Python for Data Smoothing: Exploring Moving Averages with NumPy and SciPy

Here's how to calculate moving average in Python using NumPy and SciPy:

NumPy's convolve function:

This method is efficient for calculating moving averages. It uses convolution to slide a window of a specified size over the data and calculates the mean of each window.

import numpy as np
from scipy.signal import convolve

# Sample data
data = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])

# Window size for moving average
window_size = 3

# Create a weight vector with equal weights (1/window_size) for averaging
weights = np.ones(window_size) / window_size

# Calculate moving average using convolution
smoothed_data = convolve(data, weights, mode='valid')  # 'valid' removes elements outside the window

# Print the original data and smoothed data
print("Original data:", data)
print("Smoothed data:", smoothed_data)

This code outputs:

Original data: [ 1  2  3  4  5  6  7  8  9 10]
Smoothed data: [2. 3. 4. 5. 6. 7. 8. 9.]

SciPy's ndimage.uniform_filter1d function:

This SciPy function offers another way to compute the moving average. It applies a uniform filter of a defined size to the data.

import numpy as np
from scipy.ndimage import uniform_filter1d

# Sample data
data = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])

# Window size for moving average
window_size = 3

# Calculate moving average using uniform_filter1d
smoothed_data = uniform_filter1d(data, window_size)

# Print the original data and smoothed data
print("Original data:", data)
print("Smoothed data:", smoothed_data)

This code outputs the same result as the previous example.

Key Points:

• Both methods achieve the same result of calculating the moving average.
• convolve offers more flexibility for defining custom weights for the moving average.
• uniform_filter1d might be simpler to use for basic moving averages.
• Choose the method that best suits your specific needs and preferences.

import numpy as np
from scipy.signal import convolve

# Sample data
data = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])

def calculate_moving_average_convolve(data, window_size):
  """
  This function calculates the moving average of a data series using convolution.

  Args:
      data: The data series as a NumPy array.
      window_size: The size of the moving average window.

  Returns:
      The moving average of the data series as a NumPy array.
  """
  # Create a weight vector with equal weights for averaging
  weights = np.ones(window_size) / window_size

  # Calculate moving average using convolution (removes elements outside window)
  smoothed_data = convolve(data, weights, mode='valid')

  return smoothed_data

# Example usage
window_size = 3
smoothed_data = calculate_moving_average_convolve(data.copy(), window_size)  # Avoid modifying original data

# Print the original data and smoothed data
print("Original data:", data)
print("Smoothed data:", smoothed_data)

This code defines a function calculate_moving_average_convolve that takes the data and window size as arguments, making it reusable for different data and window sizes.

import numpy as np
from scipy.ndimage import uniform_filter1d

# Sample data
data = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])

def calculate_moving_average_uniform(data, window_size):
  """
  This function calculates the moving average of a data series using uniform filter.

  Args:
      data: The data series as a NumPy array.
      window_size: The size of the moving average window.

  Returns:
      The moving average of the data series as a NumPy array.
  """

  # Calculate moving average using uniform_filter1d
  smoothed_data = uniform_filter1d(data, window_size)

  return smoothed_data

# Example usage
window_size = 3
smoothed_data = calculate_moving_average_uniform(data.copy(), window_size)  # Avoid modifying original data

# Print the original data and smoothed data
print("Original data:", data)
print("Smoothed data:", smoothed_data)

This code defines a similar function calculate_moving_average_uniform for calculating the moving average using the uniform filter. Both functions now allow for easy application to different datasets.

List comprehension and loop (for small datasets):

This method is suitable for small datasets and offers more control over the calculation.

def calculate_moving_average_loop(data, window_size):
  """
  This function calculates the moving average using a loop.

  Args:
      data: The data series as a list.
      window_size: The size of the moving average window.

  Returns:
      A list containing the moving averages for each data point.
  """

  smoothed_data = []
  for i in range(len(data)):
    # Check if enough data is available for the window
    if i < window_size - 1:
      smoothed_data.append(np.nan)  # Insert NaN for missing values
    else:
      # Calculate average for the window
      window_data = data[i - window_size + 1: i + 1]
      smoothed_data.append(sum(window_data) / window_size)

  return smoothed_data

# Example usage with sample data as a list
data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
window_size = 3
smoothed_data = calculate_moving_average_loop(data.copy(), window_size)  # Avoid modifying original data

# Print the original data and smoothed data
print("Original data:", data)
print("Smoothed data:", smoothed_data)

Pandas rolling window (for time series data):

If you're working with time series data stored in a Pandas DataFrame, the rolling window functionality is a convenient option.

import pandas as pd

# Sample data as Pandas Series
data = pd.Series([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])

# Window size for moving average
window_size = 3

# Calculate moving average using Pandas rolling window
smoothed_data = data.rolling(window=window_size).mean()

# Print the original data and smoothed data
print("Original data:")
print(data)
print("\nSmoothed data:")
print(smoothed_data)

This method is efficient for time series analysis and leverages the capabilities of Pandas for data manipulation.

Remember:

• Choose the method that best suits your data size, application, and desired level of control.
• The loop-based method offers flexibility but might be less efficient for large datasets.
• Pandas rolling is ideal for time series data analysis within the Pandas ecosystem.