sarkas.utilities.maths.correlationfunction

sarkas.utilities.maths.correlationfunction(At, Bt)

Calculate the correlation function between \(\mathbf{A}(t)\) and \(\mathbf{B}(t)\) using scipy.signal.correlate()

\[C_{AB}(\tau) = \sum_j^D \sum_i^T A_j(t_i)B_j(t_i + \tau)\]

where \(D\) is the number of dimensions and \(T\) is the total length of the simulation.

Parameters

• At (numpy.ndarray) – Observable to correlate.

• Bt (numpy.ndarray) – Observable to correlate.

Returns

full_corr (numpy.ndarray) – Correlation function \(C_{AB}(\tau)\)

Examples

>>> import numpy as np
>>> t = np.linspace( 0.0, 6.0 * np.pi, 3000)
>>> w0 = 0.5
>>> At = np.cos(w0 * t)
>>> Bt = np.sin(w0 * t)
>>> corr_t = correlationfunction(At, Bt)