var

→Tensor

var(input: Tensor, dim: _int | Sequence[_int] | None = None, unbiased: _bool | None = None, keepdim: _bool = False, correction: _int | _float | None = None)

source edit

Implementing kernel

C++var_opfree fn

Compute the variance along dim.

The sum of squared deviations from the mean, divided by $\max(n - c, 0)$ for n reduced elements and correction $c$ . correction=1 (the default) is Bessel's unbiased sample variance; correction=0 the population variance.

Parameters

inputTensor

Input tensor.

dimint or sequence of int= None

Dimension(s) to reduce. None reduces every element. A dimension named twice is refused.

unbiasedbool= None

True is correction=1, False correction=0; it overrides correction when given. A bool in the place of dim — var(x, False) — is read as this.

keepdimbool= False

Whether to retain reduced dims with size 1.

correctionint or float= None

Degrees-of-freedom correction

c

. Default 1.

Returns

Tensor

Reduced floating-point tensor.

Raises

ValueError

If dim names one dimension twice.

Notes

\sigma^2 \;=\; \frac{1}{\max(n - c, 0)} \sum_{i=1}^{n} (x_i - \bar{x})^2 .

With $n \le c$ the divisor is 0: a slice with no spread gives nan and one with spread inf — so var of a single element is nan under the default correction, as is any empty reduction.

Examples

>>> import lucid
>>> x = lucid.tensor([[1.0, 2.0, 3.0, 4.0], [2.0, 4.0, 6.0, 8.0]])
>>> lucid.var(x, 1)
tensor([1.667, 6.667])
>>> lucid.var(x, 1, False, True)
tensor([[1.25], [5.]])

var