megengine.functional.norm¶
- norm(inp, ord=None, axis=None, keepdims=False)[source]¶
Calculates the norm of tensor elements over a given axis.
This function is able to return different matrix norms, or one of an infinite number of vector norms (described below), depending on the value of the ord parameter.
- Parameters
inp (
Tensor) – input tensor. Should have a numeric data type.ord (
Optional[float]) – Order of the norm (see table under Notes). If not specified, the default is 2.axis (
Optional[int]) – Axis along which to compute vector norms. If axis is an integer, it specifies the axis of inp along which to compute the vector norms.keepdims – If this is set to
True, the axes which are normed over are left in the result as dimensions with size one.
- Returns
Norm of the matrix or vector(s).
Note
Now the following norms can be calculated:
inf: norm-\(\infty\) (maximum of absolute values).
-inf: norm-\(-\infty\) (minimum of absolute values).
2: 2-norm (largest singluar value).
The Frobenius norm is given by to
sum(abs(x)**ord)**(1./ord):\[\|A\|_F=\left[\sum_{i, j} a b s\left(a_{i, j}\right)^2\right]^{1 / 2}\]See also
Examples
>>> import math >>> x = Tensor([1, 2, 3]) >>> F.norm(x, ord=math.inf) Tensor(3, dtype=int32, device=xpux:0) >>> F.norm(x, ord=-math.inf) Tensor(1, dtype=int32, device=xpux:0)
>>> x = Tensor([[1, 2, 3], [4, 5, 6]]) >>> F.norm(x, ord=2, axis=0) Tensor([4.1231 5.3852 6.7082], device=xpux:0) >>> F.norm(x, ord=2, axis=1) Tensor([3.7417 8.775 ], device=xpux:0)