splinebox.basis_functions.

Exponential#

class splinebox.basis_functions.Exponential(M)#

Basis function for an exponential spline.

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

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

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`()	TODO: This fails the tests.

Examples

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

Create a basis function object:

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

Evaluate the basis function at a single position:

>>> basis_function(0.5)
0.5

Evaluate the basis function at multiple positions simultaneously:

>>> t = np.array([-0.2, 0, 0.5])
>>> basis_function(t)
array([0.687, 0.724, 0.5  ])

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

>>> basis_function(t, derivative=1)
array([ 0.366,  0.   , -0.865])

>>> t = np.linspace(-2.1, 2.1, 500)
>>> plt.plot(t, basis_function(t))
>>> plt.show()

../../_images/splinebox-basis_functions-Exponential-1.png

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