splinebox.basis_functions.

ExponentialHermite

class splinebox.basis_functions.ExponentialHermite(M)

Basis function for an exponential Hermite spline.

For a detailed theoretical description – including the equation and a plot of the function – refer to the Exponential Hermite basis section in the documentation.

The constructor requires M, the number of knots in the spline, as an argument.

Note: This basis function is a multigenerator and __call__ returns two values.

Methods

__call__(t[, derivative])	Evaluate the function at position(s) t.
filter_periodic(s)	Returns a filtered version of the input s, used to convert knots into control points for a closed spline.
filter_symmetric(s)	Returns a filtered version of the input s, used to convert knots into control points for an open spline.
refinement_mask()	This function is needed for local refinement (see [Badoual2016]).

Examples

>>> import splinebox
>>> import numpy as np
>>> import matplotlib.pyplot as plt

Create a basis function object:

>>> basis_function = splinebox.basis_functions.ExponentialHermite(M=5)

Evaluate the basis function at a single position:

>>> basis_function(0.5)
array([0.5  , 0.129])

Evaluate the basis function at multiple positions simultaneously:

>>> t = np.array([-0.2, 0, 0.5])
>>> basis_function(t)
array([[ 0.897, -0.13 ],
       [ 1.   ,  0.   ],
       [ 0.5  ,  0.129]])

Compute the first derivative of the basis function at multiple positions:

>>> basis_function(t, derivative=1)
array([[ 0.955,  0.336],
       [-0.   ,  1.   ],
       [-1.51 , -0.255]])

>>> t = np.linspace(-2.1, 2.1, 500)
>>> plt.plot(t, basis_function(t)[0])
>>> plt.plot(t, basis_function(t)[1], linestyle="-.")
>>> plt.show()