jax.numpy.var

jax.numpy.var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=None, correction=None)

Compute the variance along a given axis.

JAX implementation of numpy.var().

Parameters:

• a (ArrayLike) – input array.

• axis (Axis | None) – optional, int or sequence of ints, default=None. Axis along which the variance is computed. If None, variance is computed along all the axes.

• dtype (DTypeLike | None | None) – The type of the output array. Default=None.

• ddof (int) – int, default=0. Degrees of freedom. The divisor in the variance computation is N-ddof, N is number of elements along given axis.

• keepdims (bool) – bool, default=False. If true, reduced axes are left in the result with size 1.

• where (ArrayLike | None | None) – optional, boolean array, default=None. The elements to be used in the variance. Array should be broadcast compatible to the input.

• correction (int | float | None | None) – int or float, default=None. Alternative name for ddof. Both ddof and correction can’t be provided simultaneously.

• out (None | None) – Unused by JAX.

Returns:

An array of the variance along the given axis.

Return type:

Array

See also

• jax.numpy.mean(): Compute the mean of array elements over a given axis.

• jax.numpy.std(): Compute the standard deviation of array elements over given axis.

• jax.numpy.nanvar(): Compute the variance along a given axis, ignoring NaNs values.

• jax.numpy.nanstd(): Computed the standard deviation of a given axis, ignoring NaN values.

Examples

By default, jnp.var computes the variance along all axes.

>>> x = jnp.array([[1, 3, 4, 2],
...                [5, 2, 6, 3],
...                [8, 4, 2, 9]])
>>> with jnp.printoptions(precision=2, suppress=True):
...   jnp.var(x)
Array(5.74, dtype=float32)

If axis=1, variance is computed along axis 1.

>>> jnp.var(x, axis=1)
Array([1.25  , 2.5   , 8.1875], dtype=float32)

To preserve the dimensions of input, you can set keepdims=True.

>>> jnp.var(x, axis=1, keepdims=True)
Array([[1.25  ],
       [2.5   ],
       [8.1875]], dtype=float32)

If ddof=1:

>>> with jnp.printoptions(precision=2, suppress=True):
...   print(jnp.var(x, axis=1, keepdims=True, ddof=1))
[[ 1.67]
 [ 3.33]
 [10.92]]

To include specific elements of the array to compute variance, you can use where.

>>> where = jnp.array([[1, 0, 1, 0],
...                    [0, 1, 1, 0],
...                    [1, 1, 1, 0]], dtype=bool)
>>> with jnp.printoptions(precision=2, suppress=True):
...   print(jnp.var(x, axis=1, keepdims=True, where=where))
[[2.25]
 [4.  ]
 [6.22]]