalize!(opts[:type])}, tensor, axis: axis, direction: direction, stable: opts[:stable] ) 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< s32[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< s32[3] [1, 2, 3] > iex> b #Nx.Tensor< s32[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< s32[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] s32 [1, 2, 3] > iex> b #Nx.Tensor< s32[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< s32[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!(<>, 1, 0) do do_numpy_to_tensor(rest, header_size) end defp load_numpy!(<>, _, _) do do_numpy_to_tensor(rest, header_size) end defp do_numpy_to_tensor(rest, header_size) when is_binary(rest) do <> = rest {byte_order, {_, size} = type, shape, fortran_order?} = parse_header(header) bit_size_of_array = size * Nx.size(shape) <> = 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': " <> <> <> ", 'fortran_order': False, 'shape': " <> shape -> {byte_order, type} = parse_type(dtype) {byte_order, type, parse_shape(shape), false} "{'descr': " <> <> <> ", 'fortran_order': True, 'shape': " <> shape -> {byte_order, type} = parse_type(dtype) {byte_order, type, parse_shape(shape), true} end end defp parse_type(<>) 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(<>) 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 <> 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< s32[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 """ A shortcut to `covariance/3` with either `opts` or `mean` as second argument. """ @doc type: :aggregation @spec covariance(tensor :: Nx.Tensor.t(), opts :: Keyword.t()) :: Nx.Tensor.t() def covariance(tensor, opts \\ []) @spec covariance(tensor :: Nx.Tensor.t(), opts :: Keyword.t()) :: Nx.Tensor.t() def covariance(tensor, opts) when is_list(opts), do: covariance(tensor, Nx.mean(tensor, axes: [-2]), opts) @spec covariance(tensor :: Nx.Tensor.t(), mean :: Nx.Tensor.t()) :: Nx.Tensor.t() def covariance(tensor, mean), do: covariance(tensor, mean, []) @doc """ Computes the covariance matrix of the input tensor. The covariance of two random variables X and Y is calculated as $Cov(X, Y) = \\frac{1}{N}\\sum_{i=0}^{N-1}{(X_i - \\overline{X}) * (Y_i - \\overline{Y})}$. The tensor must be at least of rank 2, with shape `{n, d}`. Any additional dimension will be treated as batch dimensions. The column mean can be provided as the second argument and it must be a tensor of shape `{..., d}`, where the batch shape is broadcastable with that of the input tensor. If not provided, the mean is estimated using `Nx.mean/2`. If the `:ddof` (delta degrees of freedom) option is given, the divisor `n - ddof` is used for the sum of the products. ## Examples iex> Nx.covariance(Nx.tensor([[1, 2], [3, 4], [5, 6]])) #Nx.Tensor< f32[2][2] [ [2.6666667461395264, 2.6666667461395264], [2.6666667461395264, 2.6666667461395264] ] > iex> Nx.covariance(Nx.tensor([[[1, 2], [3, 4], [5, 6]], [[7, 8], [9, 10], [11, 12]]])) #Nx.Tensor< f32[2][2][2] [ [ [2.6666667461395264, 2.6666667461395264], [2.6666667461395264, 2.6666667461395264] ], [ [2.6666667461395264, 2.6666667461395264], [2.6666667461395264, 2.6666667461395264] ] ] > iex> Nx.covariance(Nx.tensor([[1, 2], [3, 4], [5, 6]]), ddof: 1) #Nx.Tensor< f32[2][2] [ [4.0, 4.0], [4.0, 4.0] ] > iex> Nx.covariance(Nx.tensor([[1, 2], [3, 4], [5, 6]]), Nx.tensor([4, 3])) #Nx.Tensor< f32[2][2] [ [3.6666667461395264, 1.6666666269302368], [1.6666666269302368, 3.6666667461395264] ] > """ @doc type: :aggregation @spec covariance(tensor :: Nx.Tensor.t(), mean :: Nx.Tensor.t(), opts :: Keyword.t()) :: Nx.Tensor.t() def covariance(tensor, mean, opts) do tensor = to_tensor(tensor) mean = to_tensor(mean) opts = keyword!(opts, ddof: 0) tensor_rank = Nx.rank(tensor) if tensor_rank < 2 do raise ArgumentError, "expected input tensor of rank at least 2, got #{tensor_rank}" end if Nx.rank(mean) == 0 do raise ArgumentError, "expected mean of rank at least 1, got 0" end ddof = opts[:ddof] if not is_integer(ddof) or ddof < 0 do raise ArgumentError, "expected ddof to be a non-negative integer, got #{ddof}" end tensor = tensor |> subtract(new_axis(mean, -2)) |> rename(nil) conj = if Nx.Type.complex?(Nx.type(tensor)), do: Nx.conjugate(tensor), else: tensor batch_axes = 0..(Nx.rank(tensor) - 3)//1 |> Enum.to_list() total = Nx.axis_size(tensor, -2) Nx.dot(conj, [-2], batch_axes, tensor, [-2], batch_axes) |> divide(total - ddof) 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. * `:axis` - the axis upon which the DFT will be calculated. Defaults to the last axis. ## 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] > The calculation can happen on a specific axis: iex> tensor = Nx.tensor([[1, 1, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1]]) iex> Nx.fft(tensor, axis: -1) #Nx.Tensor< c64[2][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], [5.0+0.0i, 1.0+0.0i, -1.0+0.0i, 1.0+0.0i, -1.0+0.0i, 1.0+0.0i] ] > iex> Nx.fft(tensor, axis: -2) #Nx.Tensor< c64[2][6] [ [2.0+0.0i, 2.0+0.0i, 2.0+0.0i, 0.0+0.0i, 2.0+0.0i, 2.0+0.0i], [0.0+0.0i, 0.0+0.0i, 0.0+0.0i, 0.0+0.0i, 0.0+0.0i, 0.0+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, by default, 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. * `:axis` - the axis upon which the Inverse DFT will be calculated. Defaults to the last axis. ## 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] > The calculation can happen on a specific axis: iex> tensor = Nx.tensor([[5, 1, -1, 1, -1, 1], [5, 1, -1, 1, -1, 1]]) iex> Nx.ifft(tensor, axis: -1) #Nx.Tensor< c64[2][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], [1.0+0.0i, 1.0+0.0i, 1.0+0.0i, 0.0+0.0i, 1.0+0.0i, 1.0+0.0i] ] > iex> Nx.ifft(tensor, axis: -2) #Nx.Tensor< c64[2][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], [0.0+0.0i, 0.0+0.0i, 0.0+0.0i, 0.0+0.0i, 0.0+0.0i, 0.0+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, by default,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, offset -> shape = Nx.Shape.fft(tensor.shape) opts = Keyword.validate!