View Source Nx (Nx v0.4.1)

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

References

Here is a general outline of the main references in this library:

  • For an introduction, see our Intro to Nx 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

Creating tensors

The main APIs for creating tensors are tensor/2, from_binary/2, iota/2, eye/2, random_uniform/2, random_normal/2, and broadcast/3.

The tensor types can be one of:

  • unsigned integers (u8, u16, u32, u64)
  • signed integers (s8, s16, s32, s64)
  • floats (f16, f32, f64)
  • brain floats (bf16)
  • and complex numbers (c64, c128)

The types are tracked as tuples:

iex> Nx.tensor([1, 2, 3], type: {:f, 32})
#Nx.Tensor<
  f32[3]
  [1.0, 2.0, 3.0]
>

But a shortcut atom notation is also available:

iex> Nx.tensor([1, 2, 3], type: :f32)
#Nx.Tensor<
  f32[3]
  [1.0, 2.0, 3.0]
>

The tensor dimensions can also be named, via the :names option available to all creation functions:

iex> Nx.iota({2, 3}, names: [:x, :y])
#Nx.Tensor<
  s64[x: 2][y: 3]
  [
    [0, 1, 2],
    [3, 4, 5]
  ]
>

Finally, for creating vectors and matrices, a sigil notation is available:

iex> import Nx, only: :sigils
iex> ~V[1 2 3]f32
#Nx.Tensor<
  f32[3]
  [1.0, 2.0, 3.0]
>

iex> import Nx, only: :sigils
iex> ~M'''
...> 1 2 3
...> 4 5 6
...> '''s32
#Nx.Tensor<
  s32[2][3]
  [
    [1, 2, 3],
    [4, 5, 6]
  ]
>

All other APIs accept exclusively numbers or tensors, unless explicitly noted otherwise.

broadcasting

Broadcasting

Broadcasting allows operations on two tensors of different shapes to match. For example, most often operations between tensors have the same shape:

iex> a = Nx.tensor([1, 2, 3])
iex> b = Nx.tensor([10, 20, 30])
iex> Nx.add(a, b)
#Nx.Tensor<
  s64[3]
  [11, 22, 33]
>

Now let's imagine you want to multiply a large tensor of dimensions 1000x1000x1000 by 2. If you had to create a similarly large tensor only to perform this operation, it would be inefficient. Therefore, you can simply multiply this large tensor by the scalar 2, and Nx will propagate its dimensions at the time the operation happens, without allocating a large intermediate tensor:

iex> Nx.multiply(Nx.tensor([1, 2, 3]), 2)
#Nx.Tensor<
  s64[3]
  [2, 4, 6]
>

In practice, broadcasting is not restricted only to scalars; it is a general algorithm that applies to all dimensions of a tensor. When broadcasting, Nx compares the shapes of the two tensors, starting with the trailing ones, such that:

  • If the dimensions have equal size, then they are compatible

  • If one of the dimensions have size of 1, it is "broadcast" to match the dimension of the other

In case one tensor has more dimensions than the other, the missing dimensions are considered to be of size one. Here are some examples of how broadcast would work when multiplying two tensors with the following shapes:

s64[3] * s64
#=> s64[3]

s64[255][255][3] * s64[3]
#=> s64[255][255][3]

s64[2][1] * s[1][2]
#=> s64[2][2]

s64[5][1][4][1] * s64[3][4][5]
#=> s64[5][3][4][5]

If any of the dimensions do not match or are not 1, an error is raised.

access-syntax-slicing

Access syntax (slicing)

Nx tensors implement Elixir's access syntax. This allows developers to slice tensors up and easily access sub-dimensions and values.

Access accepts integers:

iex> t = Nx.tensor([[1, 2], [3, 4]])
iex> t[0]
#Nx.Tensor<
  s64[2]
  [1, 2]
>
iex> t[1]
#Nx.Tensor<
  s64[2]
  [3, 4]
>
iex> t[1][1]
#Nx.Tensor<
  s64
  4
>

If a negative index is given, it accesses the element from the back:

iex> t = Nx.tensor([[1, 2], [3, 4]])
iex> t[-1][-1]
#Nx.Tensor<
  s64
  4
>

Out of bound access will raise:

iex> Nx.tensor([1, 2])[2]
** (ArgumentError) index 2 is out of bounds for axis 0 in shape {2}

iex> Nx.tensor([1, 2])[-3]
** (ArgumentError) index -3 is out of bounds for axis 0 in shape {2}

The index can also be another tensor but in such cases it must be a scalar between 0 and the dimension size. Out of bound dynamic indexes are always clamped to the tensor dimensions:

iex> two = Nx.tensor(2)
iex> t = Nx.tensor([[1, 2], [3, 4]])
iex> t[two][two]
#Nx.Tensor<
  s64
  4
>

For example, a minus_one dynamic index will be clamped to zero:

iex> minus_one = Nx.tensor(-1)
iex> t = Nx.tensor([[1, 2], [3, 4]])
iex> t[minus_one][minus_one]
#Nx.Tensor<
  s64
  1
>

Access also accepts ranges. Ranges in Elixir are inclusive:

iex> t = Nx.tensor([[1, 2], [3, 4], [5, 6], [7, 8]])
iex> t[0..1]
#Nx.Tensor<
  s64[2][2]
  [
    [1, 2],
    [3, 4]
  ]
>

Ranges can receive negative positions and they will read from the back. In such cases, the range step must be explicitly given and the right-side of the range must be equal or greater than the left-side:

iex> t = Nx.tensor([[1, 2], [3, 4], [5, 6], [7, 8]])
iex> t[1..-2//1]
#Nx.Tensor<
  s64[2][2]
  [
    [3, 4],
    [5, 6]
  ]
>

As you can see, accessing with a range does not eliminate the accessed axis. This means that, if you try to cascade ranges, you will always be filtering the highest dimension:

iex> t = Nx.tensor([[1, 2], [3, 4], [5, 6], [7, 8]])
iex> t[1..-1//1] # Drop the first "row"
#Nx.Tensor<
  s64[3][2]
  [
    [3, 4],
    [5, 6],
    [7, 8]
  ]
>
iex> t[1..-1//1][1..-1//1] # Drop the first "row" twice
#Nx.Tensor<
  s64[2][2]
  [
    [5, 6],
    [7, 8]
  ]
>

Therefore, if you want to slice across multiple dimensions, you can wrap the ranges in a list:

iex> t = Nx.tensor([[1, 2], [3, 4], [5, 6], [7, 8]])
iex> t[[1..-1//1, 1..-1//1]] # Drop the first "row" and the first "column"
#Nx.Tensor<
  s64[3][1]
  [
    [4],
    [6],
    [8]
  ]
>

You can also use .. as the full-slice range, which means you want to keep a given dimension as is:

iex> t = Nx.tensor([[1, 2], [3, 4], [5, 6], [7, 8]])
iex> t[[.., 1..-1//1]] # Drop only the first "column"
#Nx.Tensor<
  s64[4][1]
  [
    [2],
    [4],
    [6],
    [8]
  ]
>

You can mix both ranges and integers in the list too:

iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]])
iex> t[[1..2, 2]]
#Nx.Tensor<
  s64[2]
  [6, 9]
>

If the list has less elements than axes, the remaining dimensions are returned in full:

iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]])
iex> t[[1..2]]
#Nx.Tensor<
  s64[2][3]
  [
    [4, 5, 6],
    [7, 8, 9]
  ]
>

The access syntax also pairs nicely with named tensors. By using named tensors, you can pass only the axis you want to slice, leaving the other axes intact:

iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]], names: [:x, :y])
iex> t[x: 1..2]
#Nx.Tensor<
  s64[x: 2][y: 3]
  [
    [4, 5, 6],
    [7, 8, 9]
  ]
>
iex> t[x: 1..2, y: 0..1]
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [4, 5],
    [7, 8]
  ]
>
iex> t[x: 1, y: 0..1]
#Nx.Tensor<
  s64[y: 2]
  [4, 5]
>

For a more complex slicing rules, including strides, you can always fallback to Nx.slice/4.

backends

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 and Torchx for installation and GPU support.

To implement your own backend, check the Nx.Tensor behaviour.

Link to this section Summary

Types

t()

Represents a numerical value.

Guards

Checks whether the value is a valid numerical value.

Functions: Aggregates

Returns a scalar tensor of value 1 if all of the tensor values are not zero. Otherwise the value is 0.

Returns a scalar tensor of value 1 if all element-wise values are within tolerance of b. Otherwise returns value 0.

Returns a scalar tensor of value 1 if any of the tensor values are not zero. Otherwise the value is 0.

Returns the indices of the maximum values.

Returns the indices of the minimum values.

Returns the mean for the tensor.

Returns the median for the tensor.

Returns the mode of a tensor (the value that appears most often).

Returns the product for the tensor.

Reduces over a tensor with the given accumulator.

Returns the maximum values of the tensor.

Returns the minimum values of the tensor.

Finds the standard deviation of a tensor.

Returns the sum for the tensor.

Finds the variance of a tensor.

Returns the weighted mean for the tensor and the weights.

Functions: Backend

Deallocates data in a device.

Gets the default backend for the current process.

Sets the given backend as default in the current process.

Sets the default backend globally.

Functions: Conversion

Deserializes a serialized representation of a tensor or a container with the given options.

Loads a .npy file into a tensor.

Loads a .npz archive into a list of tensors.

Serializes the given tensor or container of tensors to iodata.

Converts the underlying tensor to a stream of tensor batches.

Returns the underlying tensor as a binary.

Returns the underlying tensor as a flat list.

Returns a heatmap struct with the tensor data.

Returns the underlying tensor as a number.

Converts a tensor (or tuples and maps of tensors) to tensor templates.

Converts the given number (or tensor) to a tensor.

Functions: Creation

Creates the identity matrix of size n.

Creates a one-dimensional tensor from a binary with the given type.

Creates a tensor with the given shape which increments along the provided axis. You may optionally provide dimension names.

Creates a diagonal tensor from a 1D tensor.

Puts the individual values from a 1D diagonal into the diagonal indices of the given 2D tensor.

Shortcut for random_normal(shape, 0.0, 1.0, opts).

Returns a normally-distributed random tensor with the given shape.

Shortcut for random_uniform(shape, 0.0, 1.0, opts).

Returns a uniformly-distributed random tensor with the given shape.

Shuffles tensor elements.

A convenient ~M sigil for building matrices (two-dimensional tensors).

A convenient ~V sigil for building vectors (one-dimensional tensors).

Extracts the diagonal of batched matrices.

Creates a tensor template.

Builds a tensor.

Functions: Cumulative

Returns the cumulative maximum of elements along an axis.

Returns the cumulative minimum of elements along an axis.

Returns the cumulative product of elements along an axis.

Returns the cumulative sum of elements along an axis.

Functions: Element-wise

Computes the absolute value of each element in the tensor.

Calculates the inverse cosine of each element in the tensor.

Calculates the inverse hyperbolic cosine of each element in the tensor.

Element-wise addition of two tensors.

Calculates the inverse sine of each element in the tensor.

Calculates the inverse hyperbolic sine of each element in the tensor.

Element-wise arc tangent of two tensors.

Calculates the inverse tangent of each element in the tensor.

Calculates the inverse hyperbolic tangent of each element in the tensor.

Element-wise bitwise AND of two tensors.

Applies bitwise not to each element in the tensor.

Element-wise bitwise OR of two tensors.

Element-wise bitwise XOR of two tensors.

Calculates the cube root of each element in the tensor.

Calculates the ceil of each element in the tensor.

Clips the values of the tensor on the closed interval [min, max].

Constructs a complex tensor from two equally-shaped tensors.

Calculates the complex conjugate of each element in the tensor.

Calculates the cosine of each element in the tensor.

Calculates the hyperbolic cosine of each element in the tensor.

Counts the number of leading zeros of each element in the tensor.

Element-wise division of two tensors.

Element-wise equality comparison of two tensors.

Calculates the error function of each element in the tensor.

Calculates the inverse error function of each element in the tensor.

Calculates the one minus error function of each element in the tensor.

Calculates the exponential of each element in the tensor.

Calculates the exponential minus one of each element in the tensor.

Calculates the floor of each element in the tensor.

Element-wise greater than comparison of two tensors.

Element-wise greater than or equal comparison of two tensors.

Returns the imaginary component of each entry in a complex tensor as a floating point tensor.

Determines if each element in tensor is Inf or -Inf.

Determines if each element in tensor is a NaN.

Element-wise left shift of two tensors.

Element-wise less than comparison of two tensors.

Element-wise less than or equal comparison of two tensors.

Calculates the natural log plus one of each element in the tensor.

Calculates the natural log of each element in the tensor.

Element-wise logical and of two tensors.

Element-wise logical not a tensor.

Element-wise logical or of two tensors.

Element-wise logical xor of two tensors.

Maps the given scalar function over the entire tensor.

Element-wise maximum of two tensors.

Element-wise minimum of two tensors.

Element-wise multiplication of two tensors.

Negates each element in the tensor.

Element-wise not-equal comparison of two tensors.

Calculates the complex phase angle of each element in the tensor. $$phase(z) = atan2(b, a), z = a + bi \in \Complex$$

Computes the bitwise population count of each element in the tensor.

Element-wise power of two tensors.

Element-wise integer division of two tensors.

Returns the real component of each entry in a complex tensor as a floating point tensor.

Element-wise remainder of two tensors.

Element-wise right shift of two tensors.

Calculates the round (away from zero) of each element in the tensor.

Calculates the reverse square root of each element in the tensor.

Constructs a tensor from two tensors, based on a predicate.

Calculates the sigmoid of each element in the tensor.

Computes the sign of each element in the tensor.

Calculates the sine of each element in the tensor.

Calculates the hyperbolic sine of each element in the tensor.

Calculates the square root of each element in the tensor.

Element-wise subtraction of two tensors.

Calculates the tangent of each element in the tensor.

Calculates the hyperbolic tangent of each element in the tensor.

Functions: Indexed

Builds a new tensor by taking individual values from the original tensor at the given indices.

Performs an indexed add operation on the target tensor, adding the updates into the corresponding indices positions.

Puts individual values from updates into the given tensor at the corresponding indices.

Puts the given slice into the given tensor at the given start_indices.

Slices a tensor from start_indices with lengths.

Slices a tensor along the given axis.

Takes and concatenates slices along an axis.

Takes the values from a tensor given an indices tensor, along the specified axis.

Functions: N-dim

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.

Concatenates tensors along the given axis.

Computes an n-D convolution (where n >= 3) as used in neural networks.

Returns the dot product of two tensors.

Computes the generalized dot product between two tensors, given the contracting axes.

Computes the generalized dot product between two tensors, given the contracting and batch axes.

Calculates the DFT of the given tensor.

Calculates the Inverse DFT of the given tensor.

Computes the outer product of two tensors.

Reverses the tensor in the given dimensions.

Sorts the tensor along the given axis according to the given direction.

Joins a list of tensors with the same shape along a new axis.

Functions: Shape

Returns all of the axes in a tensor.

Returns the index of the given axis in the tensor.

Returns the size of a given axis of a tensor.

Broadcasts tensor to the given broadcast_shape.

Returns the byte size of the data in the tensor computed from its shape and type.

Checks if two tensors have the same shape, type, and compatible names.

Flattens a n-dimensional tensor to a 1-dimensional tensor.

Returns all of the names in a tensor.

Adds a new axis of size 1 with optional name.

Pads a tensor with a given value.

Returns the rank of a tensor.

Adds (or overrides) the given names to the tensor.

Changes the shape of a tensor.

Returns the shape of the tensor as a tuple.

Returns the number of elements in the tensor.

Squeezes the given size 1 dimensions out of the tensor.

Creates a new tensor by repeating the input tensor along the given axes.

Transposes a tensor to the given axes.

Functions: Type

Changes the type of a tensor.

Changes the type of a tensor, using a bitcast.

Returns the type of the tensor.

Functions: Window

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.

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.

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.

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.

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.

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.

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.

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.

Link to this section Types

@type axes() :: Nx.Tensor.axes()
@type axis() :: Nx.Tensor.axis()
@type shape() :: number() | Nx.Tensor.t() | Nx.Tensor.shape()
@type t() :: number() | Complex.t() | Nx.Tensor.t()

Represents a numerical value.

Can be a plain number, a Complex number or an Nx.Tensor.

See also: is_tensor/1

@type template() :: Nx.Tensor.t(%Nx.TemplateBackend{})

Link to this section Guards

Checks whether the value is a valid numerical value.

Returns true if the value is a number, a Complex number or an Nx.Tensor.

See also: t/0

Link to this section Functions: Aggregates

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

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

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]
  ]
>
Link to this function

all_close(a, b, opts \\ [])

View Source

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

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

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 NaNs 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
>

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

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

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]
  ]
>
Link to this function

argmax(tensor, opts \\ [])

View Source

Returns the indices of the maximum values.

options

Options

  • :axis - the axis to aggregate on. If no axis is given, returns the index of the absolute maximum value in the tensor.

  • :keep_axis - whether or not to keep the reduced axis with a size of 1. Defaults to false.

  • :tie_break - how to break ties. one of :high, or :low. default behavior is to always return the lower index.

examples

Examples

iex> Nx.argmax(4)
#Nx.Tensor<
  s64
  0
>

iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]])
iex> Nx.argmax(t)
#Nx.Tensor<
  s64
  10
>

If a tensor of floats is given, it still returns integers:

iex> Nx.argmax(Nx.tensor([2.0, 4.0]))
#Nx.Tensor<
  s64
  1
>

aggregating-over-an-axis

Aggregating over an 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: :x)
#Nx.Tensor<
  s64[y: 2][z: 3]
  [
    [1, 0, 0],
    [1, 1, 0]
  ]
>

iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]], names: [:x, :y, :z])
iex> Nx.argmax(t, axis: :y)
#Nx.Tensor<
  s64[x: 2][z: 3]
  [
    [0, 0, 0],
    [0, 1, 0]
  ]
>

iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]], names: [:x, :y, :z])
iex> Nx.argmax(t, axis: :z)
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [0, 2],
    [0, 1]
  ]
>

tie-breaks

Tie breaks

iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]], names: [:x, :y, :z])
iex> Nx.argmax(t, tie_break: :low, axis: :y)
#Nx.Tensor<
  s64[x: 2][z: 3]
  [
    [0, 0, 0],
    [0, 1, 0]
  ]
>

iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]], names: [:x, :y, :z])
iex> Nx.argmax(t, tie_break: :high, axis: :y)
#Nx.Tensor<
  s64[x: 2][z: 3]
  [
    [0, 0, 1],
    [0, 1, 1]
  ]
>

keep-axis

Keep axis

iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]], names: [:x, :y, :z])
iex> Nx.argmax(t, axis: :y, keep_axis: true)
#Nx.Tensor<
  s64[x: 2][y: 1][z: 3]
  [
    [
      [0, 0, 0]
    ],
    [
      [0, 1, 0]
    ]
  ]
>
Link to this function

argmin(tensor, opts \\ [])

View Source

Returns the indices of the minimum values.

options

Options

  • :axis - the axis to aggregate on. If no axis is given, returns the index of the absolute minimum value in the tensor.

  • :keep_axis - whether or not to keep the reduced axis with a size of 1. Defaults to false.

  • :tie_break - how to break ties. one of :high, or :low. Default behavior is to always return the lower index.

examples

Examples

iex> Nx.argmin(4)
#Nx.Tensor<
  s64
  0
>

iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]])
iex> Nx.argmin(t)
#Nx.Tensor<
  s64
  4
>

If a tensor of floats is given, it still returns integers:

iex> Nx.argmin(Nx.tensor([2.0, 4.0]))
#Nx.Tensor<
  s64
  0
>

aggregating-over-an-axis

Aggregating over an 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: :x)
#Nx.Tensor<
  s64[y: 2][z: 3]
  [
    [0, 0, 0],
    [0, 0, 0]
  ]
>

iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]], names: [:x, :y, :z])
iex> Nx.argmin(t, axis: 1)
#Nx.Tensor<
  s64[x: 2][z: 3]
  [
    [1, 1, 0],
    [1, 0, 0]
  ]
>

iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]], names: [:x, :y, :z])
iex> Nx.argmin(t, axis: :z)
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [1, 1],
    [1, 2]
  ]
>

tie-breaks

Tie breaks

iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]], names: [:x, :y, :z])
iex> Nx.argmin(t, tie_break: :low, axis: :y)
#Nx.Tensor<
  s64[x: 2][z: 3]
  [
    [1, 1, 0],
    [1, 0, 0]
  ]
>

iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]], names: [:x, :y, :z])
iex> Nx.argmin(t, tie_break: :high, axis: :y)
#Nx.Tensor<
  s64[x: 2][z: 3]
  [
    [1, 1, 1],
    [1, 0, 1]
  ]
>

keep-axis

Keep axis

iex> t = Nx.tensor([[[4, 2, 3], [1, -5, 3]], [[6, 2, 3], [4, 8, 3]]], names: [:x, :y, :z])
iex> Nx.argmin(t, axis: :y, keep_axis: true)
#Nx.Tensor<
  s64[x: 2][y: 1][z: 3]
  [
    [
      [1, 1, 0]
    ],
    [
      [1, 0, 0]
    ]
  ]
>
Link to this function

mean(tensor, opts \\ [])

View Source

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

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

Aggregating over an axis

iex> Nx.mean(Nx.tensor([1, 2, 3], names: [:x]), 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([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]], names: [:x, :y, :z])
iex> Nx.mean(t, axes: [:x])
#Nx.Tensor<
  f32[y: 2][z: 3]
  [
    [4.0, 5.0, 6.0],
    [7.0, 8.0, 9.0]
  ]
>

iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]], names: [:x, :y, :z])
iex> Nx.mean(t, axes: [:x, :z])
#Nx.Tensor<
  f32[y: 2]
  [5.0, 8.0]
>

iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]], names: [:x, :y, :z])
iex> Nx.mean(t, axes: [-1])
#Nx.Tensor<
  f32[x: 2][y: 2]
  [
    [2.0, 5.0],
    [8.0, 11.0]
  ]
>

keeping-axes

Keeping axes

iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]], names: [:x, :y, :z])
iex> Nx.mean(t, axes: [-1], keep_axes: true)
#Nx.Tensor<
  f32[x: 2][y: 2][z: 1]
  [
    [
      [2.0],
      [5.0]
    ],
    [
      [8.0],
      [11.0]
    ]
  ]
>
Link to this function

median(tensor, opts \\ [])

View Source

Returns the median for the tensor.

