var(a, axis=None, dtype=None, keepdims=False, ddof=0, split_every=None, out=None)

This docstring was copied from numpy.var.

Some inconsistencies with the Dask version may exist.

Returns the variance of the array elements, a measure of the spread of a distribution. The variance is computed for the flattened array by default, otherwise over the specified axis.

Notes

The variance is the average of the squared deviations from the mean, i.e., var = mean(x) , where x = abs(a - a.mean())**2 .

The mean is typically calculated as x.sum() / N , where N = len(x) . If, however, :None:None:`ddof` is specified, the divisor N - ddof is used instead. In standard statistical practice, ddof=1 provides an unbiased estimator of the variance of a hypothetical infinite population. ddof=0 provides a maximum likelihood estimate of the variance for normally distributed variables.

Note that for complex numbers, the absolute value is taken before squaring, so that the result is always real and nonnegative.

For floating-point input, the variance is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for :None:None:`float32` (see example below). Specifying a higher-accuracy accumulator using the dtype keyword can alleviate this issue.

Parameters

a : array_like

Array containing numbers whose variance is desired. If a is not an array, a conversion is attempted.

axis : None or int or tuple of ints, optional

Axis or axes along which the variance is computed. The default is to compute the variance of the flattened array.

versionadded

If this is a tuple of ints, a variance is performed over multiple axes, instead of a single axis or all the axes as before.

dtype : data-type, optional

Type to use in computing the variance. For arrays of integer type the default is :None:None:`float64`; for arrays of float types it is the same as the array type.

out : ndarray, optional

Alternate output array in which to place the result. It must have the same shape as the expected output, but the type is cast if necessary.

ddof : int, optional

"Delta Degrees of Freedom": the divisor used in the calculation is N - ddof , where N represents the number of elements. By default :None:None:`ddof` is zero.

keepdims : bool, optional

If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array.

If the default value is passed, then keepdims will not be passed through to the var method of sub-classes of :None:None:`ndarray`, however any non-default value will be. If the sub-class' method does not implement keepdims any exceptions will be raised.

where : array_like of bool, optional (Not supported in Dask)

Elements to include in the variance. See :None:None:`~numpy.ufunc.reduce` for details.

versionadded

Returns

variance : ndarray, see dtype parameter above

If out=None , returns a new array containing the variance; otherwise, a reference to the output array is returned.

Compute the variance along the specified axis.

See Also

mean

nanmean

nanstd

nanvar

std

ufuncs-output-type

ref

Examples

This example is valid syntax, but we were not able to check execution

>>> a = np.array([[1, 2], [3, 4]])  # doctest: +SKIP
... np.var(a)  # doctest: +SKIP
1.25

This example is valid syntax, but we were not able to check execution

>>> np.var(a, axis=0)  # doctest: +SKIP
array([1.,  1.])

This example is valid syntax, but we were not able to check execution

>>> np.var(a, axis=1)  # doctest: +SKIP
array([0.25,  0.25])

In single precision, var() can be inaccurate:

This example is valid syntax, but we were not able to check execution

>>> a = np.zeros((2, 512*512), dtype=np.float32)  # doctest: +SKIP
... a[0, :] = 1.0  # doctest: +SKIP
... a[1, :] = 0.1  # doctest: +SKIP
... np.var(a)  # doctest: +SKIP
0.20250003

Computing the variance in float64 is more accurate:

This example is valid syntax, but we were not able to check execution

>>> np.var(a, dtype=np.float64)  # doctest: +SKIP
0.20249999932944759 # may vary

This example is valid syntax, but we were not able to check execution

>>> ((1-0.55)**2 + (0.1-0.55)**2)/2  # doctest: +SKIP
0.2025

Specifying a where argument:

This example is valid syntax, but we were not able to check execution

>>> a = np.array([[14, 8, 11, 10], [7, 9, 10, 11], [10, 15, 5, 10]])  # doctest: +SKIP
... np.var(a)  # doctest: +SKIP
6.833333333333333 # may vary

This example is valid syntax, but we were not able to check execution

>>> np.var(a, where=[[True], [True], [False]])  # doctest: +SKIP
4.0

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

dask.array.reductions.var dask.array.reductions.nanmean dask.array.reductions.mean dask.array.reductions.nanvar dask.array.reductions.std dask.array.reductions.nanstd

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them

---

File: /dask/array/reductions.py#824
type: <class 'function'>
Commit: