# View Source Nx.Random (Nx v0.7.2)

Pseudo-random number generators.

Unlike the stateful pseudo-random number generators (PRNGs)
that users of most programming languages and numerical libraries
may be accustomed to, Nx random functions require an explicit
PRNG key to be passed as a first argument (see below for more info). That key is defined by
an `Nx.Tensor`

composed of 2 unsigned 32-bit integers, usually
generated by the `Nx.Random.key/1`

function:

```
iex> Nx.Random.key(12)
#Nx.Tensor<
u32[2]
[0, 12]
>
```

This key can then be used in any of Nx’s random number generation routines:

```
iex> key = Nx.Random.key(12)
iex> {uniform, _new_key} = Nx.Random.uniform(key)
iex> uniform
#Nx.Tensor<
f32
0.7691127061843872
>
```

Now, when generating a new random number, you pass the `new_key`

to get a different number.

The function in this module also have a `*_split`

variant, which
is used when the key has been split before hand.

## Design and Context

In short, Nx's PRNGs are based on a Threefry counter PRNG associated to a functional array-oriented splitting model. To summarize, among other requirements, Nx's PRNG aims to:

Ensure reproducibility

Parallelize well, both in terms of vectorization (generating array values) and multi-replica, multi-core computation. In particular it should not use sequencing constraints between random function calls.

## The key to understanding Nx.Random keys

Most Elixir users might be used to not having to keep track of the PRNG state while their code executes.

While this works fine when we're dealing with the CPU, we can think of keeping track of the

`Nx.Random`

key as a way to isolate multiple GPU users, much like the PRNG on different BEAM nodes is isolated. Each key gets updated in its own isolated sequence of calls, and thus we don't get different results for each process using the same PRNG as we would in the normal situation.The fact that the key is a parameter for the functions also helps with the caching and operator fusion of the computational graphs. Because the PRNG functions themselves are stateless, compilers can take advantage of this to further improve execution times.

# Summary

## Functions

Generates random samples from a tensor.

Generates random samples from a tensor with specified probabilities.

Folds in new data to a PRNG key.

Sample Gumbel random values with given shape and float dtype.

Same as `gumbel/2`

, but assumes the key has been split beforehand.

Create a pseudo-random number generator (PRNG) key given an integer seed.

Returns a sample from a multivariate normal distribution with given `mean`

and `covariance`

(matrix).
The function assumes that the covariance is a positive semi-definite matrix.
Otherwise, the result will not be normally distributed.

Same as `multivariate_normal/4`

but assumes the key has already been split.

Shortcut for `normal(key, 0.0, 1.0, opts)`

.

Returns a normal distribution with the given `mean`

and `standard_deviation`

.

Same as `normal/4`

but assumes the key has already been split.

Sample uniform random integer values in the semi-open open interval `[min_value, max_value)`

.

Same as `randint/4`

but assumes the key has already been split.

Randomly shuffles tensor elements along an axis.

Splits a PRNG key into `num`

new keys by adding a leading axis.

Shortcut for `uniform(key, 0.0, 1.0, opts)`

.

Sample uniform float values in the semi-open interval `[min_val, max_val)`

.

Same as `uniform/4`

but assumes the key has already been split.

# Functions

Generates random samples from a tensor.

## Options

`:samples`

- The number of samples to take`:axis`

- The axis along which to take samples. If`nil`

, the tensor is flattened beforehand.`:replace`

- a boolean that specifies if samples will be taken with or without replacement. Defaults to`true`

.

## Examples

```
iex> k = Nx.Random.key(1)
iex> t = Nx.iota({4, 3})
iex> {result, _key} = Nx.Random.choice(k, t, samples: 4, axis: 0)
iex> result
#Nx.Tensor<
s64[4][3]
[
[6, 7, 8],
[3, 4, 5],
[6, 7, 8],
[3, 4, 5]
]
>
iex> {result, _key} = Nx.Random.choice(k, t, samples: 4, axis: 0, replace: false)
iex> result
#Nx.Tensor<
s64[4][3]
[
[3, 4, 5],
[9, 10, 11],
[6, 7, 8],
[0, 1, 2]
]
>
```

If no axis is specified, the tensor is flattened:

```
iex> k = Nx.Random.key(2)
iex> t = Nx.iota({3, 2})
iex> {result, _key} = Nx.Random.choice(k, t)
iex> result
#Nx.Tensor<
s64[1]
[3]
>
iex> {result, _key} = Nx.Random.choice(k, t, samples: 6, replace: false)
iex> result
#Nx.Tensor<
s64[6]
[2, 0, 4, 5, 1, 3]
>
```

Generates random samples from a tensor with specified probabilities.

