LpNormalization¶

LpNormalization - 22¶

Version¶

name: LpNormalization (GitHub)
domain: main
since_version: 22
function: False
support_level: SupportType.COMMON
shape inference: True

This version of the operator has been available since version 22.

Summary¶

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.

Attributes¶

axis - INT (default is -1):

The axis on which to apply normalization, -1 mean last axis.
p - INT (default is 2):

The order of the normalization, only 1 or 2 are supported.

Inputs¶

input (heterogeneous) - T:

Input matrix

Outputs¶

output (heterogeneous) - T:

Matrix after normalization

Type Constraints¶

T in ( tensor(bfloat16), tensor(double), tensor(float), tensor(float16) ):

Constrain input and output types to float tensors.

Examples¶

_l2normalization_axis_0¶

import numpy as np
import onnx

node = onnx.helper.make_node(
    "LpNormalization", inputs=["x"], outputs=["y"], axis=0, p=2
)
x = np.array(
    [[[1.0, 2.0, 2.0], [3.0, 4.0, 0.0]], [[0.0, 5.0, 5.0], [6.0, 8.0, 0.0]]],
    dtype=np.float32,
)
l2_norm_axis_0 = np.sqrt(np.sum(x**2, axis=0, keepdims=True))
# When norm is 0, output is 0 (0/0 = 0)
y = np.where(l2_norm_axis_0 == 0, 0, x / l2_norm_axis_0)
expect(node, inputs=[x], outputs=[y], name="test_l2normalization_axis_0")

_l2normalization_axis_1¶

import numpy as np
import onnx

node = onnx.helper.make_node(
    "LpNormalization", inputs=["x"], outputs=["y"], axis=1, p=2
)
x = np.array([[3.0, 4.0], [6.0, 8.0]], dtype=np.float32)
l2_norm_axis_1 = np.sqrt(np.sum(x**2, axis=1, keepdims=True))
y = x / l2_norm_axis_1
expect(node, inputs=[x], outputs=[y], name="test_l2normalization_axis_1")

_l1normalization_axis_0¶

import numpy as np
import onnx

node = onnx.helper.make_node(
    "LpNormalization", inputs=["x"], outputs=["y"], axis=0, p=1
)
x = np.array([3.0, 4.0], dtype=np.float32)
l1_norm_axis_0 = np.sum(abs(x), axis=0, keepdims=True)
y = x / l1_norm_axis_0
expect(node, inputs=[x], outputs=[y], name="test_l1normalization_axis_0")

_l1normalization_axis_1¶

import numpy as np
import onnx

node = onnx.helper.make_node(
    "LpNormalization", inputs=["x"], outputs=["y"], axis=1, p=1
)
x = np.array([[3.0, 4.0], [6.0, 8.0]], dtype=np.float32)
l1_norm_axis_1 = np.sum(abs(x), axis=1, keepdims=True)
y = x / l1_norm_axis_1
expect(node, inputs=[x], outputs=[y], name="test_l1normalization_axis_1")

_l1normalization_axis_last¶

import numpy as np
import onnx

node = onnx.helper.make_node(
    "LpNormalization", inputs=["x"], outputs=["y"], axis=-1, p=1
)
x = np.array(
    [[[1.0, 2.0, 2.0], [3.0, 4.0, 0.0]], [[0.0, 5.0, 5.0], [6.0, 8.0, 0.0]]],
    dtype=np.float32,
)
l1_norm_axis_last = np.sum(abs(x), axis=-1, keepdims=True)
y = x / l1_norm_axis_last
expect(node, inputs=[x], outputs=[y], name="test_l1normalization_axis_last")

_default¶

import numpy as np
import onnx

node = onnx.helper.make_node("LpNormalization", inputs=["x"], outputs=["y"])
x = np.array(
    [[[1.0, 2.0, 2.0], [3.0, 4.0, 0.0]], [[0.0, 5.0, 5.0], [6.0, 8.0, 0.0]]],
    dtype=np.float32,
)
lp_norm_default = np.sqrt(np.sum(x**2, axis=-1, keepdims=True))
y = x / lp_norm_default
expect(node, inputs=[x], outputs=[y], name="test_lpnormalization_default")

LpNormalization - 1 vs 22

LpNormalization - 1¶