giagrad.Tensor.std#

Tensor.std(axis=None, ddof=1, keepdims=False, eps=0.0)[source]#

Calculates the standard deviation over the axis specified by axis.

The standard deviation (\(\sigma\)) is calculated as:

\[\sigma = \sqrt{\frac{1}{N-\text{ddof}}\sum_{i=0}^{N-1}(x_i-\bar{x})^2 + \epsilon}\]

If keepdims is True, the output tensor is of the same size as input except in the axis where it is of size 1. Otherwise, every axis is squeezed, leading to an output tensor with fewer dimensions. If no axis is supplied all data is reduced to a scalar value. Optional parameter eps could be used for numerical stability.

Parameters:

  • axis ((int, ...) or int or None, default: None) – The dimension or dimension to reduce. If None, std reduces all dimensions.

  • ddof (int, default: 1) – Degrees of freedom substracted to N. ddof=1 equals sample variance, ddof=0 equals population variance.

  • keepdims (bool, default: False) – Whether te output tensor should retain the reduced dimensions.

  • eps (float, default: 0.0) – Epsilon value added to \(\mathrm{Var}[x]\) for numerical stability.

Examples

>>> a = Tensor.empty(2, 2, 3, dtype=int).uniform(0, 10)
>>> a
tensor: [[[2 8 5]
          [8 4 6]]
...
         [[7 9 6]
          [3 3 6]]]
>>> a.std()
tensor: 2.1392496 fn: Pow
>>> a.std((0, 1), keepdims=True, ddof=1)
tensor: [[[2.94392029 2.94392029 0.5       ]]] fn: Pow
>>> a.std((0, 1), keepdims=True, ddof=1).ndim
3
>>> a.std((0, 1), keepdims=True, ddof=1, eps=.1)
tensor: [[[2.96085573 2.96085573 0.59160798]]] fn: Pow
>>> (a.var((0, 1), keepdims=True, ddof=1) + .1).sqrt()
tensor: [[[2.96085573 2.96085573 0.59160798]]] fn: Pow