MFDMA (Multifractal Detrended Moving Average)

A Python library for performing 1D and 2D multifractal analysis using the Detrended Moving Average (DMA) method. Supports multifractal spectrum estimation with customizable parameters for in-depth data analysis.

Citation

📖 Citation

If you use the mfdma library in your research, please cite the following thesis:

@misc{souza2025,
  author       = {Souza, Rhimon Alves de Assis},
  title        = {MFDMA applied to Time Series Analysis},
  year         = {2025},
  version      = {1.0},
  howpublished = {\url{https://doi.org/10.5281/zenodo.17382145}},
  note         = {Zenodo repository},
  doi          = {10.5281/zenodo.17382145}
}

Features

• MFDMA_1D: Perform multifractal analysis on 1D time series data.
• MFDMA_2D: Conduct multifractal analysis on 2D data sets.

Installation

You can install the package directly from the GitHub repository using pip:

#public

pip install git+https://github.com/rhimonsouza/mfdma.git    

Usage

1D MF-DMA Analysis

To perform multifractal analysis on a 1D time series, use the MFDMA_1D function.

Parameters

• x: 1D array-like input data.
• n_min: Minimum window size for the log-spaced window sizes.
• n_max: Maximum window size for the log-spaced window sizes.
• N: Number of scales to consider between n_min and n_max.
• theta: Offset parameter controlling detrending (0 ≤ theta ≤ 1).
• q: Array of moments for multifractal analysis (can include positive and negative values).

Example

from mfdma import MFDMA_1D

# Example data
x = [your_1D_data]

# Parameters
n_min = 10
n_max = 100
N = 50
theta = 0.5
q = [-2, -1, 0, 1, 2]

# Perform 1D MF-DMA
n, Fq, tau, alpha, f = MFDMA_1D(x, n_min, n_max, N, theta, q)


## Usage

### 2D MF-DMA Analysis

To perform multifractal analysis on a 2D dataset, use the `MFDMA_2D` function.

#### Parameters

- `X`: 2D numpy array representing the spatial data to analyze.
- `n_min`: Minimum window size for the moving average.
- `n_max`: Maximum window size for the moving average.
- `N`: Number of window sizes to consider between `n_min` and `n_max`.
- `theta`: Overlap parameter, controlling the degree of overlap between windows (0 ≤ theta ≤ 1).
- `q`: Array of q-order moments used in the multifractal analysis (including positive and negative values).

#### Example

```python
from mfdma import MFDMA_2D
import numpy as np

# Example 2D data, such as an image
X = np.random.rand(100, 100)  # Replace with your 2D data

# Parameters for 2D MF-DMA analysis
n_min = 5
n_max = 50
N = 30
theta = 0.3
q = [-2, -1, 0, 1, 2]

# Perform 2D MF-DMA
n, Fq, tau, alpha, f = MFDMA_2D(X, n_min, n_max, N, theta, q)