fit_with_sum_of_exp

  • full name: tenpy.tools.fit.fit_with_sum_of_exp

  • parent module: tenpy.tools.fit

  • type: function

tenpy.tools.fit.fit_with_sum_of_exp(f, n, N=50)[source]

Approximate a decaying function f with a sum of exponentials.

MPOs can naturally represent long-range interactions with an exponential decay. A common technique for other (e.g. powerlaw) long-range interactions is to approximate them by sums of exponentials and to include them into the MPOs. This function allows to do that.

The algorithm/implementation follows the appendix of [murg2010].

Parameters:

  • f (function) – Decaying function to be approximated. Needs to accept a 1D numpy array x

  • n (int) – Number of exponentials to be used.

  • N (int) – Number of points at which to evaluate/fit f; we evaluate and fit f at the points x = np.arange(1, N+1).

Returns:

lambdas, prefactors – Such that \(f(k) \approx \sum_i x_i \lambda_i^k\) for (integer) 1 <= k <= N. The function sum_of_exp() evaluates this for given x.

Return type:

1D arrays