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TensorFlow 1 version View source on GitHub

Computes the Euclidean norm of elements across dimensions of a tensor.


  • tf.compat.v1.math.reduce_euclidean_norm
  • tf.compat.v2.math.reduce_euclidean_norm

Reduces input_tensor along the dimensions given in axis. Unless keepdims is true, the rank of the tensor is reduced by 1 for each entry in axis. If keepdims is true, the reduced dimensions are retained with length 1.

If axis is None, all dimensions are reduced, and a tensor with a single element is returned.

For example:

x = tf.constant([[1, 2, 3], [1, 1, 1]])
tf.reduce_euclidean_norm(x)  # sqrt(17)
tf.reduce_euclidean_norm(x, 0)  # [sqrt(2), sqrt(5), sqrt(10)]
tf.reduce_euclidean_norm(x, 1)  # [sqrt(14), sqrt(3)]
tf.reduce_euclidean_norm(x, 1, keepdims=True)  # [[sqrt(14)], [sqrt(3)]]
tf.reduce_euclidean_norm(x, [0, 1])  # sqrt(17)


  • input_tensor: The tensor to reduce. Should have numeric type.
  • axis: The dimensions to reduce. If None (the default), reduces all dimensions. Must be in the range [-rank(input_tensor), rank(input_tensor)).
  • keepdims: If true, retains reduced dimensions with length 1.
  • name: A name for the operation (optional).


The reduced tensor, of the same dtype as the input_tensor.