The probabilities tensor must have the same size as the axis along which the samples are being taken. If no axis is given, the size must be equal to the input tensor's size.

## Options

`:samples`

- The number of samples to take`:axis`

- The axis along which to take samples. If`nil`

, the tensor is flattened beforehand.`:replace`

- a boolean that specifies if samples will be taken with or without replacement. Defaults to`true`

.

## Examples

```
iex> k = Nx.Random.key(1)
iex> t = Nx.iota({4, 3})
iex> p = Nx.tensor([0.1, 0.7, 0.2])
iex> {result, _key} = Nx.Random.choice(k, t, p, samples: 3, axis: 1)
iex> result
#Nx.Tensor<
s64[4][3]
[
[1, 0, 1],
[4, 3, 4],
[7, 6, 7],
[10, 9, 10]
]
>
iex> {result, _key} = Nx.Random.choice(k, t, p, samples: 3, axis: 1, replace: false)
iex> result
#Nx.Tensor<
s64[4][3]
[
[1, 2, 0],
[4, 5, 3],
[7, 8, 6],
[10, 11, 9]
]
>
```

If no axis is specified, the tensor is flattened. Notice that in the first case we get a higher occurence of the entries with bigger probabilities, while in the second case, without replacements, we get those samples first.

```
iex> k = Nx.Random.key(2)
iex> t = Nx.iota({2, 3})
iex> p = Nx.tensor([0.01, 0.1, 0.19, 0.6, 0.05, 0.05])
iex> {result, _key} = Nx.Random.choice(k, t, p)
iex> result
#Nx.Tensor<
s64[1]
[3]
>
iex> {result, _key} = Nx.Random.choice(k, t, p, samples: 6)
iex> result
#Nx.Tensor<
s64[6]
[3, 3, 3, 0, 3, 3]
>
iex> {result, _key} = Nx.Random.choice(k, t, p, samples: 6, replace: false)
iex> result
#Nx.Tensor<
s64[6]
[3, 1, 2, 5, 4, 0]
>
```

Folds in new data to a PRNG key.

## Examples

```
iex> key = Nx.Random.key(42)
iex> Nx.Random.fold_in(key, 99)
#Nx.Tensor<
u32[2]
[2015327502, 1351855566]
>
iex> key = Nx.Random.key(42)
iex> Nx.Random.fold_in(key, 1234)
#Nx.Tensor<
u32[2]
[1356445167, 2917756949]
>
iex> key = Nx.Random.key(42)
iex> Nx.Random.fold_in(key, Nx.tensor([[1, 99], [1234, 13]]))
#Nx.Tensor<
u32[2][2][2]
[
[
[64467757, 2916123636],
[2015327502, 1351855566]
],
[
[1356445167, 2917756949],
[3514951389, 229662949]
]
]
>
```

Sample Gumbel random values with given shape and float dtype.

## Options

`:shape`

- the shape of the output tensor containing the random samples. Defaults to`{}`

`:type`

- the floating-point output type. Defaults to`{:f, 32}`

## Examples

```
iex> {result, _key} = Nx.Random.gumbel(Nx.Random.key(1))
iex> result
#Nx.Tensor<
f32
-0.7294610142707825
>
iex> {result, _key} = Nx.Random.gumbel(Nx.Random.key(1), shape: {2, 3})
iex> result
#Nx.Tensor<
f32[2][3]
[
[0.6247938275337219, -0.21740718185901642, 0.7678327560424805],
[0.7778404355049133, 4.0895304679870605, 0.3029090166091919]
]
>
```

Same as `gumbel/2`

, but assumes the key has been split beforehand.

