Compute the variance along the specified axis, while ignoring NaNs.
Returns the variance of the tensor elements, a measure of the spread of
a distribution. The variance is computed for the flattened tensor by
default, otherwise over the specified axis.
For all-NaN slices or slices with zero degrees of freedom, NaN is
returned and a RuntimeWarning is raised.
a (array_like) – Tensor containing numbers whose variance is desired. If a is not a
tensor, a conversion is attempted.
axis (int, optional) – Axis along which the variance is computed. The default is to compute
the variance of the flattened array.
dtype (data-type, optional) – Type to use in computing the variance. For tensors of integer type
the default is float32; for tensors of float types it is the same as
the tensor type.
out (Tensor, optional) – Alternate output tensor in which to place the result. It must have
the same shape as the expected output, but the type is cast if
ddof (int, optional) – “Delta Degrees of Freedom”: the divisor used in the calculation is
N - ddof, where N represents the number of non-NaN
elements. By default ddof is zero.
N - ddof
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 original a.
combine_size (int, optional) – The number of chunks to combine.
variance – If out is None, return a new tensor containing the variance,
otherwise return a reference to the output tensor. If ddof is >= the
number of non-NaN elements in a slice or the slice contains only
NaNs, then the result for that slice is NaN.
Tensor, see dtype parameter above
Variance while not ignoring NaNs
The variance is the average of the squared deviations from the mean,
i.e., var = mean(abs(x - x.mean())**2).
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.
x.sum() / N
N = len(x)
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 float32 (see example
below). Specifying a higher-accuracy accumulator using the dtype
keyword can alleviate this issue.
For this function to work on sub-classes of Tensor, they must define
sum with the kwarg keepdims
>>> import mars.tensor as mt
>>> a = mt.array([[1, mt.nan], [3, 4]])
>>> mt.nanvar(a, axis=0).execute()
array([ 1., 0.])
>>> mt.nanvar(a, axis=1).execute()
array([ 0., 0.25])