(opts, [:length, axis: -1, eps: 1.0e-10]) axis = Nx.Shape.normalize_axis(shape, opts[:axis], tensor.names, offset) n = elem(shape, axis) length = case opts[:length] do :power_of_two -> 2 ** Kernel.ceil(:math.log2(n)) nil -> 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.merge(opts, length: length, axis: axis) output_shape = shape |> Tuple.insert_at(axis, length) |> Tuple.delete_at(axis + 1) out = to_template(%{tensor | shape: output_shape, type: Nx.Type.to_complex(tensor.type)}) apply(impl!(tensor), kind, [out, tensor, opts]) end) end @doc """ Calculates the 2D DFT of the given tensor. ## Options * `:eps` - Threshold which backends can use for cleaning-up results. Defaults to `1.0e-10`. * `:lengths` - A 2 element list where each element is 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. * `:axes` - the 2 axes upon which the Inverse 2D DFT will be calculated. Defaults to the last 2 axes. ## Examples iex> Nx.fft2(Nx.tensor([[1, 0, 1, 0], [1, 1, 1, 1]])) #Nx.Tensor< c64[2][4] [ [6.0+0.0i, 0.0+0.0i, 2.0+0.0i, 0.0+0.0i], [-2.0+0.0i, 0.0+0.0i, 2.0+0.0i, 0.0+0.0i] ] > The calculation can happen on a specific pair of axes: iex> tensor = Nx.tensor([[[1, 0, 1, 0]], [[1, 1, 1, 1]]]) iex> Nx.fft2(tensor, axes: [0, -1]) #Nx.Tensor< c64[2][1][4] [ [ [6.0+0.0i, 0.0+0.0i, 2.0+0.0i, 0.0+0.0i] ], [ [-2.0+0.0i, 0.0+0.0i, 2.0+0.0i, 0.0+0.0i] ] ] > iex> Nx.fft2(tensor, axes: [-2, -1]) #Nx.Tensor< c64[2][1][4] [ [ [2.0+0.0i, 0.0+0.0i, 2.0+0.0i, 0.0+0.0i] ], [ [4.0+0.0i, 0.0+0.0i, 0.0+0.0i, 0.0+0.0i] ] ] > Padding and slicing can be introduced through `:lengths`: iex> tensor = Nx.tensor([[1, 1], [1, 0]]) iex> Nx.fft2(tensor, lengths: [2, 4]) #Nx.Tensor< c64[2][4] [ [3.0+0.0i, 2.0-1.0i, 1.0+0.0i, 2.0+1.0i], [1.0+0.0i, 0.0-1.0i, -1.0+0.0i, 0.0+1.0i] ] > iex> Nx.fft2(tensor, lengths: [4, 2]) #Nx.Tensor< c64[4][2] [ [3.0+0.0i, 1.0+0.0i], [2.0-1.0i, 0.0-1.0i], [1.0+0.0i, -1.0+0.0i], [2.0+1.0i, 0.0+1.0i] ] > iex> Nx.fft2(Nx.tensor([[1, 1, 0], [1, 1, 0], [1, 1, -1]]), lengths: [:power_of_two, :power_of_two]) #Nx.Tensor< c64[4][4] [ [5.0+0.0i, 4.0-3.0i, -1.0+0.0i, 4.0+3.0i], [1.0-2.0i, -2.0-1.0i, 1.0+0.0i, 0.0-1.0i], [1.0+0.0i, 2.0-1.0i, -1.0+0.0i, 2.0+1.0i], [1.0+2.0i, 0.0+1.0i, 1.0+0.0i, -2.0+1.0i] ] > iex> Nx.fft2(Nx.tensor([[[1, 1, 0, 0, 2, 3]]]), axes: [0, 2], lengths: [2, 4]) #Nx.Tensor< c64[2][1][4] [ [ [2.0+0.0i, 1.0-1.0i, 0.0+0.0i, 1.0+1.0i] ], [ [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, by default, applied to the last axes: iex> tensor = Nx.tensor([ ...> [[[1, 0, 1, 0, 10, 10], [1, 1, 1, 1, 10, 10]]], ...> [[[-2, -2, -2, -2, 20, 20], [0, 0, 0, 1, -20, -20]]]]) iex> Nx.fft2(tensor, lengths: [2, 4]) #Nx.Tensor< c64[2][1][2][4] [ [ [ [6.0+0.0i, 0.0+0.0i, 2.0+0.0i, 0.0+0.0i], [-2.0+0.0i, 0.0+0.0i, 2.0+0.0i, 0.0+0.0i] ] ], [ [ [-7.0+0.0i, 0.0+1.0i, -1.0+0.0i, 0.0-1.0i], [-9.0+0.0i, 0.0-1.0i, 1.0+0.0i, 0.0+1.0i] ] ] ] > ## Vectorized tensors Vectorized tensors work the same as N-dimensional tensors iex> tensor = Nx.tensor([ ...> [[[1, 0, 1, 0, 10, 10], [1, 1, 1, 1, 10, 10]]], ...