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).
Args
tensor
Tensor of types float32, float64, complex64, complex128
ord
Order of the norm. Supported values are 'fro', 'euclidean',
1, 2, 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 'euclidean', 'fro', 1,
2, 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.
axis
If axis is None (the default), the input is considered a vector
and a single vector norm is computed over the entire set of values in the
tensor, i.e. norm(tensor, ord=ord) is equivalent to
norm(reshape(tensor, [-1]), ord=ord).
If axis is a Python integer, the input is considered a batch of vectors,
and axis determines the axis in tensor over which to compute vector
norms.
If axis is a 2-tuple of Python integers it is considered a batch of
matrices and 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
computed.
keepdims
If True, the axis indicated in axis are kept with size 1.
Otherwise, the dimensions in axis are removed from the output shape.
name
The name of the op.
keep_dims
Deprecated alias for keepdims.
Returns
output
A 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,
if axis is an integer, the rank of output is one less than the rank
of tensor, if axis is a 2-tuple the rank of output is two less
than the rank of tensor.
Raises
ValueError
If ord or axis is invalid.
numpy compatibility
Mostly equivalent to numpy.linalg.norm.
Not supported: ord <= 0, 2-norm for matrices, nuclear norm.
Other differences:
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.
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