# Copyright (C) 2020 Jørgen S. Dokken
#
# This file is part of DOLFINX_MPC
#
# SPDX-License-Identifier:    MIT
#
# Multi point constraint problem for linear elasticity with slip conditions
# between two cubes.
from __future__ import annotations

from mpi4py import MPI
from petsc4py import PETSc

import dolfinx.fem as fem
import gmsh
import numpy as np
import numpy.testing as nt
import pytest
import scipy.sparse.linalg
import ufl
from dolfinx import default_scalar_type
from dolfinx.common import Timer, list_timings
from dolfinx.io import gmsh as gmshio

import dolfinx_mpc
import dolfinx_mpc.utils

theta = np.pi / 5


@pytest.fixture
def generate_hex_boxes():
    """
    Generate the stacked boxes [x0,y0,z0]x[y1,y1,z1] and
    [x0,y0,z1] x [x1,y1,z2] with different resolution in each box.
    The markers are is a list of arrays containing markers
    array of markers for [back, bottom, right, left, top, front] per box
    volume_markers a list of marker per volume
    """

    res = 0.2
    x0, y0, z0, x1, y1, z1, z2 = 0, 0, 0, 1, 1, 1, 2
    facet_markers = [[11, 5, 12, 13, 4, 14], [21, 9, 22, 23, 3, 24]]
    volume_markers = [1, 2]
    r_matrix = dolfinx_mpc.utils.rotation_matrix([1, 1, 0], -theta)

    # Check if GMSH is initialized
    gmsh.initialize()
    gmsh.clear()
    if MPI.COMM_WORLD.rank == 0:
        gmsh.option.setNumber("Mesh.RecombinationAlgorithm", 2)
        gmsh.option.setNumber("Mesh.RecombineAll", 2)
        gmsh.option.setNumber("General.Terminal", 0)
        bottom = gmsh.model.occ.addRectangle(x0, y0, z0, x1 - x0, y1 - y0)
        top = gmsh.model.occ.addRectangle(x0, y0, z2, x1 - x0, y1 - y0)

        # Set mesh size at point
        gmsh.model.occ.extrude([(2, bottom)], 0, 0, z1 - z0, numElements=[int(1 / (2 * res))], recombine=True)
        gmsh.model.occ.extrude([(2, top)], 0, 0, z1 - z2 - 1e-12, numElements=[int(1 / (2 * res))], recombine=True)
        # Syncronize to be able to fetch entities
        gmsh.model.occ.synchronize()

        # Create entity -> marker map (to be used after rotation)
        volumes = gmsh.model.getEntities(3)
        volume_entities = {"Top": [None, volume_markers[1]], "Bottom": [None, volume_markers[0]]}
        for i, volume in enumerate(volumes):
            com = gmsh.model.occ.getCenterOfMass(volume[0], volume[1])
            if np.isclose(com[2], (z1 - z0) / 2):
                bottom_index = i
                volume_entities["Bottom"][0] = volume
            elif np.isclose(com[2], (z2 - z1) / 2 + z1):
                top_index = i
                volume_entities["Top"][0] = volume
        surfaces = ["Top", "Bottom", "Left", "Right", "Front", "Back"]
        entities = {
            "Bottom": {key: [[], None] for key in surfaces},
            "Top": {key: [[], None] for key in surfaces},
        }
        # Identitfy entities for each surface of top and bottom cube