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

Examples

iex> Nx.median(Nx.tensor(42))
#Nx.Tensor<
  s64
  42
>

iex> Nx.median(Nx.tensor([1, 2, 3]))
#Nx.Tensor<
  s64
  2
>

iex> Nx.median(Nx.tensor([1, 2]))
#Nx.Tensor<
  f32
  1.5
>

aggregating-over-an-axis

Aggregating over an axis

iex> Nx.median(Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:x, :y]), axis: 0)
#Nx.Tensor<
  f32[y: 3]
  [2.5, 3.5, 4.5]
>

iex> Nx.median(Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:x, :y]), axis: :y)
#Nx.Tensor<
  s64[x: 2]
  [2, 5]
>

iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]], 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, axis: :x)
#Nx.Tensor<
  f32[y: 2][z: 3]
  [
    [7.0, 5.0, -3.0],
    [7.0, 8.0, 12.0]
  ]
>

iex> t = Nx.tensor([[[1, 2, 2], [3, 4, 2]], [[4, 5, 2], [7, 9, 2]]])
iex> Nx.median(t, axis: -1)
#Nx.Tensor<
  s64[2][2]
  [
    [2, 3],
    [4, 7]
  ]
>

keeping-axis

Keeping axis

iex> t = Nx.tensor([[[1, 2, 2], [3, 4, 2]], [[4, 5, 2], [7, 9, 2]]])
iex> Nx.median(t, axis: -1, keep_axis: true)
#Nx.Tensor<
  s64[2][2][1]
  [
    [
      [2],
      [3]
    ],
    [
      [4],
      [7]
    ]
  ]
>
Link to this function

mode(tensor, opts \\ [])

View Source

Returns the mode of a tensor (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

Examples

iex> Nx.mode(Nx.tensor(42))
#Nx.Tensor<
  s64
  42
>

iex> Nx.mode(Nx.tensor([[1]]))
#Nx.Tensor<
  s64
  1
>

iex> Nx.mode(Nx.tensor([1, 2, 2, 3, 5]))
#Nx.Tensor<
  s64
  2
>

iex> Nx.mode(Nx.tensor([[1, 2, 2, 3, 5], [1, 1, 76, 8, 1]]))
#Nx.Tensor<
  s64
  1
>

aggregating-over-an-axis

Aggregating over an axis

iex> Nx.mode(Nx.tensor([[1, 2, 2, 3, 5], [1, 1, 76, 8, 1]]), axis: 0)
#Nx.Tensor<
  s64[5]
  [1, 1, 2, 3, 1]
>

iex> Nx.mode(Nx.tensor([[1, 2, 2, 3, 5], [1, 1, 76, 8, 1]]), axis: 1)
#Nx.Tensor<
  s64[2]
  [2, 1]
>

iex> Nx.mode(Nx.tensor([[[[1]]]]), axis: 1)
#Nx.Tensor<
  s64[1][1][1]
  [
    [
      [1]
    ]
  ]
>

keeping-axis

Keeping axis

iex> Nx.mode(Nx.tensor([[1, 2, 2, 3, 5], [1, 1, 76, 8, 1]]), axis: 1, keep_axis: true)
#Nx.Tensor<
  s64[2][1]
  [
    [2],
    [1]
  ]
>

iex> Nx.mode(Nx.tensor(1), keep_axis: true)
#Nx.Tensor<
  s64[1]
  [1]
>

iex> Nx.mode(Nx.tensor([[[1]]]), keep_axis: true)
#Nx.Tensor<
  s64[1][1][1]
  [
    [
      [1]
    ]
  ]
>

iex> Nx.mode(Nx.tensor([[[[1]]]]), axis: 1, keep_axis: true)
#Nx.Tensor<
  s64[1][1][1][1]
  [
    [
      [
        [1]
      ]
    ]
  ]
>
Link to this function

product(tensor, opts \\ [])

View Source

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

Examples

iex> Nx.product(Nx.tensor(42))
#Nx.Tensor<
  s64
  42
>

iex> Nx.product(Nx.tensor([1, 2, 3], names: [:x]))
#Nx.Tensor<
  s64
  6
>

iex> Nx.product(Nx.tensor([[1.0, 2.0], [3.0, 4.0]], names: [:x, :y]))
#Nx.Tensor<
  f32
  24.0
>

Giving a tensor with low precision casts it to a higher precision to make sure the sum does not overflow:

iex> Nx.product(Nx.tensor([[10, 20], [30, 40]], type: :u8, names: [:x, :y]))
#Nx.Tensor<
  u64
  240000
>

iex> Nx.product(Nx.tensor([[10, 20], [30, 40]], type: :s8, names: [:x, :y]))
#Nx.Tensor<
  s64
  240000
>

aggregating-over-an-axis

Aggregating over an axis

iex> Nx.product(Nx.tensor([1, 2, 3], names: [:x]), axes: [0])
#Nx.Tensor<
  s64
  6
>

Same tensor over different axes combinations:

iex> t = Nx.tensor(
...>   [
...>     [
...>       [1, 2, 3],
...>       [4, 5, 6]
...>     ],
...>     [
...>       [7, 8, 9],
...>       [10, 11, 12]
...>     ]
...>   ],
...>   names: [:x, :y, :z]
...> )
iex> Nx.product(t, axes: [:x])
#Nx.Tensor<
  s64[y: 2][z: 3]
  [
    [7, 16, 27],
    [40, 55, 72]
  ]
>
iex> Nx.product(t, axes: [:y])
#Nx.Tensor<
  s64[x: 2][z: 3]
  [
    [4, 10, 18],
    [70, 88, 108]
  ]
>
iex> Nx.product(t, axes: [:x, :z])
#Nx.Tensor<
  s64[y: 2]
  [3024, 158400]
>
iex> Nx.product(t, axes: [:z])
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [6, 120],
    [504, 1320]
  ]
>
iex> Nx.product(t, axes: [-3])
#Nx.Tensor<
  s64[y: 2][z: 3]
  [
    [7, 16, 27],
    [40, 55, 72]
  ]
>

keeping-axes

Keeping axes

iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]], names: [:x, :y, :z])
iex> Nx.product(t, axes: [:z], keep_axes: true)
#Nx.Tensor<
  s64[x: 2][y: 2][z: 1]
  [
    [
      [6],
      [120]
    ],
    [
      [504],
      [1320]
    ]
  ]
>

errors

Errors

iex> Nx.product(Nx.tensor([[1, 2]]), axes: [2])
** (ArgumentError) given axis (2) invalid for shape with rank 2
Link to this function

reduce(tensor, acc, opts \\ [], fun)

View Source

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

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.

examples

Examples

iex> Nx.reduce(Nx.tensor(42), 0, fn x, y -> Nx.add(x, y) end)
#Nx.Tensor<
  s64
  42
>

iex> Nx.reduce(Nx.tensor([1, 2, 3]), 0, fn x, y -> Nx.add(x, y) end)
#Nx.Tensor<
  s64
  6
>

iex> Nx.reduce(Nx.tensor([[1.0, 2.0], [3.0, 4.0]]), 0, fn x, y -> Nx.add(x, y) end)
#Nx.Tensor<
  f32
  10.0
>

aggregating-over-axes

Aggregating over axes

iex> t = Nx.tensor([1, 2, 3], names: [:x])
iex> Nx.reduce(t, 0, [axes: [:x]], fn x, y -> Nx.add(x, y) end)
#Nx.Tensor<
  s64
  6
>

iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]], names: [:x, :y, :z])
iex> Nx.reduce(t, 0, [axes: [:x]], fn x, y -> Nx.add(x, y) end)
#Nx.Tensor<
  s64[y: 2][z: 3]
  [
    [8, 10, 12],
    [14, 16, 18]
  ]
>

iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]], names: [:x, :y, :z])
iex> Nx.reduce(t, 0, [axes: [:y]], fn x, y -> Nx.add(x, y) end)
#Nx.Tensor<
  s64[x: 2][z: 3]
  [
    [5, 7, 9],
    [17, 19, 21]
  ]
>

iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]], names: [:x, :y, :z])
iex> Nx.reduce(t, 0, [axes: [:x, 2]], fn x, y -> Nx.add(x, y) end)
#Nx.Tensor<
  s64[y: 2]
  [30, 48]
>

iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]], names: [:x, :y, :z])
iex> Nx.reduce(t, 0, [axes: [-1]], fn x, y -> Nx.add(x, y) end)
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [6, 15],
    [24, 33]
  ]
>

iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]], names: [:x, :y, :z])
iex> Nx.reduce(t, 0, [axes: [:x]], fn x, y -> Nx.add(x, y) end)
#Nx.Tensor<
  s64[y: 2][z: 3]
  [
    [8, 10, 12],
    [14, 16, 18]
  ]
>

iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]], names: [:x, :y, :z])
iex> Nx.reduce(t, 0, [axes: [:x], keep_axes: true], fn x, y -> Nx.add(x, y) end)
#Nx.Tensor<
  s64[x: 1][y: 2][z: 3]
  [
    [
      [8, 10, 12],
      [14, 16, 18]
    ]
  ]
>
Link to this function

reduce_max(tensor, opts \\ [])

View Source

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

Examples

iex> Nx.reduce_max(Nx.tensor(42))
#Nx.Tensor<
  s64
  42
>

iex> Nx.reduce_max(Nx.tensor(42.0))
#Nx.Tensor<
  f32
  42.0
>

iex> Nx.reduce_max(Nx.tensor([1, 2, 3]))
#Nx.Tensor<
  s64
  3
>

aggregating-over-an-axis

Aggregating over an axis

iex> t = Nx.tensor([[3, 1, 4], [2, 1, 1]], names: [:x, :y])
iex> Nx.reduce_max(t, axes: [:x])
#Nx.Tensor<
  s64[y: 3]
  [3, 1, 4]
>

iex> t = Nx.tensor([[3, 1, 4], [2, 1, 1]], names: [:x, :y])
iex> Nx.reduce_max(t, axes: [:y])
#Nx.Tensor<
  s64[x: 2]
  [4, 2]
>

iex> t = Nx.tensor([[[1, 2], [4, 5]], [[2, 4], [3, 8]]], names: [:x, :y, :z])
iex> Nx.reduce_max(t, axes: [:x, :z])
#Nx.Tensor<
  s64[y: 2]
  [4, 8]
>

keeping-axes

Keeping axes

iex> t = Nx.tensor([[[1, 2], [4, 5]], [[2, 4], [3, 8]]], names: [:x, :y, :z])
iex> Nx.reduce_max(t, axes: [:x, :z], keep_axes: true)
#Nx.Tensor<
  s64[x: 1][y: 2][z: 1]
  [
    [
      [4],
      [8]
    ]
  ]
>
Link to this function

reduce_min(tensor, opts \\ [])

View Source

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

Examples

iex> Nx.reduce_min(Nx.tensor(42))
#Nx.Tensor<
  s64
  42
>

iex> Nx.reduce_min(Nx.tensor(42.0))
#Nx.Tensor<
  f32
  42.0
>

iex> Nx.reduce_min(Nx.tensor([1, 2, 3]))
#Nx.Tensor<
  s64
  1
>

aggregating-over-an-axis

Aggregating over an axis

iex> t = Nx.tensor([[3, 1, 4], [2, 1, 1]], names: [:x, :y])
iex> Nx.reduce_min(t, axes: [:x])
#Nx.Tensor<
  s64[y: 3]
  [2, 1, 1]
>

iex> t = Nx.tensor([[3, 1, 4], [2, 1, 1]], names: [:x, :y])
iex> Nx.reduce_min(t, axes: [:y])
#Nx.Tensor<
  s64[x: 2]
  [1, 1]
>

iex> t = Nx.tensor([[[1, 2], [4, 5]], [[2, 4], [3, 8]]], names: [:x, :y, :z])
iex> Nx.reduce_min(t, axes: [:x, :z])
#Nx.Tensor<
  s64[y: 2]
  [1, 3]
>

keeping-axes

Keeping axes

iex> t = Nx.tensor([[[1, 2], [4, 5]], [[2, 4], [3, 8]]], names: [:x, :y, :z])
iex> Nx.reduce_min(t, axes: [:x, :z], keep_axes: true)
#Nx.Tensor<
  s64[x: 1][y: 2][z: 1]
  [
    [
      [1],
      [3]
    ]
  ]
>
Link to this function

standard_deviation(tensor, opts \\ [])

View Source
@spec standard_deviation(tensor :: Nx.Tensor.t(), opts :: Keyword.t()) ::
  Nx.Tensor.t()

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

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], [3, 4]]), axes: [0])
#Nx.Tensor<
  f32[2]
  [1.0, 1.0]
>

iex> Nx.standard_deviation(Nx.tensor([[1, 2], [3, 4]]), axes: [1])
#Nx.Tensor<
  f32[2]
  [0.5, 0.5]
>

iex> Nx.standard_deviation(Nx.tensor([[1, 2], [3, 4]]), axes: [0], ddof: 1)
#Nx.Tensor<
  f32[2]
  [1.4142135381698608, 1.4142135381698608]
>

iex> Nx.standard_deviation(Nx.tensor([[1, 2], [3, 4]]), axes: [1], ddof: 1)
#Nx.Tensor<
  f32[2]
  [0.7071067690849304, 0.7071067690849304]
>

keeping-axes

Keeping axes

iex> Nx.standard_deviation(Nx.tensor([[1, 2], [3, 4]]), keep_axes: true)
#Nx.Tensor<
  f32[1][1]
  [
    [1.1180340051651]
  ]
>

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

Examples

iex> Nx.sum(Nx.tensor(42))
#Nx.Tensor<
  s64
  42
>

iex> Nx.sum(Nx.tensor([1, 2, 3], names: [:x]))
#Nx.Tensor<
  s64
  6
>

iex> Nx.sum(Nx.tensor([[1.0, 2.0], [3.0, 4.0]], names: [:x, :y]))
#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, names: [:x, :y]))
#Nx.Tensor<
  s64
  410
>

iex> Nx.sum(Nx.tensor([[101, 102], [103, 104]], type: :s16, names: [:x, :y]))
#Nx.Tensor<
  s64
  410
>

aggregating-over-an-axis

Aggregating over an axis

iex> Nx.sum(Nx.tensor([1, 2, 3], names: [:x]), axes: [0])
#Nx.Tensor<
  s64
  6
>

Same tensor over different axes combinations:

iex> t = Nx.tensor(
...>   [
...>     [
...>       [1, 2, 3],
...>       [4, 5, 6]
...>     ],
...>     [
...>       [7, 8, 9],
...>       [10, 11, 12]
...>     ]
...>   ],
...>   names: [:x, :y, :z]
...> )
iex> Nx.sum(t, axes: [:x])
#Nx.Tensor<
  s64[y: 2][z: 3]
  [
    [8, 10, 12],
    [14, 16, 18]
  ]
>
iex> Nx.sum(t, axes: [:y])
#Nx.Tensor<
  s64[x: 2][z: 3]
  [
    [5, 7, 9],
    [17, 19, 21]
  ]
>
iex> Nx.sum(t, axes: [:z])
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [6, 15],
    [24, 33]
  ]
>
iex> Nx.sum(t, axes: [:x, :z])
#Nx.Tensor<
  s64[y: 2]
  [30, 48]
>
iex> Nx.sum(t, axes: [:z])
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [6, 15],
    [24, 33]
  ]
>
iex> Nx.sum(t, axes: [-3])
#Nx.Tensor<
  s64[y: 2][z: 3]
  [
    [8, 10, 12],
    [14, 16, 18]
  ]
>

keeping-axes

Keeping axes

iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]], names: [:x, :y, :z])
iex> Nx.sum(t, axes: [:z], keep_axes: true)
#Nx.Tensor<
  s64[x: 2][y: 2][z: 1]
  [
    [
      [6],
      [15]
    ],
    [
      [24],
      [33]
    ]
  ]
>

errors

Errors

iex> Nx.sum(Nx.tensor([[1, 2]]), axes: [2])
** (ArgumentError) given axis (2) invalid for shape with rank 2
Link to this function

variance(tensor, opts \\ [])

View Source
@spec variance(tensor :: Nx.Tensor.t(), opts :: Keyword.t()) :: Nx.Tensor.t()

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

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

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]
  ]
>
Link to this function

weighted_mean(tensor, weights, opts \\ [])

View Source

Returns the weighted mean for the tensor and the weights.

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 averaged axis to size 1.

examples

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-an-axis

Aggregating over an axis

iex> Nx.weighted_mean(Nx.tensor([1, 2, 3], names: [:x]), Nx.tensor([4, 5, 6]), axis: 0)
#Nx.Tensor<
  f32
  2.133333444595337
>

iex> Nx.weighted_mean(Nx.tensor([1,2,3], type: :u8, names: [:x]), Nx.tensor([1,3,5]), axis: :x)
#Nx.Tensor<
  f32
  2.444444417953491
>

iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]], 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, axis: :x)
#Nx.Tensor<
  f32[y: 2][z: 3]
  [
    [7.0, 5.0, -3.0],
    [7.0, 8.0, 12.0]
  ]
>

iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]], 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, axis: -1)
#Nx.Tensor<
  f32[x: 2][y: 2]
  [
    [2.6666667461395264, 4.5],
    [8.0, 9.0]
  ]
>

iex> t = Nx.iota({3,4})
iex> weights = Nx.tensor([1, 2, 3, 4])
iex> Nx.weighted_mean(t, weights, axis: 1)
#Nx.Tensor<
  f32[3]
  [2.0, 6.0, 10.0]
>

keeping-axis

Keeping axis

iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]], 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, axis: -1, keep_axis: true)
#Nx.Tensor<
  f32[x: 2][y: 2][z: 1]
  [
    [
      [2.6666667461395264],
      [4.5]
    ],
    [
      [8.0],
      [9.0]
    ]
  ]
>

Link to this section Functions: Backend

Link to this function

backend_copy(tensor_or_container, backend \\ Nx.Tensor)

View Source

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.

For convenience, this function accepts tensors and any container (such as maps and tuples as defined by the Nx.Container protocol) and recursively copies all tensors in them. This behaviour exists as it is common to transfer data before and after defn functions.

*Note: Nx.default_backend/1 does not affect the behaviour of this function.

examples

Examples

iex> Nx.backend_copy(Nx.tensor([[1, 2, 3], [4, 5, 6]])) #Nx.Tensor<

s64[2][3]
[
  [1, 2, 3],
  [4, 5, 6]
]
Link to this function

backend_deallocate(tensor_or_container)

View Source

Deallocates data in a device.

It returns either :ok or :already_deallocated.

For convenience, this function accepts tensors and any container (such as maps and tuples as defined by the Nx.Container protocol) and deallocates all devices in them. This behaviour exists as it is common to deallocate data after defn functions.

Link to this function

backend_transfer(tensor_or_container, backend \\ Nx.Tensor)

View Source

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.

For convenience, this function accepts tensors and any container (such as maps and tuples as defined by the Nx.Container protocol) and transfers all tensors in them. This behaviour exists as it is common to transfer data from tuples and maps before and after defn functions.

*Note: Nx.default_backend/1 does not affect the behaviour of this function.

examples

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)

Gets the default backend for the current process.

Link to this function

default_backend(backend)

View Source

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.

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.

examples

Examples

iex> Nx.default_backend({EXLA.Backend, device: :cuda})
{Nx.BinaryBackend, []}
iex> Nx.default_backend()
{EXLA.Backend, device: :cuda}
Link to this function

global_default_backend(backend)

View Source

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}]]
)

Link to this section Functions: Conversion

Link to this function

deserialize(data, opts \\ [])

View Source

Deserializes a serialized representation of a tensor or a container with the given options.

It is the opposite of Nx.serialize/2.

examples

Examples

iex> a = Nx.tensor([1, 2, 3])
iex> serialized_a = Nx.serialize(a)
iex> Nx.deserialize(serialized_a)
#Nx.Tensor<
  s64[3]
  [1, 2, 3]
>

iex> container = {Nx.tensor([1, 2, 3]), %{b: Nx.tensor([4, 5, 6])}}
iex> serialized_container = Nx.serialize(container)
iex> {a, %{b: b}} = Nx.deserialize(serialized_container)
iex> a
#Nx.Tensor<
  s64[3]
  [1, 2, 3]
>
iex> b
#Nx.Tensor<
  s64[3]
  [4, 5, 6]
>

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.

Link to this function

from_numpy_archive(archive)

View Source

Loads a .npz archive into a list of tensors.

An .npz file is a zipped, possibly compressed archive containing multiple .npy files.

Link to this function

serialize(tensor_or_container, opts \\ [])

View Source

Serializes the given tensor or container of tensors to iodata.

You may pass a tensor, tuple, or map to serialize.

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.

examples

Examples

iex> a = Nx.tensor([1, 2, 3])
iex> serialized_a = Nx.serialize(a)
iex> Nx.deserialize(serialized_a)
#Nx.Tensor<
  s64[3]
  [1, 2, 3]
>

iex> container = {Nx.tensor([1, 2, 3]), %{b: Nx.tensor([4, 5, 6])}}
iex> serialized_container = Nx.serialize(container)
iex> {a, %{b: b}} = Nx.deserialize(serialized_container)
iex> a
#Nx.Tensor<
  s64[3]
  [1, 2, 3]
>
iex> b
#Nx.Tensor<
  s64[3]
  [4, 5, 6]
>
Link to this function

to_batched(tensor, batch_size, opts \\ [])

View Source

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.

examples

Examples

In the examples below we immediately pipe to Enum.to_list/1 for convenience, but in practice you want to lazily traverse the batches to avoid allocating multiple tensors at once in certain backends:

iex> [first, second] = Nx.to_batched(Nx.iota({2, 2, 2}), 1) |> Enum.to_list()
iex> first
#Nx.Tensor<
  s64[1][2][2]
  [
    [
      [0, 1],
      [2, 3]
    ]
  ]
>
iex> second
#Nx.Tensor<
  s64[1][2][2]
  [
    [
      [4, 5],
      [6, 7]
    ]
  ]
>

If the batch size would result in uneven batches, you can repeat or discard excess data. By default, we repeat:

iex> [first, second, third] = Nx.to_batched(Nx.iota({5, 2}, names: [:x, :y]), 2) |> Enum.to_list()
iex> first
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [0, 1],
    [2, 3]
  ]
>
iex> second
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [4, 5],
    [6, 7]
  ]
>
iex> third
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [8, 9],
    [0, 1]
  ]
>

But you can also discard:

iex> [first, second] = Nx.to_batched(Nx.iota({5, 2}, names: [:x, :y]), 2, leftover: :discard) |> Enum.to_list()
iex> first
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [0, 1],
    [2, 3]
  ]
>
iex> second
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [4, 5],
    [6, 7]
  ]
>
Link to this function

to_batched_list(tensor, batch_size, opts \\ [])

View Source
This function is deprecated. Use to_batched/3 instead.
Link to this function

to_binary(tensor, opts \\ [])

View Source

Returns the underlying tensor as a binary.

Warning: converting a tensor to a binary can potentially be a very expensive operation, as it may copy a GPU tensor fully to the machine memory.

It returns the in-memory binary representation of the tensor in a row-major fashion. The binary is in the system endianness, which has to be taken into account if the binary is meant to be serialized to other systems.

options

Options

  • :limit - limit the number of entries represented in the binary

examples

Examples

iex> Nx.to_binary(1)
<<1::64-native>>

iex> Nx.to_binary(Nx.tensor([1.0, 2.0, 3.0]))
<<1.0::float-32-native, 2.0::float-32-native, 3.0::float-32-native>>

iex> Nx.to_binary(Nx.tensor([1.0, 2.0, 3.0]), limit: 2)
<<1.0::float-32-native, 2.0::float-32-native>>
Link to this function

to_flat_list(tensor, opts \\ [])

View Source

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.

examples

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]
Link to this function

to_heatmap(tensor, opts \\ [])

View Source

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

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

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

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, it raises.

examples

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
Link to this function

to_template(tensor_or_container)

View Source

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.Container protocol) and recursively converts all tensors to templates.

examples

Examples

iex> Nx.iota({2, 3}) |> Nx.to_template()
#Nx.Tensor<
  s64[2][3]
  Nx.TemplateBackend
>

iex> {int, float} = Nx.to_template({1, 2.0})
iex> int
#Nx.Tensor<
  s64
  Nx.TemplateBackend
>
iex> float
#Nx.Tensor<
  f32
  Nx.TemplateBackend
>

Although note it is impossible to perform any operation on a tensor template:

iex> t = Nx.iota({2, 3}) |> Nx.to_template()
iex> Nx.abs(t)
** (RuntimeError) cannot perform operations on a Nx.TemplateBackend tensor

To build a template from scratch, use template/3.

Converts the given number (or tensor) to a tensor.

The Nx API works with numbers, complex numbers, and tensors. This function exists to normalize those values into tensors (i.e. Nx.Tensor structs).

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.

