tf.keras.ops.norm | TensorFlow v2.16.1 (original) (raw)
tf.keras.ops.norm
Matrix or vector norm.
View aliases
Main aliases
tf.keras.ops.norm(
x, ord=None, axis=None, keepdims=False
)
This function is able to return one of eight different matrix norms, or one of an infinite number of vector norms (described below), depending on the value of the ord parameter.
| Args | |
|---|---|
| x | Input tensor. |
| ord | Order of the norm (see table under Notes). The default is None. |
| axis | If axis is an integer, it specifies the axis of x along which to compute the vector norms. If axis is a 2-tuple, it specifies the axes that hold 2-D matrices, and the matrix norms of these matrices are computed. |
| keepdims | If this is set to True, the axes which are reduced are left in the result as dimensions with size one. |
| Note |
|---|
| For values of ord < 1, the result is, strictly speaking, not a mathematical 'norm', but it may still be useful for various numerical purposes. The following norms can be calculated: For matrices: ord=None: Frobenius norm ord="fro": Frobenius norm ord="nuc": nuclear norm ord=np.inf: max(sum(abs(x), axis=1)) ord=-np.inf: min(sum(abs(x), axis=1)) ord=0: not supported ord=1: max(sum(abs(x), axis=0)) ord=-1: min(sum(abs(x), axis=0)) ord=2: 2-norm (largest sing. value) ord=-2: smallest singular value other: not supported For vectors: ord=None: 2-norm ord="fro": not supported ord="nuc": not supported ord=np.inf: max(abs(x)) ord=-np.inf: min(abs(x)) ord=0: sum(x != 0) ord=1: as below ord=-1: as below ord=2: as below ord=-2: as below other: sum(abs(x)**ord)**(1./ord) |
| Returns |
|---|
| Norm of the matrix or vector(s). |
Example:
x = keras.ops.reshape(keras.ops.arange(9, dtype="float32") - 4, (3, 3))
keras.ops.linalg.norm(x)
7.7459664
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Last updated 2024-06-07 UTC.