Create a pseudo-random number generator (PRNG) key given an integer seed.

## Examples

```
iex> Nx.Random.key(12)
#Nx.Tensor<
u32[2]
[0, 12]
>
iex> Nx.Random.key(999999999999)
#Nx.Tensor<
u32[2]
[232, 3567587327]
>
```

Returns a sample from a multivariate normal distribution with given `mean`

and `covariance`

(matrix).
The function assumes that the covariance is a positive semi-definite matrix.
Otherwise, the result will not be normally distributed.

## Options

`:type`

- a float type for the returned tensor`:shape`

- batch shape of the returned tensor, i.e. the prefix of the result shape excluding the last axis`:names`

- the names of the returned tensor`:method`

- a decomposition method used for the covariance. Must be one of :svd, :eigh, and :cholesky. Defaults to :cholesky. For singular covariance matrices, use :svd or :eigh.

## Examples

```
iex> key = Nx.Random.key(12)
iex> {multivariate_normal, _new_key} = Nx.Random.multivariate_normal(key, Nx.tensor([0]), Nx.tensor([[1]]))
iex> multivariate_normal
#Nx.Tensor<
f32[1]
[0.735927939414978]
>
iex> key = Nx.Random.key(12)
iex> {multivariate_normal, _new_key} = Nx.Random.multivariate_normal(key, Nx.tensor([0, 0]), Nx.tensor([[1, 0], [0, 1]]))
iex> multivariate_normal
#Nx.Tensor<
f32[2]
[-1.3425945043563843, -0.40812060236930847]
>
iex> key = Nx.Random.key(12)
iex> {multivariate_normal, _new_key} = Nx.Random.multivariate_normal(key, Nx.tensor([0]), Nx.tensor([[1]]), shape: {3, 2}, type: :f16)
iex> multivariate_normal
#Nx.Tensor<
f16[3][2][1]
[
[
[0.326904296875],
[0.2176513671875]
],
[
[0.316650390625],
[0.1109619140625]
],
[
[0.53955078125],
[-0.8857421875]
]
]
>
iex> key = Nx.Random.key(12)
iex> {multivariate_normal, _new_key} = Nx.Random.multivariate_normal(key, Nx.tensor([0, 0]), Nx.tensor([[1, 0], [0, 1]]), shape: {3, 2})
iex> multivariate_normal
#Nx.Tensor<
f32[3][2][2]
[
[
[0.9891449809074402, 1.0795185565948486],
[-0.9467806220054626, 1.47813880443573]
],
[
[2.2095863819122314, -1.529456377029419],
[-0.7933920621871948, 1.121195673942566]
],
[
[0.10976295918226242, -0.9959557056427002],
[0.4754556119441986, 1.1413804292678833]
]
]
>
```

Same as `multivariate_normal/4`

but assumes the key has already been split.

Shortcut for `normal(key, 0.0, 1.0, opts)`

.

Returns a normal distribution with the given `mean`

and `standard_deviation`

.

## Options

`:type`

- a float or complex type for the returned tensor`:shape`

- shape of the returned tensor`:names`

- the names of the returned tensor

## Examples

```
iex> key = Nx.Random.key(42)
iex> {normal, _new_key} = Nx.Random.normal(key)
iex> normal
#Nx.Tensor<
f32
1.3694695234298706
>
iex> key = Nx.Random.key(42)
iex> {normal, _new_key} = Nx.Random.normal(key, 0, 1, shape: {3, 2}, type: :f16)
iex> normal
#Nx.Tensor<
f16[3][2]
[
[-0.32568359375, -0.77197265625],
[0.39208984375, 0.5341796875],
[0.270751953125, -2.080078125]
]
>
iex> key = Nx.Random.key(42)
iex> {normal, _new_key} = Nx.Random.normal(key, 0, 1, shape: {2, 2}, type: :c64)
iex> normal
#Nx.Tensor<
c64[2][2]
[
[-0.7632761001586914+0.8661127686500549i, -0.14282889664173126-0.7384796142578125i],
[0.678461492061615+0.4118310809135437i, -2.269538402557373-0.3689095079898834i]
]
>
iex> key = Nx.Random.key(1337)
iex> {normal, _new_key} = Nx.Random.normal(key, 10, 5, shape: {1_000})
iex> Nx.mean(normal)
#Nx.Tensor<
f32
9.70022201538086
>
iex> Nx.standard_deviation(normal)
#Nx.Tensor<
f32
5.051416397094727
>
```

Same as `normal/4`

but assumes the key has already been split.