Link to this section Functions: Creation

Link to this function

eye(n_or_tensor_or_shape, opts \\ [])

View Source

Creates the identity matrix of size n.

examples

Examples

iex> Nx.eye(2)
#Nx.Tensor<
  s64[2][2]
  [
    [1, 0],
    [0, 1]
  ]
>

iex> Nx.eye(3, type: :f32, names: [:height, :width])
#Nx.Tensor<
  f32[height: 3][width: 3]
  [
    [1.0, 0.0, 0.0],
    [0.0, 1.0, 0.0],
    [0.0, 0.0, 1.0]
  ]
>

The first argument can also be a shape of a matrix:

iex> Nx.eye({1, 2})
#Nx.Tensor<
  s64[1][2]
  [
    [1, 0]
  ]
>

The shape can also represent a tensor batch. In this case, the last two axes will represent the same identity matrix.

iex> Nx.eye({2, 4, 3})
#Nx.Tensor<
  s64[2][4][3]
  [
    [
      [1, 0, 0],
      [0, 1, 0],
      [0, 0, 1],
      [0, 0, 0]
    ],
    [
      [1, 0, 0],
      [0, 1, 0],
      [0, 0, 1],
      [0, 0, 0]
    ]
  ]
>

options

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

Link to this function

from_binary(binary, type, opts \\ [])

View Source

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

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

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
Link to this function

iota(tensor_or_shape, opts \\ [])

View Source

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.

examples

Examples

iex> Nx.iota({})
#Nx.Tensor<
  s64
  0
>

iex> Nx.iota({5})
#Nx.Tensor<
  s64[5]
  [0, 1, 2, 3, 4]
>

iex> Nx.iota({3, 2, 3}, names: [:batch, :height, :width])
#Nx.Tensor<
  s64[batch: 3][height: 2][width: 3]
  [
    [
      [0, 1, 2],
      [3, 4, 5]
    ],
    [
      [6, 7, 8],
      [9, 10, 11]
    ],
    [
      [12, 13, 14],
      [15, 16, 17]
    ]
  ]
>

iex> Nx.iota({3, 3}, axis: 1, names: [:batch, nil])
#Nx.Tensor<
  s64[batch: 3][3]
  [
    [0, 1, 2],
    [0, 1, 2],
    [0, 1, 2]
  ]
>

iex> Nx.iota({3, 3}, axis: -1)
#Nx.Tensor<
  s64[3][3]
  [
    [0, 1, 2],
    [0, 1, 2],
    [0, 1, 2]
  ]
>

iex> Nx.iota({3, 4, 3}, axis: 0, type: :f64)
#Nx.Tensor<
  f64[3][4][3]
  [
    [
      [0.0, 0.0, 0.0],
      [0.0, 0.0, 0.0],
      [0.0, 0.0, 0.0],
      [0.0, 0.0, 0.0]
    ],
    [
      [1.0, 1.0, 1.0],
      [1.0, 1.0, 1.0],
      [1.0, 1.0, 1.0],
      [1.0, 1.0, 1.0]
    ],
    [
      [2.0, 2.0, 2.0],
      [2.0, 2.0, 2.0],
      [2.0, 2.0, 2.0],
      [2.0, 2.0, 2.0]
    ]
  ]
>

iex> Nx.iota({1, 3, 2}, axis: 2)
#Nx.Tensor<
  s64[1][3][2]
  [
    [
      [0, 1],
      [0, 1],
      [0, 1]
    ]
  ]
>

options

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

Link to this function

make_diagonal(tensor, opts \\ [])

View Source

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.

examples

Examples

Given a 1D tensor:

iex> Nx.make_diagonal(Nx.tensor([1, 2, 3, 4]))
#Nx.Tensor<
  s64[4][4]
  [
    [1, 0, 0, 0],
    [0, 2, 0, 0],
    [0, 0, 3, 0],
    [0, 0, 0, 4]
  ]
>

Given a 1D tensor with an offset:

iex> Nx.make_diagonal(Nx.tensor([1, 2, 3]), offset: 1)
#Nx.Tensor<
  s64[4][4]
  [
    [0, 1, 0, 0],
    [0, 0, 2, 0],
    [0, 0, 0, 3],
    [0, 0, 0, 0]
  ]
>

iex> Nx.make_diagonal(Nx.tensor([1, 2, 3]), offset: -1)
#Nx.Tensor<
  s64[4][4]
  [
    [0, 0, 0, 0],
    [1, 0, 0, 0],
    [0, 2, 0, 0],
    [0, 0, 3, 0]
  ]
>

You can also have offsets with an abs greater than the tensor length:

iex> Nx.make_diagonal(Nx.tensor([1, 2, 3]), offset: -4)
#Nx.Tensor<
  s64[7][7]
  [
    [0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0],
    [1, 0, 0, 0, 0, 0, 0],
    [0, 2, 0, 0, 0, 0, 0],
    [0, 0, 3, 0, 0, 0, 0]
  ]
>

iex> Nx.make_diagonal(Nx.tensor([1, 2, 3]), offset: 4)
#Nx.Tensor<
  s64[7][7]
  [
    [0, 0, 0, 0, 1, 0, 0],
    [0, 0, 0, 0, 0, 2, 0],
    [0, 0, 0, 0, 0, 0, 3],
    [0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0]
  ]
>

options

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.

error-cases

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
Link to this function

put_diagonal(tensor, diagonal, opts \\ [])

View Source

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

Examples

Given a 2D tensor and a 1D diagonal:

iex> t = Nx.broadcast(0, {4, 4})
#Nx.Tensor<
  s64[4][4]
  [
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0]
  ]
>
iex> Nx.put_diagonal(t, Nx.tensor([1, 2, 3, 4]))
#Nx.Tensor<
  s64[4][4]
  [
    [1, 0, 0, 0],
    [0, 2, 0, 0],
    [0, 0, 3, 0],
    [0, 0, 0, 4]
  ]
>

iex> t = Nx.broadcast(0, {4, 3})
#Nx.Tensor<
  s64[4][3]
  [
    [0, 0, 0],
    [0, 0, 0],
    [0, 0, 0],
    [0, 0, 0]
  ]
>
iex> Nx.put_diagonal(t, Nx.tensor([1, 2, 3]))
#Nx.Tensor<
  s64[4][3]
  [
    [1, 0, 0],
    [0, 2, 0],
    [0, 0, 3],
    [0, 0, 0]
  ]
>

Given a 2D tensor and a 1D diagonal with a positive offset:

iex> Nx.put_diagonal(Nx.broadcast(0, {4, 4}), Nx.tensor([1, 2, 3]), offset: 1)
#Nx.Tensor<
  s64[4][4]
  [
    [0, 1, 0, 0],
    [0, 0, 2, 0],
    [0, 0, 0, 3],
    [0, 0, 0, 0]
  ]
>

iex> Nx.put_diagonal(Nx.broadcast(0, {4, 3}), Nx.tensor([1, 2]), offset: 1)
#Nx.Tensor<
  s64[4][3]
  [
    [0, 1, 0],
    [0, 0, 2],
    [0, 0, 0],
    [0, 0, 0]
  ]
>

Given a 2D tensor and a 1D diagonal with a negative offset:

iex> Nx.put_diagonal(Nx.broadcast(0, {4, 4}), Nx.tensor([1, 2, 3]), offset: -1)
#Nx.Tensor<
  s64[4][4]
  [
    [0, 0, 0, 0],
    [1, 0, 0, 0],
    [0, 2, 0, 0],
    [0, 0, 3, 0]
  ]
>

iex> Nx.put_diagonal(Nx.broadcast(0, {4, 3}), Nx.tensor([1, 2, 3]), offset: -1)
#Nx.Tensor<
  s64[4][3]
  [
    [0, 0, 0],
    [1, 0, 0],
    [0, 2, 0],
    [0, 0, 3]
  ]
>

options

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

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
Link to this function

random_normal(tensor_or_shape, opts \\ [])

View Source
This function is deprecated. Use Nx.Random instead.

Shortcut for random_normal(shape, 0.0, 1.0, opts).

Link to this function

random_normal(tensor_or_shape, mu, sigma, opts \\ [])

View Source
This function is deprecated. Use Nx.Random instead.

Returns a normally-distributed random tensor with the given shape.

The distribution has mean of mu and standard deviation of sigma. Return type is one of {:bf, 16}, {:f, 32} or {:f, 64}.

If a tensor or a number are given, the shape is taken from the tensor.

examples

Examples

iex> t = Nx.random_normal({10})
iex> Nx.shape(t)
{10}
iex> Nx.type(t)
{:f, 32}

iex> t = Nx.random_normal({5, 5}, 2.0, 1.0, type: :bf16)
iex> Nx.shape(t)
{5, 5}
iex> Nx.type(t)
{:bf, 16}

iex> t = Nx.random_normal({3, 3, 3}, -1.0, 1.0, type: :f32)
iex> Nx.shape(t)
{3, 3, 3}
iex> Nx.type(t)
{:f, 32}

If given a tensor as a shape, it takes the shape, names, and default type from the tensor:

iex> t = Nx.tensor([[1.0, 2.0], [3.0, 4.0]], names: [:batch, :data])
iex> t = Nx.random_normal(t)
iex> Nx.shape(t)
{2, 2}
iex> Nx.type(t)
{:f, 32}
iex> Nx.names(t)
[:batch, :data]

iex> t = Nx.tensor([[1.0, 2.0], [3.0, 4.0]])
iex> t = Nx.random_normal(t, type: :f32)
iex> Nx.shape(t)
{2, 2}
iex> Nx.type(t)
{:f, 32}
iex> Nx.names(t)
[nil, nil]

The same applies to numbers:

iex> t = Nx.random_normal(10.0)
iex> Nx.shape(t)
{}
iex> Nx.type(t)
{:f, 32}
iex> Nx.names(t)
[]

If you pass the :names option, the resulting tensor will take on those names:

iex> t = Nx.tensor([[1, 2], [3, 4]], names: [:batch, :data])
iex> t = Nx.random_normal(t, names: [:batch, nil])
iex> Nx.shape(t)
{2, 2}
iex> Nx.type(t)
{:f, 32}
iex> Nx.names(t)
[:batch, nil]

options

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

Link to this function

random_uniform(tensor_or_shape, opts \\ [])

View Source
This function is deprecated. Use Nx.Random.uniform/2 instead.

Shortcut for random_uniform(shape, 0.0, 1.0, opts).

Link to this function

random_uniform(tensor_or_shape, min, max, opts \\ [])

View Source
This function is deprecated. Use Nx.Random.uniform/2 instead.

Returns a uniformly-distributed random tensor with the given shape.

The distribution is bounded on the semi-open interval [min, max). If min and max are integers, then the tensor has type {:s, 64}. Otherwise, a {:f, 64} tensor is returned. You can also pass any valid type via the :type option.

If a tensor or a number are given, the shape and default type are taken from them.

examples

Examples

generating-floats

Generating Floats

iex> t = Nx.random_uniform({10})
iex> for <<x::float-32-native <- Nx.to_binary(t)>> do
...>   true = x >= 0.0 and x < 1.0
...> end
iex> Nx.shape(t)
{10}
iex> Nx.type(t)
{:f, 32}

iex> t = Nx.random_uniform({5, 5}, type: :bf16)
iex> byte_size(Nx.to_binary(t))
50
iex> Nx.shape(t)
{5, 5}
iex> Nx.type(t)
{:bf, 16}

iex> t = Nx.random_uniform({5, 5}, -1.0, 1.0, type: :f64)
iex> for <<x::float-64-native <- Nx.to_binary(t)>> do
...>   true = x >= -1.0 and x < 1.0
...> end
iex> Nx.shape(t)
{5, 5}
iex> Nx.type(t)
{:f, 64}

generating-integers

Generating Integers

iex> t = Nx.random_uniform({10}, 5, 10, type: :u8)
iex> for <<x::8-unsigned-native <- Nx.to_binary(t)>> do
...>   true = x >= 5 and x < 10
...> end
iex> Nx.shape(t)
{10}
iex> Nx.type(t)
{:u, 8}

iex> t = Nx.random_uniform({5, 5}, -5, 5, type: :s64)
iex> for <<x::64-signed-native <- Nx.to_binary(t)>> do
...>   true = x >= -5 and x < 5
...> end
iex> Nx.shape(t)
{5, 5}
iex> Nx.type(t)
{:s, 64}

tensors-as-shapes

Tensors as shapes

If given a tensor as a shape, it takes the shape and names from the tensor:

iex> t = Nx.tensor([[1, 2], [3, 4]], names: [:batch, :data])
iex> t = Nx.random_uniform(t)
iex> Nx.shape(t)
{2, 2}
iex> Nx.type(t)
{:f, 32}
iex> Nx.names(t)
[:batch, :data]

iex> t = Nx.tensor([[1, 2], [3, 4]])
iex> t = Nx.random_uniform(t, type: :f32)
iex> Nx.shape(t)
{2, 2}
iex> Nx.type(t)
{:f, 32}
iex> Nx.names(t)
[nil, nil]

The same applies to numbers:

iex> t = Nx.random_uniform(10)
iex> Nx.shape(t)
{}
iex> Nx.type(t)
{:f, 32}

iex> t = Nx.random_uniform(10.0)
iex> Nx.shape(t)
{}
iex> Nx.type(t)
{:f, 32}
iex> Nx.names(t)
[]

If you pass :names as an option, the resulting tensor will take on those names:

iex> t = Nx.tensor([[1, 2], [3, 4]], names: [:batch, :data])
iex> t = Nx.random_uniform(t, names: [:batch, nil])
iex> Nx.shape(t)
{2, 2}
iex> Nx.type(t)
{:f, 32}
iex> Nx.names(t)
[:batch, nil]

options

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

Link to this function

shuffle(tensor, opts \\ [])

View Source

Shuffles tensor elements.

By default, shuffles elements within the whole tensor. When :axis is given, shuffles the tensor along the specific axis instead.

options

Options

  • :axis - the axis to shuffle along

examples

Examples

Shuffling all elements:

t = Nx.tensor([[1, 2], [3, 4], [5, 6]])
Nx.shuffle(t)
#=>
#Nx.Tensor<
  s64[3][2]
  [
    [5, 1],
    [2, 3],
    [6, 4]
  ]
>

Shuffling rows in a two-dimensional tensor:

t = Nx.tensor([[1, 2], [3, 4], [5, 6]])
Nx.shuffle(t, axis: 0)
#=>
#Nx.Tensor<
  s64[3][2]
  [
    [5, 6],
    [1, 2],
    [3, 4]
  ]
>
Link to this macro

sigil_M(arg, modifiers)

View Source (macro)

A convenient ~M sigil for building matrices (two-dimensional tensors).

examples

Examples

Before using sigils, you must first import them:

import Nx, only: :sigils

Then you use the sigil to create matrices. The sigil:

~M<
  -1 0 0 1
  0 2 0 0
  0 0 3 0
  0 0 0 4
>

Is equivalent to:

Nx.tensor([
  [-1, 0, 0, 1],
  [0, 2, 0, 0],
  [0, 0, 3, 0],
  [0, 0, 0, 4]
])

If the tensor has any complex type, it defaults to c64. If the tensor has any float type, it defaults to f32. Otherwise, it is s64. You can specify the tensor type as a sigil modifier:

iex> import Nx, only: :sigils
iex> ~M[0.1 0.2 0.3 0.4]f16
#Nx.Tensor<
  f16[1][4]
  [
    [0.0999755859375, 0.199951171875, 0.300048828125, 0.39990234375]
  ]
>
iex> ~M[1+1i 2-2.0i -3]
#Nx.Tensor<
  c64[1][3]
  [
    [1.0+1.0i, 2.0-2.0i, -3.0+0.0i]
  ]
>
iex> ~M[1 Inf NaN]
#Nx.Tensor<
  f32[1][3]
  [
    [1.0, Inf, NaN]
  ]
>
iex> ~M[1i Inf NaN]
#Nx.Tensor<
  c64[1][3]
  [
    [0.0+1.0i, Inf+0.0i, NaN+0.0i]
  ]
>
iex> ~M[1i Inf+2i NaN-Infi]
#Nx.Tensor<
  c64[1][3]
  [
    [0.0+1.0i, Inf+2.0i, NaN-Infi]
  ]
>
Link to this macro

sigil_V(arg, modifiers)

View Source (macro)

A convenient ~V sigil for building vectors (one-dimensional tensors).

examples

Examples

Before using sigils, you must first import them:

import Nx, only: :sigils

Then you use the sigil to create vectors. The sigil:

~V[-1 0 0 1]

Is equivalent to:

Nx.tensor([-1, 0, 0, 1])

If the tensor has any complex type, it defaults to c64. If the tensor has any float type, it defaults to f32. Otherwise, it is s64. You can specify the tensor type as a sigil modifier:

iex> import Nx, only: :sigils
iex> ~V[0.1 0.2 0.3 0.4]f16
#Nx.Tensor<
  f16[4]
  [0.0999755859375, 0.199951171875, 0.300048828125, 0.39990234375]
>
iex> ~V[1+1i 2-2.0i -3]
#Nx.Tensor<
  c64[3]
  [1.0+1.0i, 2.0-2.0i, -3.0+0.0i]
>
iex> ~V[1 Inf NaN]
#Nx.Tensor<
  f32[3]
  [1.0, Inf, NaN]
>
iex> ~V[1i Inf NaN]
#Nx.Tensor<
  c64[3]
  [0.0+1.0i, Inf+0.0i, NaN+0.0i]
>
iex> ~V[1i Inf+2i NaN-Infi]
#Nx.Tensor<
  c64[3]
  [0.0+1.0i, Inf+2.0i, NaN-Infi]
>
Link to this function

take_diagonal(tensor, opts \\ [])

View Source

Extracts the diagonal of batched matrices.

Converse of make_diagonal/2.

examples

Examples

Given a matrix without offset:

iex> Nx.take_diagonal(Nx.tensor([
...> [0, 1, 2],
...> [3, 4, 5],
...> [6, 7, 8]
...> ]))
#Nx.Tensor<
  s64[3]
  [0, 4, 8]
>

And if given a matrix along with an offset:

iex> Nx.take_diagonal(Nx.iota({3, 3}), offset: 1)
#Nx.Tensor<
  s64[2]
  [1, 5]
>

iex> Nx.take_diagonal(Nx.iota({3, 3}), offset: -1)
#Nx.Tensor<
  s64[2]
  [3, 7]
>

Given batched matrix:

iex> Nx.take_diagonal(Nx.iota({3, 2, 2}))
#Nx.Tensor<
  s64[3][2]
  [
    [0, 3],
    [4, 7],
    [8, 11]
  ]
>

iex> Nx.take_diagonal(Nx.iota({3, 2, 2}), offset: -1)
#Nx.Tensor<
  s64[3][1]
  [
    [2],
    [6],
    [10]
  ]
>

options

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

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
Link to this function

template(shape, type, opts \\ [])

View Source

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

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.

Builds a tensor.

The argument is either a number, which means the tensor is a scalar (zero-dimensions), a list of those (the tensor is a vector) or a list of n-lists of those, leading to n-dimensional tensors. The tensor will be allocated in Nx.default_backend/0, unless the :backend option is given, which overrides the default one.

examples

Examples

A number returns a tensor of zero dimensions:

iex> Nx.tensor(0)
#Nx.Tensor<
  s64
  0
>

iex> Nx.tensor(1.0)
#Nx.Tensor<
  f32
  1.0
>

Giving a list returns a vector (a one-dimensional tensor):

iex> Nx.tensor([1, 2, 3])
#Nx.Tensor<
  s64[3]
  [1, 2, 3]
>

iex> Nx.tensor([1.2, 2.3, 3.4, 4.5])
#Nx.Tensor<
  f32[4]
  [1.2000000476837158, 2.299999952316284, 3.4000000953674316, 4.5]
>

The type can be explicitly given. Integers and floats bigger than the given size overflow:

iex> Nx.tensor([300, 301, 302], type: :s8)
#Nx.Tensor<
  s8[3]
  [44, 45, 46]
>

Mixed types give higher priority to floats:

iex> Nx.tensor([1, 2, 3.0])
#Nx.Tensor<
  f32[3]
  [1.0, 2.0, 3.0]
>

Boolean values are also accepted, where true is converted to 1 and false to 0, with the type being inferred as {:u, 8}

iex> Nx.tensor(true)
#Nx.Tensor<
  u8
  1
>

iex> Nx.tensor(false)
#Nx.Tensor<
  u8
  0
>

iex> Nx.tensor([true, false])
#Nx.Tensor<
  u8[2]
  [1, 0]
>

Multi-dimensional tensors are also possible:

iex> Nx.tensor([[1, 2, 3], [4, 5, 6]])
#Nx.Tensor<
  s64[2][3]
  [
    [1, 2, 3],
    [4, 5, 6]
  ]
>

iex> Nx.tensor([[1, 2], [3, 4], [5, 6]])
#Nx.Tensor<
  s64[3][2]
  [
    [1, 2],
    [3, 4],
    [5, 6]
  ]
>

iex> Nx.tensor([[[1, 2], [3, 4], [5, 6]], [[-1, -2], [-3, -4], [-5, -6]]])
#Nx.Tensor<
  s64[2][3][2]
  [
    [
      [1, 2],
      [3, 4],
      [5, 6]
    ],
    [
      [-1, -2],
      [-3, -4],
      [-5, -6]
    ]
  ]
>

floats-and-complex-numbers

Floats and complex numbers

Besides single-precision (32 bits), floats can also have half-precision (16) or double-precision (64):

iex> Nx.tensor([1, 2, 3], type: :f16)
#Nx.Tensor<
  f16[3]
  [1.0, 2.0, 3.0]
>

iex> Nx.tensor([1, 2, 3], type: :f64)
#Nx.Tensor<
  f64[3]
  [1.0, 2.0, 3.0]
>

Brain-floating points are also supported:

iex> Nx.tensor([1, 2, 3], type: :bf16)
#Nx.Tensor<
  bf16[3]
  [1.0, 2.0, 3.0]
>

In all cases, the non-finite values negative infinity (-Inf), infinity (Inf), and "not a number" (NaN) can be represented by the atoms :neg_infinity, :infinity, and :nan respectively:

iex> Nx.tensor([:neg_infinity, :nan, :infinity])
#Nx.Tensor<
  f32[3]
  [-Inf, NaN, Inf]
>

Finally, complex numbers are also supported in tensors:

iex> Nx.tensor(Complex.new(1, -1))
#Nx.Tensor<
  c64
  1.0-1.0i
>

naming-dimensions

Naming dimensions

You can provide names for tensor dimensions. Names are atoms:

iex> Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:x, :y])
#Nx.Tensor<
  s64[x: 2][y: 3]
  [
    [1, 2, 3],
    [4, 5, 6]
  ]
>

Names make your code more expressive:

iex> Nx.tensor([[[1, 2, 3], [4, 5, 6], [7, 8, 9]]], names: [:batch, :height, :width])
#Nx.Tensor<
  s64[batch: 1][height: 3][width: 3]
  [
    [
      [1, 2, 3],
      [4, 5, 6],
      [7, 8, 9]
    ]
  ]
>

You can also leave dimension names as nil:

iex> Nx.tensor([[[1, 2, 3], [4, 5, 6], [7, 8, 9]]], names: [:batch, nil, nil])
#Nx.Tensor<
  s64[batch: 1][3][3]
  [
    [
      [1, 2, 3],
      [4, 5, 6],
      [7, 8, 9]
    ]
  ]
>

However, you must provide a name for every dimension in the tensor:

iex> Nx.tensor([[[1, 2, 3], [4, 5, 6], [7, 8, 9]]], names: [:batch])
** (ArgumentError) invalid names for tensor of rank 3, when specifying names every dimension must have a name or be nil

options

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}. This option is ignored inside defn

Link to this section Functions: Cumulative

Link to this function

cumulative_max(tensor, opts \\ [])

View Source

Returns the cumulative maximum of elements along an axis.

options

Options

  • :axis - the axis to compare elements along. Defaults to 0
  • :reverse - whether to perform accumulation in the opposite direction. Defaults to false

examples

Examples

iex> Nx.cumulative_max(Nx.tensor([3, 4, 2, 1]))
#Nx.Tensor<
  s64[4]
  [3, 4, 4, 4]
>

iex> Nx.cumulative_max(Nx.tensor([[2, 3, 1], [1, 3, 2], [2, 1, 3]]), axis: 0)
#Nx.Tensor<
  s64[3][3]
  [
    [2, 3, 1],
    [2, 3, 2],
    [2, 3, 3]
  ]
>

iex> Nx.cumulative_max(Nx.tensor([[2, 3, 1], [1, 3, 2], [2, 1, 3]]), axis: 1)
#Nx.Tensor<
  s64[3][3]
  [
    [2, 3, 3],
    [1, 3, 3],
    [2, 2, 3]
  ]
>

iex> Nx.cumulative_max(Nx.tensor([[2, 3, 1], [1, 3, 2], [2, 1, 3]]), axis: 0, reverse: true)
#Nx.Tensor<
  s64[3][3]
  [
    [2, 3, 3],
    [2, 3, 3],
    [2, 1, 3]
  ]
>

iex> Nx.cumulative_max(Nx.tensor([[2, 3, 1], [1, 3, 2], [2, 1, 3]]), axis: 1, reverse: true)
#Nx.Tensor<
  s64[3][3]
  [
    [3, 3, 1],
    [3, 3, 2],
    [3, 3, 3]
  ]
>
Link to this function

cumulative_min(tensor, opts \\ [])

View Source

Returns the cumulative minimum of elements along an axis.

