mars.tensor.nanvar(a, axis=None, dtype=None, out=None, ddof=0, keepdims=None, combine_size=None)[source]#

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 necessary.

  • 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.

  • 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.

Return type

Tensor, see dtype parameter above

See also


Standard deviation




Variance while not ignoring NaNs

nanstd, nanmean


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.

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).execute()
>>> mt.nanvar(a, axis=0).execute()
array([ 1.,  0.])
>>> mt.nanvar(a, axis=1).execute()
array([ 0.,  0.25])