        # Physical markers for bottom cube
        bottom_surfaces = gmsh.model.getBoundary([volumes[bottom_index]], recursive=False, oriented=False)
        for entity in bottom_surfaces:
            com = gmsh.model.occ.getCenterOfMass(entity[0], entity[1])
            if np.allclose(com, [(x1 - x0) / 2, y1, (z1 - z0) / 2]):
                entities["Bottom"]["Back"][0].append(entity[1])
                entities["Bottom"]["Back"][1] = facet_markers[0][0]
            elif np.allclose(com, [(x1 - x0) / 2, (y1 - y0) / 2, z0]):
                entities["Bottom"]["Bottom"][0].append(entity[1])
                entities["Bottom"]["Bottom"][1] = facet_markers[0][1]
            elif np.allclose(com, [x1, (y1 - y0) / 2, (z1 - z0) / 2]):
                entities["Bottom"]["Right"][0].append(entity[1])
                entities["Bottom"]["Right"][1] = facet_markers[0][2]
            elif np.allclose(com, [x0, (y1 - y0) / 2, (z1 - z0) / 2]):
                entities["Bottom"]["Left"][0].append(entity[1])
                entities["Bottom"]["Left"][1] = facet_markers[0][3]
            elif np.allclose(com, [(x1 - x0) / 2, (y1 - y0) / 2, z1]):
                entities["Bottom"]["Top"][0].append(entity[1])
                entities["Bottom"]["Top"][1] = facet_markers[0][4]
            elif np.allclose(com, [(x1 - x0) / 2, y0, (z1 - z0) / 2]):
                entities["Bottom"]["Front"][0].append(entity[1])
                entities["Bottom"]["Front"][1] = facet_markers[0][5]
        # Physical markers for top
        top_surfaces = gmsh.model.getBoundary([volumes[top_index]], recursive=False, oriented=False)
        for entity in top_surfaces:
            com = gmsh.model.occ.getCenterOfMass(entity[0], entity[1])
            if np.allclose(com, [(x1 - x0) / 2, y1, (z2 - z1) / 2 + z1]):
                entities["Top"]["Back"][0].append(entity[1])
                entities["Top"]["Back"][1] = facet_markers[1][0]
            elif np.allclose(com, [(x1 - x0) / 2, (y1 - y0) / 2, z1]):
                entities["Top"]["Bottom"][0].append(entity[1])
                entities["Top"]["Bottom"][1] = facet_markers[1][1]
            elif np.allclose(com, [x1, (y1 - y0) / 2, (z2 - z1) / 2 + z1]):
                entities["Top"]["Right"][0].append(entity[1])
                entities["Top"]["Right"][1] = facet_markers[1][2]
            elif np.allclose(com, [x0, (y1 - y0) / 2, (z2 - z1) / 2 + z1]):
                entities["Top"]["Left"][0].append(entity[1])
                entities["Top"]["Left"][1] = facet_markers[1][3]
            elif np.allclose(com, [(x1 - x0) / 2, (y1 - y0) / 2, z2]):
                entities["Top"]["Top"][0].append(entity[1])
                entities["Top"]["Top"][1] = facet_markers[1][4]
            elif np.allclose(com, [(x1 - x0) / 2, y0, (z2 - z1) / 2 + z1]):
                entities["Top"]["Front"][0].append(entity[1])
                entities["Top"]["Front"][1] = facet_markers[1][5]

        # gmsh.model.occ.rotate(volumes, 0, 0, 0,
        #                       1 / np.sqrt(2), 1 / np.sqrt(2), 0, theta)
        # Note: Rotation cannot be used on recombined surfaces
        gmsh.model.occ.synchronize()

        for volume in volume_entities.keys():
            gmsh.model.addPhysicalGroup(
                volume_entities[volume][0][0],
                [volume_entities[volume][0][1]],
                tag=volume_entities[volume][1],
            )
            gmsh.model.setPhysicalName(volume_entities[volume][0][0], volume_entities[volume][1], volume)

        for box in entities.keys():
            for surface in entities[box].keys():
                gmsh.model.addPhysicalGroup(2, entities[box][surface][0], tag=entities[box][surface][1])
                gmsh.model.setPhysicalName(2, entities[box][surface][1], box + ":" + surface)
        # Set mesh sizes on the points from the surface we are extruding
        bottom_nodes = gmsh.model.getBoundary([(2, bottom)], recursive=True, oriented=False)
        gmsh.model.occ.mesh.setSize(bottom_nodes, res)
        top_nodes = gmsh.model.getBoundary([(2, top)], recursive=True, oriented=False)
        gmsh.model.occ.mesh.setSize(top_nodes, 2 * res)
        # NOTE: Need to synchronize after setting mesh sizes
        gmsh.model.occ.synchronize()
        # Generate mesh
        gmsh.model.mesh.generate(3)
        gmsh.model.mesh.setOrder(1)
    MPI.COMM_WORLD.barrier()
    mesh_data = gmshio.model_to_mesh(gmsh.model, MPI.COMM_WORLD, 0)
    gmsh.clear()
    gmsh.finalize()
    # NOTE: Hex mesh must be rotated after generation due to gmsh API
    mesh_data.mesh.geometry.x[:] = np.dot(r_matrix, mesh_data.mesh.geometry.x.T).T
    assert mesh_data.facet_tags is not None
    return (mesh_data.mesh, mesh_data.facet_tags)


@pytest.mark.parametrize("get_assemblers", ["C++", "numba"], indirect=True)
@pytest.mark.parametrize("nonslip", [True, False])
def test_cube_contact(generate_hex_boxes, nonslip, get_assemblers):
    assemble_matrix, assemble_vector = get_assemblers
    comm = MPI.COMM_WORLD
    root = 0
    # Generate mesh
    mesh_data = generate_hex_boxes
    mesh, mt = mesh_data
    fdim = mesh.topology.dim - 1
    # Create functionspaces
    V = fem.functionspace(mesh, ("Lagrange", 1, (mesh.geometry.dim,)))

