torch.linalg.vector_norm¶
- torch.linalg.vector_norm(x, ord=2, dim=None, keepdim=False, *, dtype=None, out=None) Tensor ¶
Computes a vector norm.
If
x
is complex valued, it computes the norm ofx
.abs()Supports input of float, double, cfloat and cdouble dtypes.
This function does not necessarily treat multidimensional
x
as a batch of vectors, instead:If
dim
= None,x
will be flattened before the norm is computed.If
dim
is an int or a tuple, the norm will be computed over these dimensions and the other dimensions will be treated as batch dimensions.
This behavior is for consistency with
torch.linalg.norm()
.ord
defines the vector norm that is computed. The following norms are supported:ord
vector norm
2 (default)
2-norm (see below)
inf
max(abs(x))
-inf
min(abs(x))
0
sum(x != 0)
other int or float
sum(abs(x)^{ord})^{(1 / ord)}
where inf refers to float(‘inf’), NumPy’s inf object, or any equivalent object.
dtype
may be used to perform the computation in a more precise dtype. It is semantically equivalent to callinglinalg.vector_norm(x.to(dtype))
but it is faster in some cases.See also
torch.linalg.matrix_norm()
computes a matrix norm.- Parameters
x (Tensor) – tensor, flattened by default, but this behavior can be controlled using
dim
.ord (int, float, inf, -inf, 'fro', 'nuc', optional) – order of norm. Default: 2
dim (int, Tuple[int], optional) – dimensions over which to compute the norm. See above for the behavior when
dim
= None. Default: Nonekeepdim (bool, optional) – If set to True, the reduced dimensions are retained in the result as dimensions with size one. Default: False
- Keyword Arguments
out (Tensor, optional) – output tensor. Ignored if None. Default: None.
dtype (
torch.dtype
, optional) – type used to perform the accumulation and the return. If specified,x
is cast todtype
before performing the operation, and the returned tensor’s type will bedtype
if real and of its real counterpart if complex.dtype
may be complex ifx
is complex, otherwise it must be real.x
should be convertible without narrowing todtype
. Default: None
- Returns
A real-valued tensor, even when
x
is complex.
Examples:
>>> from torch import linalg as LA >>> a = torch.arange(9, dtype=torch.float) - 4 >>> a tensor([-4., -3., -2., -1., 0., 1., 2., 3., 4.]) >>> B = a.reshape((3, 3)) >>> B tensor([[-4., -3., -2.], [-1., 0., 1.], [ 2., 3., 4.]]) >>> LA.vector_norm(a, ord=3.5) tensor(5.4345) >>> LA.vector_norm(B, ord=3.5) tensor(5.4345)