options

Options

  • :axis - the axis to compare elements along. Defaults to 0
  • :reverse - whether to perform accumulation in the opposite direction. Defaults to false

examples

Examples

iex> Nx.cumulative_min(Nx.tensor([3, 4, 2, 1]))
#Nx.Tensor<
  s64[4]
  [3, 3, 2, 1]
>

iex> Nx.cumulative_min(Nx.tensor([[2, 3, 1], [1, 3, 2], [2, 1, 3]]), axis: 0)
#Nx.Tensor<
  s64[3][3]
  [
    [2, 3, 1],
    [1, 3, 1],
    [1, 1, 1]
  ]
>

iex> Nx.cumulative_min(Nx.tensor([[2, 3, 1], [1, 3, 2], [2, 1, 3]]), axis: 1)
#Nx.Tensor<
  s64[3][3]
  [
    [2, 2, 1],
    [1, 1, 1],
    [2, 1, 1]
  ]
>

iex> Nx.cumulative_min(Nx.tensor([[2, 3, 1], [1, 3, 2], [2, 1, 3]]), axis: 0, reverse: true)
#Nx.Tensor<
  s64[3][3]
  [
    [1, 1, 1],
    [1, 1, 2],
    [2, 1, 3]
  ]
>

iex> Nx.cumulative_min(Nx.tensor([[2, 3, 1], [1, 3, 2], [2, 1, 3]]), axis: 1, reverse: true)
#Nx.Tensor<
  s64[3][3]
  [
    [1, 1, 1],
    [1, 2, 2],
    [1, 1, 3]
  ]
>
Link to this function

cumulative_product(tensor, opts \\ [])

View Source

Returns the cumulative product of elements along an axis.

options

Options

  • :axis - the axis to multiply elements along. Defaults to 0
  • :reverse - whether to perform accumulation in the opposite direction. Defaults to false

examples

Examples

iex> Nx.cumulative_product(Nx.tensor([1, 2, 3, 4]))
#Nx.Tensor<
  s64[4]
  [1, 2, 6, 24]
>

iex> Nx.cumulative_product(Nx.iota({3, 3}), axis: 0)
#Nx.Tensor<
  s64[3][3]
  [
    [0, 1, 2],
    [0, 4, 10],
    [0, 28, 80]
  ]
>

iex> Nx.cumulative_product(Nx.iota({3, 3}), axis: 1)
#Nx.Tensor<
  s64[3][3]
  [
    [0, 0, 0],
    [3, 12, 60],
    [6, 42, 336]
  ]
>

iex> Nx.cumulative_product(Nx.iota({3, 3}), axis: 0, reverse: true)
#Nx.Tensor<
  s64[3][3]
  [
    [0, 28, 80],
    [18, 28, 40],
    [6, 7, 8]
  ]
>

iex> Nx.cumulative_product(Nx.iota({3, 3}), axis: 1, reverse: true)
#Nx.Tensor<
  s64[3][3]
  [
    [0, 2, 2],
    [60, 20, 5],
    [336, 56, 8]
  ]
>
Link to this function

cumulative_sum(tensor, opts \\ [])

View Source

Returns the cumulative sum of elements along an axis.

options

Options

  • :axis - the axis to sum elements along. Defaults to 0
  • :reverse - whether to perform accumulation in the opposite direction. Defaults to false

examples

Examples

iex> Nx.cumulative_sum(Nx.tensor([1, 2, 3, 4]))
#Nx.Tensor<
  s64[4]
  [1, 3, 6, 10]
>

iex> Nx.cumulative_sum(Nx.iota({3, 3}), axis: 0)
#Nx.Tensor<
  s64[3][3]
  [
    [0, 1, 2],
    [3, 5, 7],
    [9, 12, 15]
  ]
>

iex> Nx.cumulative_sum(Nx.iota({3, 3}), axis: 1)
#Nx.Tensor<
  s64[3][3]
  [
    [0, 1, 3],
    [3, 7, 12],
    [6, 13, 21]
  ]
>

iex> Nx.cumulative_sum(Nx.iota({3, 3}), axis: 0, reverse: true)
#Nx.Tensor<
  s64[3][3]
  [
    [9, 12, 15],
    [9, 11, 13],
    [6, 7, 8]
  ]
>

iex> Nx.cumulative_sum(Nx.iota({3, 3}), axis: 1, reverse: true)
#Nx.Tensor<
  s64[3][3]
  [
    [3, 3, 2],
    [12, 9, 5],
    [21, 15, 8]
  ]
>

Link to this section Functions: Element-wise

Computes the absolute value of each element in the tensor.

examples

Examples

iex> Nx.abs(Nx.tensor([-2, -1, 0, 1, 2], names: [:x]))
#Nx.Tensor<
  s64[x: 5]
  [2, 1, 0, 1, 2]
>

Calculates the inverse cosine of each element in the tensor.

It is equivalent to:

$$acos(cos(z)) = z$$

examples

Examples

iex> Nx.acos(0.10000000149011612)
#Nx.Tensor<
  f32
  1.4706288576126099
>

iex> Nx.acos(Nx.tensor([0.10000000149011612, 0.5, 0.8999999761581421], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [1.4706288576126099, 1.0471975803375244, 0.4510268568992615]
>

Calculates the inverse hyperbolic cosine of each element in the tensor.

It is equivalent to:

$$acosh(cosh(z)) = z$$

examples

Examples

iex> Nx.acosh(1)
#Nx.Tensor<
  f32
  0.0
>

iex> Nx.acosh(Nx.tensor([1, 2, 3], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [0.0, 1.316957950592041, 1.7627471685409546]
>

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

Examples

adding-scalars

Adding scalars

iex> Nx.add(1, 2)
#Nx.Tensor<
  s64
  3
>

iex> Nx.add(1, 2.2)
#Nx.Tensor<
  f32
  3.200000047683716
>

adding-a-scalar-to-a-tensor

Adding a scalar to a tensor

iex> Nx.add(Nx.tensor([1, 2, 3], names: [:data]), 1)
#Nx.Tensor<
  s64[data: 3]
  [2, 3, 4]
>

iex> Nx.add(1, Nx.tensor([1, 2, 3], names: [:data]))
#Nx.Tensor<
  s64[data: 3]
  [2, 3, 4]
>

Given a float scalar converts the tensor to a float:

iex> Nx.add(Nx.tensor([1, 2, 3], names: [:data]), 1.0)
#Nx.Tensor<
  f32[data: 3]
  [2.0, 3.0, 4.0]
>

iex> Nx.add(Nx.tensor([1.0, 2.0, 3.0], names: [:data]), 1)
#Nx.Tensor<
  f32[data: 3]
  [2.0, 3.0, 4.0]
>

iex> Nx.add(Nx.tensor([1.0, 2.0, 3.0], type: :f32, names: [:data]), 1)
#Nx.Tensor<
  f32[data: 3]
  [2.0, 3.0, 4.0]
>

Unsigned tensors become signed and double their size if a negative number is given:

iex> Nx.add(Nx.tensor([0, 1, 2], type: :u8, names: [:data]), -1)
#Nx.Tensor<
  s16[data: 3]
  [-1, 0, 1]
>

adding-tensors-of-the-same-shape

Adding tensors of the same shape

iex> left = Nx.tensor([[1, 2], [3, 4]], names: [:x, :y])
iex> right = Nx.tensor([[10, 20], [30, 40]], names: [nil, :y])
iex> Nx.add(left, right)
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [11, 22],
    [33, 44]
  ]
>

adding-tensors-with-broadcasting

Adding tensors with broadcasting

iex> left = Nx.tensor([[1], [2]], names: [nil, :y])
iex> right = Nx.tensor([[10, 20]], names: [:x, nil])
iex> Nx.add(left, right)
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [11, 21],
    [12, 22]
  ]
>

iex> left = Nx.tensor([[10, 20]], names: [:x, nil])
iex> right = Nx.tensor([[1], [2]], names: [nil, :y])
iex> Nx.add(left, right)
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [11, 21],
    [12, 22]
  ]
>

iex> left = Nx.tensor([[1], [2]], names: [:x, nil])
iex> right = Nx.tensor([[10, 20], [30, 40]])
iex> Nx.add(left, right)
#Nx.Tensor<
  s64[x: 2][2]
  [
    [11, 21],
    [32, 42]
  ]
>

iex> left = Nx.tensor([[1, 2]])
iex> right = Nx.tensor([[10, 20], [30, 40]])
iex> Nx.add(left, right)
#Nx.Tensor<
  s64[2][2]
  [
    [11, 22],
    [31, 42]
  ]
>

Calculates the inverse sine of each element in the tensor.

It is equivalent to:

$$asin(sin(z)) = z$$

examples

Examples

iex> Nx.asin(0.10000000149011612)
#Nx.Tensor<
  f32
  0.1001674234867096
>

iex> Nx.asin(Nx.tensor([0.10000000149011612, 0.5, 0.8999999761581421], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [0.1001674234867096, 0.5235987901687622, 1.1197694540023804]
>

Calculates the inverse hyperbolic sine of each element in the tensor.

It is equivalent to:

$$asinh(sinh(z)) = z$$

examples

Examples

iex> Nx.asinh(1)
#Nx.Tensor<
  f32
  0.8813735842704773
>

iex> Nx.asinh(Nx.tensor([1, 2, 3], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [0.8813735842704773, 1.4436354637145996, 1.8184465169906616]
>

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

Examples

arc-tangent-between-scalars

Arc tangent between scalars

iex> Nx.atan2(1, 2)
#Nx.Tensor<
  f32
  0.46364760398864746
>

arc-tangent-between-tensors-and-scalars

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

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]
  ]
>

Calculates the inverse tangent of each element in the tensor.

It is equivalent to:

$$atan(tan(z)) = z$$

examples

Examples

iex> Nx.atan(0.10000000149011612)
#Nx.Tensor<
  f32
  0.09966865181922913
>

iex> Nx.atan(Nx.tensor([0.10000000149011612, 0.5, 0.8999999761581421], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [0.09966865181922913, 0.46364760398864746, 0.7328150868415833]
>

Calculates the inverse hyperbolic tangent of each element in the tensor.

It is equivalent to:

$$atanh(tanh(z)) = z$$

examples

Examples

iex> Nx.atanh(0.10000000149011612)
#Nx.Tensor<
  f32
  0.10033535212278366
>

iex> Nx.atanh(Nx.tensor([0.10000000149011612, 0.5, 0.8999999761581421], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [0.10033535212278366, 0.5493061542510986, 1.4722193479537964]
>
Link to this function

bitwise_and(left, right)

View Source

Element-wise bitwise AND of two tensors.

Only integer tensors are supported. If a float or complex tensor is given, an error is raised.

It will broadcast tensors whenever the dimensions do not match and broadcasting is possible.

If you're using Nx.Defn.defn/2, you can use the &&& operator in place of this function: left &&& right.

examples

Examples

bitwise-and-between-scalars

bitwise and between scalars

iex> Nx.bitwise_and(1, 0)
#Nx.Tensor<
  s64
  0
>

bitwise-and-between-tensors-and-scalars

bitwise and between tensors and scalars

iex> Nx.bitwise_and(Nx.tensor([0, 1, 2], names: [:data]), 1)
#Nx.Tensor<
  s64[data: 3]
  [0, 1, 0]
>

iex> Nx.bitwise_and(Nx.tensor([0, -1, -2], names: [:data]), -1)
#Nx.Tensor<
  s64[data: 3]
  [0, -1, -2]
>

bitwise-and-between-tensors

bitwise and between tensors

iex> Nx.bitwise_and(Nx.tensor([0, 0, 1, 1], names: [:data]), Nx.tensor([0, 1, 0, 1]))
#Nx.Tensor<
  s64[data: 4]
  [0, 0, 0, 1]
>

error-cases

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}

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

Examples

iex> Nx.bitwise_not(1)
#Nx.Tensor<
  s64
  -2
>

iex> Nx.bitwise_not(Nx.tensor([-1, 0, 1], type: :s8, names: [:x]))
#Nx.Tensor<
  s8[x: 3]
  [0, -1, -2]
>

iex> Nx.bitwise_not(Nx.tensor([0, 1, 254, 255], type: :u8, names: [:x]))
#Nx.Tensor<
  u8[x: 4]
  [255, 254, 1, 0]
>

error-cases

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}

Element-wise bitwise OR of two tensors.

Only integer tensors are supported. If a float or complex tensor is given, an error is raised.

It will broadcast tensors whenever the dimensions do not match and broadcasting is possible.

If you're using Nx.Defn.defn/2, you can use the ||| operator in place of this function: left ||| right.

examples

Examples

bitwise-or-between-scalars

bitwise or between scalars

iex> Nx.bitwise_or(1, 0)
#Nx.Tensor<
  s64
  1
>

bitwise-or-between-tensors-and-scalars

bitwise or between tensors and scalars

iex> Nx.bitwise_or(Nx.tensor([0, 1, 2], names: [:data]), 1)
#Nx.Tensor<
  s64[data: 3]
  [1, 1, 3]
>

iex> Nx.bitwise_or(Nx.tensor([0, -1, -2], names: [:data]), -1)
#Nx.Tensor<
  s64[data: 3]
  [-1, -1, -1]
>

bitwise-or-between-tensors

bitwise or between tensors

iex> Nx.bitwise_or(Nx.tensor([0, 0, 1, 1], names: [:data]), Nx.tensor([0, 1, 0, 1], names: [:data]))
#Nx.Tensor<
  s64[data: 4]
  [0, 1, 1, 1]
>

error-cases

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}
Link to this function

bitwise_xor(left, right)

View Source

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

Examples

bitwise-xor-between-scalars

Bitwise xor between scalars

iex> Nx.bitwise_xor(1, 0)
#Nx.Tensor<
  s64
  1
>

bitwise-xor-and-between-tensors-and-scalars

Bitwise xor and between tensors and scalars

iex> Nx.bitwise_xor(Nx.tensor([1, 2, 3], names: [:data]), 2)
#Nx.Tensor<
  s64[data: 3]
  [3, 0, 1]
>

iex> Nx.bitwise_xor(Nx.tensor([-1, -2, -3], names: [:data]), 2)
#Nx.Tensor<
  s64[data: 3]
  [-3, -4, -1]
>

bitwise-xor-between-tensors

Bitwise xor between tensors

iex> Nx.bitwise_xor(Nx.tensor([0, 0, 1, 1]), Nx.tensor([0, 1, 0, 1], names: [:data]))
#Nx.Tensor<
  s64[data: 4]
  [0, 1, 1, 0]
>

error-cases

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}

Calculates the cube root of each element in the tensor.

It is equivalent to:

$$cbrt(z) = z^{\frac{1}{3}}$$

examples

Examples

iex> Nx.cbrt(1)
#Nx.Tensor<
  f32
  1.0
>

iex> Nx.cbrt(Nx.tensor([1, 2, 3], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [1.0, 1.2599210739135742, 1.4422495365142822]
>

Calculates the ceil 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

Examples

iex> Nx.ceil(Nx.tensor([-1, 0, 1], names: [:x]))
#Nx.Tensor<
  s64[x: 3]
  [-1, 0, 1]
>

iex> Nx.ceil(Nx.tensor([-1.5, -0.5, 0.5, 1.5], names: [:x]))
#Nx.Tensor<
  f32[x: 4]
  [-1.0, 0.0, 1.0, 2.0]
>

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

Examples

iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:x, :y])
iex> Nx.clip(t, 2, 4)
#Nx.Tensor<
  s64[x: 2][y: 3]
  [
    [2, 2, 3],
    [4, 4, 4]
  ]
>

iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:x, :y])
iex> Nx.clip(t, 2.0, 3)
#Nx.Tensor<
  f32[x: 2][y: 3]
  [
    [2.0, 2.0, 3.0],
    [3.0, 3.0, 3.0]
  ]
>

iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:x, :y])
iex> Nx.clip(t, Nx.tensor(2.0), Nx.max(1.0, 3.0))
#Nx.Tensor<
  f32[x: 2][y: 3]
  [
    [2.0, 2.0, 3.0],
    [3.0, 3.0, 3.0]
  ]
>

iex> t = Nx.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]], names: [:x, :y])
iex> Nx.clip(t, 2, 6.0)
#Nx.Tensor<
  f32[x: 2][y: 3]
  [
    [2.0, 2.0, 3.0],
    [4.0, 5.0, 6.0]
  ]
>

iex> t = Nx.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]], type: :f32, names: [:x, :y])
iex> Nx.clip(t, 1, 4)
#Nx.Tensor<
  f32[x: 2][y: 3]
  [
    [1.0, 2.0, 3.0],
    [4.0, 4.0, 4.0]
  ]
>

Constructs a complex tensor from two equally-shaped tensors.

Does not accept complex tensors as inputs.

examples

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]
>

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

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]
 >

Calculates the cosine of each element in the tensor.

It is equivalent to:

$$cos(z) = \frac{e^{iz} + e^{-iz}}{2}$$

examples

Examples

iex> Nx.cos(1)
#Nx.Tensor<
  f32
  0.5403022766113281
>

iex> Nx.cos(Nx.tensor([1, 2, 3], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [0.5403022766113281, -0.416146844625473, -0.9899924993515015]
>

Calculates the hyperbolic cosine of each element in the tensor.

It is equivalent to:

$$cosh(z) = \frac{e^z + e^{-z}}{2}$$

examples

Examples

iex> Nx.cosh(1)
#Nx.Tensor<
  f32
  1.5430806875228882
>

iex> Nx.cosh(Nx.tensor([1, 2, 3], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [1.5430806875228882, 3.762195587158203, 10.067662239074707]
>
Link to this function

count_leading_zeros(tensor)

View Source

Counts the number of leading zeros of each element in the tensor.

examples

Examples

iex> Nx.count_leading_zeros(1)
#Nx.Tensor<
  s64
  63
>

iex> Nx.count_leading_zeros(-1)
#Nx.Tensor<
  s64
  0
>

iex> Nx.count_leading_zeros(Nx.tensor([0, 0xF, 0xFF, 0xFFFF], names: [:x]))
#Nx.Tensor<
  s64[x: 4]
  [64, 60, 56, 48]
>

iex> Nx.count_leading_zeros(Nx.tensor([0xF000000000000000, 0x0F00000000000000], names: [:x]))
#Nx.Tensor<
  s64[x: 2]
  [0, 4]
>

iex> Nx.count_leading_zeros(Nx.tensor([0, 0xF, 0xFF, 0xFFFF], type: :s32, names: [:x]))
#Nx.Tensor<
  s32[x: 4]
  [32, 28, 24, 16]
>

iex> Nx.count_leading_zeros(Nx.tensor([0, 0xF, 0xFF, 0xFFFF], type: :s16, names: [:x]))
#Nx.Tensor<
  s16[x: 4]
  [16, 12, 8, 0]
>

iex> Nx.count_leading_zeros(Nx.tensor([0, 1, 2, 4, 8, 16, 32, 64, -1, -128], type: :s8, names: [:x]))
#Nx.Tensor<
  s8[x: 10]
  [8, 7, 6, 5, 4, 3, 2, 1, 0, 0]
>

iex> Nx.count_leading_zeros(Nx.tensor([0, 1, 2, 4, 8, 16, 32, 64, 128], type: :u8, names: [:x]))
#Nx.Tensor<
  u8[x: 9]
  [8, 7, 6, 5, 4, 3, 2, 1, 0]
>

error-cases

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}

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

Examples

dividing-scalars

Dividing scalars

iex> Nx.divide(1, 2)
#Nx.Tensor<
  f32
  0.5
>

dividing-tensors-and-scalars

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

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]
  ]
>

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

Examples

comparison-of-scalars

Comparison of scalars

iex> Nx.equal(1, 2)
#Nx.Tensor<
  u8
  0
>

comparison-of-tensors-and-scalars

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

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]
  ]
>

Calculates the error function of each element in the tensor.

It is equivalent to:

$$erf(z) = \frac{2}{\sqrt{\pi}} \int_{0}^{z} e^{-t^2}dt$$

examples

Examples

iex> Nx.erf(1)
#Nx.Tensor<
  f32
  0.8427007794380188
>

iex> Nx.erf(Nx.tensor([1, 2, 3], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [0.8427007794380188, 0.9953222870826721, 0.9999778866767883]
>

Calculates the inverse error function of each element in the tensor.

It is equivalent to:

$$erf\text{\textunderscore}inv(erf(z)) = z$$

examples

Examples

iex> Nx.erf_inv(0.10000000149011612)
#Nx.Tensor<
  f32
  0.08885598927736282
>

iex> Nx.erf_inv(Nx.tensor([0.10000000149011612, 0.5, 0.8999999761581421], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [0.08885598927736282, 0.4769362807273865, 1.163087010383606]
>

Calculates the one minus error function of each element in the tensor.

It is equivalent to:

$$erfc(z) = 1 - erf(z)$$

examples

Examples

iex> Nx.erfc(1)
#Nx.Tensor<
  f32
  0.15729920566082
>

iex> Nx.erfc(Nx.tensor([1, 2, 3], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [0.15729920566082, 0.004677734803408384, 2.2090496713644825e-5]
>

Calculates the exponential of each element in the tensor.

It is equivalent to:

$$exp(z) = e^z$$

examples

Examples

iex> Nx.exp(1)
#Nx.Tensor<
  f32
  2.7182817459106445
>

iex> Nx.exp(Nx.tensor([1, 2, 3], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [2.7182817459106445, 7.389056205749512, 20.08553695678711]
>

Calculates the exponential minus one of each element in the tensor.

It is equivalent to:

$$expm1(z) = e^z - 1$$

examples

Examples

iex> Nx.expm1(1)
#Nx.Tensor<
  f32
  1.718281865119934
>

iex> Nx.expm1(Nx.tensor([1, 2, 3], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [1.718281865119934, 6.389056205749512, 19.08553695678711]
>

Calculates the floor 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

Examples

iex> Nx.floor(Nx.tensor([-1, 0, 1], names: [:x]))
#Nx.Tensor<
  s64[x: 3]
  [-1, 0, 1]
>

iex> Nx.floor(Nx.tensor([-1.5, -0.5, 0.5, 1.5], names: [:x]))
#Nx.Tensor<
  f32[x: 4]
  [-2.0, -1.0, 0.0, 1.0]
>

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

Examples

comparison-of-scalars

Comparison of scalars

iex> Nx.greater(1, 2)
#Nx.Tensor<
  u8
  0
>

comparison-of-tensors-and-scalars

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

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]
  ]
>
Link to this function

greater_equal(left, right)

View Source

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

Examples

comparison-of-scalars

Comparison of scalars

iex> Nx.greater_equal(1, 2)
#Nx.Tensor<
  u8
  0
>

comparison-of-tensors-and-scalars

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

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]
  ]
>

Returns the imaginary component of each entry in a complex tensor as a floating point tensor.

examples

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]
>

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

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]
>

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

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]
>

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

Examples

left-shift-between-scalars

Left shift between scalars

iex> Nx.left_shift(1, 0)
#Nx.Tensor<
  s64
  1
>

left-shift-between-tensors-and-scalars

Left shift between tensors and scalars

iex> Nx.left_shift(Nx.tensor([1, 2, 3], names: [:data]), 2)
#Nx.Tensor<
  s64[data: 3]
  [4, 8, 12]
>

left-shift-between-tensors

Left shift between tensors

iex> left = Nx.tensor([1, 1, -1, -1], names: [:data])
iex> right = Nx.tensor([1, 2, 3, 4], names: [:data])
iex> Nx.left_shift(left, right)
#Nx.Tensor<
  s64[data: 4]
  [2, 4, -8, -16]
>

error-cases

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}

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

Examples

comparison-of-scalars

Comparison of scalars

iex> Nx.less(1, 2)
#Nx.Tensor<
  u8
  1
>

comparison-of-tensors-and-scalars

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

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]
  ]
>

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

Examples

comparison-of-scalars

Comparison of scalars

iex> Nx.less_equal(1, 2)
#Nx.Tensor<
  u8
  1
>

comparison-of-tensors-and-scalars

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

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]
  ]
>

Calculates the natural log plus one of each element in the tensor.

It is equivalent to:

$$log1p(z) = log(z + 1)$$

examples

Examples

iex> Nx.log1p(1)
#Nx.Tensor<
  f32
  0.6931471824645996
>

iex> Nx.log1p(Nx.tensor([1, 2, 3], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [0.6931471824645996, 1.0986123085021973, 1.3862943649291992]
>

Calculates the natural log of each element in the tensor.

