NormInducedMetric

class skfda.misc.metrics.NormInducedMetric(norm)

Metric induced by a norm.

Given a norm \(\| \cdot \|: X \rightarrow \mathbb{R}\), returns the metric \(d: X \times X \rightarrow \mathbb{R}\) induced by the norm:

\[d(f,g) = \|f - g\|\]

Parameters:

norm (Norm[VectorType]) – Norm used to induce the metric.

Examples

Computes the \(\mathbb{L}^2\) distance between an object containing functional data corresponding to the function \(y(x) = x\) defined over the interval [0, 1] and another one containing data of the function \(y(x) = x/2\).

Firstly we create the functional data.

>>> import skfda
>>> import numpy as np
>>> from skfda.misc.metrics import l2_norm, NormInducedMetric
>>>
>>> x = np.linspace(0, 1, 1001)
>>> fd = skfda.FDataGrid([x], x)
>>> fd2 = skfda.FDataGrid([x/2], x)

To construct the \(\mathbb{L}^2\) distance it is used the \(\mathbb{L}^2\) norm wich it is used to compute the distance.

>>> l2_distance = NormInducedMetric(l2_norm)
>>> d = l2_distance(fd, fd2)
>>> float(d[0])
0.288...

Methods