r"""Solves a 2D Poisson PDE with Dirichlet BCs using the Deep Ritz method and PINNs.

.. math::

    -\mu \delta u & = f in \Omega \times M \\
    u & = g on \partial \Omega \times M

where :math:`x = (x_1, x_2) \in \Omega = (0, 1) \times (0, 1)`, :math:`f` such that :math:`u(x_1, x_2, \mu) = \mu \sin(2\pi x_1) \sin(2\pi x_2)`, :math:`g = 0` and :math:`\mu \in M = [0.5, 1]`. Boundary conditions are enforced weakly.
"""

import matplotlib.pyplot as plt
import torch

from scimba_torch.approximation_space.nn_space import NNxSpace
from scimba_torch.domain.meshless_domain.domain_2d import Square2D
from scimba_torch.integration.monte_carlo import DomainSampler, TensorizedSampler
from scimba_torch.integration.monte_carlo_parameters import UniformParametricSampler
from scimba_torch.neural_nets.coordinates_based_nets.mlp import GenericMLP
from scimba_torch.numerical_solvers.elliptic_pde.deep_ritz import (
    DeepRitzElliptic,
    NaturalGradientDeepRitzElliptic,
)
from scimba_torch.numerical_solvers.elliptic_pde.pinns import (
    NaturalGradientPinnsElliptic,
)
from scimba_torch.physical_models.elliptic_pde.laplacians import (
    Laplacian2DDirichletRitzForm,
    Laplacian2DDirichletStrongForm,
)
from scimba_torch.plots.plots_nd import plot_abstract_approx_spaces
from scimba_torch.utils.scimba_tensors import LabelTensor


def exact_sol(x: LabelTensor, mu: LabelTensor):
    x1, x2 = x.get_components()
    mu1 = mu.get_components()
    return mu1 * torch.sin(2.0 * torch.pi * x1) * torch.sin(2.0 * torch.pi * x2)


def f_rhs(x: LabelTensor, mu: LabelTensor):
    x1, x2 = x.get_components()
    mu1 = mu.get_components()
    return (
        8.0
        * mu1
        * mu1
        * (torch.pi**2)
        * torch.sin(2.0 * torch.pi * x1)
        * torch.sin(2.0 * torch.pi * x2)
    )


def f_bc(x: LabelTensor, mu: LabelTensor):
    x1, _ = x.get_components()
    return torch.zeros_like(x1)


bc_weight = 10.0

domain_x = Square2D([(0.0, 1), (0.0, 1)], is_main_domain=True)
# domain_mu= []
domain_mu = [[0.5, 1.0]]
sampler = TensorizedSampler(
    [DomainSampler(domain_x), UniformParametricSampler(domain_mu)]
)

space = NNxSpace(
    1,
    1,
    GenericMLP,
    domain_x,
    sampler,
    layer_sizes=[64],
)

pde = Laplacian2DDirichletStrongForm(space, f=f_rhs, g=f_bc)

pinns = NaturalGradientPinnsElliptic(
    pde,
    bc_type="weak",
    bc_weight=bc_weight,
)

new_solve = False
if new_solve or not pinns.load(__file__, "pinn_strong_ENG"):
    pinns.solve(epochs=300, n_collocation=900, n_bc_collocation=200, verbose=True)
    pinns.save(__file__, "pinn_strong_ENG")

###### second space ############
bc_weight = 10.0

space2 = NNxSpace(
    1,
    1,
    GenericMLP,
    domain_x,
    sampler,
    layer_sizes=[64],
)

pde2 = Laplacian2DDirichletRitzForm(space2, f=f_rhs, g=f_bc)

ritz = DeepRitzElliptic(
    pde2,
    bc_type="weak",
    bc_weight=bc_weight,
)

new_solve = False
if new_solve or not ritz.load(__file__, "ritz_strong_no_precond"):
    ritz.solve(epochs=1000, n_collocation=40000, n_bc_collocation=4000, verbose=True)
    ritz.save(__file__, "ritz_strong_no_precond")

space3 = NNxSpace(
    1,
    1,
    GenericMLP,
    domain_x,
    sampler,
    layer_sizes=[64],
)

pde3 = Laplacian2DDirichletRitzForm(space3, f=f_rhs, g=f_bc)

bc_weight = 10.0

ritz2 = NaturalGradientDeepRitzElliptic(
    pde3,
    bc_type="weak",
    bc_weight=bc_weight,
)

new_solve = True
if new_solve or not ritz2.load(__file__, "ritz_strong_ENG"):
    ritz2.solve(epochs=200, n_collocation=40000, n_bc_collocation=4000, verbose=True)
    ritz2.save(__file__, "ritz_strong_ENG")

plot_abstract_approx_spaces(
    (
        pinns.space,
        ritz.space,
        ritz2.space,
    ),
    (domain_x,),
    (domain_mu,),
    loss=(
        pinns.losses,
        ritz.losses,
        ritz2.losses,
    ),
    error=exact_sol,
    draw_contours=True,
    n_drawn_contours=20,
    parameters_values="mean",
    title=r"Solving $-\mu \Delta u = 8 \mu^2 \pi^2 \sin(2\pi x) \sin(2\pi y)$",
    titles=(
        "PINN with ENG preconditioning",
        "RITZ with no preconditioning",
        "RITZ with ENG preconditioning",
    ),
)
plt.show()