jax.numpy.var#

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

Compute the variance along a given axis.

JAX implementation of numpy.var().

Parameters:

  • a (ArrayLike) – input array.

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

  • mean (ArrayLike | None) – optional, mean of the input array, computed along the given axis. If provided, it will be used to compute the variance instead of computing it from the input array. If specified, mean must be broadcast-compatible with the input array. In the general case, this can be achieved by computing the mean with keepdims=True and axis matching this function’s axis argument.

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

  • out (None) – Unused by JAX.

Returns:

An array of the variance along the given axis.

Return type:

Array

See also

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]]