# %% [markdown]
# # Ball refinement
# This is a simple grid refinement and coarsening example.
# We define a simple time dependent indicator function to
# mark elements for refinement and coarsening.


# %%

import numpy as np
from dune.common import FieldVector
from dune.grid import Marker
from dune.alugrid import aluCubeGrid, aluConformGrid
from dune.grid import cartesianDomain

lbMethod=14 # help(aluConformGrid) for more information

domain = cartesianDomain([0,0], [1,1], [16,16])
# view = aluCubeGrid( domain )
view = aluConformGrid( domain, lbMethod=lbMethod )

maxLevel = 5
t = 0.

# %% [markdown]
# As an example we implement a simple refinement indicator.
# \begin{equation}
#  \eta_E = \left \{ \begin{array}{ll}
#                        1 & \mbox{ if } \quad 0.15 < |c_E - y(t)| < 0.25 \\
#                        0 & \mbox{ else }.
#                       \end{array} \right .
# \end{equation}
# where $c_E$ is the elements center and $y(t) = (r_0\cos(t 2 \pi ) + 0.5, r_0\sin(t 2 \pi) + 0.5 )^T$ and $r_0 = 0.3$.
# Mark an element $E$ for refinement, if $\eta_E = 1$, otherwise mark for coarsening.
#
# Implement $\eta_E$ and a marking function with the following signature:
# ```
# def eta( element ):
#     return 0.
#
# def markh( element ):
#     return Marker.keep
# ```


# %%
##### TASK

# %% [markdown]
# We invoke some initial refinement


# %%

# initial refinement
view.hierarchicalGrid.globalRefine(maxLevel-1)

from dune.grid import gridFunction
@gridFunction(view)
def levelFct(e, x):
    return e.level

# %% [markdown]
# Adapt the grid in each time step in the time interval $[0,T]$ with $T=1.5$ and
# use a time step of $\Delta t = 0.01$.
# Use the hierarchical grids adapt function:
# ```
# view.hierarchicalGrid.adapt(markh)
# ```


# %%
##### TASK

# %% [markdown]
# Lets do the same using a UFL expression for the characteristic function
# $\eta_E$ and use the marking and adapt routines from dune-fem.
#


# %%

import dune.fem
from dune.fem.view import adaptiveLeafGridView
from dune.fem.space import finiteVolume
from dune.fem.function import gridFunction

from ufl import SpatialCoordinate, sin, cos, pi, sqrt, dot, as_vector, conditional
from dune.ufl import Constant

# create an adaptiveLeafGridView over a standard grid view
view = adaptiveLeafGridView( aluConformGrid( domain, lbMethod=lbMethod ) )
# initial refinement
view.hierarchicalGrid.globalRefine(maxLevel-1)

# a space to store the indicator
space = finiteVolume( view )

# %% [markdown]
# Task: Write $\eta_E$ as UFL expression and use the routines
# ```
# dune.fem.mark(indicator, refineTolerance=0.7, coarsenTolerance=0.1, maxLevel=maxLevel )
# dune.fem.adapt( view.hierarchicalGrid )
# ```
# to carry out the adaptation.
#


# %%
##### TASK