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Function is used. The following script finds the dot product between the inverse of matrix A and the matrix B, which is the solution of the Equation 1.B = np.array([20, 26])X = np.linalg.inv(A).dot(B)print(X)Output:Check out our hands-on, practical guide to learning Git, with best-practices, industry-accepted standards, and included cheat sheet. Stop Googling Git commands and actually learn it![2. 4.]Here, 2 and 4 are the respective values for the unknowns x and y in Equation 1. To verify, if you plug 2 in place of the unknown x and 4 in the place of the unknown y in equation 4x + 3y, you will see that the result will be 20.Let's now solve a system of three linear equations, as shown below:4x + 3y + 2z = 25-2x + 2y + 3z = -103x -5y + 2z = -4The above equation can be solved using the Numpy library as follows:Equation 2:A = np.array([[4, 3, 2], [-2, 2, 3], [3, -5, 2]])B = np.array([25, -10, -4])X = np.linalg.inv(A).dot(B)print(X)In the script above the linalg.inv() and the linalg.dot() methods are chained together. The variable X contains the solution for Equation 2, and is printed as follows:[ 5. 3. -2.]The value for the unknowns x, y, and z are 5, 3, and -2, respectively. You can plug these values in Equation 2 and verify their correctness.Using the solve() MethodIn the previous two examples, we used linalg.inv() and linalg.dot() methods to find the solution of system of equations. However, the Numpy library contains the linalg.solve() method, which can be used to directly find the solution of a system of linear equations:A = np.array([[4, 3, 2], [-2, 2, 3], [3, -5, 2]])B = np.array([25, -10, -4])X2 = np.linalg.solve(A,B)print(X2)Output:[ 5. 3. -2.]You can see that the output is same as before.A Real-World ExampleLet's see how a system of linear

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PoissonpyPlug-and-play standalone library for solving 2D Poisson equations. Useful tool in scientific computing prototyping, image and video processing, computer graphics.FeaturesSolves the Poisson equation on sqaure or non-square rectangular grids.Solves the Poisson equation on regions with arbitrary shape.Supports arbitrary boundary and interior conditions using sympy function experssions or numpy arrays.Supports Dirichlet, Neumann, or mixed boundary conditions.DisclaimerThis package is only used to solve 2D Poisson equations. If you are looking for a general purpose and optimized PDE library, you might want to checkout the FEniCSx project.UsageImport necessary libraries. poissonpy utilizes numpy and sympy greatly, so its best to import both:import numpy as npfrom sympy import sin, cosfrom sympy.abc import x, yfrom poissonpy import functional, utils, sovlersDefining sympy functionsIn the following examples, we use a ground truth function to create a mock Poisson equation and compare the solver's solution with the analytical solution.Define functions using sympy function expressions or numpy arrays:f_expr = sin(x) + cos(y) # create sympy function expressionlaplacian_expr = functional.get_sp_laplacian_expr(f_expr) # create sympy laplacian function expressionf = functional.get_sp_function(f_expr) # create sympy functionlaplacian = functional.get_sp_function(laplacian_expr) # create sympy functionDirichlet Boundary ConditionsDefine interior and Dirichlet boundary conditions:interior = laplacianboundary = { "left": (f, "dirichlet"), "right": (f, "dirichlet"), "top": (f, "dirichlet"), "bottom": (f, "dirichlet")}Initialize solver and solve Poisson equation:solver = Poisson2DRectangle(((-2*np.pi, -2*np.pi), (2*np.pi, 2*np.pi)), interior, boundary, X=100, Y=100)solution = solver.solve()Plot solution and ground truth:poissonpy.plot_3d(solver.x_grid, solver.y_grid, solution)poissonpy.plot_3d(solver.x_grid, solver.y_grid, f(solver.x_grid, solver.y_grid))SolutionGround truthErrorNeumann Boundary ConditionsYou can also define Neumann boundary conditions by specifying neumann_x and neumann_y in the boundary condition parameter.x_derivative_expr = functional.get_sp_derivative_expr(f_expr, x)y_derivative_expr = functional.get_sp_derivative_expr(f_expr, y)interior