Why interpolation estimates between data points in SciPy

Introduction

Interpolation helps us find values between known data points. It fills gaps in data smoothly and logically.

You have temperature readings every hour but want to know the temperature at half past the hour.

You know sales numbers for some months and want to estimate sales for missing months.

You have GPS locations recorded every minute and want to estimate position at a specific second.

You want to draw a smooth curve through scattered data points for visualization.

Syntax

SciPy

from scipy.interpolate import interp1d

# Create interpolation function
f = interp1d(x, y, kind='linear')

# Estimate value at new point
new_y = f(new_x)

x and y are arrays of known data points.

kind defines the interpolation method, like 'linear' or 'cubic'.

Examples

Linear interpolation estimates the value at 1.5 between points (1,1) and (2,4).

SciPy

from scipy.interpolate import interp1d

x = [0, 1, 2]
y = [0, 1, 4]
f = interp1d(x, y)
print(f(1.5))

Cubic interpolation gives a smoother estimate at 1.5 using more points.

SciPy

from scipy.interpolate import interp1d

x = [0, 1, 2, 3]
y = [0, 1, 4, 9]
f = interp1d(x, y, kind='cubic')
print(f(1.5))

Sample Program

This program estimates the temperature at 2.5 hours using linear interpolation between known hourly temperatures.

SciPy

from scipy.interpolate import interp1d
import numpy as np

# Known data points: hours and temperature
hours = np.array([0, 1, 2, 3, 4])
temps = np.array([15, 17, 20, 22, 21])

# Create linear interpolation function
interp_func = interp1d(hours, temps, kind='linear')

# Estimate temperature at 2.5 hours
temp_2_5 = interp_func(2.5)

print(f"Estimated temperature at 2.5 hours: {temp_2_5:.1f} degrees")

Important Notes

Interpolation only estimates within the range of known data points, not outside.

Choosing the right interpolation method affects smoothness and accuracy.

Summary

Interpolation fills in missing values between known data points.

It helps make smooth predictions or visualizations.

Scipy's interp1d is a simple way to do interpolation in Python.