fftl.transforms.laplace

fftl.transforms.laplace(r, ar, *args, **kwargs)

Laplace transform

The Laplace transform is defined as

\[\tilde{a}(k) = \int_{0}^{\infty} \! a(r) \, e^{-kr} \, dr \;.\]

Examples

Compute the Laplace transform.

>>> # some test function
>>> p, q = 2.0, 0.5
>>> r = np.logspace(-2, 2, 1000)
>>> ar = r**p*np.exp(-q*r)
>>>
>>> # compute a biased transform
>>> from fftl.transforms import laplace
>>> k, ak = laplace(r, ar, q=0.7)

Compare with the analytical result.

>>> from scipy.special import gamma
>>> res = gamma(p+1)/(q + k)**(p+1)
>>>
>>> import matplotlib.pyplot as plt
>>> plt.loglog(k, ak, '-k', label='numerical')
>>> plt.loglog(k, res, ':r', label='analytical')
>>> plt.legend()
>>> plt.show()