Computes the norm of vectors, matrices, and tensors.
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`tf.compat.v2.linalg.norm`
tf.compat.v2.norm(
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).
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.
|
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.