A Guide to Using Numpy.interp for 1D Interpolation

Understanding Numpy.interp: 1-D Linear Interpolation in Python

numpy.interp is a function that performs 1-dimensional linear interpolation. It is used to estimate intermediate values between given data points. This is especially useful in signal processing, numerical modeling, and data visualization.

Syntax:

numpy.interp(x, xp, fp, left=None, right=None, period=None)

Parameters:

1. x (array_like): The x-coordinates at which to evaluate the interpolated values.

2. xp (1-D sequence): The x-coordinates of the data points. Must be strictly increasing.

3. fp (1-D sequence): The y-coordinates of the data points corresponding to xp.

4. left (scalar, optional): Value to return for x < xp[0]. Defaults to the first value in fp.

5. right (scalar, optional): Value to return for x > xp[-1]. Defaults to the last value in fp.

6. period (scalar, optional): Period for periodic interpolation.

Returns:

An array of interpolated values.

Examples and Code:

Example 1: Basic Interpolation

Code:

import numpy as np

# Define known data points
xp = [0, 1, 2, 3]
fp = [0, 1, 4, 9]

# Interpolate at new x-coordinates
x = [0.5, 1.5, 2.5]
y = np.interp(x, xp, fp)

# Print interpolated values
print("Interpolated values:", y)

Output:

Interpolated values: [0.5 2.5 6.5]

Explanation:

The function estimates values at 0.5, 1.5, and 2.5 using linear interpolation between the data points.

Example 2: Using left and right Parameters

Code:

import numpy as np

# Define known data points
xp = [0, 1, 2, 3]
fp = [0, 1, 4, 9]

# Extrapolate values outside the given range
x = [-1, 4]
y = np.interp(x, xp, fp, left=-10, right=100)

# Print results
print("Values with left and right parameters:", y)

Output:

Values with left and right parameters: [-10. 100.]

Explanation:
For x < xp[0], left is returned. For x > xp[-1], right is returned.

Example 3: Periodic Interpolation

Code:

import numpy as np

# Define known data points
xp = [0, 1, 2, 3]
fp = [0, 1, 4, 9]

# Define periodic x-coordinates
x = [3.5, 4.5, 5.5]
y = np.interp(x, xp, fp, period=4)

# Print periodic interpolated values
print("Periodic interpolated values:", y)

Output:

Periodic interpolated values: [4.5 0.5 2.5]

Explanation:
The data is treated as periodic with a period of 4. The function wraps around and performs interpolation.

Example 4: Interpolation with Uneven Data Points

Code:

import numpy as np

# Unevenly spaced data points
xp = [0, 2, 5]
fp = [0, 4, 25]

# Interpolation
x = [1, 3, 4]
y = np.interp(x, xp, fp)

# Print results
print("Interpolated values for uneven points:", y)

Output:

Interpolated values for uneven points: [ 2. 11. 18.].]

Explanation:
The function performs linear interpolation between the unevenly spaced data points.

Key Notes:

1. Input Validity: The xp array must be strictly increasing; otherwise, the function raises an error.

2. Efficiency: numpy.interp is optimized for large datasets and performs efficiently even for complex arrays.

3. Extrapolation: Values outside the xp range can be handled using left and right.

4. Periodic Data: Use the period parameter for cyclic interpolation.

Use Cases:

1. Signal Processing: Filling missing points in time-series data.

2. Data Visualization: Smoothing graphs by adding interpolated points.

3. Scientific Simulations: Estimating intermediate values for experimental data.

Additional Tips:

• For higher-dimensional interpolation, consider using scipy.interpolate functions.
• Combine with matplotlib for visualizing the results of interpolation.

Practical Guides to NumPy Snippets and Examples.