> [[[-2, -2, -2, -2, 20, 20], [0, 0, 0, 1, -20, -20]]] ...> ]) |> Nx.vectorize(:x) iex> Nx.fft2(tensor, lengths: [2, 4]) #Nx.Tensor< vectorized[x: 2] c64[1][2][4] [ [ [ [6.0+0.0i, 0.0+0.0i, 2.0+0.0i, 0.0+0.0i], [-2.0+0.0i, 0.0+0.0i, 2.0+0.0i, 0.0+0.0i] ] ], [ [ [-7.0+0.0i, 0.0+1.0i, -1.0+0.0i, 0.0-1.0i], [-9.0+0.0i, 0.0-1.0i, 1.0+0.0i, 0.0+1.0i] ] ] ] > ## Error Cases iex> Nx.fft2(Nx.tensor([[1, 1]]), lengths: [:invalid, 2]) ** (ArgumentError) expected :lengths to be a list of lengths or :power_of_two, got: [:invalid, 2] iex> Nx.fft2(Nx.tensor([1, 1]), length: :invalid) ** (ArgumentError) expected a tensor with rank > 1, got tensor with rank 1 """ @doc type: :ndim def fft2(tensor, opts \\ []), do: call_fft2(tensor, opts, :fft2) @doc """ Calculates the Inverse 2D DFT of the given tensor. ## Options * `:eps` - Threshold which backends can use for cleaning-up results. Defaults to `1.0e-10`. * `:lengths` - A 2 element list where each element is 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. * `:axes` - the 2 axes upon which the Inverse 2D DFT will be calculated. Defaults to the last 2 axes. ## Examples iex> Nx.ifft2(Nx.tensor([[6, 0, 2, 0], [-2, 0, 2, 0]])) #Nx.Tensor< c64[2][4] [ [1.0+0.0i, 0.0+0.0i, 1.0+0.0i, 0.0+0.0i], [1.0+0.0i, 1.0+0.0i, 1.0+0.0i, 1.0+0.0i] ] > The calculation can happen on a specific pair of axes: iex> tensor = Nx.tensor([[[6, 0, 2, 0]], [[-2, 0, 2, 0]]]) iex> Nx.ifft2(tensor, axes: [0, -1]) #Nx.Tensor< c64[2][1][4] [ [ [1.0+0.0i, 0.0+0.0i, 1.0+0.0i, 0.0+0.0i] ], [ [1.0+0.0i, 1.0+0.0i, 1.0+0.0i, 1.0+0.0i] ] ] > iex> Nx.ifft2(tensor, axes: [-2, -1]) #Nx.Tensor< c64[2][1][4] [ [ [2.0+0.0i, 1.0+0.0i, 2.0+0.0i, 1.0+0.0i] ], [ [0.0+0.0i, -1.0+0.0i, 0.0+0.0i, -1.0+0.0i] ] ] > Padding and slicing can be introduced through `:lengths`: iex> tensor = Nx.tensor([[8, 8], [8, 0]]) iex> Nx.ifft2(tensor, lengths: [2, 4]) #Nx.Tensor< c64[2][4] [ [3.0+0.0i, 2.0+1.0i, 1.0+0.0i, 2.0-1.0i], [1.0+0.0i, 0.0+1.0i, -1.0+0.0i, 0.0-1.0i] ] > iex> Nx.ifft2(tensor, lengths: [4, 2]) #Nx.Tensor< c64[4][2] [ [3.0+0.0i, 1.0+0.0i], [2.0+1.0i, 0.0+1.0i], [1.0+0.0i, -1.0+0.0i], [2.0-1.0i, 0.0-1.0i] ] > iex> Nx.ifft2(Nx.tensor([[16, 16, 0], [16, 16, 0], [16, 16, -16]]), lengths: [:power_of_two, :power_of_two]) #Nx.Tensor< c64[4][4] [ [5.0+0.0i, 4.0+3.0i, -1.0+0.0i, 4.0-3.0i], [1.0+2.0i, -2.0+1.0i, 1.0+0.0i, 0.0+1.0i], [1.0+0.0i, 2.0+1.0i, -1.0+0.0i, 2.0-1.0i], [1.0-2.0i, 0.0-1.0i, 1.0+0.0i, -2.0-1.0i] ] > iex> Nx.ifft2(Nx.tensor([[[8, 8, 0, 0, 2, 3]]]), axes: [0, 2], lengths: [2, 4]) #Nx.Tensor< c64[2][1][4] [ [ [2.0+0.0i, 1.0+1.0i, 0.0+0.0i, 1.0-1.0i] ], [ [2.0+0.0i, 1.0+1.0i, 0.0+0.0i, 1.0-1.0i] ] ] > If an N-dimensional tensor is passed, the Inverse DFT is, by default, applied to the last axes: iex> tensor = Nx.tensor([ ...> [[[8, 0, 8, 0, 10, 10], [8, 8, 8, 8, 10, 10]]], ...