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() |
Output:
