tf.norm

tf.norm

tf.norm

norm(
    tensor,
    ord='euclidean',
    axis=None,
    keep_dims=False,
    name=None
)

Defined in tensorflow/python/ops/linalg_ops.py.

See the guide: Math > Matrix Math Functions

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, and inf-norm).

Args:

• tensor: Tensor of types float32, float64, complex64, complex128
• ord: Order of the norm. Supported values are 'fro', 'euclidean', 0, 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, 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.
• keep_dims: 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 keep_dims 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.