  import argparse
import sys
import numpy as np
import matplotlib.pyplot as plt
from scipy.sparse import linalg
from mumps import MumpsSolver
from fealpy.mesh import TriangleMesh
from fealpy.time import UniformTimeLine
from fealpy.finite_element import LagrangeFiniteElementSpace
from fealpy.form import BilinearForm, MixedBilinearForm
from fealpy.integrator import DomainIntegrator
from fealpy.solver import NewtonSolver

# Define command-line argument parser
parser = argparse.ArgumentParser()
parser.add_argument('--motion_degree', type=int, default=1)
parser.add_argument('--pressure_degree', type=int, default=1)
parser.add_argument('--time_divisions', type=int, default=10)
parser.add_argument('--end_time', type=float, default=1.0)
parser.add_argument('--output_dir', type=str, default='output')
parser.add_argument('--steps', type=int, default=100)
parser.add_argument('--nonlinear_method', type=str, default='newton')

# Parse command-line arguments
args = parser.parse_args()

# Define variables
mesh = TriangleMesh.unit_square()
time_line = UniformTimeLine(args.time_divisions, 0.0, args.end_time)
motion_space = LagrangeFiniteElementSpace(mesh, args.motion_degree)
pressure_space = LagrangeFiniteElementSpace(mesh, args.pressure_degree)
motion_dofs = motion_space.num_dofs
pressure_dofs = pressure_space.num_dofs

# Define forms and integrators
bilform = BilinearForm(motion_space, pressure_space)
mixed_bilform = MixedBilinearForm(motion_space, pressure_space)
domain_integrator = DomainIntegrator(bilform)

# Assemble forms and get matrices
A = bilform.assemble()
M = mixed_bilform.assemble()

# Calculate mass matrix and initialize error matrix
mass_matrix = np.zeros((motion_dofs, motion_dofs))
error_matrix = np.zeros((motion_dofs, pressure_dofs))

# Set up boundary conditions
boundary_conditions = [
    {'type': 'Dirichlet', 'dofs': motion_space.get_dofs_on_boundary(), 'value': 0.0}
]

# Set up solver
solver = NewtonSolver(A, M, mass_matrix, boundary_conditions)

# Set up output directory
output_dir = args.output_dir
if not os.path.exists(output_dir):
    os.makedirs(output_dir)

# Set up time stepping
dt = time_line.dt
t = 0.0

# Set up convergence criteria
tol = 1e-6
max_iter = 100

# Set up nonlinear solver
nonlinear_solver = MumpsSolver()

# Loop over time steps
for i in range(args.steps):
    # Advance to next time level
    t += dt

    # Add convection integrator to bilinear form
    convection_integrator = ScalarConvectionIntegrator(motion_space, pressure_space, dt)
    convection_bilform = BilinearForm(motion_space, pressure_space)
    convection_bilform.add_integrator(convection_integrator)

    # Assemble convection bilinear form
    convection_A = convection_bilform.assemble()

    # Calculate divergence matrix
    divergence_matrix = np.zeros((pressure_dofs, motion_dofs))

    # Calculate new matrix M
    M = np.vstack((M, convection_A))

    # Calculate source vector
    source_vector = np.zeros(pressure_dofs)

    # Set up boundary conditions
    boundary_conditions = [
        {'type': 'Dirichlet', 'dofs': motion_space.get_dofs_on_boundary(), 'value': 0.0}
    ]

    # Solve system of equations
    solver.solve(source_vector, error_matrix, tol, max_iter, nonlinear_solver)

    # Update motion and pressure functions
    motion_space.update_dofs(solver.u)
    pressure_space.update_dofs(solver.p)

    # Calculate L2 error and maximum error
    l2_error = np.linalg.norm(error_matrix)
    max_error = np.max(np.abs(error_matrix))

    # Print sum of absolute values of motion function
    print(f'Time: {t:.2f}, L2 error: {l2_error:.2e}, Max error: {max_error:.2e}')

    # Save solution to file
    np.save(os.path.join(output_dir, f'solution_{i:04d}.npy'), solver.u)

    # Save error to file
    np.save(os.path.join(output_dir, f'error_{i:04d}.npy'), error_matrix)

# Plot solution
plt.figure()
plt.pcolor(mesh.nodes[:, 0], mesh.nodes[:, 1], solver.u.reshape(mesh.num_elements, -1).T, cmap='RdBu')
plt.colorbar()
plt.show()