It is equivalent to:

$$log(z) = ln(z),\quad \text{if z} \in \Reals$$

$$log(z) = ln(r) + i\theta,\quad\text{if }z = re^{i\theta} \in \Complex$$

examples

Examples

iex> Nx.log(1)
#Nx.Tensor<
  f32
  0.0
>

iex> Nx.log(Nx.tensor([1, 2, 3], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [0.0, 0.6931471824645996, 1.0986123085021973]
>
Link to this function

logical_and(left, right)

View Source

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

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]
  ]
>

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

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]
>

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

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]
  ]
>
Link to this function

logical_xor(left, right)

View Source

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

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]
  ]
>
Link to this function

map(tensor, opts \\ [], fun)

View Source

Maps the given scalar function over the entire tensor.

The type of the returned tensor will be of the same type as the input tensor, unless the :type option is given. Therefore, you may need to explicitly cast the tensor to avoid errors. For example, if you have an integer tensor and you convert it to a float, as below, it will fail:

tensor = Nx.tensor([[1, 2, 3], [4, 5, 6]]),
Nx.map(tensor, fn x -> Nx.multiply(x, 1.0) end)

You need to explicitly pass the output type in such cases:

iex> tensor = Nx.tensor([[1, 2, 3], [4, 5, 6]])
iex> Nx.map(tensor, [type: :f32], fn x -> Nx.multiply(x, 1.0) end)
#Nx.Tensor<
  f32[2][3]
  [
    [1.0, 2.0, 3.0],
    [4.0, 5.0, 6.0]
  ]
>

limitations

Limitations

Given this function relies on anonymous functions, it may not be available or efficient on all Nx backends. Therefore, you should avoid using map/2 whenever possible and use other functions in the Nx module to achieve the desired result.

examples

Examples

iex> Nx.map(Nx.tensor([[1, 2, 3], [4, 5, 6]]), fn x -> Nx.add(x, 1) end)
#Nx.Tensor<
  s64[2][3]
  [
    [2, 3, 4],
    [5, 6, 7]
  ]
>

iex> Nx.map(Nx.tensor(1), fn x -> Nx.add(x, 1) end)
#Nx.Tensor<
  s64
  2
>

iex> Nx.map(Nx.tensor([[1, 2, 3], [4, 5, 6]]), [type: :f64], fn x -> Nx.add(x, 1) end)
#Nx.Tensor<
  f64[2][3]
  [
    [2.0, 3.0, 4.0],
    [5.0, 6.0, 7.0]
  ]
>

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

Examples

max-between-scalars

Max between scalars

iex> Nx.max(1, 2)
#Nx.Tensor<
  s64
  2
>

max-between-tensors-and-scalars

Max between tensors and scalars

iex> Nx.max(Nx.tensor([1, 2, 3], names: [:data]), 1)
#Nx.Tensor<
  s64[data: 3]
  [1, 2, 3]
>

iex> Nx.max(1, Nx.tensor([1.0, 2.0, 3.0], names: [:data]))
#Nx.Tensor<
  f32[data: 3]
  [1.0, 2.0, 3.0]
>

max-between-tensors

Max between tensors

iex> left = Nx.tensor([[1], [2]], names: [:x, :y])
iex> right = Nx.tensor([[10, 20]])
iex> Nx.max(left, right)
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [10, 20],
    [10, 20]
  ]
>

iex> left = Nx.tensor([[1], [2]], type: :s8, names: [:x, nil])
iex> right = Nx.tensor([[10, 20]], type: :s8)
iex> Nx.max(left, right)
#Nx.Tensor<
  s8[x: 2][2]
  [
    [10, 20],
    [10, 20]
  ]
>

iex> left = Nx.tensor([[1], [2]], type: :f32, names: [:x, nil])
iex> right = Nx.tensor([[10, 20]], type: :f32, names: [nil, :y])
iex> Nx.max(left, right)
#Nx.Tensor<
  f32[x: 2][y: 2]
  [
    [10.0, 20.0],
    [10.0, 20.0]
  ]
>

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

Examples

min-between-scalars

Min between scalars

iex> Nx.min(1, 2)
#Nx.Tensor<
  s64
  1
>

min-between-tensors-and-scalars

Min between tensors and scalars

iex> Nx.min(Nx.tensor([1, 2, 3], names: [:data]), 1)
#Nx.Tensor<
  s64[data: 3]
  [1, 1, 1]
>

iex> Nx.min(1, Nx.tensor([1.0, 2.0, 3.0], names: [:data]))
#Nx.Tensor<
  f32[data: 3]
  [1.0, 1.0, 1.0]
>

min-between-tensors

Min between tensors

iex> left = Nx.tensor([[1], [2]], names: [:x, nil])
iex> right = Nx.tensor([[10, 20]])
iex> Nx.min(left, right)
#Nx.Tensor<
  s64[x: 2][2]
  [
    [1, 1],
    [2, 2]
  ]
>

iex> left = Nx.tensor([[1], [2]], type: :s8, names: [:x, :y])
iex> right = Nx.tensor([[10, 20]], type: :s8)
iex> Nx.min(left, right)
#Nx.Tensor<
  s8[x: 2][y: 2]
  [
    [1, 1],
    [2, 2]
  ]
>

iex> left = Nx.tensor([[1], [2]], type: :f32, names: [:x, nil])
iex> right = Nx.tensor([[10, 20]], type: :f32, names: [nil, :y])
iex> Nx.min(left, right)
#Nx.Tensor<
  f32[x: 2][y: 2]
  [
    [1.0, 1.0],
    [2.0, 2.0]
  ]
>

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

Examples

multiplying-scalars

Multiplying scalars

iex> Nx.multiply(1, 2)
#Nx.Tensor<
  s64
  2
>

multiplying-tensors-and-scalars

Multiplying tensors and scalars

iex> Nx.multiply(Nx.tensor([1, 2, 3], names: [:data]), 1)
#Nx.Tensor<
  s64[data: 3]
  [1, 2, 3]
>

iex> Nx.multiply(1, Nx.tensor([1.0, 2.0, 3.0], names: [:data]))
#Nx.Tensor<
  f32[data: 3]
  [1.0, 2.0, 3.0]
>

multiplying-tensors

Multiplying tensors

iex> left = Nx.tensor([[1], [2]], names: [:x, :y])
iex> right = Nx.tensor([[10, 20]], names: [:x, :y])
iex> Nx.multiply(left, right)
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [10, 20],
    [20, 40]
  ]
>

iex> left = Nx.tensor([[1], [2]], type: :s8, names: [:x, nil])
iex> right = Nx.tensor([[10, 20]], type: :s8, names: [nil, :y])
iex> Nx.multiply(left, right)
#Nx.Tensor<
  s8[x: 2][y: 2]
  [
    [10, 20],
    [20, 40]
  ]
>

iex> left = Nx.tensor([[1], [2]], type: :f32, names: [nil, :y])
iex> right = Nx.tensor([[10, 20]], type: :f32, names: [:x, nil])
iex> Nx.multiply(left, right)
#Nx.Tensor<
  f32[x: 2][y: 2]
  [
    [10.0, 20.0],
    [20.0, 40.0]
  ]
>

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

Examples

iex> Nx.negate(1)
#Nx.Tensor<
  s64
  -1
>

iex> Nx.negate(Nx.tensor([-1, 0, 1]))
#Nx.Tensor<
  s64[3]
  [1, 0, -1]
>

iex> Nx.negate(Nx.tensor([1.0, 2.0, 3.0], type: :f32))
#Nx.Tensor<
  f32[3]
  [-1.0, -2.0, -3.0]
>

If an unsigned tensor is given, it works as bitwise_not:

iex> Nx.negate(Nx.tensor([0, 1, 2], type: :u8, names: [:x]))
#Nx.Tensor<
  u8[x: 3]
  [0, 255, 254]
>

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

Examples

comparison-of-scalars

Comparison of scalars

iex> Nx.not_equal(1, 2)
#Nx.Tensor<
  u8
  1
>

comparison-of-tensor-and-scalar

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

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]
  ]
>

Calculates the complex phase angle of each element in the tensor. $$phase(z) = atan2(b, a), z = a + bi \in \Complex$$

examples

Examples

 iex> Nx.phase(Complex.new(1, 2))
 #Nx.Tensor<
   f32
   1.1071487665176392
 >

 iex> Nx.phase(1)
 #Nx.Tensor<
   f32
   0.0
 >

 iex> import Nx, only: [sigil_V: 2]
 iex> Nx.phase(~V[1+2i -2+1i])
 #Nx.Tensor<
   f32[2]
   [1.1071487665176392, 2.677945137023926]
 >
Link to this function

population_count(tensor)

View Source

Computes the bitwise population count of each element in the tensor.

examples

Examples

iex> Nx.population_count(1)
#Nx.Tensor<
  s64
  1
>

iex> Nx.population_count(-128)
#Nx.Tensor<
  s64
  57
>

iex> Nx.population_count(Nx.tensor([0, 1, 254, 255], names: [:x]))
#Nx.Tensor<
  s64[x: 4]
  [0, 1, 7, 8]
>

iex> Nx.population_count(Nx.tensor([0, 1, 126, 127, -1, -127, -128], type: :s8, names: [:x]))
#Nx.Tensor<
  s8[x: 7]
  [0, 1, 6, 7, 8, 2, 1]
>

error-cases

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}

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

Examples

power-of-scalars

Power of scalars

iex> Nx.power(2, 4)
#Nx.Tensor<
  s64
  16
>

power-of-tensors-and-scalars

Power of tensors and scalars

iex> Nx.power(Nx.tensor([1, 2, 3], names: [:data]), 2)
#Nx.Tensor<
  s64[data: 3]
  [1, 4, 9]
>

iex> Nx.power(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

Power of tensors

iex> Nx.power(Nx.tensor([[2], [3]], names: [:x, nil]), Nx.tensor([[4, 5]], names: [nil, :y]))
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [16, 32],
    [81, 243]
  ]
>

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

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

Examples

integer-dividing-scalars

Integer dividing scalars

iex> Nx.quotient(11, 2)
#Nx.Tensor<
  s64
  5
>

integer-dividing-tensors-and-scalars

Integer dividing tensors and scalars

iex> Nx.quotient(Nx.tensor([2, 4, 5], names: [:data]), 2)
#Nx.Tensor<
  s64[data: 3]
  [1, 2, 2]
>

iex> Nx.quotient(10, Nx.tensor([1, 2, 3], names: [:data]))
#Nx.Tensor<
  s64[data: 3]
  [10, 5, 3]
>

dividing-tensors

Dividing tensors

iex> left = Nx.tensor([[10, 20]], names: [nil, :y])
iex> right = Nx.tensor([[1], [2]], names: [:x, nil])
iex> Nx.quotient(left, right)
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [10, 20],
    [5, 10]
  ]
>

iex> left = Nx.tensor([[10, 20]], type: :s8, names: [:x, :y])
iex> right = Nx.tensor([[1], [2]], type: :s8)
iex> Nx.quotient(left, right)
#Nx.Tensor<
  s8[x: 2][y: 2]
  [
    [10, 20],
    [5, 10]
  ]
>

iex> left = Nx.tensor([[10, 20]], type: :u8, names: [:x, :y])
iex> right = Nx.tensor([[1], [2]], type: :u32)
iex> Nx.quotient(left, right)
#Nx.Tensor<
  u32[x: 2][y: 2]
  [
    [10, 20],
    [5, 10]
  ]
>

Returns the real component of each entry in a complex tensor as a floating point tensor.

examples

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]
>

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

Examples

remainder-of-scalars

Remainder of scalars

iex> Nx.remainder(1, 2)
#Nx.Tensor<
  s64
  1
>

remainder-of-tensors-and-scalars

Remainder of tensors and scalars

iex> Nx.remainder(Nx.tensor([1, 2, 3], names: [:data]), 2)
#Nx.Tensor<
  s64[data: 3]
  [1, 0, 1]
>

iex> Nx.remainder(2, Nx.tensor([1.0, 2.0, 3.0], names: [:data]))
#Nx.Tensor<
  f32[data: 3]
  [0.0, 0.0, 2.0]
>

remainder-of-tensors

Remainder of tensors

iex> left = Nx.tensor([[10], [20]], names: [:x, :y])
iex> right = Nx.tensor([[3, 4]], names: [nil, :y])
iex> Nx.remainder(left, right)
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [1, 2],
    [2, 0]
  ]
>

remainder-involving-negative-values

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
>
Link to this function

right_shift(left, right)

View Source

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

Examples

right-shift-between-scalars

Right shift between scalars

iex> Nx.right_shift(1, 0)
#Nx.Tensor<
  s64
  1
>

right-shift-between-tensors-and-scalars

Right shift between tensors and scalars

iex> Nx.right_shift(Nx.tensor([2, 4, 8], names: [:data]), 2)
#Nx.Tensor<
  s64[data: 3]
  [0, 1, 2]
>

right-shift-between-tensors

Right shift between tensors

iex> left = Nx.tensor([16, 32, -64, -128], names: [:data])
iex> right = Nx.tensor([1, 2, 3, 4])
iex> Nx.right_shift(left, right)
#Nx.Tensor<
  s64[data: 4]
  [8, 8, -8, -8]
>

error-cases

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}

Calculates the round (away from zero) 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

Examples

iex> Nx.round(Nx.tensor([-1, 0, 1], names: [:x]))
#Nx.Tensor<
  s64[x: 3]
  [-1, 0, 1]
>

iex> Nx.round(Nx.tensor([-1.5, -0.5, 0.5, 1.5], names: [:x]))
#Nx.Tensor<
  f32[x: 4]
  [-2.0, -1.0, 1.0, 2.0]
>

Calculates the reverse square root of each element in the tensor.

It is equivalent to:

$$rsqrt(z) = \frac{1}{\sqrt{z}}$$

examples

Examples

iex> Nx.rsqrt(1)
#Nx.Tensor<
  f32
  1.0
>

iex> Nx.rsqrt(Nx.tensor([1, 2, 3], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [1.0, 0.7071067690849304, 0.5773502588272095]
>
Link to this function

select(pred, on_true, on_false)

View Source

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

Examples

When the first argument is a scalar:

iex> Nx.select(1, Nx.tensor([1, 2, 3], names: [:x]), Nx.tensor([4, 5, 6], names: [:x]))
#Nx.Tensor<
  s64[x: 3]
  [1, 2, 3]
>

iex> Nx.select(0, Nx.tensor([1, 2, 3], names: [:y]), Nx.tensor([4, 5, 6], names: [:y]))
#Nx.Tensor<
  s64[y: 3]
  [4, 5, 6]
>

iex> Nx.select(0, Nx.tensor([[1, 2]], names: [:x, :y]), Nx.tensor([[3], [4]], names: [:x, :y]))
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [3, 3],
    [4, 4]
  ]
>

When the first argument is a tensor:

iex> Nx.select(Nx.tensor([0, 1, 0], names: [:x]), Nx.tensor([1, 2, 3], names: [:y]), Nx.tensor([4, 5, 6], names: [:z]))
#Nx.Tensor<
  s64[x: 3]
  [4, 2, 6]
>

iex> x = Nx.tensor([2, 4, 6], names: [:x])
iex> y = Nx.tensor([3, 2, 1])
iex> Nx.select(Nx.greater(x, y), Nx.tensor([2, 4, 6], names: [:i]), Nx.tensor([1, 3, 5], names: [:j]))
#Nx.Tensor<
  s64[x: 3]
  [1, 4, 6]
>

iex> x = Nx.tensor([2, 4, 6, 8, 10], names: [:x])
iex> y = Nx.tensor([1, 6, 2, 11, 2], names: [:x])
iex> Nx.select(Nx.greater(x, y), Nx.tensor(2), Nx.tensor([1, 3, 5, 7, 9], names: [:x]))
#Nx.Tensor<
  s64[x: 5]
  [2, 3, 2, 7, 2]
>

If the tensor has other values, any non-zero value is considered true:

iex> Nx.select(Nx.tensor([0, 1, 2], type: :u8), Nx.tensor([0, 0, 0]), Nx.tensor([1, 1, 1]))
#Nx.Tensor<
  s64[3]
  [1, 0, 0]
>

iex> Nx.select(Nx.tensor([0, 1, 0]), Nx.tensor([1, 1, 1]), Nx.tensor([2.0, 2.0, 2.0]))
#Nx.Tensor<
  f32[3]
  [2.0, 1.0, 2.0]
>

Calculates the sigmoid of each element in the tensor.

It is equivalent to:

$$sigmoid(z) = \frac{1}{1 + e^{-z}}$$

examples

Examples

iex> Nx.sigmoid(1)
#Nx.Tensor<
  f32
  0.7310585975646973
>

iex> Nx.sigmoid(Nx.tensor([1, 2, 3], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [0.7310585975646973, 0.8807970881462097, 0.9525741338729858]
>

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

Examples

iex> Nx.sign(Nx.tensor([-2, -1, 0, 1, 2], names: [:x]))
#Nx.Tensor<
  s64[x: 5]
  [-1, -1, 0, 1, 1]
>

Calculates the sine of each element in the tensor.

It is equivalent to:

$$sin(z) = \frac{e^{iz} - e^{-iz}}{2i}$$

examples

Examples

iex> Nx.sin(1)
#Nx.Tensor<
  f32
  0.8414709568023682
>

iex> Nx.sin(Nx.tensor([1, 2, 3], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [0.8414709568023682, 0.9092974066734314, 0.14112000167369843]
>

Calculates the hyperbolic sine of each element in the tensor.

It is equivalent to:

$$sinh(z) = \frac{e^z - e^{-z}}{2}$$

examples

Examples

iex> Nx.sinh(1)
#Nx.Tensor<
  f32
  1.175201177597046
>

iex> Nx.sinh(Nx.tensor([1, 2, 3], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [1.175201177597046, 3.6268603801727295, 10.017874717712402]
>

Calculates the square root of each element in the tensor.

It is equivalent to:

$$sqrt(z) = \sqrt{z}$$

examples

Examples

iex> Nx.sqrt(1)
#Nx.Tensor<
  f32
  1.0
>

iex> Nx.sqrt(Nx.tensor([1, 2, 3], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [1.0, 1.4142135381698608, 1.7320507764816284]
>

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

Examples

subtracting-scalars

Subtracting scalars

iex> Nx.subtract(1, 2)
#Nx.Tensor<
  s64
  -1
>

subtracting-tensors-and-scalars

Subtracting tensors and scalars

iex> Nx.subtract(Nx.tensor([1, 2, 3], names: [:data]), 1)
#Nx.Tensor<
  s64[data: 3]
  [0, 1, 2]
>

iex> Nx.subtract(1, Nx.tensor([1.0, 2.0, 3.0], names: [:data]))
#Nx.Tensor<
  f32[data: 3]
  [0.0, -1.0, -2.0]
>

subtracting-tensors

Subtracting tensors

iex> left = Nx.tensor([[1], [2]], names: [:x, :y])
iex> right = Nx.tensor([[10, 20]], names: [:x, :y])
iex> Nx.subtract(left, right)
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [-9, -19],
    [-8, -18]
  ]
>

iex> left = Nx.tensor([[1], [2]], type: :s8, names: [:x, nil])
iex> right = Nx.tensor([[10, 20]], type: :s8, names: [nil, :y])
iex> Nx.subtract(left, right)
#Nx.Tensor<
  s8[x: 2][y: 2]
  [
    [-9, -19],
    [-8, -18]
  ]
>

iex> left = Nx.tensor([[1], [2]], type: :f32, names: [nil, :y])
iex> right = Nx.tensor([[10, 20]], type: :f32, names: [:x, nil])
iex> Nx.subtract(left, right)
#Nx.Tensor<
  f32[x: 2][y: 2]
  [
    [-9.0, -19.0],
    [-8.0, -18.0]
  ]
>

Calculates the tangent of each element in the tensor.

It is equivalent to:

$$tan(z) = \frac{sin(z)}{cos(z)}$$

examples

Examples

iex> Nx.tan(1)
#Nx.Tensor<
  f32
  1.5574077367782593
>

iex> Nx.tan(Nx.tensor([1, 2, 3], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [1.5574077367782593, -2.185039758682251, -0.14254654943943024]
>

Calculates the hyperbolic tangent of each element in the tensor.

It is equivalent to:

$$sinh(z) = \frac{e^z - e^{-z}}{e^z + e^{-z}}$$

examples

Examples

iex> Nx.tanh(1)
#Nx.Tensor<
  f32
  0.7615941762924194
>

iex> Nx.tanh(Nx.tensor([1, 2, 3], names: [:x]))
#Nx.Tensor<
  f32[x: 3]
  [0.7615941762924194, 0.9640275835990906, 0.9950547814369202]
>

Link to this section Functions: Indexed

Builds a new tensor by taking individual values from the original tensor at the given indices.

The last dimension in indices must have the same size as the tensor rank, think of it as one value per axis.

examples

Examples

iex> t = Nx.tensor([[1, 2], [3, 4]])
iex> Nx.gather(t, Nx.tensor([[1, 1], [0, 1], [1, 0]]))
#Nx.Tensor<
  s64[3]
  [4, 2, 3]
>

iex> t = Nx.tensor([[1, 2], [3, 4]])
iex> Nx.gather(t, Nx.tensor([[[1, 1], [0, 0]], [[1, 0], [0, 1]]]))
#Nx.Tensor<
  s64[2][2]
  [
    [4, 1],
    [3, 2]
  ]
>

iex> t = Nx.tensor([[[1, 2], [11, 12]], [[101, 102], [111, 112]]])
iex> Nx.gather(t, Nx.tensor([[0, 0, 0], [0, 1, 1], [1, 1, 1]]))
#Nx.Tensor<
  s64[3]
  [1, 12, 112]
>

error-cases

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}
Link to this function

indexed_add(target, indices, updates)

View Source

Performs an indexed add operation on the target tensor, adding the updates into the corresponding indices positions.

This operation is the grad for gather/2 and gather-like operations such as take/3 and take_along_axis/3.

indices must be a fully qualified tensor of shape {n, Nx.rank(target)}, with n being an arbitrary number of indices, while updates must have a compatible {n} shape.

See also: indexed_add/3, gather/2, take/3, take_along_axis/3

examples

Examples

iex> t = Nx.iota({1, 2, 3})
#Nx.Tensor<
  s64[1][2][3]
  [
    [
      [0, 1, 2],
      [3, 4, 5]
    ]
  ]
>
iex> indices = Nx.tensor([[0, 0, 0], [0, 1, 1], [0, 0, 0], [0, 0, 2], [0, 1, 2]])
iex> updates = Nx.tensor([1, 3, 1, -2, 5])
iex> Nx.indexed_add(t, indices, updates)
#Nx.Tensor<
  s64[1][2][3]
  [
    [
      [2, 1, 0],
      [3, 7, 10]
    ]
  ]
>

Type promotions should happen automatically, with the resulting type being the combination of the target type and the updates type.

iex> Nx.indexed_add(Nx.tensor([1.0]), Nx.tensor([[0], [0]]), Nx.tensor([1, 1]))
#Nx.Tensor<
  f32[1]
  [3.0]
>

iex> Nx.indexed_add(Nx.tensor([1]), Nx.tensor([[0], [0]]), Nx.tensor([1.0, 1.0]))
#Nx.Tensor<
  f32[1]
  [3.0]
>

iex> Nx.indexed_add(Nx.tensor([1], type: :s32), Nx.tensor([[0], [0]]), Nx.tensor([1, 1], type: :s64))
#Nx.Tensor<
  s64[1]
  [3]
>

error-cases

Error cases

iex> Nx.indexed_add(Nx.tensor([[1], [2]]), Nx.tensor([[[1, 2, 3]]]), Nx.tensor([0]))
** (ArgumentError) indices must be a rank 2 tensor, got: 3

iex> Nx.indexed_add(Nx.tensor([[1], [2]]), Nx.tensor([[1, 2]]), Nx.tensor([[0]]))
** (ArgumentError) updates must be a rank 1 tensor, got: 2

iex> Nx.indexed_add(Nx.tensor([[1], [2]]), Nx.tensor([[1, 2, 3]]), Nx.tensor([0]))
** (ArgumentError) expected indices to have shape {*, 2}, got: {1, 3}

iex> Nx.indexed_add(Nx.tensor([[1], [2]]), Nx.tensor([[1, 2]]), Nx.tensor([0, 1]))
** (ArgumentError) expected updates tensor to match the first axis of indices tensor with shape {1, 2}, got {2}
Link to this function

indexed_put(target, indices, updates)

View Source

Puts individual values from updates into the given tensor at the corresponding indices.

indices must be a fully qualified tensor of shape {n, Nx.rank(target)}, with n being an arbitrary number of indices, while updates must have a compatible {n} shape.

