Numpy - Interpolation
Interpolation is a method of estimating the value of a function at a point within the range of a set of known data points. NumPy provides several functions for performing interpolation, including linear, nearest-neighbor, and polynomial interpolation.
To perform linear interpolation, you can use the interp function from NumPy, which takes the data points (specified as two arrays for the independent and dependent variables), the point at which to interpolate, and the kind of interpolation to use (specified by the kind argument). For example:
import numpy as np
# Interpolate the value of y at x = 3 using linear interpolation
x = np.array([0, 1, 2, 3, 4])
y = np.array([0, 1, 4, 9, 16])
x_interp = 3
y_interp = np.interp(x_interp, x, y)
print(y_interp) # 6.0
To perform nearest-neighbor interpolation, you can set the kind argument to 'nearest'. For example:
# Interpolate the value of y at x = 3.5 using nearest-neighbor interpolation
x_interp = 3.5
y_interp = np.interp(x_interp, x, y, kind='nearest')
print(y_interp) # 9.0
To perform polynomial interpolation, you can use the polyfit and polyval functions from NumPy, as I described in a previous message. For example:
# Fit a polynomial of degree 2 to the data points (0, 0), (1, 1), (2, 4), (3, 9), and (4, 16)
coeffs = np.polyfit(x, y, 2)
# Interpolate the value of y at x = 3 using the polynomial
x_interp = 3
y_interp = np.polyval(coeffs, x_interp)
print(y_interp) # 6.0
I hope this helps! Let me know if you have any questions.