# Copyright (C) 2020 Jørgen S. Dokken
#
# This file is part of DOLFINX_MPC
#
# SPDX-License-Identifier:    MIT
#
# This demo demonstrates how to solve a contact problem between
# two stacked cubes.
# The bottom cube is fixed at the bottom surface
# The top cube has a force applied normal to its to surface.
# A slip condition is implemented at the interface of the cube.
# Additional constraints to avoid tangential movement is
# added to the to left corner of the top cube.
from __future__ import annotations

import warnings
from argparse import ArgumentDefaultsHelpFormatter, ArgumentParser
from pathlib import Path

from mpi4py import MPI
from petsc4py import PETSc

import numpy as np
import scipy.sparse.linalg
from dolfinx import default_real_type, default_scalar_type
from dolfinx.common import Timer, list_timings
from dolfinx.fem import Constant, Function, dirichletbc, form, functionspace, locate_dofs_geometrical
from dolfinx.fem.petsc import apply_lifting, assemble_matrix, assemble_vector, set_bc
from dolfinx.io import XDMFFile
from dolfinx.log import LogLevel, set_log_level
from dolfinx.mesh import locate_entities_boundary, meshtags
from ufl import Identity, Measure, TestFunction, TrialFunction, dx, grad, inner, sym, tr

from create_and_export_mesh import gmsh_2D_stacked, mesh_2D_dolfin
from dolfinx_mpc import LinearProblem, MultiPointConstraint
from dolfinx_mpc.utils import (
    compare_mpc_lhs,
    compare_mpc_rhs,
    facet_normal_approximation,
    gather_PETScMatrix,
    gather_PETScVector,
    gather_transformation_matrix,
    log_info,
    rigid_motions_nullspace,
    rotation_matrix,
)

set_log_level(LogLevel.ERROR)


def demo_stacked_cubes(
    outfile: XDMFFile,
    theta: float,
    gmsh: bool = True,
    quad: bool = False,
    compare: bool = False,
    res: float = 0.1,
):
    log_info(f"Run theta:{theta:.2f}, Quad: {quad}, Gmsh {gmsh}, Res {res:.2e}")

    celltype = "quadrilateral" if quad else "triangle"
    meshdir = Path("meshes")
    meshdir.mkdir(exist_ok=True, parents=True)
    if gmsh:
        mesh, mt = gmsh_2D_stacked(celltype, theta)
        mesh.name = f"mesh_{celltype}_{theta:.2f}_gmsh"

    else:
        if default_real_type == np.float32:
            warnings.warn("Demo does not run for single float precision due to limited xdmf support")
            exit(0)
        mesh_name = "mesh"
        filename = meshdir / f"mesh_{celltype}_{theta:.2f}.xdmf"

        mesh_2D_dolfin(celltype, theta)
        with XDMFFile(MPI.COMM_WORLD, filename, "r") as xdmf:
            mesh = xdmf.read_mesh(name=mesh_name)
            mesh.name = f"mesh_{celltype}_{theta:.2f}"
            tdim = mesh.topology.dim
            fdim = tdim - 1
            mesh.topology.create_connectivity(tdim, tdim)
            mesh.topology.create_connectivity(fdim, tdim)
            mt = xdmf.read_meshtags(mesh, name="facet_tags")

    # Helper until meshtags can be read in from xdmf
    V = functionspace(mesh, ("Lagrange", 1, (mesh.geometry.dim,)))
    r_matrix = rotation_matrix([0, 0, 1], theta)
    g_vec = np.dot(r_matrix, [0, -1.25e2, 0])
    g = Constant(mesh, default_scalar_type(g_vec[:2]))

    def bottom_corner(x):
        return np.isclose(x, [[0], [0], [0]], atol=5e2 * np.finfo(default_scalar_type).resolution).all(axis=0)

    # Fix bottom corner
    bc_value = np.array((0,) * mesh.geometry.dim, dtype=default_scalar_type)  # type: ignore
    bottom_dofs = locate_dofs_geometrical(V, bottom_corner)
    bc_bottom = dirichletbc(bc_value, bottom_dofs, V)
    bcs = [bc_bottom]

    # Elasticity parameters
    E = 1.0e3
    nu = 0
    mu = Constant(mesh, default_scalar_type(E / (2.0 * (1.0 + nu))))
    lmbda = Constant(mesh, default_scalar_type(E * nu / ((1.0 + nu) * (1.0 - 2.0 * nu))))

    # Stress computation
    def sigma(v):
        return 2.0 * mu * sym(grad(v)) + lmbda * tr(sym(grad(v))) * Identity(len(v))

    # Define variational problem
    u = TrialFunction(V)
    v = TestFunction(V)
    a = inner(sigma(u), grad(v)) * dx
    ds = Measure("ds", domain=mesh, subdomain_data=mt, subdomain_id=3)
    rhs = inner(Constant(mesh, default_scalar_type((0, 0))), v) * dx + inner(g, v) * ds  # type: ignore
    tol = float(5e2 * np.finfo(default_scalar_type).resolution)

    def left_corner(x):
        return np.isclose(x.T, np.dot(r_matrix, [0, 2, 0]), atol=tol).all(axis=1)