In case of repeating indices, the result is non-determinstic, since the operation happens in parallel when running on devices such as the GPU.

See also: indexed_add/3, put_slice/3.

examples

Examples

iex> Nx.indexed_put(Nx.tensor([0, 0, 0]), Nx.tensor([[1], [2]]), Nx.tensor([2, 4]))
#Nx.Tensor<
  s64[3]
  [0, 2, 4]
>

iex> Nx.indexed_put(Nx.tensor([0, 0, 0]), Nx.tensor([[1], [2], [1]]), Nx.tensor([3, 4, 2]))
#Nx.Tensor<
  s64[3]
  [0, 2, 4]
>

iex> t = Nx.iota({1, 2, 3})
#Nx.Tensor<
  s64[1][2][3]
  [
    [
      [0, 1, 2],
      [3, 4, 5]
    ]
  ]
>
iex> indices = Nx.tensor([[0, 0, 0], [0, 1, 1], [0, 0, 2]])
iex> updates = Nx.tensor([1, 3, -2])
iex> Nx.indexed_put(t, indices, updates)
#Nx.Tensor<
  s64[1][2][3]
  [
    [
      [1, 1, -2],
      [3, 3, 5]
    ]
  ]
>

Type promotions should happen automatically, with the resulting type being the combination of the target type and the updates type.

iex> Nx.indexed_put(Nx.tensor([1.0]), Nx.tensor([[0]]), Nx.tensor([3]))
#Nx.Tensor<
  f32[1]
  [3.0]
>

iex> Nx.indexed_put(Nx.tensor([1]), Nx.tensor([[0]]), Nx.tensor([3.0]))
#Nx.Tensor<
  f32[1]
  [3.0]
>

iex> Nx.indexed_put(Nx.tensor([1], type: :s32), Nx.tensor([[0]]), Nx.tensor([3], type: :s64))
#Nx.Tensor<
  s64[1]
  [3]
>

error-cases

Error cases

iex> Nx.indexed_put(Nx.tensor([[1], [2]]), Nx.tensor([[[1, 2, 3]]]), Nx.tensor([0]))
** (ArgumentError) indices must be a rank 2 tensor, got: 3

iex> Nx.indexed_put(Nx.tensor([[1], [2]]), Nx.tensor([[1, 2]]), Nx.tensor([[0]]))
** (ArgumentError) updates must be a rank 1 tensor, got: 2

iex> Nx.indexed_put(Nx.tensor([[1], [2]]), Nx.tensor([[1, 2, 3]]), Nx.tensor([0]))
** (ArgumentError) expected indices to have shape {*, 2}, got: {1, 3}

iex> Nx.indexed_put(Nx.tensor([[1], [2]]), Nx.tensor([[1, 2]]), Nx.tensor([0, 1]))
** (ArgumentError) expected updates tensor to match the first axis of indices tensor with shape {1, 2}, got {2}
Link to this function

put_slice(tensor, start_indices, slice)

View Source

Puts the given slice into the given tensor at the given start_indices.

The given slice must be of the same rank as tensor. Each axis must be less than or equal to the size to the equivalent axis in the tensor.

The number of elements in start_indices should match the rank of the tensor.

See also: indexed_add/3, put_slice/3.

examples

Examples

iex> t = Nx.tensor([0, 1, 2, 3, 4])
iex> Nx.put_slice(t, [2], Nx.tensor([5, 6]))
#Nx.Tensor<
  s64[5]
  [0, 1, 5, 6, 4]
>

iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]])
iex> Nx.put_slice(t, [0, 1], Nx.tensor([[7, 8], [9, 10]]))
#Nx.Tensor<
  s64[2][3]
  [
    [1, 7, 8],
    [4, 9, 10]
  ]
>

Similar to slice/3, dynamic start indexes are also supported:

iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]])
iex> Nx.put_slice(t, [Nx.tensor(0), Nx.tensor(1)], Nx.tensor([[10.0, 11.0]]))
#Nx.Tensor<
  f32[2][3]
  [
    [1.0, 10.0, 11.0],
    [4.0, 5.0, 6.0]
  ]
>

Also similar to slice/3, if start_index + slice_dimension > dimension, the start index will be clipped in order to put the whole slice:

iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]])
iex> Nx.put_slice(t, [1, 1], Nx.tensor([[7, 8], [9, 10]]))
#Nx.Tensor<
  s64[2][3]
  [
    [1, 7, 8],
    [4, 9, 10]
  ]
>
Link to this function

slice(tensor, start_indices, lengths, opts \\ [])

View Source

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

Examples

iex> Nx.slice(Nx.tensor([1, 2, 3, 4, 5, 6]), [0], [3])
#Nx.Tensor<
  s64[3]
  [1, 2, 3]
>

iex> Nx.slice(Nx.tensor([1, 2, 3, 4, 5, 6]), [0], [6], strides: [2])
#Nx.Tensor<
  s64[3]
  [1, 3, 5]
>

iex> Nx.slice(Nx.tensor([[1, 2], [3, 4], [5, 6]]), [0, 0], [3, 2], strides: [2, 1])
#Nx.Tensor<
  s64[2][2]
  [
    [1, 2],
    [5, 6]
  ]
>

Strides can also be a number that applies to all dimensions:

iex> t = Nx.tensor([[1, 2], [3, 4], [5, 6]])
iex> Nx.slice(t, [0, 0], [3, 2], strides: 2)
#Nx.Tensor<
  s64[2][1]
  [
    [1],
    [5]
  ]
>

A more complex example:

iex> t = Nx.iota({900})
iex> t = Nx.reshape(t, {2, 15, 30})
iex> Nx.slice(t, [0, 4, 11], [2, 3, 9], strides: [2, 1, 3])
#Nx.Tensor<
  s64[1][3][3]
  [
    [
      [131, 134, 137],
      [161, 164, 167],
      [191, 194, 197]
    ]
  ]
>

tensors-as-start_indices

Tensors as start_indices

The start_indices list can be made of scalar tensors:

iex> Nx.slice(Nx.tensor([[1, 2, 3], [4, 5, 6]]), [Nx.tensor(1), Nx.tensor(2)], [1, 1])
#Nx.Tensor<
  s64[1][1]
  [
    [6]
  ]
>

iex> t = Nx.tensor([
...>   [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
...>   [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
...>   [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],
...>   [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],
...>   [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],
...>   [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]
...> ])
iex> Nx.slice(t, [Nx.tensor(0), Nx.tensor(0)], [6, 7], strides: [5, 3])
#Nx.Tensor<
  f32[2][3]
  [
    [0.0, 0.0, 0.0],
    [1.0, 1.0, 1.0]
  ]
>

clipping

Clipping

slice/3 will always guarantee the return tensor has the given lengths. See the following example:

iex> Nx.slice(Nx.iota({3, 3}), [2, 2], [1, 1])
#Nx.Tensor<
  s64[1][1]
  [
    [8]
  ]
>

In the example above, start_index + length <= dimension, so there is no clipping. However, if the start_index + length is to exceed the dimension, the index will be clipped in order to guarantee the given lengths:

iex> Nx.slice(Nx.iota({3, 3}), [2, 2], [2, 2])
#Nx.Tensor<
  s64[2][2]
  [
    [4, 5],
    [7, 8]
  ]
>

This also applies when the start index is given by tensors:

iex> Nx.slice(Nx.iota({3, 3}), [Nx.tensor(2), Nx.tensor(2)], [2, 2])
#Nx.Tensor<
  s64[2][2]
  [
    [4, 5],
    [7, 8]
  ]
>

error-cases

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
Link to this function

slice_along_axis(tensor, start_index, len, opts \\ [])

View Source

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

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

Examples

iex> Nx.slice_along_axis(Nx.iota({5, 2}), 1, 2, axis: 0)
#Nx.Tensor<
  s64[2][2]
  [
    [2, 3],
    [4, 5]
  ]
>

iex> Nx.slice_along_axis(Nx.iota({2, 5}), 1, 2, axis: 1)
#Nx.Tensor<
  s64[2][2]
  [
    [1, 2],
    [6, 7]
  ]
>

iex> Nx.slice_along_axis(Nx.iota({2, 5}, names: [:x, :y]), 0, 1, axis: :x)
#Nx.Tensor<
  s64[x: 1][y: 5]
  [
    [0, 1, 2, 3, 4]
  ]
>

iex> Nx.slice_along_axis(Nx.iota({2, 5}, names: [:x, :y]), Nx.tensor(0), 1, axis: :x)
#Nx.Tensor<
  s64[x: 1][y: 5]
  [
    [0, 1, 2, 3, 4]
  ]
>

iex> Nx.slice_along_axis(Nx.iota({2, 5}), 0, 3, axis: -1, strides: 2)
#Nx.Tensor<
  s64[2][2]
  [
    [0, 2],
    [5, 7]
  ]
>
Link to this function

take(tensor, indices, opts \\ [])

View Source

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

Options

  • :axis - an axis to take tensor slices over. Defaults to 0.

examples

Examples

iex> t = Nx.tensor([[1, 2], [3, 4]])
iex> Nx.take(t, Nx.tensor([1, 0, 1]))
#Nx.Tensor<
  s64[3][2]
  [
    [3, 4],
    [1, 2],
    [3, 4]
  ]
>

iex> t = Nx.tensor([[1, 2], [3, 4]])
iex> Nx.take(t, Nx.tensor([1, 0, 1]), axis: 1)
#Nx.Tensor<
  s64[2][3]
  [
    [2, 1, 2],
    [4, 3, 4]
  ]
>


iex> t = Nx.tensor([[1, 2], [3, 4]], names: [:x, :y])
iex> Nx.take(t, Nx.tensor([1, 0, 1]), axis: :y)
#Nx.Tensor<
  s64[x: 2][y: 3]
  [
    [2, 1, 2],
    [4, 3, 4]
  ]
>

iex> t = Nx.tensor([[[1, 2], [11, 12]], [[101, 102], [111, 112]]])
iex> Nx.take(t, Nx.tensor([1, 0, 1]), axis: 1)
#Nx.Tensor<
  s64[2][3][2]
  [
    [
      [11, 12],
      [1, 2],
      [11, 12]
    ],
    [
      [111, 112],
      [101, 102],
      [111, 112]
    ]
  ]
>

Multi-dimensional indices tensor:

iex> t = Nx.tensor([[1, 2], [11, 12]])
iex> Nx.take(t, Nx.tensor([[0, 0], [1, 1], [0, 0]]), axis: 1)
#Nx.Tensor<
  s64[2][3][2]
  [
    [
      [1, 1],
      [2, 2],
      [1, 1]
    ],
    [
      [11, 11],
      [12, 12],
      [11, 11]
    ]
  ]
>

iex> t = Nx.tensor([[[1, 2], [11, 12]], [[101, 102], [111, 112]]])
iex> Nx.take(t, Nx.tensor([[0, 0, 0], [1, 1, 1], [0, 0, 0]]), axis: 1)
#Nx.Tensor<
  s64[2][3][3][2]
  [
    [
      [
        [1, 2],
        [1, 2],
        [1, 2]
      ],
      [
        [11, 12],
        [11, 12],
        [11, 12]
      ],
      [
        [1, 2],
        [1, 2],
        [1, 2]
      ]
    ],
    [
      [
        [101, 102],
        [101, 102],
        [101, 102]
      ],
      [
        [111, 112],
        [111, 112],
        [111, 112]
      ],
      [
        [101, 102],
        [101, 102],
        [101, 102]
      ]
    ]
  ]
>

error-cases

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}
Link to this function

take_along_axis(tensor, indices, opts \\ [])

View Source

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

Options

  • :axis - The axis along which to take the values from. Defaults to 0.

examples

Examples

iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]])
iex> Nx.take_along_axis(t, Nx.tensor([[0, 0, 2, 2, 1, 1], [2, 2, 1, 1, 0, 0]]), axis: 1)
#Nx.Tensor<
  s64[2][6]
  [
    [1, 1, 3, 3, 2, 2],
    [6, 6, 5, 5, 4, 4]
  ]
>

iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]])
iex> Nx.take_along_axis(t, Nx.tensor([[0, 1, 1], [1, 0, 0], [0, 1, 0]]), axis: 0)
#Nx.Tensor<
  s64[3][3]
  [
    [1, 5, 6],
    [4, 2, 3],
    [1, 5, 3]
  ]
>

The indices returned from Nx.argsort/2 can be used with Nx.take_along_axis/3 to produce the sorted tensor (or to sort more tensors according to the same criteria).

iex> tensor = Nx.tensor([[[1, 2], [3, 4], [5, 6]]])
#Nx.Tensor<
  s64[1][3][2]
  [
    [
      [1, 2],
      [3, 4],
      [5, 6]
    ]
  ]
>
iex> idx1 = Nx.argsort(tensor, axis: 1, direction: :desc)
#Nx.Tensor<
  s64[1][3][2]
  [
    [
      [2, 2],
      [1, 1],
      [0, 0]
    ]
  ]
>
iex> Nx.take_along_axis(tensor, idx1, axis: 1)
#Nx.Tensor<
  s64[1][3][2]
  [
    [
      [5, 6],
      [3, 4],
      [1, 2]
    ]
  ]
>
iex> idx2 = Nx.argsort(tensor, axis: 2, direction: :desc)
#Nx.Tensor<
  s64[1][3][2]
  [
    [
      [1, 0],
      [1, 0],
      [1, 0]
    ]
  ]
>
iex> Nx.take_along_axis(tensor, idx2, axis: 2)
#Nx.Tensor<
  s64[1][3][2]
  [
    [
      [2, 1],
      [4, 3],
      [6, 5]
    ]
  ]
>

error-cases

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}

Link to this section Functions: N-dim

Link to this function

argsort(tensor, opts \\ [])

View Source

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.

options

Options

  • :axis - The name or number of the corresponding axis on which the sort should be applied
  • :direction - Can be :asc or :desc. Defaults to :asc

examples

Examples

iex> Nx.argsort(Nx.tensor([16, 23, 42, 4, 8, 15]))
#Nx.Tensor<
  s64[6]
  [3, 4, 5, 0, 1, 2]
>

iex> t = Nx.tensor([[3, 1, 7], [2, 5, 4]], names: [:x, :y])
iex> Nx.argsort(t, axis: :x)
#Nx.Tensor<
  s64[x: 2][y: 3]
  [
    [1, 0, 1],
    [0, 1, 0]
  ]
>

iex> t = Nx.tensor([[3, 1, 7], [2, 5, 4]], names: [:x, :y])
iex> Nx.argsort(t, axis: :y)
#Nx.Tensor<
  s64[x: 2][y: 3]
  [
    [1, 0, 2],
    [0, 2, 1]
  ]
>

iex> t = Nx.tensor([[3, 1, 7], [2, 5, 4]], names: [:x, :y])
iex> Nx.argsort(t, axis: :y, direction: :asc)
#Nx.Tensor<
  s64[x: 2][y: 3]
  [
    [1, 0, 2],
    [0, 2, 1]
  ]
>

Same tensor sorted over different axes:

iex> t = Nx.tensor(
...>   [
...>     [
...>       [4, 5, 2],
...>       [2, 5, 3],
...>       [5, 0, 2]
...>     ],
...>     [
...>       [1, 9, 8],
...>       [2, 1, 3],
...>       [2, 1, 4]
...>     ]
...>   ],
...>   names: [:x, :y, :z]
...> )
iex> Nx.argsort(t, axis: :x)
#Nx.Tensor<
  s64[x: 2][y: 3][z: 3]
  [
    [
      [1, 0, 0],
      [0, 1, 0],
      [1, 0, 0]
    ],
    [
      [0, 1, 1],
      [1, 0, 1],
      [0, 1, 1]
    ]
  ]
>
iex> Nx.argsort(t, axis: :y)
#Nx.Tensor<
  s64[x: 2][y: 3][z: 3]
  [
    [
      [1, 2, 0],
      [0, 0, 2],
      [2, 1, 1]
    ],
    [
      [0, 1, 1],
      [1, 2, 2],
      [2, 0, 0]
    ]
  ]
>
iex> Nx.argsort(t, axis: :z)
#Nx.Tensor<
  s64[x: 2][y: 3][z: 3]
  [
    [
      [2, 0, 1],
      [0, 2, 1],
      [1, 2, 0]
    ],
    [
      [0, 2, 1],
      [1, 0, 2],
      [1, 0, 2]
    ]
  ]
>
Link to this function

concatenate(tensors, opts \\ [])

View Source

Concatenates tensors along the given axis.

If no axis is provided, defaults to 0.

All tensors must have the same rank and all of their dimension sizes but the concatenated dimension must match.

If tensors are named, the names must be able to be merged.

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.

examples

Examples

iex> Nx.concatenate([Nx.tensor([1, 2, 3])])
#Nx.Tensor<
  s64[3]
  [1, 2, 3]
>

iex> Nx.concatenate([Nx.tensor([1, 2, 3]), Nx.tensor([4, 5, 6])])
#Nx.Tensor<
  s64[6]
  [1, 2, 3, 4, 5, 6]
>

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]
    ]
  ]
>

iex> t1 = Nx.iota({1, 3, 2}, names: [:x, :y, :z])
iex> t2 = Nx.iota({1, 1, 2}, names: [:x, :y, :z])
iex> t3 = Nx.iota({1, 2, 2}, names: [:x, :y, :z])
iex> Nx.concatenate([t1, t2, t3], axis: :y)
#Nx.Tensor<
  s64[x: 1][y: 6][z: 2]
  [
    [
      [0, 1],
      [2, 3],
      [4, 5],
      [0, 1],
      [0, 1],
      [2, 3]
    ]
  ]
>

iex> t1 = Nx.iota({2, 1, 4}, names: [:x, :y, :z])
iex> t2 = Nx.iota({2, 1, 1}, names: [:x, :y, :z])
iex> t3 = Nx.iota({2, 1, 3}, names: [:x, :y, :z])
iex> Nx.concatenate([t1, t2, t3], axis: :z)
#Nx.Tensor<
  s64[x: 2][y: 1][z: 8]
  [
    [
      [0, 1, 2, 3, 0, 0, 1, 2]
    ],
    [
      [4, 5, 6, 7, 1, 3, 4, 5]
    ]
  ]
>

iex> t1 = Nx.iota({2, 1, 4}, names: [:x, :y, :z])
iex> Nx.concatenate([t1], axis: :z)
#Nx.Tensor<
  s64[x: 2][y: 1][z: 4]
  [
    [
      [0, 1, 2, 3]
    ],
    [
      [4, 5, 6, 7]
    ]
  ]
>
Link to this function

conv(tensor, kernel, opts \\ [])

View Source

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

Examples

iex> left = Nx.iota({9})
iex> left = Nx.reshape(left, {1, 1, 3, 3})
iex> right = Nx.iota({4})
iex> right = Nx.reshape(right, {4, 1, 1, 1})
iex> Nx.conv(left, right, strides: [1, 1])
#Nx.Tensor<
  f32[1][4][3][3]
  [
    [
      [
        [0.0, 0.0, 0.0],
        [0.0, 0.0, 0.0],
        [0.0, 0.0, 0.0]
      ],
      [
        [0.0, 1.0, 2.0],
        [3.0, 4.0, 5.0],
        [6.0, 7.0, 8.0]
      ],
      [
        [0.0, 2.0, 4.0],
        [6.0, 8.0, 10.0],
        [12.0, 14.0, 16.0]
      ],
      [
        [0.0, 3.0, 6.0],
        [9.0, 12.0, 15.0],
        [18.0, 21.0, 24.0]
      ]
    ]
  ]
>

iex> left = Nx.iota({9})
iex> left = Nx.reshape(left, {1, 1, 3, 3})
iex> right = Nx.iota({8})
iex> right = Nx.reshape(right, {4, 1, 2, 1})
iex> Nx.conv(left, right, strides: 2, padding: :same, kernel_dilation: [2, 1])
#Nx.Tensor<
  f32[1][4][2][2]
  [
    [
      [
        [3.0, 5.0],
        [0.0, 0.0]
      ],
      [
        [9.0, 15.0],
        [6.0, 10.0]
      ],
      [
        [15.0, 25.0],
        [12.0, 20.0]
      ],
      [
        [21.0, 35.0],
        [18.0, 30.0]
      ]
    ]
  ]
>

Complex tensors are also supported:

iex> left = Nx.tensor([[[Complex.new(1, 1), 2, Complex.new(3, -3)]]])
iex> right = Nx.tensor([[[1, Complex.new(0, 2), Complex.new(0, 3)]]])
iex> Nx.conv(left, right, padding: [{2, 2}])
#Nx.Tensor<
  c64[1][1][5]
  [
    [
      [-3.0+3.0i, -2.0+8.0i, 10.0+14.0i, 8.0+6.0i, 3.0-3.0i]
    ]
  ]
>

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

Examples

dot-product-of-scalars

Dot product of scalars

iex> Nx.dot(5, 5)
#Nx.Tensor<
  s64
  25
>

iex> Nx.dot(-2.0, 5.0)
#Nx.Tensor<
  f32
  -10.0
>

iex> Nx.dot(2, 2.0)
#Nx.Tensor<
  f32
  4.0
>

dot-product-of-vectors

Dot product of vectors

iex> Nx.dot(Nx.tensor([1, 2, 3]), Nx.tensor([4, 5, 6]))
#Nx.Tensor<
  s64
  32
>

iex> Nx.dot(Nx.tensor([2.0, 4.0, 3.0, 5.0]), Nx.tensor([1.0, 2.0, 3.0, 4.0]))
#Nx.Tensor<
  f32
  39.0
>

iex> Nx.dot(Nx.tensor([1.0, 2.0, 3.0]), Nx.tensor([1, 2, 3]))
#Nx.Tensor<
  f32
  14.0
>

dot-product-of-matrices

Dot product of matrices

iex> left = Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:i, :j])
iex> right = Nx.tensor([[7, 8], [9, 10], [11, 12]], names: [:x, :y])
iex> Nx.dot(left, right)
#Nx.Tensor<
  s64[i: 2][y: 2]
  [
    [58, 64],
    [139, 154]
  ]
>

iex> left = Nx.tensor([[10.0, 13.0, 14.0, 15.0], [59.0, 20.0, 10.0, 30.0]], names: [:i, :j])
iex> right = Nx.tensor([[2.0, 4.0], [5.0, 1.0], [6.0, 8.0], [9.0, 10.0]], names: [:x, :y])
iex> Nx.dot(left, right)
#Nx.Tensor<
  f32[i: 2][y: 2]
  [
    [304.0, 315.0],
    [548.0, 636.0]
  ]
>

iex> left = Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:i, :j])
iex> right = Nx.tensor([[7.0, 8.0], [9.0, 10.0], [11.0, 12.0]], names: [:x, :y])
iex> Nx.dot(left, right)
#Nx.Tensor<
  f32[i: 2][y: 2]
  [
    [58.0, 64.0],
    [139.0, 154.0]
  ]
>

dot-product-of-vector-and-n-d-tensor

Dot product of vector and n-d tensor

iex> left = Nx.tensor([[[1, 2], [3, 4]], [[5, 6], [7, 8]]], names: [:i, :j, :k])
iex> right = Nx.tensor([5, 10], names: [:x])
iex> Nx.dot(left, right)
#Nx.Tensor<
  s64[i: 2][j: 2]
  [
    [25, 55],
    [85, 115]
  ]
>

iex> left = Nx.tensor([5, 10], names: [:x])
iex> right = Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:i, :j])
iex> Nx.dot(left, right)
#Nx.Tensor<
  s64[j: 3]
  [45, 60, 75]
>

iex> left = Nx.tensor([[[[[1.0, 2.0], [3.0, 4.0]], [[5.0, 6.0], [7.0, 8.0]]]]], names: [:shard, :batch, :x, :y, :z])
iex> right = Nx.tensor([2.0, 2.0], names: [:data])
iex> Nx.dot(left, right)
#Nx.Tensor<
  f32[shard: 1][batch: 1][x: 2][y: 2]
  [
    [
      [
        [6.0, 14.0],
        [22.0, 30.0]
      ]
    ]
  ]
>

dot-product-of-n-d-and-m-d-tensor

Dot product of n-D and m-D tensor

iex> left = Nx.tensor([[[1, 2, 3], [4, 5, 6], [7, 8, 9]], [[1, 2, 3], [4, 5, 6], [7, 8, 9]]], names: [:x, :y, :z])
iex> right = Nx.tensor([[[1, 2, 3], [3, 4, 5], [5, 6, 7]]], names: [:i, :j, :k])
iex> Nx.dot(left, right)
#Nx.Tensor<
  s64[x: 2][y: 3][i: 1][k: 3]
  [
    [
      [
        [22, 28, 34]
      ],
      [
        [49, 64, 79]
      ],
      [
        [76, 100, 124]
      ]
    ],
    [
      [
        [22, 28, 34]
      ],
      [
        [49, 64, 79]
      ],
      [
        [76, 100, 124]
      ]
    ]
  ]
>

error-cases

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)
Link to this function

dot(t1, contract_axes1, t2, contract_axes2)

