How to Calculate a Running Mean of a 1D Array Using NumPy\'s `np.convolve` Function?

How to Calculate Running Mean of a 1D Array Using SciPy or NumPy

The running mean, also known as the moving average, is a statistical measure that calculates the mean of a subset of data points within a specified window as the window slides across the data. In Python, there are several ways to calculate the running mean using SciPy and NumPy functions.

SciPy Function

SciPy does not have a dedicated function for calculating the running mean. However, you can use the np.convolve function from NumPy to implement the running mean calculation.

NumPy Function

NumPy's np.convolve function performs convolution operations. Convolution, in the context of the running mean, is the process of applying a kernel to the data and summing the results. For calculating the running mean, the kernel is a uniform distribution, which gives equal weight to each data point within the window.

To use np.convolve for the running mean, you can use the following code:

running_mean = np.convolve(array, np.ones(window_size) / window_size, mode='valid')

where:

• array is the 1D array for which you want to calculate the running mean.
• window_size is the size of the window over which the mean is calculated.
• mode='valid' specifies that the edges of the array are ignored, resulting in an output array that is shorter than the input array by window_size - 1.

Explanation

The np.ones(window_size) / window_size creates a kernel with uniform weights. np.convolve applies this kernel to the array, resulting in an array of means for each window. The mode='valid' argument ensures that the edges of the array are not included in the calculation, producing an output array that reflects the running mean over the entire data.

Edge Handling

The mode argument of np.convolve specifies how to handle the edges of the array. Different modes result in different edge behaviors. The table below lists the commonly used modes:

Mode	Edge Handling
full	Pads the array with zeros and returns an output array that is the same size as the input array.
same	Pads the array with zeros to match the kernel size and returns an output array that is the same size as the input array.
valid	Ignores the edges of the array, resulting in an output array that is shorter than the input array.

The choice of mode depends on your specific requirements and the interpretation you want for the running mean at the edges of the array.

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