std

→Tensor

std(x: Tensor, dim: _int | list[_int] | None = None, keepdim: _bool = False, correction: _int = 1)

source

Compute the sample standard deviation along dim.

Defined as the square root of the (corrected) sample variance. The correction keyword selects between Bessel-corrected (correction=1, the default — divides by $n-1$ ) and biased (correction=0 — divides by $n$ ) estimates.

Parameters

xTensor

Input tensor.

dimint or list of int= None

Dimension(s) to reduce.

keepdimbool= False

Whether to retain reduced dims with size 1.

correctionint= 1

Degrees-of-freedom correction. 1 for unbiased, 0 for biased.

Returns

Tensor

Reduced floating-point tensor.

Notes

\sigma \;=\; \sqrt{ \frac{1}{n - c} \sum_{i=1}^{n} (x_i - \bar{x})^2 } ,

where $c$ is the correction and $\bar{x}$ is the sample mean.

Examples

>>> import lucid
>>> x = lucid.tensor([1.0, 2.0, 3.0, 4.0])
>>> lucid.std(x)
Tensor(1.2910)