Usage

This section introduces the basic usage of GenML. GenML provides several interfaces for efficiently generating M-L noise sequences in batches and computing actual and theoretical autocorrelation functions. The following are detailed explanations:

Parameters

  • N [type int]: Number of noise sequences to generate.

  • T [type int]: Length of the noise sequences to generate.

  • C [type float]: Amplitude coefficient.

  • lamda [type float]: Mittag-Leffler exponent, range (0, 2).

  • tau [type int]: Characteristic memory time, range (0, 10000).

  • seed [default=None]: Random seed for generating noise.

    • Set to None for different noise sequences each time; set to a specific value for identical noise sequences each time.

  • xi [type ndarray]: Generated noise sequences, shape (N, T).

  • tmax [type int]: Maximum value for computing autocorrelation functions, range (0, T).

  • dt [type int]: Interval for computing autocorrelation functions, range (0, tmax).

  • nc [default=1]: Number of cores to use for parallel computation of autocorrelation functions.

Note: When lamda approaches 2 and tau is large, generating noise sequences may take a long time and consume a significant amount of memory. It is recommended to use caution in such cases.

Generating Mittag-Leffler Correlated Noise

To generate M-L noise, use the mln interface with the following method: genml.mln(N, T, C, lamda, tau, seed).

Example usage:

import genml

# Parameters
N = 10  # Number of sequences
T = 500  # Length of each sequence
C = 1.0  # Amplitude coefficient
lamda = 0.5  # Mittag-Leffler exponent
tau = 10  # Characteristic memory time
seed = 42 # Random seed

# Generate M-L noise sequences
xi = genml.mln(N, T, C, lamda, tau, seed)

Calculating Autocorrelation Function

To calculate the autocorrelation function (ACF) values of the generated noise sequences, you can use the acf function for actual ACF values and the acft function for theoretical ACF values. Usage: genml.acf(xi, tmax, dt, nc) and genml.acft(tmax, dt, C, lamda, tau).

Example usage:

tmax = 100  # Max lag for ACF calculation
dt = 1  # Step size between lags
nc = 4  # Number of CPU cores for parallel processing

# Calculate actual ACF values
acfv = genml.acf(xi, tmax, dt, nc)

# Calculate theoretical ACF values
acftv = genml.acft(tmax, dt, C, lamda, tau)