View Source

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

Examples

iex> t1 = Nx.tensor([[1, 2], [3, 4]], names: [:x, :y])
iex> t2 = Nx.tensor([[10, 20], [30, 40]], names: [:height, :width])
iex> Nx.dot(t1, [0], t2, [0])
#Nx.Tensor<
  s64[y: 2][width: 2]
  [
    [100, 140],
    [140, 200]
  ]
>

iex> t1 = Nx.tensor([[0.0, 1.0, 2.0], [3.0, 4.0, 5.0]])
iex> t2 = Nx.tensor([[0.0, 1.0], [2.0, 3.0], [4.0, 5.0]])
iex> Nx.dot(t1, [0, 1], t2, [1, 0])
#Nx.Tensor<
  f32
  50.0
>
Link to this function

dot(t1, contract_axes1, batch_axes1, t2, contract_axes2, batch_axes2)

View Source

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

Examples

contracting-along-axes

Contracting along axes

iex> t1 = Nx.tensor([[1, 2], [3, 4]], names: [:x, :y])
iex> t2 = Nx.tensor([[10, 20], [30, 40]], names: [:height, :width])
iex> Nx.dot(t1, [0], [], t2, [0], [])
#Nx.Tensor<
  s64[y: 2][width: 2]
  [
    [100, 140],
    [140, 200]
  ]
>
iex> Nx.dot(t1, [0], [], t2, [1], [])
#Nx.Tensor<
  s64[y: 2][height: 2]
  [
    [70, 150],
    [100, 220]
  ]
>
iex> Nx.dot(t1, [1], [], t2, [0], [])
#Nx.Tensor<
  s64[x: 2][width: 2]
  [
    [70, 100],
    [150, 220]
  ]
>
iex> Nx.dot(t1, [1], [], t2, [1], [])
#Nx.Tensor<
  s64[x: 2][height: 2]
  [
    [50, 110],
    [110, 250]
  ]
>
iex> Nx.dot(t1, [0, 1], [], t2, [0, 1], [])
#Nx.Tensor<
  s64
  300
>

If no axes are given, it works like outer/2:

iex> t1 = Nx.tensor([[1, 2], [3, 4]])
iex> t2 = Nx.tensor([[10, 20], [30, 40]])
iex> Nx.dot(t1, [], [], t2, [], [])
#Nx.Tensor<
  s64[2][2][2][2]
  [
    [
      [
        [10, 20],
        [30, 40]
      ],
      [
        [20, 40],
        [60, 80]
      ]
    ],
    [
      [
        [30, 60],
        [90, 120]
      ],
      [
        [40, 80],
        [120, 160]
      ]
    ]
  ]
>

dot-product-between-two-batched-tensors

Dot product between two batched tensors

iex> u = Nx.tensor([[[1]], [[2]]])
iex> v = Nx.tensor([[[3]], [[4]]])
iex> Nx.dot(u, [2], [0], v, [2], [0])
#Nx.Tensor<
  s64[2][1][1]
  [
    [
      [3]
    ],
    [
      [8]
    ]
  ]
>

iex> u = Nx.tensor([[[1, 1]], [[2, 2]]])
iex> v = Nx.tensor([[[3], [3]], [[4], [4]]])
iex> Nx.dot(u, [2], [0], v, [1], [0])
#Nx.Tensor<
  s64[2][1][1]
  [
    [
      [6]
    ],
    [
      [16]
    ]
  ]
>

error-cases

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])

Calculates the DFT of the given tensor.

options

Options

  • :eps - Threshold which backends can use for cleaning-up results. Defaults to 1.0e-10.
  • :length - Either a positive integer or :power_of_two. Will pad or slice the tensor accordingly. :power_of_two will automatically pad to the next power of two.

examples

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, 0, 0, 0]))
#Nx.Tensor<
  c64[5]
  [2.0+0.0i, 1.3090169429779053-0.9510565400123596i, 0.19098301231861115-0.5877852439880371i, 0.19098301231861115+0.5877852439880371i, 1.3090169429779053+0.9510565400123596i]
>

iex> Nx.fft(Nx.tensor([1, 1, 1, 0, 1, 1]))
#Nx.Tensor<
  c64[6]
  [5.0+0.0i, 1.0+0.0i, -1.0+0.0i, 1.0+0.0i, -1.0+0.0i, 1.0+0.0i]
>

Padding and slicing can be introduced through :length:

iex> Nx.fft(Nx.tensor([1, 1]), length: 4)
#Nx.Tensor<
  c64[4]
  [2.0+0.0i, 1.0-1.0i, 0.0+0.0i, 1.0+1.0i]
>

iex> Nx.fft(Nx.tensor([1, 1, 0]), length: :power_of_two)
#Nx.Tensor<
  c64[4]
  [2.0+0.0i, 1.0-1.0i, 0.0+0.0i, 1.0+1.0i]
>

iex> Nx.fft(Nx.tensor([1, 1, 0, 0, 2, 3]), length: 4)
#Nx.Tensor<
  c64[4]
  [2.0+0.0i, 1.0-1.0i, 0.0+0.0i, 1.0+1.0i]
>

If an N-dimensional tensor is passed, the DFT is applied to its last axis:

iex> Nx.fft(Nx.tensor([[1, 1, 0, 0, 2, 3], [1, 0, 0, 0, 2, 3]]), length: 4)
#Nx.Tensor<
  c64[2][4]
  [
    [2.0+0.0i, 1.0-1.0i, 0.0+0.0i, 1.0+1.0i],
    [1.0+0.0i, 1.0+0.0i, 1.0+0.0i, 1.0+0.0i]
  ]
>

error-cases

Error Cases

iex> Nx.fft(Nx.tensor([1, 1]), length: :invalid)
** (RuntimeError) expected an integer or :power_of_two as length, got: :invalid
Link to this function

ifft(tensor, opts \\ [])

View Source

Calculates the Inverse DFT of the given tensor.

options

Options

  • :eps - Threshold which backends can use for cleaning-up results. Defaults to 1.0e-10.
  • :length - Either a positive integer or :power_of_two. Will pad or slice the tensor accordingly. :power_of_two will automatically pad to the next power of two.

examples

Examples

iex> Nx.ifft(Nx.tensor([2, Complex.new(1, -1), 0, Complex.new(1, 1)]))
#Nx.Tensor<
  c64[4]
  [1.0+0.0i, 1.0+0.0i, 0.0+0.0i, 0.0+0.0i]
>

iex> Nx.ifft(Nx.tensor([5, 1, -1, 1, -1, 1]))
#Nx.Tensor<
  c64[6]
  [1.0+0.0i, 1.0+0.0i, 1.0+0.0i, 0.0+0.0i, 1.0+0.0i, 1.0+0.0i]
>

Padding and slicing can be introduced through :length:

iex> Nx.ifft(Nx.tensor([1, 1]), length: 4)
#Nx.Tensor<
  c64[4]
  [0.5+0.0i, 0.25+0.25i, 0.0+0.0i, 0.25-0.25i]
>

iex> Nx.ifft(Nx.tensor([1, 1, 0]), length: :power_of_two)
#Nx.Tensor<
  c64[4]
  [0.5+0.0i, 0.25+0.25i, 0.0+0.0i, 0.25-0.25i]
>

iex> Nx.ifft(Nx.tensor([1, 1, 0, 0, 2, 3]), length: 4)
#Nx.Tensor<
  c64[4]
  [0.5+0.0i, 0.25+0.25i, 0.0+0.0i, 0.25-0.25i]
>

If an N-dimensional tensor is passed, the Inverse DFT is applied to its last axis:

iex> Nx.ifft(Nx.tensor([[1, 1, 0, 0, 2, 3], [1, 0, 0, 0, 2, 3]]), length: 4)
#Nx.Tensor<
  c64[2][4]
  [
    [0.5+0.0i, 0.25+0.25i, 0.0+0.0i, 0.25-0.25i],
    [0.25+0.0i, 0.25+0.0i, 0.25+0.0i, 0.25+0.0i]
  ]
>

error-cases

Error Cases

iex> Nx.ifft(Nx.tensor([1, 1]), length: :invalid)
** (RuntimeError) expected an integer or :power_of_two as length, got: :invalid

Computes the outer product of two tensors.

The output is always a two-dimensional tensor.

examples

Examples

iex> Nx.outer(Nx.tensor([1, 2, 3], names: [:x]), 100)
#Nx.Tensor<
  s64[x: 3][1]
  [
    [100],
    [200],
    [300]
  ]
>

iex> Nx.outer(Nx.tensor([1, 2, 3], names: [:x]), Nx.tensor([10, 20], names: [:y]))
#Nx.Tensor<
  s64[x: 3][y: 2]
  [
    [10, 20],
    [20, 40],
    [30, 60]
  ]
>

iex> Nx.outer(Nx.tensor([[1, 2], [3, 4]], names: [:x, :y]), Nx.tensor([10, 20, 30], names: [:z]))
#Nx.Tensor<
  s64[x: 4][z: 3]
  [
    [10, 20, 30],
    [20, 40, 60],
    [30, 60, 90],
    [40, 80, 120]
  ]
>
Link to this function

reverse(tensor, opts \\ [])

View Source

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

Examples

iex> Nx.reverse(Nx.tensor([1, 2, 3]))
#Nx.Tensor<
  s64[3]
  [3, 2, 1]
>

iex> Nx.reverse(Nx.tensor([[1, 2, 3], [4, 5, 6]]))
#Nx.Tensor<
  s64[2][3]
  [
    [6, 5, 4],
    [3, 2, 1]
  ]
>

iex> Nx.reverse(Nx.tensor([1, 2, 3], names: [:x]), axes: [:x])
#Nx.Tensor<
  s64[x: 3]
  [3, 2, 1]
>

iex> Nx.reverse(Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:x, :y]), axes: [:x])
#Nx.Tensor<
  s64[x: 2][y: 3]
  [
    [4, 5, 6],
    [1, 2, 3]
  ]
>

iex> Nx.reverse(Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:x, :y]), axes: [:y])
#Nx.Tensor<
  s64[x: 2][y: 3]
  [
    [3, 2, 1],
    [6, 5, 4]
  ]
>

iex> Nx.reverse(Nx.iota({2, 2, 2}, type: :f32, names: [:x, :y, :z]), axes: [:x, :z])
#Nx.Tensor<
  f32[x: 2][y: 2][z: 2]
  [
    [
      [5.0, 4.0],
      [7.0, 6.0]
    ],
    [
      [1.0, 0.0],
      [3.0, 2.0]
    ]
  ]
>
Link to this function

sort(tensor, opts \\ [])

View Source

Sorts the tensor along the given axis according to the given direction.

If no axis is given, defaults to 0.

options

Options

  • :axis - The name or number of the corresponding axis on which the sort should be applied
  • :direction - Can be :asc or :desc. Defaults to :asc

examples

Examples

iex> Nx.sort(Nx.tensor([16, 23, 42, 4, 8, 15]))
#Nx.Tensor<
  s64[6]
  [4, 8, 15, 16, 23, 42]
>

iex> t = Nx.tensor([[3, 1, 7], [2, 5, 4]], names: [:x, :y])
iex> Nx.sort(t, axis: :x)
#Nx.Tensor<
  s64[x: 2][y: 3]
  [
    [2, 1, 4],
    [3, 5, 7]
  ]
>

iex> t = Nx.tensor([[3, 1, 7], [2, 5, 4]], names: [:x, :y])
iex> Nx.sort(t, axis: :y)
#Nx.Tensor<
  s64[x: 2][y: 3]
  [
    [1, 3, 7],
    [2, 4, 5]
  ]
>

iex> t = Nx.tensor([[3, 1, 7], [2, 5, 4]], names: [:x, :y])
iex> Nx.sort(t, axis: :y, direction: :asc)
#Nx.Tensor<
  s64[x: 2][y: 3]
  [
    [1, 3, 7],
    [2, 4, 5]
  ]
>

iex> t = Nx.tensor(
...>   [
...>     [[4, 5], [2, 5], [5, 0]],
...>     [[1, 9], [2, 1], [2, 1]],
...>     [[0, -1], [-1, 0], [0, -1]],
...>     [[-1, 0], [0, -1], [-1, 0]]
...>   ],
...>   names: [:x, :y, :z]
...> )
iex> Nx.sort(t, axis: :x)
#Nx.Tensor<
  s64[x: 4][y: 3][z: 2]
  [
    [
      [-1, -1],
      [-1, -1],
      [-1, -1]
    ],
    [
      [0, 0],
      [0, 0],
      [0, 0]
    ],
    [
      [1, 5],
      [2, 1],
      [2, 0]
    ],
    [
      [4, 9],
      [2, 5],
      [5, 1]
    ]
  ]
>

Same tensor sorted over different axes:

iex> t = Nx.tensor(
...>   [
...>     [
...>       [4, 5, 2],
...>       [2, 5, 3],
...>       [5, 0, 2]
...>     ],
...>     [
...>       [1, 9, 8],
...>       [2, 1, 3],
...>       [2, 1, 4]
...>     ]
...>   ],
...>   names: [:x, :y, :z]
...> )
iex> Nx.sort(t, axis: :x)
#Nx.Tensor<
  s64[x: 2][y: 3][z: 3]
  [
    [
      [1, 5, 2],
      [2, 1, 3],
      [2, 0, 2]
    ],
    [
      [4, 9, 8],
      [2, 5, 3],
      [5, 1, 4]
    ]
  ]
>
iex> Nx.sort(t, axis: :y)
#Nx.Tensor<
  s64[x: 2][y: 3][z: 3]
  [
    [
      [2, 0, 2],
      [4, 5, 2],
      [5, 5, 3]
    ],
    [
      [1, 1, 3],
      [2, 1, 4],
      [2, 9, 8]
    ]
  ]
>
iex> Nx.sort(t, axis: :z)
#Nx.Tensor<
  s64[x: 2][y: 3][z: 3]
  [
    [
      [2, 4, 5],
      [2, 3, 5],
      [0, 2, 5]
    ],
    [
      [1, 8, 9],
      [1, 2, 3],
      [1, 2, 4]
    ]
  ]
>
Link to this function

stack(tensors, opts \\ [])

View Source

Joins a list of tensors with the same shape along a new axis.

options

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

Examples

iex> Nx.stack([1, 2, 3])
#Nx.Tensor<
  s64[3]
  [1, 2, 3]
>

iex> Nx.stack([Nx.tensor([1, 2, 3]), Nx.tensor([4, 5, 6])])
#Nx.Tensor<
  s64[2][3]
  [
    [1, 2, 3],
    [4, 5, 6]
  ]
>

iex> t1 = Nx.iota({2, 1, 4})
iex> t2 = Nx.iota({2, 1, 4})
iex> t3 = Nx.iota({2, 1, 4})
iex> Nx.stack([t1, t2, t3], axis: -1)
#Nx.Tensor<
  s64[2][1][4][3]
  [
    [
      [
        [0, 0, 0],
        [1, 1, 1],
        [2, 2, 2],
        [3, 3, 3]
      ]
    ],
    [
      [
        [4, 4, 4],
        [5, 5, 5],
        [6, 6, 6],
        [7, 7, 7]
      ]
    ]
  ]
>

iex> t1 = Nx.iota({2, 1, 4})
iex> t2 = Nx.iota({2, 1, 4})
iex> t3 = Nx.iota({2, 1, 4})
iex> Nx.stack([t1, t2, t3], axis: 1)
#Nx.Tensor<
  s64[2][3][1][4]
  [
    [
      [
        [0, 1, 2, 3]
      ],
      [
        [0, 1, 2, 3]
      ],
      [
        [0, 1, 2, 3]
      ]
    ],
    [
      [
        [4, 5, 6, 7]
      ],
      [
        [4, 5, 6, 7]
      ],
      [
        [4, 5, 6, 7]
      ]
    ]
  ]
>

iex> Nx.stack([Nx.tensor(1), Nx.tensor(2)], name: :x)
#Nx.Tensor<
  s64[x: 2]
  [1, 2]
>

Link to this section Functions: Shape

Returns all of the axes in a tensor.

If a shape is given, it returns the axes for the given shape.

examples

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]
Link to this function

axis_index(tensor, axis)

View Source

Returns the index of the given axis in the tensor.

examples

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

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) key :z not found in tensor with names [:batch, :x, :y]

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

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
Link to this function

broadcast(tensor, shape, opts \\ [])

View Source

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

Examples

without-axes

Without axes

examples-1

Examples

iex> Nx.broadcast(1, {1, 2, 3})
#Nx.Tensor<
  s64[1][2][3]
  [
    [
      [1, 1, 1],
      [1, 1, 1]
    ]
  ]
>

iex> Nx.broadcast(Nx.tensor([[1], [2]], names: [:x, :y]), Nx.tensor([[10, 20], [30, 40]], names: [:i, :j]))
#Nx.Tensor<
  s64[i: 2][j: 2]
  [
    [1, 1],
    [2, 2]
  ]
>

iex> Nx.broadcast(Nx.tensor([[1, 2]], names: [:x, :y]), Nx.tensor([[10, 20], [30, 40]], names: [:i, :j]))
#Nx.Tensor<
  s64[i: 2][j: 2]
  [
    [1, 2],
    [1, 2]
  ]
>

Note that, even if there is no broadcasting because the shape is the same, names are discarded if none are given:

iex> Nx.broadcast(Nx.iota({2, 2}, names: [:x, :y]), {2, 2})
#Nx.Tensor<
  s64[2][2]
  [
    [0, 1],
    [2, 3]
  ]
>

iex> Nx.broadcast(Nx.iota({2, 2}, names: [:x, :y]), {2, 2}, names: [:i, :j])
#Nx.Tensor<
  s64[i: 2][j: 2]
  [
    [0, 1],
    [2, 3]
  ]
>

with-axes

With axes

Using the default broadcast rules, we cannot broadcast a tensor of shape (3) to the shape (3, 2), because the lower dimensions must match. But with Nx.broadcast/3 we can configure how the dimensions match:

iex> t = Nx.tensor([1, 2, 3])
iex> Nx.broadcast(t, {3, 2}, axes: [0], names: [:x, :y])
#Nx.Tensor<
  s64[x: 3][y: 2]
  [
    [1, 1],
    [2, 2],
    [3, 3]
  ]
>

Or a more complex example:

iex> t = Nx.tensor([1, 2, 3])
iex> Nx.broadcast(t, {2, 3, 2}, axes: [1], names: [:x, :y, :z])
#Nx.Tensor<
  s64[x: 2][y: 3][z: 2]
  [
    [
      [1, 1],
      [2, 2],
      [3, 3]
    ],
    [
      [1, 1],
      [2, 2],
      [3, 3]
    ]
  ]
>

Returns the byte size of the data in the tensor computed from its shape and type.

examples

Examples

iex> Nx.byte_size(Nx.tensor([[1, 2, 3], [4, 5, 6]]))
48
iex> Nx.byte_size(Nx.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]]))
24
iex> Nx.byte_size(Nx.tensor([[1, 2, 3], [4, 5, 6]], type: :u8))
6
iex> Nx.byte_size(1)
8
Link to this function

compatible?(left, right)

View Source

Checks if two tensors have the same shape, type, and compatible names.

The data in the tensor is ignored.

For convenience, this function accepts tensors and any container (such as maps and tuples as defined by the Nx.Container protocol) and recursively compares them, observing their container data structures are also the same.

examples

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

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

Examples

iex> t = Nx.iota({2, 2, 2, 2})
#Nx.Tensor<
  s64[2][2][2][2]
  [
    [
      [
        [0, 1],
        [2, 3]
      ],
      [
        [4, 5],
        [6, 7]
      ]
    ],
    [
      [
        [8, 9],
        [10, 11]
      ],
      [
        [12, 13],
        [14, 15]
      ]
    ]
  ]
>
iex> Nx.flatten(t)
#Nx.Tensor<
  s64[16]
  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
>

And if the tensor is already 1-dimensional:

iex> t = Nx.iota({16})
#Nx.Tensor<
  s64[16]
  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
>
iex> Nx.flatten(t)
#Nx.Tensor<
  s64[16]
  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
>

Returns all of the names in a tensor.

examples

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)
[]
Link to this function

new_axis(tensor, axis, name \\ nil)

View Source

Adds a new axis of size 1 with optional name.

examples

Examples

iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]])
iex> Nx.new_axis(t, 0, :new)
#Nx.Tensor<
  s64[new: 1][2][3]
  [
    [
      [1, 2, 3],
      [4, 5, 6]
    ]
  ]
>
iex> Nx.new_axis(t, 1, :new)
#Nx.Tensor<
  s64[2][new: 1][3]
  [
    [
      [1, 2, 3]
    ],
    [
      [4, 5, 6]
    ]
  ]
>
iex> Nx.new_axis(t, 2, :new)
#Nx.Tensor<
  s64[2][3][new: 1]
  [
    [
      [1],
      [2],
      [3]
    ],
    [
      [4],
      [5],
      [6]
    ]
  ]
>

Axis can also be negative, which will start from the back:

iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]])
iex> Nx.new_axis(t, -1, :new)
#Nx.Tensor<
  s64[2][3][new: 1]
  [
    [
      [1],
      [2],
      [3]
    ],
    [
      [4],
      [5],
      [6]
    ]
  ]
>
Link to this function

pad(tensor, pad_value, padding_config)

View Source

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.

examples

Examples

iex> Nx.pad(Nx.tensor(1), 0, [])
#Nx.Tensor<
  s64
  1
>

iex> Nx.pad(Nx.tensor([1, 2, 3], names: [:data]), 0, [{1, 1, 0}])
#Nx.Tensor<
  s64[data: 5]
  [0, 1, 2, 3, 0]
>

iex> Nx.pad(Nx.tensor([[1, 2, 3], [4, 5, 6]]), 0, [{0, 0, 1}, {0, 0, 1}])
#Nx.Tensor<
  s64[3][5]
  [
    [1, 0, 2, 0, 3],
    [0, 0, 0, 0, 0],
    [4, 0, 5, 0, 6]
  ]
>

iex> Nx.pad(Nx.tensor([[1, 2, 3], [4, 5, 6]]), 0, [{1, 1, 0}, {1, 1, 0}])
#Nx.Tensor<
  s64[4][5]
  [
    [0, 0, 0, 0, 0],
    [0, 1, 2, 3, 0],
    [0, 4, 5, 6, 0],
    [0, 0, 0, 0, 0]
  ]
>

iex> tensor = Nx.tensor([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])
iex> Nx.pad(tensor, 0, [{0, 2, 0}, {1, 1, 0}, {1, 0, 0}])
#Nx.Tensor<
  s64[4][4][3]
  [
    [
      [0, 0, 0],
      [0, 1, 2],
      [0, 3, 4],
      [0, 0, 0]
    ],
    [
      [0, 0, 0],
      [0, 5, 6],
      [0, 7, 8],
      [0, 0, 0]
    ],
    [
      [0, 0, 0],
      [0, 0, 0],
      [0, 0, 0],
      [0, 0, 0]
    ],
    [
      [0, 0, 0],
      [0, 0, 0],
      [0, 0, 0],
      [0, 0, 0]
    ]
  ]
>

iex> tensor = Nx.tensor([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])
iex> Nx.pad(tensor, 0, [{1, 0, 0}, {1, 1, 0}, {0, 1, 0}])
#Nx.Tensor<
  s64[3][4][3]
  [
    [
      [0, 0, 0],
      [0, 0, 0],
      [0, 0, 0],
      [0, 0, 0]
    ],
    [
      [0, 0, 0],
      [1, 2, 0],
      [3, 4, 0],
      [0, 0, 0]
    ],
    [
      [0, 0, 0],
      [5, 6, 0],
      [7, 8, 0],
      [0, 0, 0]
    ]
  ]
>

iex> tensor = Nx.tensor([[[1.0, 2.0], [3.0, 4.0]], [[5.0, 6.0], [7.0, 8.0]]])
iex> Nx.pad(tensor, 0.0, [{1, 2, 0}, {1, 0, 0}, {0, 1, 0}])
#Nx.Tensor<
  f32[5][3][3]
  [
    [
      [0.0, 0.0, 0.0],
      [0.0, 0.0, 0.0],
      [0.0, 0.0, 0.0]
    ],
    [
      [0.0, 0.0, 0.0],
      [1.0, 2.0, 0.0],
      [3.0, 4.0, 0.0]
    ],
    [
      [0.0, 0.0, 0.0],
      [5.0, 6.0, 0.0],
      [7.0, 8.0, 0.0]
    ],
    [
      [0.0, 0.0, 0.0],
      [0.0, 0.0, 0.0],
      [0.0, 0.0, 0.0]
    ],
    [
      [0.0, 0.0, 0.0],
      [0.0, 0.0, 0.0],
      [0.0, 0.0, 0.0]
    ]
  ]
>

iex> Nx.pad(Nx.tensor([0, 1, 2, 3, 0]), 0, [{-1, -1, 0}])
#Nx.Tensor<
  s64[3]
  [1, 2, 3]
>

iex> tensor = Nx.tensor([
...>   [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]],
...>   [[0, 0, 0], [1, 2, 0], [3, 4, 0], [0, 0, 0]],
...>   [[0, 0, 0], [5, 6, 0], [7, 8, 0], [0, 0, 0]]
...> ])
iex> Nx.pad(tensor, 0, [{-1, 0, 0}, {-1, -1, 0}, {0, -1, 0}])
#Nx.Tensor<
  s64[2][2][2]
  [
    [
      [1, 2],
      [3, 4]
    ],
    [
      [5, 6],
      [7, 8]
    ]
  ]
>

iex> tensor = Nx.tensor([[0, 1, 2, 3], [0, 4, 5, 6]])
iex> Nx.pad(tensor, 0, [{0, 0, 0}, {-1, 1, 0}])
#Nx.Tensor<
  s64[2][4]
  [
    [1, 2, 3, 0],
    [4, 5, 6, 0]
  ]
>

iex> tensor = Nx.tensor([[0, 1, 2], [3, 4, 5]], type: :f32)
iex> Nx.pad(tensor, 0, [{-1, 2, 0}, {1, -1, 0}])
#Nx.Tensor<
  f32[3][3]
  [
    [0.0, 3.0, 4.0],
    [0.0, 0.0, 0.0],
    [0.0, 0.0, 0.0]
  ]
>

Returns the rank of a tensor.

