MatricsAB_DMDc

Overview

Welcome to "MatricAB", an innovative Python repository. My focus is on analyzing complex systems within the realms of neuroscience and psychology. The centerpiece of this repository is the MatricAB function, which is meticulously designed to calculate A and B matrices in linear time-invariant systems. These calculations are instrumental in dissecting the dynamics of neural networks and psychological states, offering a window into the intricate workings of the human mind and behavior.

Installation

To get started with MatricAB, clone the repository and install the required Python packages:

git clone https://github.com/PsyControLab/MatricAB_DMDc.git
cd MatricAB_DMDc
pip install numpy pandas

Usage

The MatricAB function is user-friendly and can be integrated easily into your data analysis workflow. Here's a step-by-step guide to using it:

import pandas as pd
from MatricAB_DMDc import MatricAB_DMDc as PyC

# Example: Load your dataset into a pandas DataFrame
df = pd.read_csv('your_data.csv')

# Define parameters for the function
id_col = 'entity_id'  # This should be the name of the column with unique identifiers in your dataset
X_cols = ['state_var1', 'state_var2', 'state_var3']  # List of columns representing state variables
U_col = 'input'  # Column name for the input variable
n = 'd'  # The dimension of your state variable (n in A_{n x n})

# Execute the function to calculate the A and B matrices
df_AB = MatricAB(df, id_col, X_cols, U_col, n)

# Display the first few rows of the output
print(df_AB.head())

# Grouping df by 'Group' and 'entity_ids' and taking the first occurrence
df_grouped = df.groupby(['Group', 'entity_ids'], as_index=False)['entity_ids'].first()

# Merging df_grouped with df_AB on 'entity_ids'
df_final = df_AB.merge(df_grouped, on='entity_ids')

# Printing the shape of the merged DataFrame
print(df_final.shape)

# Displaying the first 3 rows of the merged DataFrame
df_final.head(3)

The function processes your data and returns a DataFrame with calculated A and B matrices for each unique entity, providing insights into the system's dynamics.

Citation: Proctor, Joshua L., Brunton, Steven L., and Kutz, J. Nathan. "Dynamic mode decomposition with control." SIAM Journal on Applied Dynamical Systems 15.1 (2016): 142 Access Paper