  import fealpy

class BoxDomain:
    def __init__(self, Lx, Ly, Nx, Ny):
        self.Lx = Lx
        self.Ly = Ly
        self.Nx = Nx
        self.Ny = Ny
        self.mesh = fealpy.Mesh(self.Lx, self.Ly, self.Nx, self.Ny)

    def initialize_mesh(self):
        self.mesh.initialize()

    def define_displacement(self, u):
        self.mesh.define_displacement(u)

    def define_strain(self, e):
        self.mesh.define_strain(e)

    def define_stress(self, s):
        self.mesh.define_stress(s)

    def define_source(self, f):
        self.mesh.define_source(f)

    def define_Dirichlet_boundary_conditions(self, bc):
        self.mesh.define_Dirichlet_boundary_conditions(bc)

    def define_Neumann_boundary_conditions(self, bc):
        self.mesh.define_Neumann_boundary_conditions(bc)

    def is_on_Dirichlet_boundary(self, x):
        return self.mesh.is_on_Dirichlet_boundary(x)

    def is_on_Neumann_boundary(self, x):
        return self.mesh.is_on_Neumann_boundary(x)

    def is_on_fracture_boundary(self, x):
        return self.mesh.is_on_fracture_boundary(x)

class IterationCounter:
    def __init__(self):
        self.iterations = 0

    def increment(self):
        self.iterations += 1

class FastSolver:
    def __init__(self, A, b, x0, tol, max_iter):
        self.A = A
        self.b = b
        self.x0 = x0
        self.tol = tol
        self.max_iter = max_iter

    def precondition(self, A):
        return A

    def solve(self, b):
        x = self.x0
        r = b - self.A @ x
        p = r
        r_old = np.linalg.norm(r)
        for i in range(self.max_iter):
            Ap = self.A @ p
            alpha = r_old / np.dot(p, Ap)
            x += alpha * p
            r -= alpha * Ap
            r_new = np.linalg.norm(r)
            if r_new < self.tol:
                break
            p = r + (r_new / r_old) * p
            r_old = r_new
        return x

def main():
    # Initialize the box domain
    Lx = 1.0
    Ly = 1.0
    Nx = 10
    Ny = 10
    domain = BoxDomain(Lx, Ly, Nx, Ny)
    domain.initialize_mesh()

    # Create a mesh
    mesh = fealpy.Mesh(Lx, Ly, Nx, Ny)
    mesh.initialize()

    # Define a Lagrange finite element space
    V = fealpy.FunctionSpace(mesh, 'Lagrange', 1)

    # Define Dirichlet and Neumann boundary conditions
    bc = fealpy.DirichletBC(V, 0.0, lambda x: x[0] == 0.0 or x[0] == Lx or x[1] == 0.0 or x[1] == Ly)
    bc.apply(V)

    # Define a source term
    f = fealpy.Function(V)
    f.set_expression('sin(pi*x[0])*sin(pi*x[1])')

    # Define the solution
    u = fealpy.Function(V)

    # Define the stiffness matrix
    K = fealpy.StiffnessMatrix(V, mesh)

    # Define the linear elasticity matrix
    C = fealpy.LinearElasticityMatrix(V, mesh)

    # Set up the system of equations
    A = K + C
    b = f - K @ u

    # Apply the boundary conditions
    bc.apply(A)
    bc.apply(b)

    # Solve the system of equations
    tic = time.time()
    x = FastSolver(A, b, u, 1e-10, 1000).solve()
    toc = time.time()
    print(f'Solved in {toc - tic:.2f} seconds')

    # Plot the original mesh
    mesh.plot()

    # Print the shape of the matrix
    print(A.shape)

if __name__ == '__main__':
    main()