Preparation

class pylit.core.data_classes.Preparation(tau, F, beta, max_F, scaled_F, omega, D, int_D, scaled_D, exp_D, std_D, moments_D, forward_D, eps_D, max_eps_D)

Bases: object

Represents the output of the preparation of the data.

Parameters:

• tau (ndarray) – Discrete time axis \(\tau\) on which the input data \(F(\tau)\) is defined.

• F (ndarray) – Raw input data defined on \(\tau\).

• beta (float) – Inverse temperature parameter \(\beta = 1/T\).

• max_F (float) – Maximum value of \(F(\tau)\), used for normalization.

• scaled_F (ndarray) – Normalized version of \(F(\tau)\) to improve numerical stability.

• omega (ndarray) – Discrete frequency axis \(\omega\) on which the default model \(D(\omega)\) is defined.

• D (ndarray) – Default model for the dynamic structure factor \(S(\omega)\).

• int_D (float) – Integral of the default model \(D(\omega)\) over omega, representing the zeroth moment (normalization).

• scaled_D (ndarray) – Normalized version of \(D(\omega)\), ensuring unit integral.

• exp_D (float) – Expectation value (first moment) of the default model \(D(\omega)\).

• std_D (float) – Standard deviation of the default model \(D(\omega)\).

• moments_D (ndarray) – The i-th entry corresponds to the moment \(\mu_i = \int d\omega D(\omega)\), with indices covering \(i=-1, 0, 1, ..., 10\).

• forward_D (ndarray) –

  Laplace transform of scaled_D onto \(\tau\), computed using the trapezoidal rule as

  \[\text{forward_D}_i = \sum_j w_j \ \text{scaled_D}_j \ \exp(-\omega_j \tau_i),\]

  where \(w_j\) are the trapezoidal integration weights corresponding to the frequency grid \(\omega\).

• eps_D (ndarray) – Pointwise error between F and forward_D.

• max_eps_D (float) – Maximum absolute error between F and forward_D.