# Basic application to load a mesh from file and view it in a window

# Python imports

import sys, os

import euclid as eu

import time

import numpy as np

import scipy.sparse as sps

import scipy.sparse.linalg

from scipy.sparse.linalg.dsolve import linsolve

from scipy.sparse.linalg import dsolve

from scipy.sparse import csr_matrix

## Imports from this project

sys.path.append(os.path.join(os.path.dirname(__file__), '..', 'core')) # hack to allow local imports without creaing a module or modifying the path variable

from InputOutput import *

from MeshDisplay import MeshDisplay

#from HalfEdgeMesh import *

from HalfEdgeMesh_ListImplementation import *

from Utilities import *

"""

an important misunderstanding about

the cotan-Laplace matrix L:

it does not represent the Laplace operator.

Instead, it represents the 'conformal Laplacian'

it gives you the laplacian integrated over each dual cell

TLM says:

We are computing the Laplace operator on a surface

We are not solving for some potential-flow satisfying various constraints

The only 'constraint' is the shape of the space. --- A closed manifold.

No extra conditions. Just compute

d*d(u) = rho

"""

"""

import pydec

import numpy as np

from scipy.linalg import lu

A = np.array([[1., 2., 3.], [4., 5., 6.], [7., 8., 9.]])

p, l, u = lu(A)

from scipy.sparse import csr_matrix # row format

#"""

def main(inputfile, show=False,