nlcpy.var

nlcpy.var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=nlcpy._NoValue)

Computes the variance along the specified axis.

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.

Parameters

aarray_like: Array containing numbers whose variance is desired. If a is not an array, a conversion is attempted.
axisNone or int, optional: Axis along which the variance is computed. The default is to compute the variance of the flattened array.
dtypedata-type, optional: Type to use in computing the variance. For arrays of integer type the default is float32; for arrays of float types it is the same as the array type.
outndarray, 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.
ddofint, optional: “Delta Degrees of Freedom”: the divisor used in the calculation is N - ddof, where N represents the number of elements. By default, ddof is zero. The array or list to be shuffled.
keepdimsbool, optional: If this is set to True, the axis 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.

Returns

variancendarray, see dtype parameter above: If out=None, returns a new array containing the variance; otherwise, a reference to the output array is returned.

See also

std: Computes the standard deviation along the specified axis.
mean: Computes the arithmetic mean along the specified axis.
nanmean: Computes the arithmetic mean along the specified axis, ignoring NaNs.
nanstd: Computes the standard deviation along the specified axis, while ignoring NaNs.
nanvar: Computes the variance along the specified axis, while ignoring NaNs.

Note

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

The mean is normally calculated as x.sum() / N, where N = len(x). If, however, 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.

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 float32 (see example below). Specifying a higher-accuracy accumulator using the dtype keyword can alleviate this issue.

Restriction

If axis is neither a scalar nor None : NotImplementedError occurs.
For complex numbers, NotImplementedError occurs.

Examples

>>> import nlcpy as vp
>>> a = vp.array([[1, 2], [3, 4]])
>>> vp.var(a)
array(1.25)
>>> vp.var(a, axis=0)
array([1., 1.])
>>> vp.var(a, axis=1)
array([0.25, 0.25])

In single precision, var() can be inaccurate:

>>> a = vp.zeros((2, 512*512), dtype=vp.float32)
>>> a[0, :] = 1.0
>>> a[1, :] = 0.1
>>> vp.var(a)
array(0.2024999, dtype=float32)

Computing the variance in float64 is more accurate:

>>> vp.var(a, dtype=vp.float64)   
array(0.2025) # may vary
>>> ((1-0.55)**2 + (0.1-0.55)**2)/2
0.2025