Function norm_v2

tensorflow/python/ops/linalg_ops.py:427–493

r"""Computes the norm of vectors, matrices, and tensors. 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` o

(tensor,
            ord='euclidean',
            axis=None,
            keepdims=None,
            name=None)

# pylint: disable=redefined-builtin
@tf_export('norm', 'linalg.norm', v1=[])
def norm_v2(tensor,
            ord='euclidean',
            axis=None,
            keepdims=None,
            name=None):
  r"""Computes the norm of vectors, matrices, and tensors.

  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.

  @compatibility(numpy)
  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.