> [[[-16, -16, -16, -16, 20, 20], [0, 0, 0, 8, -20, -20]]]]) iex> Nx.ifft2(tensor, lengths: [2, 4]) #Nx.Tensor< c64[2][1][2][4] [ [ [ [6.0+0.0i, 0.0+0.0i, 2.0+0.0i, 0.0+0.0i], [-2.0+0.0i, 0.0+0.0i, 2.0+0.0i, 0.0+0.0i] ] ], [ [ [-7.0+0.0i, 0.0-1.0i, -1.0+0.0i, 0.0+1.0i], [-9.0+0.0i, 0.0+1.0i, 1.0+0.0i, 0.0-1.0i] ] ] ] > ## Vectorized tensors Vectorized tensors work the same as N-dimensional tensors iex> tensor = Nx.tensor([ ...> [[[8, 0, 8, 0, 10, 10], [8, 8, 8, 8, 10, 10]]], ...> [[[-16, -16, -16, -16, 20, 20], [0, 0, 0, 8, -20, -20]]] ...> ]) |> Nx.vectorize(:x) iex> Nx.ifft2(tensor, lengths: [2, 4]) #Nx.Tensor< vectorized[x: 2] c64[1][2][4] [ [ [ [6.0+0.0i, 0.0+0.0i, 2.0+0.0i, 0.0+0.0i], [-2.0+0.0i, 0.0+0.0i, 2.0+0.0i, 0.0+0.0i] ] ], [ [ [-7.0+0.0i, 0.0-1.0i, -1.0+0.0i, 0.0+1.0i], [-9.0+0.0i, 0.0+1.0i, 1.0+0.0i, 0.0-1.0i] ] ] ] > ## Error Cases iex> Nx.ifft2(Nx.tensor([[1, 1]]), lengths: [:invalid, 2]) ** (ArgumentError) expected :lengths to be a list of lengths or :power_of_two, got: [:invalid, 2] iex> Nx.ifft2(Nx.tensor([1, 1]), length: :invalid) ** (ArgumentError) expected a tensor with rank > 1, got tensor with rank 1 """ @doc type: :ndim def ifft2(tensor, opts \\ []), do: call_fft2(tensor, opts, :ifft2) defp call_fft2(tensor, opts, kind) do apply_vectorized(tensor, fn tensor, offset -> shape = Nx.Shape.fft2(tensor.shape) opts = Keyword.validate!(opts, [:lengths, axes: [-2, -1], eps: 1.0e-10]) [ax1, ax2] = case opts[:axes] do [ax1, ax2] -> Nx.Shape.normalize_axes(tensor.shape, [ax1, ax2], tensor.names, offset) axes -> raise ArgumentError, "expected :axes to be a list with 2 axes, got: #{inspect(axes)}" end m = elem(shape, ax1) n = elem(shape, ax2) [l1, l2] = case opts[:lengths] do [l1, l2] when (is_integer(l1) or l1 == :power_of_two) and (is_integer(l2) or l2 == :power_of_two) -> [l1, l2] nil -> [m, n] lengths -> raise ArgumentError, "expected :lengths to be a list of lengths or :power_of_two, got: #{inspect(lengths)}" end l1 = case l1 do :power_of_two -> 2 ** Kernel.ceil(:math.log2(m)) m when is_integer(m) and m > 0 -> m end l2 = case l2 do :power_of_two -> 2 ** Kernel.ceil(:math.log2(n)) n when is_integer(n) and n > 0 -> n end output_shape = shape |> Tuple.insert_at(ax1, l1) |> Tuple.delete_at(ax1 + 1) |> Tuple.insert_at(ax2, l2) |> Tuple.delete_at(ax2 + 1) out = to_template(%{tensor | shape: output_shape, type: Nx.Type.to_complex(tensor.type)}) opts = Keyword.take(opts, [:eps]) |> Keyword.merge(lengths: [l1, l2], axes: [ax1, ax2]) Nx.Shared.optional(kind, [tensor, opts], out, fn tensor, opts -> [ax1, ax2] = opts[:axes] [l1, l2] = opts[:lengths] eps = opts[:eps] if kind == :fft2 do tensor |> fft(axis: ax2, length: l2, eps: eps) |> fft(axis: ax1, length: l1, eps: eps) else tensor |> ifft(axis: ax2, length: l2, eps: eps) |> ifft(axis: ax1, length: l1, eps: eps) end end) 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, 32}, endpoint: false) #Nx.Tensor< s32[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 """ Creates an Nx-tensor from an already-allocated memory space. This function should be used with caution, as it can lead to segmentation faults. The `backend` argument is either the backend module (such as `Nx.BinaryBackend`), or a tuple of `{module, keyword()}` with specific backend configuration. `pointer` is the corresponding value that would be returned from a call to `get_pointer/2`. ## Options Besides the options listed below, all other options are forwarded to the underlying implementation. * `:names` - refer to `tensor/2` ## Examples pointer = %Nx.Pointer{kind: :local, address: 1234} Nx.from_pointer(MyBackend, pointer, {:s, 32}, {1, 3}) #Nx.Tensor< s32[1][3] [ [10, 20, 30] ] > pointer = %Nx.Pointer{kind: :ipc, handle: "some-ipc-handle"} Nx.from_pointer({MyBackend, some: :opt}, pointer, {:s, 32}, {1, 3}, names: [nil, :col]) #Nx.Tensor< s32[1][col: 3] [ [10, 20, 30] ] > """ @doc type: :creation def from_pointer(backend, pointer, type, shape, opts \\ []) when is_atom(backend) or is_tuple(backend) do Nx.Shape.validate!(shape, :shape) type = Nx.Type.normalize!(type) opts = Keyword.put_new_lazy(opts, :names, fn -> List.duplicate(nil, tuple_size(shape)) end) {backend, backend_opts} = case backend do {backend, opts} when is_list(opts) -> {backend, opts} backend -> {backend, []} end backend.from_pointer(pointer, type, shape, backend_opts, opts) end @doc """ Returns an `Nx.Pointer` that represents either a local pointer or an IPC handle for the given tensor. Can be used in conjunction with `from_pointer/5` to share the same memory for multiple tensors, as well as for interoperability with other programming languages. ## Options * `:kind` - one of `:local`, `:ipc`. `:local` means the returned value represents a pointer internal to the current process. `:ipc` means the returned value represents an IPC handle that can be shared between processes. Defaults to `:local`. Other options are relayed to the backend. ## Examples t = Nx.u8([10, 20, 30]) Nx.to_pointer(t, kind: :local) %Nx.Pointer{kind: :local, address: 1234, data_size: 3, handle: nil} t = Nx.s32([1, 2, 3]) Nx.to_pointer(t, kind: :ipc) %Nx.Pointer{kind: :ipc, address: nil, data_size: 32, handle: "some-ipc-handle"} """ @doc type: :creation def to_pointer(tensor, opts \\ []) do tensor = to_tensor(tensor) impl!(tensor).to_pointer(tensor, opts) 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< s32[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< s32[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 @doc """ Replaces every value in `tensor` with `value`. The returned tensor has the same shape, names and vectorized axes as the given one. The type will be computed based on the type of `tensor` and `value`. You can also pass a `:type` option to change this behaviour. ## Options * `:type` - sets the type of the returned tensor. If one is not given, it is automatically inferred based on the inputs, with type promotions ## Examples iex> tensor = Nx.iota({2, 2}) iex> Nx.fill(tensor, 5) #Nx.Tensor< s32[2][2] [ [5, 5], [5, 5] ] > iex> tensor = Nx.iota({2, 2}) |> Nx.vectorize(:x) iex> Nx.fill(tensor, 5) #Nx.Tensor< vectorized[x: 2] s32[2] [ [5, 5], [5, 5] ] > iex> tensor = Nx.iota({2, 2}) iex> Nx.fill(tensor, 5, type: :u8) #Nx.Tensor< u8[2][2] [ [5, 5], [5, 5] ] > ### Type promotions Type promotions should happen automatically, with the resulting type being the combination of the `tensor` type and the `value` type. iex> tensor = Nx.iota({2, 2}) iex> Nx.fill(tensor, 5.0) #Nx.Tensor< f32[2][2] [ [5.0, 5.0], [5.0, 5.0] ] > """ @doc type: :element def fill(tensor, value, opts \\ []) do opts = Keyword.validate!