DFA code for python

python/dfa.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+def dfa(data, scales, order=1, plot=True):
+
+    """Perform Detrended Fluctuation Analysis on data
+
+    Inputs:
+        data: 1D numpy array of time series to be analyzed.
+        scales: List or array of scales to calculate fluctuations
+        order: Integer of polynomial fit (default=1 for linear)
+        plot: Return loglog plot (default=True to return plot)
+
+    Outputs:
+        scales: The scales that were entered as input
+        fluctuations: Variability measured at each scale with RMS
+        alpha value: Value quantifying the relationship between the scales 
+                     and fluctuations
+        
+....References:
+........Damouras, S., Chang, M. D., Sejdi, E., & Chau, T. (2010). An empirical 
+..........examination of detrended fluctuation analysis for gait data. Gait & 
+..........posture, 31(3), 336-340.
+........Mirzayof, D., & Ashkenazy, Y. (2010). Preservation of long range
+..........temporal correlations under extreme random dilution. Physica A: 
+..........Statistical Mechanics and its Applications, 389(24), 5573-5580.
+........Peng, C. K., Havlin, S., Stanley, H. E., & Goldberger, A. L. (1995).
+..........Quantification of scaling exponents and crossover phenomena in 
+..........nonstationary heartbeat time series. Chaos: An Interdisciplinary 
+..........Journal of Nonlinear Science, 5(1), 82-87.
+# =============================================================================
+                            ------ EXAMPLE ------
+
+      - Generate random data
+      data = np.random.randn(5000) 
+      
+      - Create a vector of the scales you want to use
+      scales = [10, 20, 40, 80, 160, 320, 640, 1280, 2560]
+      
+      - Set a detrending order. Use 1 for a linear detrend.
+      order = 1
+      
+      - run dfa function
+      s, f, a = dfa(data, scales, order, plot=True)
+# =============================================================================
+"""
+
+    # Check if data is a column vector (2D array with one column)
+    if data.shape[0] == 1:
+        # Reshape the data to be a column vector
+        data = data.reshape(-1, 1)
+    else:
+        # Data is already a column vector
+        data = data
+
+# =============================================================================
+##########################   START DFA CALCULATION   ##########################
+# =============================================================================
+
+    # Step 1: Integrate the data
+    integrated_data = np.cumsum(data - np.mean(data))
+
+    fluctuation = []
+
+    for scale in scales:
+        # Step 2: Divide data into non-overlapping window of size 'scale'
+        chunks = len(data) // scale
+        ms = 0.0
+
+        for i in range(chunks):
+            this_chunk = integrated_data[i*scale:(i+1)*scale]
+            x = np.arange(len(this_chunk))
+
+            # Step 3: Fit polynomial (default is linear, i.e., order=1)
+            coeffs = np.polyfit(x, this_chunk, order)
+            fit = np.polyval(coeffs, x)
+
+            # Detrend and calculate RMS for the current window
+            ms += np.mean((this_chunk - fit) ** 2)            
+
+        # Calculate average RMS for this scale
+        fluctuation.append(np.sqrt(ms / chunks))
+
+        # Perform linear regression
+    alpha, intercept = np.polyfit(np.log(scales), np.log(fluctuation), 1)
+
+
+    # Create a log-log plot to visualize the results
+    if plot:
+        plt.figure(figsize=(8, 6))
+        plt.loglog(scales, fluctuation, marker='o', markerfacecolor = 'red', markersize=8, 
+                   linestyle='-', color = 'black', linewidth=1.7, label=f'Alpha = {alpha:.3f}')
+        plt.xlabel('Scale (log)')
+        plt.ylabel('Fluctuation (log)')
+        plt.legend()
+        plt.title('Detrended Fluctuation Analysis')
+        plt.grid(True)
+        plt.show()
+
+    # Return the scales used, fluctuation functions and the alpha value
+    return scales, fluctuation, alpha
+
+
+