View Source Nx.Defn.Kernel (Nx v0.6.0)
All imported functionality available inside defn
blocks.
This module can be used in defn
.
Summary
Functions
Element-wise bitwise AND operation.
Element-wise power operator.
Element-wise multiplication operator.
Element-wise unary plus operator.
Element-wise addition operator.
Element-wise unary plus operator.
Element-wise subtraction operator.
Creates the full-slice range 0..-1//1
.
Builds a range.
Builds a range with step.
Element-wise division operator.
Element-wise inequality operation.
Element-wise less than operation.
Element-wise left shift operation.
Element-wise less-equal operation.
Concatenates two strings.
Element-wise equality operation.
Element-wise greater than operation.
Element-wise greater-equal operation.
Element-wise right shift operation.
Reads a module attribute at compilation time.
Defines an alias, as in Kernel.SpecialForms.alias/2
.
Element-wise logical AND operation.
Asserts the keyword list has the given keys.
Attaches a token to an expression. See hook/3
.
Pattern matches the result of expr
against the given clauses.
Evaluates the expression corresponding to the first clause that evaluates to a truthy value.
Creates a token for hooks. See hook/3
.
Defines a custom gradient for the given expression.
Element-wise quotient operator.
Gets the element at the zero-based index in tuple.
Shortcut for hook/3
.
Defines a hook.
Shortcut for hook_token/4
.
Defines a hook with an existing token. See hook/3
.
Provides if/else expressions.
Imports functions and macros into the current scope,
as in Kernel.SpecialForms.import/2
.
Converts the given expression into a string.
Ensures the first argument is a keyword
with the given
keys and default values.
Element-wise maximum operation.
Element-wise minimum operation.
Element-wise logical NOT operation.
Element-wise logical OR operation.
Prints the given expression to the terminal.
Prints the value at runtime to the terminal.
Raises a runtime exception with the given message
.
Raises an exception
with the given arguments
.
Element-wise remainder operation.
Requires a module in order to use its macros, as in Kernel.SpecialForms.require/2
.
Rewrites the types of expr
recursively according to opts
Stops computing the gradient for the given expression.
Pipes value
to the given fun
and returns the value
itself.
Pipes value
into the given fun
.
Defines a while
loop.
Pipes the argument on the left to the function call on the right.
Element-wise bitwise OR operation.
Element-wise bitwise not operation.
Functions
Element-wise bitwise AND operation.
Only integer tensors are supported.
It delegates to Nx.bitwise_and/2
(supports broadcasting).
Examples
defn and_or(a, b) do
{a &&& b, a ||| b}
end
Element-wise power operator.
It delegates to Nx.pow/2
(supports broadcasting).
Examples
defn pow(a, b) do
a ** b
end
Element-wise multiplication operator.
It delegates to Nx.multiply/2
(supports broadcasting).
Examples
defn multiply(a, b) do
a * b
end
Element-wise unary plus operator.
Simply returns the given argument.
Examples
defn plus_and_minus(a) do
{+a, -a}
end
Element-wise addition operator.
It delegates to Nx.add/2
(supports broadcasting).
Examples
defn add(a, b) do
a + b
end
Element-wise unary plus operator.
It delegates to Nx.negate/1
.
Examples
defn plus_and_minus(a) do
{+a, -a}
end
Element-wise subtraction operator.
It delegates to Nx.subtract/2
(supports broadcasting).
Examples
defn subtract(a, b) do
a - b
end
Creates the full-slice range 0..-1//1
.
This function returns a range with the following properties:
When enumerated, it is empty
When used as a
slice
, it returns the sliced element as is
Examples
iex> t = Nx.tensor([1, 2, 3])
iex> t[..]
#Nx.Tensor<
s64[3]
[1, 2, 3]
>
Builds a range.
Ranges are inclusive and both sides must be integers.
The step of the range is computed based on the first and last values of the range.
Examples
iex> t = Nx.tensor([1, 2, 3])
iex> t[1..2]
#Nx.Tensor<
s64[2]
[2, 3]
>
Builds a range with step.
Ranges are inclusive and both sides must be integers.
Examples
iex> t = Nx.tensor([1, 2, 3])
iex> t[1..2//1]
#Nx.Tensor<
s64[2]
[2, 3]
>
Element-wise division operator.
It delegates to Nx.divide/2
(supports broadcasting).
Examples
defn divide(a, b) do
a / b
end
Element-wise inequality operation.
It delegates to Nx.not_equal/2
.
Examples
defn check_inequality(a, b) do
a != b
end
Element-wise less than operation.
It delegates to Nx.less/2
.
Examples
defn check_less_than(a, b) do
a < b
end
Element-wise left shift operation.
Only integer tensors are supported.
It delegates to Nx.left_shift/2
(supports broadcasting).
Examples
defn shift_left_and_right(a, b) do
{a <<< b, a >>> b}
end
Element-wise less-equal operation.
It delegates to Nx.less_equal/2
.
Examples
defn check_less_equal(a, b) do
a <= b
end
Concatenates two strings.
Equivalent to Kernel.<>/2
.
Element-wise equality operation.
It delegates to Nx.equal/2
.
Examples
defn check_equality(a, b) do
a == b
end
Element-wise greater than operation.
It delegates to Nx.greater/2
.
Examples
defn check_greater_than(a, b) do
a > b
end
Element-wise greater-equal operation.
It delegates to Nx.greater_equal/2
.
Examples
defn check_greater_equal(a, b) do
a >= b
end
Element-wise right shift operation.
Only integer tensors are supported.
It delegates to Nx.right_shift/2
(supports broadcasting).
Examples
defn shift_left_and_right(a, b) do
{a <<< b, a >>> b}
end
Reads a module attribute at compilation time.
It is useful to inject code constants into defn
.
It delegates to Kernel.@/1
.
Examples
@two_per_two Nx.tensor([[1, 2], [3, 4]])
defn add_2x2_attribute(t), do: t + @two_per_two
Defines an alias, as in Kernel.SpecialForms.alias/2
.
An alias allows you to refer to a module using its aliased name. For example:
defn some_fun(t) do
alias Math.Helpers, as: MH
MH.fft(t)
end
If the :as
option is not given, the alias defaults to
the last part of the given alias. For example,
alias Math.Helpers
is equivalent to:
alias Math.Helpers, as: Helpers
Finally, note that aliases define outside of a function also apply to the function, as they have lexical scope:
alias Math.Helpers, as: MH
defn some_fun(t) do
MH.fft(t)
end
Element-wise logical AND operation.
Zero is considered false, all other numbers are considered true.
It delegates to Nx.logical_and/2
(supports broadcasting).
Examples
defn and_or(a, b) do
{a and b, a or b}
end
Asserts the keyword list has the given keys.
If it succeeds, it returns the given keyword list. Raises an error otherwise.
Examples
To assert the tensor is a scalar, you can pass the empty tuple shape
:
iex> assert_keys([one: 1, two: 2], [:one, :two])
[one: 1, two: 2]
If the keys are not available, an error is raised:
iex> assert_keys([one: 1, two: 2], [:three])
** (ArgumentError) expected key :three in keyword list, got: [one: 1, two: 2]
Attaches a token to an expression. See hook/3
.
Pattern matches the result of expr
against the given clauses.
For example:
case Nx.shape(tensor) do
{_} -> implementation_for_rank_one(tensor)
{_, _} -> implementation_for_rank_two(tensor)
_ -> implementation_for_rank_n(tensor)
end
Opposite to cond/2
and if/2
, which can execute the branching
in the device, case
s are always expanded when building the
expression, and never on the device. This allows case/2
to work
very similarly to Elixir's own Kernel.SpecialForms.case/2
,
with only the following restrictions in place:
case
inside defn only accepts structs, atoms, integers, and tuples as argumentscase
can match on struct names but not on its fields- guards in
case
inside defn can only access variables defined within the pattern
Here is an example of case
with guards:
case Nx.shape(tensor) do
{x, y} when x > y -> implementation_for_tall(tensor)
{x, y} when x < y -> implementation_for_wide(tensor)
{x, x} -> implementation_for_square(tensor)
end
Evaluates the expression corresponding to the first clause that evaluates to a truthy value.
It has the format of:
cond do
condition1 ->
expr1
condition2 ->
expr2
true ->
expr3
end
The conditions must be a scalar. Zero is considered false,
any other number is considered true. The booleans false
and
true
are supported, but any other value will raise.
All clauses are normalized to the same type and are broadcast to the same shape. The last condition must always evaluate to true. All clauses are executed in the device, unless they can be determined to always be true/false while building the numerical expression.
Examples
cond do
Nx.all(Nx.greater(a, 0)) -> b * c
Nx.all(Nx.less(a, 0)) -> b + c
true -> b - c
end
When a defn
is invoked, all cond
clauses are traversed
and expanded in order to build their expressions. This means that,
if you attempt to raise in any clause, then it will always raise.
You can only raise
in limited situations inside defn
, see
raise/2
for more information.
Creates a token for hooks. See hook/3
.
Defines a custom gradient for the given expression.
It also expects a list of inputs of the gradient and a fun
to compute the gradient. The function will be called with the
current gradient. It must return a list of arguments and their
updated gradient to continue applying grad
on.
Examples
For example, if the gradient of cos(t)
were to be
implemented by hand:
def cos(t) do
custom_grad(Nx.cos(t), [t], fn g ->
[-g * Nx.sin(t)]
end)
end
Element-wise quotient operator.
It delegates to Nx.quotient/2
(supports broadcasting).
Examples
defn quotient(a, b) do
div(a, b)
end
Gets the element at the zero-based index in tuple.
It raises ArgumentError when index is negative or it is out of range of the tuple elements.
Examples
iex> tuple = {1, 2, 3}
iex> elem(tuple, 0)
1
Shortcut for hook/3
.
Defines a hook.
Hooks are a mechanism to execute an anonymous function for side-effects with runtime tensor values.
Let's see an example:
defmodule Hooks do
import Nx.Defn
defn add_and_mult(a, b) do
add = hook(a + b, fn tensor -> IO.inspect({:add, tensor}) end)
mult = hook(a * b, fn tensor -> IO.inspect({:mult, tensor}) end)
{add, mult}
end
end
Note a hook can only access the variables passed as arguments
to the hook. It cannot access any other variable defined in
defn
outside of the hook.
The defn
above defines two hooks, one is called with the
value of a + b
and another with a * b
. Once you invoke
the function above, you should see this printed:
Hooks.add_and_mult(2, 3)
{:add, #Nx.Tensor<
s64
5
>}
{:mult, #Nx.Tensor<
s64
6
>}
In other words, the hook
function accepts a tensor
expression as argument and it will invoke a custom
function with a tensor value at runtime. hook
returns
the result of the given expression. The expression can
be any tensor or a Nx.Container
.
Note you must return the result of the hook
call.
For example, the code below won't inspect the :add
tuple, because the hook is not returned from defn
:
defn add_and_mult(a, b) do
_add = hook(a + b, fn tensor -> IO.inspect({:add, tensor}) end)
mult = hook(a * b, fn tensor -> IO.inspect({:mult, tensor}) end)
mult
end
We will learn how to hook into a value that is not part of the result in the "Hooks and tokens" section.
Named hooks
It is possible to give names to the hooks. This allows them
to be defined or overridden by calling Nx.Defn.jit/2
or
Nx.Defn.stream/2
. Let's see an example:
defmodule Hooks do
import Nx.Defn
defn add_and_mult(a, b) do
add = hook(a + b, :hooks_add)
mult = hook(a * b, :hooks_mult)
{add, mult}
end
end
Now you can pass the hook as argument as follows:
hooks = %{
hooks_add: fn tensor ->
IO.inspect {:add, tensor}
end
}
fun = Nx.Defn.jit(&Hooks.add_and_mult/2, hooks: hooks)
fun.(Nx.tensor(2), Nx.tensor(3))
Important! We recommend to prefix your hook names by the name of your project to avoid conflicts.
If a named hook is not given, compilers can optimize that away and not transfer the tensor from the device in the first place.
