Computes the norm of vectors, matrices, and tensors.
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tensor, ord='euclidean', axis=None, keepdims=None, name=None
This function can compute several different vector norms (the 1-norm, the
Euclidean or 2-norm, the inf-norm, and in general the p-norm for p > 0) and
matrix norms (Frobenius, 1-norm, 2-norm and inf-norm).
Tensor of types
Order of the norm. Supported values are
np.inf and any positive real number yielding the corresponding
p-norm. Default is
'euclidean' which is equivalent to Frobenius norm if
tensor is a matrix and equivalent to 2-norm for vectors.
Some restrictions apply:
a) The Frobenius norm
'fro' is not defined for vectors,
b) If axis is a 2-tuple (matrix norm), only
np.inf are supported.
See the description of
axis on how to compute norms for a batch of
vectors or matrices stored in a tensor.
None (the default), the input is considered a vector
and a single vector norm is computed over the entire set of values in the
norm(tensor, ord=ord) is equivalent to
norm(reshape(tensor, [-1]), ord=ord).
axis is a Python integer, the input is considered a batch of vectors,
axis determines the axis in
tensor over which to compute vector
axis is a 2-tuple of Python integers it is considered a batch of
axis determines the axes in
tensor over which to compute
a matrix norm.
Negative indices are supported. Example: If you are passing a tensor that
can be either a matrix or a batch of matrices at runtime, pass
axis=[-2,-1] instead of
axis=None to make sure that matrix norms are
If True, the axis indicated in
axis are kept with size 1.
Otherwise, the dimensions in
axis are removed from the output shape.
The name of the op.
Tensor of the same type as tensor, containing the vector or
matrix norms. If
keepdims is True then the rank of output is equal to
the rank of
tensor. Otherwise, if
axis is none the output is a scalar,
axis is an integer, the rank of
output is one less than the rank
axis is a 2-tuple the rank of
output is two less
than the rank of
axis is invalid.
Mostly equivalent to numpy.linalg.norm.
Not supported: ord <= 0, 2-norm for matrices, nuclear norm.
a) If axis is
None, treats the flattened
tensor as a vector
regardless of rank.
b) Explicitly supports 'euclidean' norm as the default, including for
higher order tensors.