    # Helper for orienting traction

    # Bottom boundary is fixed in all directions
    u_bc = fem.Function(V)
    with u_bc.x.petsc_vec.localForm() as u_local:
        u_local.set(0.0)
    u_bc.x.petsc_vec.destroy()

    bottom_dofs = fem.locate_dofs_topological(V, fdim, mt.find(5))
    bc_bottom = fem.dirichletbc(u_bc, bottom_dofs)

    g_vec = [0, 0, -4.25e-1]
    if not nonslip:
        # Helper for orienting traction
        r_matrix = dolfinx_mpc.utils.rotation_matrix([1 / np.sqrt(2), 1 / np.sqrt(2), 0], -theta)

        # Top boundary has a given deformation normal to the interface
        g_vec = np.dot(r_matrix, [0, 0, -4.25e-1])

    # Top boundary has a given deformation normal to the interface
    def top_v(x):
        values = np.empty((3, x.shape[1]))
        values[0] = g_vec[0]
        values[1] = g_vec[1]
        values[2] = g_vec[2]
        return values

    u_top = fem.Function(V)
    u_top.interpolate(top_v)

    top_dofs = fem.locate_dofs_topological(V, fdim, mt.find(3))
    bc_top = fem.dirichletbc(u_top, top_dofs)

    bcs = [bc_bottom, bc_top]

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

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

    # Define variational problem
    u = ufl.TrialFunction(V)
    v = ufl.TestFunction(V)
    a = ufl.inner(sigma(u), ufl.grad(v)) * ufl.dx
    rhs = ufl.inner(fem.Constant(mesh, default_scalar_type((0, 0, 0))), v) * ufl.dx
    bilinear_form = fem.form(a)

    linear_form = fem.form(rhs)

    # Create LU solver
    solver = PETSc.KSP().create(comm)
    solver.setType("preonly")
    solver.setTolerances(rtol=1.0e-14)
    solver.getPC().setType("lu")

    # Create MPC contact condition and assemble matrices
    mpc = dolfinx_mpc.MultiPointConstraint(V)
    if nonslip:
        with Timer("~Contact: Create non-elastic constraint"):
            mpc.create_contact_inelastic_condition(mt, 4, 9, eps2=500 * np.finfo(default_scalar_type).resolution)
    else:
        with Timer("~Contact: Create contact constraint"):
            nh = dolfinx_mpc.utils.create_normal_approximation(V, mt, 4)
            mpc.create_contact_slip_condition(mt, 4, 9, nh, eps2=500 * np.finfo(default_scalar_type).resolution)

    mpc.finalize()

    with Timer("~TEST: Assemble bilinear form"):
        A = assemble_matrix(bilinear_form, mpc, bcs=bcs)
    with Timer("~TEST: Assemble vector"):
        b = assemble_vector(linear_form, mpc)

    dolfinx_mpc.apply_lifting(b, [bilinear_form], [bcs], mpc)
    b.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE)
    fem.petsc.set_bc(b, bcs)

    with Timer("~MPC: Solve"):
        solver.setOperators(A)
        uh = fem.Function(mpc.function_space)
        uh.x.array[:] = 0
        u_vec = uh.x.petsc_vec
        solver.solve(b, u_vec)

    u_vec.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD)
    mpc.backsubstitution(uh)

    # Solve the MPC problem using a global transformation matrix
    # and numpy solvers to get reference values
    dolfinx_mpc.utils.log_info("Solving reference problem with global matrix (using numpy)")

    with Timer("~TEST: Assemble bilinear form (unconstrained)"):
        A_org = fem.petsc.assemble_matrix(bilinear_form, bcs)
        A_org.assemble()
        L_org = fem.petsc.assemble_vector(linear_form)
        fem.petsc.apply_lifting(L_org, [bilinear_form], [bcs])
        L_org.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE)
        fem.petsc.set_bc(L_org, bcs)

    with Timer("~TEST: Compare"):
        dolfinx_mpc.utils.compare_mpc_lhs(A_org, A, mpc, root=root)
        dolfinx_mpc.utils.compare_mpc_rhs(L_org, b, mpc, root=root)

        # Gather LHS, RHS and solution on one process
        A_csr = dolfinx_mpc.utils.gather_PETScMatrix(A_org, root=root)
        K = dolfinx_mpc.utils.gather_transformation_matrix(mpc, root=root)
        L_np = dolfinx_mpc.utils.gather_PETScVector(L_org, root=root)
        u_mpc = dolfinx_mpc.utils.gather_PETScVector(u_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
            atol = 1000 * np.finfo(default_scalar_type).resolution
            nt.assert_allclose(uh_numpy, u_mpc, atol=atol)
    L_org.destroy()
    b.destroy()
    solver.destroy()

    list_timings(comm)