You can also mix named hooks with callbacks:
defn add_and_mult(a, b) do
add = hook(a + b, :hooks_add, fn tensor -> IO.inspect({:add, tensor}) end)
mult = hook(a * b, :hooks_mult, fn tensor -> IO.inspect({:mult, tensor}) end)
{add, mult}
end
If a hook with the same name is given to Nx.Defn.jit/2
or Nx.Defn.stream/2
, then it will override the default
callback.
Hooks and tokens
So far, we have always returned the result of the hook
call. However, what happens if the values we want to
hook are not part of the return value, such as below?
defn add_and_mult(a, b) do
_add = hook(a + b, :hooks_add, &IO.inspect({:add, &1}))
mult = hook(a * b, :hooks_mult, &IO.inspect({:mult, &1}))
mult
end
In such cases, you must use tokens. Tokens are used to create an ordering over hooks, ensuring hooks execute in a certain sequence:
defn add_and_mult(a, b) do
token = create_token()
{token, _add} = hook_token(token, a + b, :hooks_add, &IO.inspect({:add, &1}))
{token, mult} = hook_token(token, a * b, :hooks_mult, &IO.inspect({:mult, &1}))
attach_token(token, mult)
end
The example above creates a token and uses hook_token/4
to create hooks attached to their respective tokens. By using a token,
we guarantee that those hooks will be invoked in the order
in which they were defined. Then, at the end of the function,
we attach the token (and its associated hooks) to the result mult
.
In fact, the hook/3
function is implemented roughly like this:
def hook(tensor_expr, name, function) do
{token, result} = hook_token(create_token(), tensor_expr, name, function)
attach_token(token, result)
end
Note you must attach the token at the end, otherwise the hooks will be "lost", as if they were not defined. This also applies to conditionals and loops. The token must be attached within the branch they are used. For example, this won't work:
token = create_token()
{token, result} =
if Nx.any(value) do
hook_token(token, some_value)
else
hook_token(token, another_value)
end
attach_token(token, result)
Instead, you must write:
token = create_token()
if Nx.any(value) do
{token, result} = hook_token(token, some_value)
attach_token(token, result)
else
{token, result} = hook_token(token, another_value)
attach_token(token, result)
end
Shortcut for hook_token/4
.
Defines a hook with an existing token. See hook/3
.
Provides if/else expressions.
The first argument must be a scalar. Zero is considered false,
any other number is considered true. The booleans false
and
true
are supported, but any other value will raise.
The second argument is a keyword list with do
and else
blocks. The sides are broadcast to return the same shape
and normalized to return the same type.
Examples
if Nx.any(Nx.equal(t, 0)) do
0.0
else
1 / t
end
In case else is not given, it is assumed to be 0 with the
same as the do clause. If you want to nest multiple conditionals,
see cond/1
instead.
When a defn
is invoked, both do
/else
clauses are traversed
and expanded in order to build their expressions. This means that,
if you attempt to raise in any clause, then it will always raise.
You can only raise
in limited situations inside defn
, see
raise/2
for more information.
Imports functions and macros into the current scope,
as in Kernel.SpecialForms.import/2
.
Imports are typically discouraged in favor of alias/2
.
Examples
defn some_fun(t) do
import Math.Helpers
fft(t)
end
Converts the given expression into a string.
inspect/2
is used to convert expressions into strings, typically
to be used as part of error messages. If you want to inspect for
debugging, consider using print_expr/2
, to print the underlying
expression, or print_value/2
to print the value during execution.
defn square_shape(tensor) do
case Nx.shape(tensor) do
{n, n} -> n
shape -> raise ArgumentError, "expected a square tensor: #{inspect(shape)}"
end
end
Ensures the first argument is a keyword
with the given
keys and default values.
The second argument must be a list of atoms, specifying
a given key, or tuples specifying a key and a default value.
If any of the keys in the keyword
is not defined on
values
, it raises an error.
This does not validate required keys. For such, use assert_keys/2
instead.
This is equivalent to Elixir's Keyword.validate!/2
.
Examples
iex> keyword!([], [one: 1, two: 2]) |> Enum.sort()
[one: 1, two: 2]
iex> keyword!([two: 3], [one: 1, two: 2]) |> Enum.sort()
[one: 1, two: 3]
If atoms are given, they are supported as keys but do not provide a default value:
iex> keyword!([], [:one, two: 2]) |> Enum.sort()
[two: 2]
iex> keyword!([one: 1], [:one, two: 2]) |> Enum.sort()
[one: 1, two: 2]
Passing an unknown key raises:
iex> keyword!([three: 3], [one: 1, two: 2])
** (ArgumentError) unknown key :three in [three: 3], expected one of [:one, :two]
Element-wise maximum operation.
It delegates to Nx.max/2
(supports broadcasting).
Examples
defn min_max(a, b) do
{min(a, b), max(a, b)}
end
Element-wise minimum operation.
It delegates to Nx.min/2
(supports broadcasting).
Examples
defn min_max(a, b) do
{min(a, b), max(a, b)}
end
Element-wise logical NOT operation.
Zero is considered false, all other numbers are considered true.
It delegates to Nx.logical_not/1
.
Examples
defn logical_not(a), do: not a
Element-wise logical OR operation.
Zero is considered false, all other numbers are considered true.
It delegates to Nx.logical_or/2
(supports broadcasting).
Examples
defn and_or(a, b) do
{a and b, a or b}
end
Prints the given expression to the terminal.
It returns the given expressions.
Examples
defn tanh_grad(t) do
grad(t, &Nx.tanh/1) |> print_expr()
end
When invoked, it will print the expression being built by defn
:
#Nx.Tensor<
Nx.Defn.Expr
parameter a s64
parameter c s64
b = tanh [ a ] f64
d = pow [ c, 2 ] s64
e = add [ b, d ] f64
>
Prints the value at runtime to the terminal.
This function is implemented on top of hook/3
and therefore
has the following restrictions:
- It can only inspect tensors and
Nx.Container
- The return value of this function must be part of the output
All options are passed to IO.inspect/2
.
Examples
defn tanh_grad(t) do
grad(t, fn t ->
t
|> Nx.tanh()
|> print_value()
end)
end
defn tanh_grad(t) do
grad(t, fn t ->
t
|> Nx.tanh()
|> print_value(label: "tanh")
end)
end
Raises a runtime exception with the given message
.
See raise/2
for more information on exceptions inside defn
.
Raises an exception
with the given arguments
.
raise/2
is invoked while building the numerical expression,
not inside the device. This means that raise
may be invoked
on unexpected situations, as we build the numerical expression.
To better understand those cases, let's see some examples.
First, let's start with a valid use case for raise/2
: raise
on mismatched shapes. Inside defn
, we know the tensor shapes
and types, but not their values, so we can assert on the shape
while building the numerical expression:
defn square_shape(tensor) do
case Nx.shape(tensor) do
{n, n} -> n
shape -> raise ArgumentError, "expected a square tensor: #{inspect(shape)}"
end
end
In the example above, only the matching branch of the case is executed, so if you give it a 2x2 tensor, it will return 2. However, if you give it a non-square tensor, it will raise.
Now consider this code:
defn some_check(a, b) do
if a != b do
a * b
else
raise "expected different tensors, got: #{inspect(a)} and #{inspect(b)}"
end
end
In this case, both a
and b
are tensors and we are comparing their values.
However, their values are unknown, which means we need to convert the whole
if
to a numerical expression and run it on the device. Therefore, once we
convert the else
branch, it will execute raise/2
, making it so the code
above always raises!
In such cases, there are no alternatives. We can't execute exceptions in the CPU/GPU, so you need to approach the problem under a different perspective.
Element-wise remainder operation.
It delegates to Nx.remainder/2
(supports broadcasting).
Examples
defn divides_by_5?(a) do
rem(a, 5)
|> Nx.any()
|> Nx.equal(Nx.tensor(1))
end
Requires a module in order to use its macros, as in Kernel.SpecialForms.require/2
.
Examples
defn some_fun(t) do
require NumericalMacros
NumericalMacros.some_macro t do
...
end
end
Rewrites the types of expr
recursively according to opts
Options
:max_unsigned_type
- replaces all signed tensors with size equal to or greater then the given type by the given type:max_signed_type
- replaces all signed tensors with size equal to or greater then the given type by the given type:max_float_type
- replaces all float tensors with size equal to or greater then the given type by the given type
Examples
rewrite_types(expr, max_float_type: {:f, 32})
Stops computing the gradient for the given expression.
