Lp norm function

\[f(x) = \left \| x \right \|_p = \sqrt[p]{\sum\limits_{i}^{nx}\left | x_i \right |^p},\]

Usage

import matplotlib.pyplot as plt
import numpy as np

from smt.problems import LpNorm

ndim = 2
problem = LpNorm(ndim=ndim, order=2)

num = 100
x = np.ones((num, ndim))
x[:, 0] = np.linspace(-1.0, 1.0, num)
x[:, 1] = np.linspace(-1.0, 1.0, num)
y = problem(x)

yd = np.empty((num, ndim))
for i in range(ndim):
    yd[:, i] = problem(x, kx=i).flatten()

print(y.shape)
print(yd.shape)

plt.plot(x[:, 0], y[:, 0])
plt.xlabel("x")
plt.ylabel("y")
plt.show()

(100, 1)
(100, 2)

Options

List of options

Option	Default	Acceptable values	Acceptable types	Description
ndim	1	None	[‘int’]
return_complex	False	None	[‘bool’]
order	2	None	[‘int’]
name	LpNorm	None	[‘str’]