JIYIK CN >

Linear interpolation is used for curve fitting with the help of linear polynomials.

Bilinear interpolation is an extension of linear interpolation and is used to interpolate functions of any two given variables with the help of linear interpolation.

Let's demonstrate different ways to implement bilinear interpolation in Python.

用户定义Creating a function to implement bilinear interpolation in Python

Here, we create a 用户定义function associated with four points and utilize bilinear interpolation in Python.

def bilinterpol(a, b, pts):
    i = sorted(pts)
    (a1, b1, x11), (_a1, b2, x12), (a2, _b1, x21), (_a2, _b2, x22) = i
    if a1 != _a1 or a2 != _a2 or b1 != _b1 or b2 != _b2:
        print("The given points do not form a rectangle")
    if not a1 <= a <= a2 or not b1 <= b <= b2:
        print("The (a, b) coordinates are not within the rectangle")
    Y = (
        x11 * (a2 - a) * (b2 - b)
        + x21 * (a - a1) * (b2 - b)
        + x12 * (a2 - a) * (b - b1)
        + x22 * (a - a1) * (b - b1)
    ) / ((a2 - a1) * (b2 - b1) + 0.0)
    return Y


pts = [
    (0, 1, 12),
    (4, 1, 0),
    (0, 3, -4),
    (4, 3, 8),
]
print(bilinterpol(2, 3, pts))

Output:

2.0

scipy.interpolate.interp2d()Implementing bilinear interpolation in Python using

SciPyLibrary is Scientific Pythonshort for and is open source.

Consists of a large number of utility functions that help with data science, optimization, interpolation, linear algebra, signal processing, etc. SciPyThe library uses and depends on NumPythe library.

This method can handle NumPyvery complex problems of manipulating arrays. scipy.interpolate.interp2d()The function in our case implements bilinear interpolation on a 2d grid.

grammar:

scipy.interpolate.interp2d(
    x, y, z, kind="linear", copy=True, bounds_error=False, fill_value=None
)

This function contains three important parameters that need to be understood in order to use it correctly.

• x, yBoth contain array-like values ​​describing the data point at a given coordinate. represents the column coordinates. In contrast, represents the coordinates x, considering that the data points lie on a grid .y行
• zContains an array-like value that specifies the value of the function to be interpolated using the given set of data points.
• kindSpecifies the type of interpolation to use. It can be either linear, , cubicor quintic. If no argument is passed, the value defaults to linear.

scipy.interpolate.interp2d()The following code implements bilinear interpolation in Python using .

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

x = np.arange(-15.01, 15.01, 1.00)
y = np.arange(-15.01, 15.01, 1.00)
xx, yy = np.meshgrid(x, y)
z = np.cos(xx ** 2 + yy ** 2)
f = interpolate.interp2d(x, y, z, kind="quintic")
xnew = np.arange(-15.01, 15.01, 1e-2)
ynew = np.arange(-15.01, 15.01, 1e-2)
znew = f(xnew, ynew)
plt.plot(x, z[0, :], "ro-", xnew, znew[0, :], "b-")
plt.show()

Output:

Code Explanation:

• All three essential libraries, viz. SciPy, , NumPycand MatPlotLib, are imported into the code.
• Then use numpy.arrange()the function to insert the values ​​into the variable in the form of an array x 和 y.
• Execution continues with meshgrid()the function, which generates an 1darray with x 和 yas the Cartesian index.
• The function is then used cos()to find the cosine value, which determines the value of the main function in the code z.
• Finally, matplotlibthe results are described with the help of library functions.