.. _op_ai_onnx_LpNormalization:

LpNormalization
===============

- **Domain**: ``ai.onnx``
- **Since version**: 22

Given a matrix, apply Lp-normalization along the provided axis.
The output is computed as: ``output = input / Lp_norm(input, axis)``.
When the Lp norm is zero (i.e., all elements along the axis are zero),
the output is defined to be zero to avoid division by zero.

**Inputs**

- **input** (*T*): Input matrix

**Outputs**

- **output** (*T*): Matrix after normalization

**Attributes**

- **axis** (*int*): The axis on which to apply normalization, -1 mean last axis.
- **p** (*int*): The order of the normalization, only 1 or 2 are supported.

**Type Constraints**

- **T**: Constrain input and output types to float tensors.
  Allowed types: tensor(bfloat16), tensor(double), tensor(float), tensor(float16).

Examples
--------

**test_cc_lpnormalization_axis0_p1**

.. code-block:: text

    Node:
      LpNormalization(x) -> (y)
      Attributes:
        axis = 0
        p = 1

.. code-block:: text

    Inputs:
      x: shape=(2, 2, 3), dtype=float32
        [[[1., 2., 2.],
          [3., 4., 0.]],
        
         [[0., 5., 5.],
          [6., 8., 0.]]]

    Outputs:
      y: shape=(2, 2, 3), dtype=float32
        [[[1.        , 0.2857143 , 0.2857143 ],
          [0.33333334, 0.33333334, 0.        ]],
        
         [[0.        , 0.71428573, 0.71428573],
          [0.6666667 , 0.6666667 , 0.        ]]]

**test_cc_lpnormalization_default**

.. code-block:: text

    Node:
      LpNormalization(x) -> (y)

.. code-block:: text

    Inputs:
      x: shape=(2, 2, 3), dtype=float32
        [[[1., 2., 2.],
          [3., 4., 0.]],
        
         [[0., 5., 5.],
          [6., 8., 0.]]]

    Outputs:
      y: shape=(2, 2, 3), dtype=float32
        [[[0.33333334, 0.6666667 , 0.6666667 ],
          [0.6       , 0.8       , 0.        ]],
        
         [[0.        , 0.70710677, 0.70710677],
          [0.6       , 0.8       , 0.        ]]]

**test_l1normalization_axis_0**

.. code-block:: text

    Node:
      LpNormalization(x) -> (y)
      Attributes:
        axis = 0
        p = 1

.. code-block:: text

    Inputs:
      x: shape=(2,), dtype=float32
        [3., 4.]

    Outputs:
      y: shape=(2,), dtype=float32
        [0.42857143, 0.5714286 ]

**test_l1normalization_axis_1**

.. code-block:: text

    Node:
      LpNormalization(x) -> (y)
      Attributes:
        axis = 1
        p = 1

.. code-block:: text

    Inputs:
      x: shape=(2, 2), dtype=float32
        [[3., 4.],
         [6., 8.]]

    Outputs:
      y: shape=(2, 2), dtype=float32
        [[0.42857143, 0.5714286 ],
         [0.42857143, 0.5714286 ]]

**test_l1normalization_axis_last**

.. code-block:: text

    Node:
      LpNormalization(x) -> (y)
      Attributes:
        axis = -1
        p = 1

.. code-block:: text

    Inputs:
      x: shape=(2, 2, 3), dtype=float32
        [[[1., 2., 2.],
          [3., 4., 0.]],
        
         [[0., 5., 5.],
          [6., 8., 0.]]]

    Outputs:
      y: shape=(2, 2, 3), dtype=float32
        [[[0.2       , 0.4       , 0.4       ],
          [0.42857143, 0.5714286 , 0.        ]],
        
         [[0.        , 0.5       , 0.5       ],
          [0.42857143, 0.5714286 , 0.        ]]]

**test_l2normalization_axis_0**

.. code-block:: text

    Node:
      LpNormalization(x) -> (y)
      Attributes:
        axis = 0
        p = 2

.. code-block:: text

    Inputs:
      x: shape=(2, 2, 3), dtype=float32
        [[[1., 2., 2.],
          [3., 4., 0.]],
        
         [[0., 5., 5.],
          [6., 8., 0.]]]

    Outputs:
      y: shape=(2, 2, 3), dtype=float32
        [[[1.        , 0.37139067, 0.37139067],
          [0.4472136 , 0.4472136 , 0.        ]],
        
         [[0.        , 0.9284767 , 0.9284767 ],
          [0.8944272 , 0.8944272 , 0.        ]]]

**test_l2normalization_axis_1**

.. code-block:: text

    Node:
      LpNormalization(x) -> (y)
      Attributes:
        axis = 1
        p = 2

.. code-block:: text

    Inputs:
      x: shape=(2, 2), dtype=float32
        [[3., 4.],
         [6., 8.]]

    Outputs:
      y: shape=(2, 2), dtype=float32
        [[0.6, 0.8],
         [0.6, 0.8]]

Differences with previous version (1)
-------------------------------------

**SchemaDiff**: ``LpNormalization`` (domain ``'ai.onnx'``)

* old version: 1
* new version: 22
* breaking: no

**Type constraints:**

* changed 'T': added types: ['tensor(bfloat16)']

Version History
---------------

- :doc:`Version 1 <LpNormalization-1>`