If a tuple is given as a shape, it computes the rank of the given tuple.

examples

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

Adds (or overrides) the given names to the tensor.

examples

Examples

iex> Nx.rename(Nx.iota({2, 3}), [:foo, :bar])
#Nx.Tensor<
  s64[foo: 2][bar: 3]
  [
    [0, 1, 2],
    [3, 4, 5]
  ]
>
Link to this function

reshape(tensor, new_shape, opts \\ [])

View Source

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

Examples

iex> t = Nx.tensor([1, 2, 3, 4], names: [:x])
iex> Nx.reshape(t, {2, 2}, names: [:x, :y])
#Nx.Tensor<
  s64[x: 2][y: 2]
  [
    [1, 2],
    [3, 4]
  ]
>

The shape can also be an existing tensor:

iex> shape = Nx.tensor([[0], [0], [0], [0]], names: [:x, :y])
iex> Nx.reshape(Nx.tensor([1, 2, 3, 4]), shape)
#Nx.Tensor<
  s64[x: 4][y: 1]
  [
    [1],
    [2],
    [3],
    [4]
  ]
>

Even a scalar can be transformed into a 3-dimensional tensor:

iex> t = Nx.tensor(1)
iex> Nx.reshape(t, {1, 1, 1}, names: [:x, :y, :z])
#Nx.Tensor<
  s64[x: 1][y: 1][z: 1]
  [
    [
      [1]
    ]
  ]
>

You can use :auto to infer dimension sizes. This is useful when you don't know the size some dimension should be ahead of time:

iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]])
iex> Nx.reshape(t, {:auto, 2}, names: [:x, :y])
#Nx.Tensor<
  s64[x: 3][y: 2]
  [
    [1, 2],
    [3, 4],
    [5, 6]
  ]
>

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

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}

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.

examples

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
Link to this function

squeeze(tensor, opts \\ [])

View Source

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

Examples

iex> Nx.squeeze(Nx.tensor([[[[[1]]]]]))
#Nx.Tensor<
  s64
  1
>

iex> Nx.squeeze(Nx.tensor([[[[1]]], [[[2]]]], names: [:x, :y, :z, :i]))
#Nx.Tensor<
  s64[x: 2]
  [1, 2]
>

iex> Nx.squeeze(Nx.tensor([[1, 2, 3]], names: [:x, :y]), axes: [:x])
#Nx.Tensor<
  s64[y: 3]
  [1, 2, 3]
>

iex> Nx.squeeze(Nx.tensor([[1], [2]], names: [:x, :y]), axes: [:y])
#Nx.Tensor<
  s64[x: 2]
  [1, 2]
>

error-cases

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
Link to this function

tile(tensor, repetitions)

View Source

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

Examples

iex> a = Nx.tensor([0, 1, 2])
iex> Nx.tile(a, [2])
#Nx.Tensor<
  s64[6]
  [0, 1, 2, 0, 1, 2]
>
iex> Nx.tile(a, [1, 2])
#Nx.Tensor<
  s64[1][6]
  [
    [0, 1, 2, 0, 1, 2]
  ]
>
iex> Nx.tile(a, [2, 2])
#Nx.Tensor<
  s64[2][6]
  [
    [0, 1, 2, 0, 1, 2],
    [0, 1, 2, 0, 1, 2]
  ]
>
iex> Nx.tile(a, [2, 1])
#Nx.Tensor<
  s64[2][3]
  [
    [0, 1, 2],
    [0, 1, 2]
  ]
>
iex> Nx.tile(a, [2, 1, 2])
#Nx.Tensor<
  s64[2][1][6]
  [
    [
      [0, 1, 2, 0, 1, 2]
    ],
    [
      [0, 1, 2, 0, 1, 2]
    ]
  ]
>

iex> b = Nx.tensor([[1,2],[3,4]])
iex> Nx.tile(b, [2])
#Nx.Tensor<
  s64[2][4]
  [
    [1, 2, 1, 2],
    [3, 4, 3, 4]
  ]
>
iex> Nx.tile(b, [2, 1])
#Nx.Tensor<
  s64[4][2]
  [
    [1, 2],
    [3, 4],
    [1, 2],
    [3, 4]
  ]
>
iex> Nx.tile(b, [1, 2])
#Nx.Tensor<
  s64[2][4]
  [
    [1, 2, 1, 2],
    [3, 4, 3, 4]
  ]
>

iex> c = Nx.tensor([1,2,3,4])
iex> Nx.tile(c, [4,1])
#Nx.Tensor<
  s64[4][4]
  [
    [1, 2, 3, 4],
    [1, 2, 3, 4],
    [1, 2, 3, 4],
    [1, 2, 3, 4]
  ]
>

error-cases

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
Link to this function

transpose(tensor, opts \\ [])

View Source

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

Examples

iex> Nx.transpose(Nx.tensor(1))
#Nx.Tensor<
  s64
  1
>

iex> Nx.transpose(Nx.iota({2, 3, 4}, names: [:x, :y, :z]))
#Nx.Tensor<
  s64[z: 4][y: 3][x: 2]
  [
    [
      [0, 12],
      [4, 16],
      [8, 20]
    ],
    [
      [1, 13],
      [5, 17],
      [9, 21]
    ],
    [
      [2, 14],
      [6, 18],
      [10, 22]
    ],
    [
      [3, 15],
      [7, 19],
      [11, 23]
    ]
  ]
>

iex> Nx.transpose(Nx.tensor(1), axes: [])
#Nx.Tensor<
  s64
  1
>

iex> Nx.transpose(Nx.iota({2, 3, 4}, names: [:batch, :x, :y]), axes: [2, 1, :batch])
#Nx.Tensor<
  s64[y: 4][x: 3][batch: 2]
  [
    [
      [0, 12],
      [4, 16],
      [8, 20]
    ],
    [
      [1, 13],
      [5, 17],
      [9, 21]
    ],
    [
      [2, 14],
      [6, 18],
      [10, 22]
    ],
    [
      [3, 15],
      [7, 19],
      [11, 23]
    ]
  ]
>

iex> Nx.transpose(Nx.iota({2, 3, 4}, names: [:batch, :x, :y]), axes: [:y, :batch, :x])
#Nx.Tensor<
  s64[y: 4][batch: 2][x: 3]
  [
    [
      [0, 4, 8],
      [12, 16, 20]
    ],
    [
      [1, 5, 9],
      [13, 17, 21]
    ],
    [
      [2, 6, 10],
      [14, 18, 22]
    ],
    [
      [3, 7, 11],
      [15, 19, 23]
    ]
  ]
>

iex> Nx.transpose(Nx.iota({2, 3, 4}, names: [:batch, :x, :y]), axes: [:batch, :y, :x])
#Nx.Tensor<
  s64[batch: 2][y: 4][x: 3]
  [
    [
      [0, 4, 8],
      [1, 5, 9],
      [2, 6, 10],
      [3, 7, 11]
    ],
    [
      [12, 16, 20],
      [13, 17, 21],
      [14, 18, 22],
      [15, 19, 23]
    ]
  ]
>

errors

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

Link to this section Functions: Type

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

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]
>

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

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]
>

error-cases

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

Returns the type of the tensor.

See Nx.Type for more information.

examples

Examples

iex> Nx.type(Nx.tensor([1, 2, 3]))
{:s, 64}

iex> Nx.type(Nx.tensor([1, 2, 3], type: :f32))
{:f, 32}

iex> Nx.type(1)
{:s, 64}

iex> Nx.type(1.0)
{:f, 32}

Link to this section Functions: Window

Link to this function

window_max(tensor, window_dimensions, opts \\ [])

View Source

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

Examples

iex> Nx.window_max(Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]]]), {1, 2, 1})
#Nx.Tensor<
  s64[2][1][3]
  [
    [
      [4, 5, 6]
    ],
    [
      [4, 5, 6]
    ]
  ]
>

iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]]])
iex> Nx.window_max(t, {2, 2, 1}, strides: [1, 2, 3], padding: [{0, 1}, {2, 0}, {1, 1}])
#Nx.Tensor<
  s64[2][2][2]
  [
    [
      [-9223372036854775808, -9223372036854775808],
      [-9223372036854775808, 6]
    ],
    [
      [-9223372036854775808, -9223372036854775808],
      [-9223372036854775808, 6]
    ]
  ]
>

iex> t = Nx.tensor([[[4.0, 2.0, 3.0], [2.0, 5.0, 6.5]], [[1.2, 2.2, 3.2], [4.0, 5.0, 6.2]]])
iex> Nx.window_max(t, {2, 1, 1}, strides: [2, 1, 1], padding: [{1, 1}, {0, 0}, {1, 1}])
#Nx.Tensor<
  f32[2][2][5]
  [
    [
      [-Inf, 4.0, 2.0, 3.0, -Inf],
      [-Inf, 2.0, 5.0, 6.5, -Inf]
    ],
    [
      [-Inf, 1.2000000476837158, 2.200000047683716, 3.200000047683716, -Inf],
      [-Inf, 4.0, 5.0, 6.199999809265137, -Inf]
    ]
  ]
>

iex> t = Nx.tensor([[[4, 2, 1, 3], [4, 2, 1, 7]], [[1, 2, 5, 7], [1, 8, 9, 2]]])
iex> opts = [strides: [2, 1, 1], padding: :valid, window_dilations: [1, 2, 2]]
iex> Nx.window_max(t, {1, 1, 2}, opts)
#Nx.Tensor<
  s64[1][2][2]
  [
    [
      [4, 3],
      [4, 7]
    ]
  ]
>
Link to this function

window_mean(tensor, window_dimensions, opts \\ [])

View Source

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

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]
    ]
  ]
>
Link to this function

window_min(tensor, window_dimensions, opts \\ [])

View Source

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

Examples

iex> Nx.window_min(Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]]]), {1, 2, 1})
#Nx.Tensor<
  s64[2][1][3]
  [
    [
      [1, 2, 3]
    ],
    [
      [1, 2, 3]
    ]
  ]
>

iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]]])
iex> Nx.window_min(t, {2, 2, 1}, strides: [1, 2, 3], padding: [{0, 1}, {2, 0}, {1, 1}])
#Nx.Tensor<
  s64[2][2][2]
  [
    [
      [9223372036854775807, 9223372036854775807],
      [9223372036854775807, 3]
    ],
    [
      [9223372036854775807, 9223372036854775807],
      [9223372036854775807, 3]
    ]
  ]
>

iex> t = Nx.tensor([[[4.0, 2.0, 3.0], [2.0, 5.0, 6.5]], [[1.2, 2.2, 3.2], [4.0, 5.0, 6.2]]])
iex> Nx.window_min(t, {2, 1, 1}, strides: [2, 1, 1], padding: [{1, 1}, {0, 0}, {1, 1}])
#Nx.Tensor<
  f32[2][2][5]
  [
    [
      [Inf, 4.0, 2.0, 3.0, Inf],
      [Inf, 2.0, 5.0, 6.5, Inf]
    ],
    [
      [Inf, 1.2000000476837158, 2.200000047683716, 3.200000047683716, Inf],
      [Inf, 4.0, 5.0, 6.199999809265137, Inf]
    ]
  ]
>

iex> t = Nx.tensor([[[4, 2, 1, 3], [4, 2, 1, 7]], [[1, 2, 5, 7], [1, 8, 9, 2]]])
iex> opts = [strides: [2, 1, 1], padding: :valid, window_dilations: [1, 2, 2]]
iex> Nx.window_min(t, {1, 1, 2}, opts)
#Nx.Tensor<
  s64[1][2][2]
  [
    [
      [1, 2],
      [1, 2]
    ]
  ]
>
Link to this function

window_product(tensor, window_dimensions, opts \\ [])

View Source

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

Examples

iex> Nx.window_product(Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]]]), {1, 2, 1})
#Nx.Tensor<
  s64[2][1][3]
  [
    [
      [4, 10, 18]
    ],
    [
      [4, 10, 18]
    ]
  ]
>

iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]]])
iex> Nx.window_product(t, {2, 2, 1}, strides: [1, 2, 3], padding: [{0, 1}, {2, 0}, {1, 1}])
#Nx.Tensor<
  s64[2][2][2]
  [
    [
      [1, 1],
      [1, 324]
    ],
    [
      [1, 1],
      [1, 18]
    ]
  ]
>

iex> t = Nx.tensor([[[4.0, 2.0, 3.0], [2.0, 5.0, 6.5]], [[1.2, 2.2, 3.2], [4.0, 5.0, 6.2]]])
iex> Nx.window_product(t, {2, 1, 1}, strides: [2, 1, 1], padding: [{1, 1}, {0, 0}, {1, 1}])
#Nx.Tensor<
  f32[2][2][5]
  [
    [
      [1.0, 4.0, 2.0, 3.0, 1.0],
      [1.0, 2.0, 5.0, 6.5, 1.0]
    ],
    [
      [1.0, 1.2000000476837158, 2.200000047683716, 3.200000047683716, 1.0],
      [1.0, 4.0, 5.0, 6.199999809265137, 1.0]
    ]
  ]
>

iex> t = Nx.tensor([[[4, 2, 1, 3], [4, 2, 1, 7]], [[1, 2, 5, 7], [1, 8, 9, 2]]])
iex> opts = [strides: [2, 1, 1], padding: :valid, window_dilations: [1, 2, 2]]
iex> Nx.window_product(t, {1, 1, 2}, opts)
#Nx.Tensor<
  s64[1][2][2]
  [
    [
      [4, 6],
      [4, 14]
    ]
  ]
>
Link to this function

window_reduce(tensor, acc, window_dimensions, opts \\ [], fun)

View Source

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

Examples

iex> init_value = Nx.Constants.min_finite(:s64)
iex> t = Nx.tensor([[1, 2, 3, 4], [4, 5, 6, 7], [7, 8, 9, 10], [11, 12, 13, 14]])
iex> Nx.window_reduce(t, init_value, {2, 2}, fn x, acc -> Nx.max(x, acc) end)
#Nx.Tensor<
  s64[3][3]
  [
    [5, 6, 7],
    [8, 9, 10],
    [12, 13, 14]
  ]
>

iex> init_value = Nx.Constants.min_finite(:s64)
iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
iex> opts = [padding: :same, strides: [1, 1]]
iex> Nx.window_reduce(t, init_value, {2, 2}, opts, fn x, acc -> Nx.max(x, acc) end)
#Nx.Tensor<
  s64[3][3]
  [
    [5, 6, 6],
    [8, 9, 9],
    [8, 9, 9]
  ]
>

iex> t = Nx.tensor([[1, 2, 3], [4, 5, 6]])
iex> opts = [padding: :same, strides: [1, 1]]
iex> Nx.window_reduce(t, 0, {1, 2}, opts, fn x, acc -> Nx.add(x, acc) end)
#Nx.Tensor<
  s64[2][3]
  [
    [3, 5, 3],
    [9, 11, 6]
  ]
>

iex> t = Nx.tensor([[[4, 2, 1, 3], [4, 2, 1, 7]], [[1, 2, 5, 7], [1, 8, 9, 2]]])
iex> opts = [padding: :valid, strides: [2, 1, 1], window_dilations: [1, 1, 2]]
iex> Nx.window_reduce(t, 0, {1, 1, 2}, opts, fn x, acc -> Nx.add(x, acc) end)
#Nx.Tensor<
  s64[1][2][2]
  [
    [
      [5, 5],
      [5, 9]
    ]
  ]
>
Link to this function

window_scatter_max(tensor, source, init_value, window_dimensions, opts \\ [])

View Source

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

Examples

iex> t = Nx.tensor([
...>   [7, 2, 5, 3, 10, 2],
...>   [3, 8, 9, 3, 4, 2],
...>   [1, 5, 7, 5, 6, 1],
...>   [0, 6, 2, 7, 2, 8]
...> ])
iex> opts = [strides: [2, 3], padding: :valid]
iex> Nx.window_scatter_max(t, Nx.tensor([[2, 6], [3, 1]]), 0, {2, 3}, opts)
#Nx.Tensor<
  s64[4][6]
  [
    [0, 0, 0, 0, 6, 0],
    [0, 0, 2, 0, 0, 0],
    [0, 0, 3, 0, 0, 0],
    [0, 0, 0, 0, 0, 1]
  ]
>

iex> t = Nx.tensor([
...>   [7, 2, 5, 3, 8],
...>   [3, 8, 9, 3, 4],
...>   [1, 5, 7, 5, 6],
...>   [0, 6, 2, 10, 2]
...> ])
iex> opts = [strides: [2, 2], padding: :valid]
iex> Nx.window_scatter_max(t, Nx.tensor([[2, 6], [3, 1]]), 0, {2, 3}, opts)
#Nx.Tensor<
  s64[4][5]
  [
    [0, 0, 0, 0, 0],
    [0, 0, 8, 0, 0],
    [0, 0, 3, 0, 0],
    [0, 0, 0, 1, 0]
  ]
>
Link to this function

window_scatter_min(tensor, source, init_value, window_dimensions, opts \\ [])

View Source

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

Examples

iex> t = Nx.tensor([
...>   [7, 2, 5, 3, 10, 2],
...>   [3, 8, 9, 3, 4, 2],
...>   [1, 5, 7, 5, 6, 1],
...>   [0, 6, 2, 7, 2, 8]
...> ])
iex> opts = [strides: [2, 3], padding: :valid]
iex> Nx.window_scatter_min(t, Nx.tensor([[2, 6], [3, 1]]), 0, {2, 3}, opts)
#Nx.Tensor<
  s64[4][6]
  [
    [0, 2, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 6],
    [0, 0, 0, 0, 0, 1],
    [3, 0, 0, 0, 0, 0]
  ]
>

iex> t = Nx.tensor([
...>   [7, 2, 5, 3, 8],
...>   [3, 8, 9, 3, 4],
...>   [1, 5, 7, 5, 6],
...>   [0, 6, 2, 10, 2]
...> ])
iex> opts = [strides: [2, 2], padding: :valid]
iex> Nx.window_scatter_min(t, Nx.tensor([[2, 6], [3, 1]]), 0, {2, 3}, opts)
#Nx.Tensor<
  s64[4][5]
  [
    [0, 2, 0, 0, 0],
    [0, 0, 0, 6, 0],
    [0, 0, 0, 0, 0],
    [3, 0, 0, 0, 1]
  ]
>
Link to this function

window_sum(tensor, window_dimensions, opts \\ [])

View Source

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

Examples

iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]]])
iex> Nx.window_sum(t, {1, 2, 1})
#Nx.Tensor<
  s64[2][1][3]
  [
    [
      [5, 7, 9]
    ],
    [
      [5, 7, 9]
    ]
  ]
>

iex> t = Nx.tensor([[[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]]])
iex> Nx.window_sum(t, {2, 2, 1}, strides: [1, 2, 3], padding: [{0, 1}, {2, 0}, {1, 1}])
#Nx.Tensor<
  s64[2][2][2]
  [
    [
      [0, 0],
      [0, 18]
    ],
    [
      [0, 0],
      [0, 9]
    ]
  ]
>

iex> t = Nx.tensor([[[4.0, 2.0, 3.0], [2.0, 5.0, 6.5]], [[1.2, 2.2, 3.2], [4.0, 5.0, 6.2]]])
iex> Nx.window_sum(t, {2, 1, 1}, strides: [2, 1, 1], padding: [{1, 1}, {0, 0}, {1, 1}])
#Nx.Tensor<
  f32[2][2][5]
  [
    [
      [0.0, 4.0, 2.0, 3.0, 0.0],
      [0.0, 2.0, 5.0, 6.5, 0.0]
    ],
    [
      [0.0, 1.2000000476837158, 2.200000047683716, 3.200000047683716, 0.0],
      [0.0, 4.0, 5.0, 6.199999809265137, 0.0]
    ]
  ]
>

iex> t = Nx.tensor([[[4, 2, 1, 3], [4, 2, 1, 7]], [[1, 2, 5, 7], [1, 8, 9, 2]]])
iex> opts = [strides: [2, 1, 1], padding: :valid, window_dilations: [1, 2, 1]]
iex> Nx.window_sum(t, {1, 1, 2}, opts)
#Nx.Tensor<
  s64[1][2][3]
  [
    [
      [6, 3, 4],
      [6, 3, 8]
    ]
  ]
>

iex> t = Nx.tensor([[[4, 2, 1, 3], [4, 2, 1, 7]], [[1, 2, 5, 7], [1, 8, 9, 2]]])
iex> opts = [strides: [2, 1, 1], padding: :valid, window_dilations: [1, 2, 2]]
iex> Nx.window_sum(t, {1, 1, 2}, opts)
#Nx.Tensor<
  s64[1][2][2]
  [
    [
      [5, 5],
      [5, 9]
    ]
  ]
>

iex> t = Nx.tensor([[[4, 2, 1, 3], [4, 2, 1, 7]], [[1, 2, 5, 7], [1, 8, 9, 2]]])
iex> opts = [strides: [2, 1, 1], padding: [{2, 1}, {3, 1}, {1, 0}], window_dilations: [1, 2, 2]]
iex> Nx.window_sum(t, {2, 1, 2}, opts)
#Nx.Tensor<
  s64[2][6][3]
  [
    [
      [0, 0, 0],
      [0, 0, 0],
      [0, 0, 0],
      [0, 0, 0],
      [0, 0, 0],
      [0, 0, 0]
    ],
    [
      [0, 0, 0],
      [0, 0, 0],
      [0, 0, 0],
      [4, 11, 14],
      [10, 15, 19],
      [0, 0, 0]
    ]
  ]
>