(opts, [:type]) type = Nx.Type.normalize!(opts[:type] || binary_type(tensor, value)) value = to_tensor(value) %{shape: shape, names: names} = devectorize(tensor) value |> as_type(type) |> broadcast(shape, names: names) |> vectorize(tensor.vectorized_axes) end ## Sigils @doc false @deprecated "Use ~MAT instead" defmacro sigil_M({:<<>>, _meta, [string]}, modifiers) do {numbers, type} = string |> String.trim() |> binary_to_numbers() numbers_to_tensor(numbers, type, modifiers) end @doc false @deprecated "Use ~VEC instead" 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 @doc """ A convenient `~MAT` 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: ~MAT< -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> ~MAT[0.1 0.2 0.3 0.4]f16 #Nx.Tensor< f16[1][4] [ [0.0999755859375, 0.199951171875, 0.300048828125, 0.39990234375] ] > iex> ~MAT[1+1i 2-2.0i -3] #Nx.Tensor< c64[1][3] [ [1.0+1.0i, 2.0-2.0i, -3.0+0.0i] ] > iex> ~MAT[1 Inf NaN] #Nx.Tensor< f32[1][3] [ [1.0, Inf, NaN] ] > iex> ~MAT[1i Inf NaN] #Nx.Tensor< c64[1][3] [ [0.0+1.0i, Inf+0.0i, NaN+0.0i] ] > iex> ~MAT[1i Inf+2i NaN-Infi] #Nx.Tensor< c64[1][3] [ [0.0+1.0i, Inf+2.0i, NaN-Infi] ] > """ @doc type: :creation defmacro sigil_MAT({:<<>>, _meta, [string]}, modifiers) do {numbers, type} = string |> String.trim() |> binary_to_numbers() numbers_to_tensor(numbers, type, modifiers) end @doc """ A convenient `~VEC` 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: ~VEC[-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> ~VEC[0.1 0.2 0.3 0.4]f16 #Nx.Tensor< f16[4] [0.0999755859375, 0.199951171875, 0.300048828125, 0.39990234375] > iex> ~VEC[1+1i 2-2.0i -3] #Nx.Tensor< c64[3] [1.0+1.0i, 2.0-2.0i, -3.0+0.0i] > iex> ~VEC[1 Inf NaN] #Nx.Tensor< f32[3] [1.0, Inf, NaN] > iex> ~VEC[1i Inf NaN] #Nx.Tensor< c64[3] [0.0+1.0i, Inf+0.0i, NaN+0.0i] > iex> ~VEC[1i Inf+2i NaN-Infi] #Nx.Tensor< c64[3] [0.0+1.0i, Inf+2.0i, NaN-Infi] > """ @doc type: :creation defmacro sigil_VEC({:<<>>, _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, 32}, 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: <>) 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 output_type = Enum.reduce(start_indices, &binary_type/2) Enum.with_index(start_indices, fn index, _i when is_integer(index) -> {backend, options} = default_backend() out = %T{shape: {}, type: output_type, names: []} backend.constant(out, index, options) 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) max = case max do %T{data: %Nx.Defn.Expr{}} = t -> Nx.Defn.Kernel.stop_grad(t) t -> t end 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