Solve Linear Equation and return 3D Graph in Python

Last Updated : 27 Jun, 2022

In this article, we will make the 3D graph by solving the linear equations using Python.

Solve Linear Equation in Python

Here we are going to create a different variable for assigning the value into a linear equation and then calculate the value by using linalg.solve() methods.

Python3

# Python program to solve linear
# equation and return 3-d graph

# IMport the libraries
import numpy as np

x1, y1, z1, w1 = 1, -2, 3, 9

# Take the input for equation-2
x2, y2, z2, w2 = -1, 3, -1, -6

# Take the input for equation-3
x3, y3, z3, w3 = 2, -5, 5, 17

# Create an array for LHS variables
LHS = np.array([[x1, y1, z1], 
                [x2, y2, z2], 
                [x3, y3, z3]])

# Create another array for RHS variables
RHS = np.array([w1, w2, w3])

# Apply linear algebra on any numpy
# array created and printing the output
sol = np.linalg.solve(LHS, RHS)
print(sol)

Output:

[ 1. -1.  2.]

Solve Linear Equation and return 3D Graph

After getting the linear equation we will plot the 3d graph using matplotlib. we create the 3D graphics using figure() function. Moreover, we use add_subplot() method figure module of matplotlib library for adding axes to the figure as part of a subplot arrangement.

Python3

import matplotlib.pyplot as plt
from matplotlib import cm

# Returns number spaces evenly w.r.t
# interval
x_axis, y_axis = np.linspace(0, 20, 10), 
np.linspace(0, 20, 10)

# Create a rectangular grid out of
# two given one-dimensional arrays
X, Y = np.meshgrid(x_axis, y_axis)

# Make a rectangular grid
# 3-dimensional by calculating z1, z2, z3
Z1 = (w1-x1*X-y1*Y)/z1
Z2 = (w2-x2*X-y2*Y)/z2
Z3 = (w3+X-Y)/z3

# Create 3D graphics and add
# an add an axes to the figure
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

# Create a 3D Surface Plot
ax.plot_surface(X, Y, Z1, alpha=1, 
                cmap=cm.Accent, 
                rstride=100, cstride=100)
ax.plot_surface(X, Y, Z2, alpha=1, 
                cmap=cm.Paired, 
                rstride=100, cstride=100)
ax.plot_surface(X, Y, Z3, alpha=1,
                cmap=cm.Pastel1, 
                rstride=100, cstride=100)

# Draw points and make lines
ax.plot((sol[0],), (sol[1],), (sol[2],),
        lw=2, c='k', marker='o',
        markersize=7, markeredgecolor='g',
        markerfacecolor='white')

# Set the label for x-axis, y-axis and
# z-axis
ax.set_xlabel('X axis')
ax.set_ylabel('Y axis')
ax.set_zlabel('Z axis')

# Display all figures
plt.show()