- mars.tensor.nanstd(a, axis=None, dtype=None, out=None, ddof=0, keepdims=None, combine_size=None)#
Compute the standard deviation along the specified axis, while ignoring NaNs.
Returns the standard deviation, a measure of the spread of a distribution, of the non-NaN tensor elements. The standard deviation 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) – Calculate the standard deviation of the non-NaN values.
axis (int, optional) – Axis along which the standard deviation is computed. The default is to compute the standard deviation of the flattened tensor.
dtype (dtype, optional) – Type to use in computing the standard deviation. For tensors of integer type the default is float64, for tensors of float types it is the same as the tensor type.
out (Tensor, optional) – Alternative output tensor in which to place the result. It must have the same shape as the expected output but the type (of the calculated values) will be cast if necessary.
ddof (int, optional) – Means Delta Degrees of Freedom. The divisor used in calculations is
N - ddof, where
Nrepresents 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.
If this value is anything but the default it is passed through as-is to the relevant functions of the sub-classes. If these functions do not have a keepdims kwarg, a RuntimeError will be raised.
combine_size (int, optional) – The number of chunks to combine.
standard_deviation – If out is None, return a new array containing the standard deviation, 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
ndarray, see dtype parameter above.
The standard deviation is the square root of the average of the squared deviations from the mean:
std = sqrt(mean(abs(x - x.mean())**2)).
The average squared deviation is normally calculated as
x.sum() / N, where
N = len(x). If, however, ddof is specified, the divisor
N - ddofis used instead. In standard statistical practice,
ddof=1provides an unbiased estimator of the variance of the infinite population.
ddof=0provides a maximum likelihood estimate of the variance for normally distributed variables. The standard deviation computed in this function is the square root of the estimated variance, so even with
ddof=1, it will not be an unbiased estimate of the standard deviation per se.
Note that, for complex numbers, std takes the absolute value before squaring, so that the result is always real and nonnegative.
For floating-point input, the std 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.
>>> import mars.tensor as mt
>>> a = mt.array([[1, mt.nan], [3, 4]]) >>> mt.nanstd(a).execute() 1.247219128924647 >>> mt.nanstd(a, axis=0).execute() array([ 1., 0.]) >>> mt.nanstd(a, axis=1).execute() array([ 0., 0.5])