    # Create multi point constraint
    mpc = MultiPointConstraint(V)

    with Timer("~Contact: Create contact constraint"):
        mpc.create_contact_inelastic_condition(mt, 4, 9, eps2=tol, allow_missing_masters=True)
    with Timer("~Contact: Add non-slip condition at bottom interface"):
        bottom_normal = facet_normal_approximation(V, mt, 5)
        mpc.create_slip_constraint(V, (mt, 5), bottom_normal, bcs=bcs)

    with Timer("~Contact: Add tangential constraint at one point"):
        vertex = locate_entities_boundary(mesh, 0, left_corner)

        tangent = facet_normal_approximation(V, mt, 3, tangent=True)
        mtv = meshtags(mesh, 0, vertex, np.full(len(vertex), 6, dtype=np.int32))
        mpc.create_slip_constraint(V, (mtv, 6), tangent, bcs=bcs)

    mpc.finalize()
    tol = float(5e2 * np.finfo(default_scalar_type).resolution)
    petsc_options = {
        "ksp_rtol": tol,
        "ksp_atol": tol,
        "ksp_error_if_not_converged": True,
        "pc_type": "gamg",
        "pc_gamg_type": "agg",
        "pc_gamg_square_graph": 2,
        "pc_gamg_threshold": 0.02,
        "pc_gamg_coarse_eq_limit": 1000,
        "pc_gamg_sym_graph": True,
        "mg_levels_ksp_type": "chebyshev",
        "mg_levels_pc_type": "jacobi",
        "mg_levels_esteig_ksp_type": "cg",
        #  , "help": None, "ksp_view": None
    }

    # Solve Linear problem
    problem = LinearProblem(a, rhs, mpc, bcs=bcs, petsc_options=petsc_options)

    # Build near nullspace
    null_space = rigid_motions_nullspace(mpc.function_space)
    problem.A.setNearNullSpace(null_space)
    u_h = problem.solve()
    assert isinstance(u_h, Function)

    it = problem.solver.getIterationNumber()
    if MPI.COMM_WORLD.rank == 0:
        print("Number of iterations: {0:d}".format(it))

    unorm = u_h.x.petsc_vec.norm()
    if MPI.COMM_WORLD.rank == 0:
        print(f"Norm of u: {unorm}")
    # Write solution to file
    ext = "_gmsh" if gmsh else ""
    u_h.name = "u_mpc_{0:s}_{1:.2f}{2:s}".format(celltype, theta, ext)

    outfile.write_mesh(mesh)
    outfile.write_function(u_h, 0.0, f"Xdmf/Domain/Grid[@Name='{mesh.name}'][1]")

    # Solve the MPC problem using a global transformation matrix
    # and numpy solvers to get reference values
    if not compare:
        return
    log_info("Solving reference problem with global matrix (using numpy)")
    with Timer("~MPC: Reference problem"):
        # Generate reference matrices and unconstrained solution
        A_org = assemble_matrix(form(a), bcs)
        A_org.assemble()
        L_org = assemble_vector(form(rhs))
        apply_lifting(L_org, [form(a)], [bcs])
        L_org.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE)  # type: ignore
        set_bc(L_org, bcs)

    root = 0
    with Timer("~MPC: Verification"):
        compare_mpc_lhs(A_org, problem.A, mpc, root=root)
        compare_mpc_rhs(L_org, problem.b, mpc, root=root)
        # Gather LHS, RHS and solution on one process
        A_csr = gather_PETScMatrix(A_org, root=root)
        K = gather_transformation_matrix(mpc, root=root)
        L_np = gather_PETScVector(L_org, root=root)
        u_mpc = gather_PETScVector(u_h.x.petsc_vec, root=root)

        if MPI.COMM_WORLD.rank == root:
            KTAK = K.T * A_csr * K
            reduced_L = K.T @ L_np
            # Solve linear system
            d = scipy.sparse.linalg.spsolve(KTAK, reduced_L)
            # Back substitution to full solution vector
            uh_numpy = K @ d
            np.testing.assert_allclose(uh_numpy, u_mpc, rtol=tol, atol=tol)
    L_org.destroy()
    A_org.destroy()


if __name__ == "__main__":
    parser = ArgumentParser(formatter_class=ArgumentDefaultsHelpFormatter)
    parser.add_argument("--res", default=0.1, type=np.float64, dest="res", help="Resolution of Mesh")
    parser.add_argument(
        "--theta",
        default=np.pi / 3,
        type=np.float64,
        dest="theta",
        help="Rotation angle around axis [1, 1, 0]",
    )
    quad = parser.add_mutually_exclusive_group(required=False)
    quad.add_argument("--quad", dest="quad", action="store_true", help="Use quadrilateral mesh", default=False)
    gmsh = parser.add_mutually_exclusive_group(required=False)
    gmsh.add_argument(
        "--gmsh",
        dest="gmsh",
        action="store_true",
        help="Gmsh mesh instead of built-in grid",
        default=False,
    )
    comp = parser.add_mutually_exclusive_group(required=False)
    comp.add_argument(
        "--compare",
        dest="compare",
        action="store_true",
        help="Compare with global solution",
        default=False,
    )
    time = parser.add_mutually_exclusive_group(required=False)
    time.add_argument("--timing", dest="timing", action="store_true", help="List timings", default=False)

    args = parser.parse_args()

    # Create results file
    outdir = Path("results")
    outdir.mkdir(parents=True, exist_ok=True)
    outfile = XDMFFile(MPI.COMM_WORLD, outdir / "demo_contact_2D.xdmf", "w")

    # Run demo for input parameters
    demo_stacked_cubes(
        outfile,
        theta=args.theta,
        gmsh=args.gmsh,
        quad=args.quad,
        compare=args.compare,
        res=args.res,
    )

    outfile.close()
    if args.timing:
        list_timings(MPI.COMM_WORLD)