Sample uniform random integer values in the semi-open open interval `[min_value, max_value)`

.

## Options

`:type`

- the integer type for the returned tensor`:shape`

- shape of the returned tensor`:names`

- the names of the returned tensor

## Examples

```
iex> key = Nx.Random.key(1701)
iex> {randint, _new_key} = Nx.Random.randint(key, 1, 100)
iex> randint
#Nx.Tensor<
s64
66
>
iex> key = Nx.Random.key(1701)
iex> {randint, _new_key} = Nx.Random.randint(key, 1, 100, shape: {3, 2}, type: :u32)
iex> randint
#Nx.Tensor<
u32[3][2]
[
[9, 20],
[19, 6],
[71, 15]
]
>
```

Same as `randint/4`

but assumes the key has already been split.

Randomly shuffles tensor elements along an axis.

## Options

`:axis`

- the axis along which to shuffle. Defaults to`0`

`:independent`

- a boolean that indicates wether the permutations are independent along the given axis. Defaults to`false`

## Examples

```
iex> key = Nx.Random.key(42)
iex> {shuffled, _new_key} = Nx.Random.shuffle(key, Nx.iota({3, 4}, axis: 0))
iex> shuffled
#Nx.Tensor<
s64[3][4]
[
[2, 2, 2, 2],
[0, 0, 0, 0],
[1, 1, 1, 1]
]
>
iex> key = Nx.Random.key(10)
iex> {shuffled, _new_key} = Nx.Random.shuffle(key, Nx.iota({3, 4}, axis: 1), independent: true, axis: 1)
iex> shuffled
#Nx.Tensor<
s64[3][4]
[
[2, 1, 3, 0],
[3, 0, 1, 2],
[2, 3, 0, 1]
]
>
```

Splits a PRNG key into `num`

new keys by adding a leading axis.

## Examples

```
iex> key = Nx.Random.key(1701)
iex> Nx.Random.split(key)
#Nx.Tensor<
u32[2][2]
[
[56197195, 1801093307],
[961309823, 1704866707]
]
>
iex> key = Nx.Random.key(999999999999)
iex> Nx.Random.split(key, parts: 4)
#Nx.Tensor<
u32[4][2]
[
[3959978897, 4079927650],
[3769699049, 3585271160],
[3182829676, 333122445],
[3185556048, 1258545461]
]
>
```

Shortcut for `uniform(key, 0.0, 1.0, opts)`

.

Sample uniform float values in the semi-open interval `[min_val, max_val)`

.

## Options

`:type`

- a float type for the returned tensor`:shape`

- shape of the returned tensor`:names`

- the names of the returned tensor

## Examples

```
iex> key = Nx.Random.key(1701)
iex> {uniform, _new_key} = Nx.Random.uniform(key)
iex> uniform
#Nx.Tensor<
f32
0.9728643894195557
>
iex> key = Nx.Random.key(1701)
iex> {uniform, _new_key} = Nx.Random.uniform(key, shape: {3, 2}, type: :f16)
iex> uniform
#Nx.Tensor<
f16[3][2]
[
[0.75390625, 0.6484375],
[0.7294921875, 0.21484375],
[0.09765625, 0.0693359375]
]
>
iex> key = Nx.Random.key(1701)
iex> {uniform, _new_key} = Nx.Random.uniform(key, shape: {2, 2}, type: :c64)
iex> uniform
#Nx.Tensor<
c64[2][2]
[
[0.18404805660247803+0.6546461582183838i, 0.5525915622711182+0.11568140983581543i],
[0.6074584722518921+0.8104375600814819i, 0.247686505317688+0.21975469589233398i]
]
>
```

Same as `uniform/4`

but assumes the key has already been split.