It effectively annotates the gradient for the given expression is 1.0.
Examples
expr = stop_grad(expr)
Pipes value
to the given fun
and returns the value
itself.
Useful for running synchronous side effects in a pipeline.
Examples
Let's suppose you want to inspect an expression in the middle of a pipeline. You could write:
a
|> Nx.add(b)
|> tap(&print_expr/1)
|> Nx.multiply(c)
Pipes value
into the given fun
.
In other words, it invokes fun
with value
as argument.
This is most commonly used in pipelines, allowing you
to pipe a value to a function outside of its first argument.
Examples
a
|> Nx.add(b)
|> then(&Nx.subtract(c, &1))
Defines a while
loop.
It expects the initial
arguments, a condition
expression, and
a block
:
while initial, condition do
block
end
condition
must return a scalar tensor where 0 is false and any
other number is true. The given block
will be executed while
condition
is true. Each invocation of block
must return a
value in the same shape as initial
arguments.
while
will return the value of the last execution of block
.
If block
is never executed because the initial condition
is
false, it returns initial
.
Note: you must prefer to use the operations in the
Nx
module, whenever available, instead of writing your own loops.
Examples
A simple loop that increments x
until it is 10
can be written as:
while x = 0, Nx.less(x, 10) do
x + 1
end
However, it is important to note that all variables you intend
to use inside the "while" must be explicitly given as argument
to "while". For example, imagine the amount we want to increment
by in the example above is given by a variable y
. The following
example is invalid:
while x = 0, Nx.less(x, 10) do
x + y
end
Instead, both x
and y
must be passed as variables to while
:
while {x = 0, y}, Nx.less(x, 10) do
{x + y, y}
end
Similarly, to compute the factorial of x
using while
:
defn factorial(x) do
{factorial, _} =
while {factorial = 1, x}, Nx.greater(x, 1) do
{factorial * x, x - 1}
end
factorial
end
Generators
Inspired by Elixir's for-comprehensions,
while
in defn
supports generators. Generators may be tensors or ranges.
Tensor generators
When the generator is a tensor, Nx will traverse its highest dimension. For example, you could sum a one dimensional tensor as follows:
while acc = 0, i <- tensor do
acc + i
end
Note: implementing
sum
usingwhile
, as above, is done as an example. In practice, you must prefer to use the operations in theNx
module, whenever available, instead of writing your own loops.
One advantage of using generators is that you can also unroll the loop for performance:
while acc = 0, i <- tensor, unroll: true do
acc + i
end
Or unroll it in batches:
while acc = 0, i <- tensor, unroll: 4 do
acc + i
end
Unrolling means that the the while
body is automatically duplicated
a certain amount of times, as if you wrote all iterations by hand. This
makes the final expression larger, which causes a longer compilation
time, however it enables additional compile-time optimizations (such as
fusion), improving the runtime efficiency.
In case the tensor for generator is vectorized, :unroll
will only
affect the non-vectorized part. For instance, if a tensor has shape {4}
and vectorized axes [x: 2][y: 3]
, unroll: true
will only unroll
the 4
inner iterations.
Range generators
A range can also be given as a generator. The range may be increasing or decreasing. Also remember that ranges in Elixir are inclusive on both begin and end. The sum example from the previous section could also be written with ranges:
while {tensor, acc = 0}, i <- 0..Nx.axis_size(tensor, 0)-1 do
acc + tensor[i]
end
Pipes the argument on the left to the function call on the right.
It delegates to Kernel.|>/2
.
Examples
defn exp_sum(t) do
t
|> Nx.exp()
|> Nx.sum()
end
Element-wise bitwise OR operation.
Only integer tensors are supported.
It delegates to Nx.bitwise_or/2
(supports broadcasting).
Examples
defn and_or(a, b) do
{a &&& b, a ||| b}
end
Element-wise bitwise not operation.
Only integer tensors are supported.
It delegates to Nx.bitwise_not/1
.
Examples
defn bnot(a), do: ~~~a