SciPy — Interpolation

Linear interpolation

from scipy.interpolate import interp1d
import numpy as np

x = np.array([0, 1, 2, 3, 4])
y = np.array([0, 2, 1, 3, 2])

f = interp1d(x, y)
print(f"Value at 1.5 = {f(1.5):.2f}")
print(f"Value at 2.5 = {f(2.5):.2f}")

Cubic interpolation

f_cubic = interp1d(x, y, kind='cubic')
print(f"Cubic at 1.5 = {f_cubic(1.5):.2f}")

2D interpolation

from scipy.interpolate import griddata
import numpy as np

x = np.array([0, 0, 1, 1])
y = np.array([0, 1, 0, 1])
z = np.array([1, 2, 3, 4])

# Create grid
xi = np.linspace(0, 1, 10)
yi = np.linspace(0, 1, 10)
XI, YI = np.meshgrid(xi, yi)

# Interpolate
ZI = griddata((x, y), z, (XI, YI), method='cubic')

Spline interpolation

from scipy.interpolate import UnivariateSpline
import numpy as np

x = np.array([0, 1, 2, 3, 4, 5])
y = np.array([0, 1, 4, 9, 16, 25])

spline = UnivariateSpline(x, y)
print(f"Spline at 2.5 = {spline(2.5):.2f}")

RBF interpolation

from scipy.interpolate import RBFInterpolator
import numpy as np

points = np.array([[0, 0], [1, 0], [0, 1], [1, 1]])
values = np.array([1, 2, 3, 4])

rbf = RBFInterpolator(points, values)
print(f"Value at (0.5, 0.5) = {rbf([[0.5, 0.5]])[0]:.2f}")

Extrapolation

f = interp1d(x, y, fill_value='extrapolate')
print(f"Extrapolated at 6 = {f(6):.2f}")

Mini Practice

1. Interpolate 1D data
2. Use cubic splines
3. Interpolate 2D data
4. Compare interpolation methods

Up Next

Continue with Integration - Numerical integration.