SciPy Interpolation

What is SciPy Interpolation?

Interpolation is the process of estimating unknown values that fall between known values. SciPy's interpolate module provides several methods for interpolation.

Example: Linear Interpolation

1. Create Sample Data: We'll create some sample data points that we want to interpolate between.

2. Interpolate the Data: We'll use scipy.interpolate.interp1d to create an interpolation function.

3. Plot the Results: We'll use matplotlib to visualize the original data points and the interpolated values.

Step-by-Step Example

                        import numpy as np
                        from scipy.interpolate import interp1d
                        import matplotlib.pyplot as plt

                        # Step 1: Create sample data
                        x = np.linspace(0, 10, num=11, endpoint=True)  # 11 points from 0 to 10
                        y = np.cos(-x**2/9.0)  # Some function of x

                        # Step 2: Create an interpolation function
                        f_linear = interp1d(x, y)

                        # Interpolating with more points for a smoother curve
                        x_new = np.linspace(0, 10, num=100, endpoint=True)
                        y_new = f_linear(x_new)

                        # Step 3: Plot the results
                        plt.figure(figsize=(8, 4))
                        plt.plot(x, y, 'o', label='Original data points')
                        plt.plot(x_new, y_new, '-', label='Linear interpolation')
                        plt.xlabel('x')
                        plt.ylabel('y')
                        plt.legend(loc='best')
                        plt.title('Linear Interpolation using scipy.interpolate.interp1d')
                        plt.show()

                    

Explanation

1. Creating Sample Data:

   • x is an array of 11 evenly spaced points from 0 to 10.
   • y is an array of cosine values of -x^2/9.0.

2. Creating an Interpolation Function:

   • interp1d(x, y) creates a linear interpolation function f_linear based on the original data points.

3. Interpolating and Plotting:

   • x_new is an array of 100 evenly spaced points from 0 to 10 for a smoother interpolation curve.
   • y_new is the interpolated values at the points in x_new.
   • We plot the original data points and the interpolated values for comparison.

Output

When you run the above code, you'll get a plot showing the original data points and the interpolated curve:

This plot demonstrates how linear interpolation can estimate values between the known data points, resulting in a smooth curve that approximates the underlying function.

Additional Interpolation Methods

SciPy also supports other interpolation methods such as cubic interpolation (kind='cubic') and nearest-neighbor interpolation (kind='nearest'). You can specify the interpolation method when creating the interpolation function:

                        f_cubic = interp1d(x, y, kind='cubic')
                        y_new_cubic = f_cubic(x_new)

                        plt.plot(x_new, y_new_cubic, '--', label='Cubic interpolation')
                        plt.legend(loc='best')
                        plt.show()

                    

This will create and plot a cubic interpolation, which can provide a smoother curve than linear interpolation.