def _to_delaunay(data_dict):
for name, data in data_dict.items():
mesh = Delaunay(data['coord'])
mesh.simplices = data['connect'].astype(np.int32)
data_dict[name]['mesh'] = mesh
return data_dict
def generateMesh(self):
points = self.generatePointCloud()
tri = Delaunay(points)
tri.simplices = self.filterTriangles(tri)
self.plotMesh(points,tri)
return Mesh2D(tri.points,tri.simplices)
print("Generate Mesh Done")
def wet_circles(A, B, thetaA, thetaB):
"""Generates a mesh that wets the surface of circles A and B.
Parameters
-------------
A,B : Circle
theta : list
the number of radians that the wet covers and number of the points on
the surface range
"""
vector = B.center - A.center
if vector.x > 0:
angleA = np.arctan(vector.y / vector.x)
angleB = PI + angleA
else:
angleB = np.arctan(vector.y / vector.x)
angleA = PI + angleB
# print(vector)
rA = A.radius
rB = B.radius
points = []
for t in ((np.arange(0, thetaA[1]) / (thetaA[1] - 1) - 0.5) * thetaA[0] +
angleA):
x = rA * np.cos(t) + A.center.x
y = rA * np.sin(t) + A.center.y
points.append([x, y])
mid = len(points)
for t in ((np.arange(0, thetaB[1]) / (thetaB[1] - 1) - 0.5) * thetaB[0] +
angleB):
x = rB * np.cos(t) + B.center.x
y = rB * np.sin(t) + B.center.y
points.append([x, y])
points = np.array(points)
# Triangulate the polygon
tri = Delaunay(points)
# Remove extra triangles
# print(tri.simplices)
mask = np.sum(tri.simplices < mid, 1)
mask = np.logical_and(mask < 3, mask > 0)
tri.simplices = tri.simplices[mask, :]
# print(tri.simplices)
m = Mesh()
for t in tri.simplices:
m.append(
Triangle(Point([points[t[0], 0], points[t[0], 1]]),
Point([points[t[1], 0], points[t[1], 1]]),
Point([points[t[2], 0], points[t[2], 1]])))
return m
def _mesh(self):
"""Create mesh of all the atoms in the cluster.
:return: Mesh
:rtype: scipy.spatial.Delaunay
"""
from scipy.spatial import Delaunay
points = self.cluster.get_positions()
delaunay = Delaunay(points)
simplices = self._filter_max_dist_in_element(delaunay.simplices)
delaunay.simplices = simplices
return delaunay
def Omega_mesh(self, dx, landmark):
x, y, z = np.meshgrid(np.arange(-1,1+dx,dx), np.arange(-1,1+dx,dx), np.arange(-1,1+dx,dx))
v = np.hstack((x.reshape(-1, 1), y.reshape(-1, 1), z.reshape(-1, 1)))
# v is of size l-by-3
l = v.shape[0]
ll = landmark.ndim
if not ll == 1:
num_landmark = landmark.shape[0]
else:
num_landmark = 1
landmark_index = np.zeros(num_landmark)
for i in range(num_landmark):
if not ll == 1:
check = landmark[i, :] == v
else:
check = landmark == v
result = np.matmul(check, np.ones((3, 1)))
if np.isin(3, result):
landmark_index[i] = np.argmax(result)
else:
v = np.vstack((v, landmark))
landmark_index[i] = l
l += 1
tri = Delaunay(v)
faces = tri.simplices
numf = np.shape(faces)[0]
planar = np.zeros(numf)
for i in range(numf):
facet = faces[i, :]
diff = v[facet[0:3], :] - np.tile(v[facet[3], :], (3, 1))
if not np.linalg.matrix_rank(diff) == args.dimension:
planar[i] = 1
# else:
# print(np.linalg.det(diff))
new_face = faces[planar==0, :]
tri.simplices = new_face
file2 = open('mesh.txt','w')
file2.write('triangulation: \n')
for i in range(new_face.shape[0]):
for j in range(4):
file2.write(str(new_face[i, j]))
file2.write(' ')
file2.write('\n')
file2.write('vertices: \n')
for i in range(v.shape[0]):
for j in range(3):
file2.write(str(v[i, j]))
file2.write(' ')
file2.write('\n')
file2.close()
return v, new_face, landmark_index
def delaunayTriangulation(points):
# https://stackoverflow.com/questions/36604172/difference-between-matlab-delaunayn-and-scipy-delaunay
N = points.ndim # The dimensions of points
options = 'Qt Qbb Qc' if N <= 3 else 'Qt Qbb Qc Qx' # Set the QHull options
DT = Delaunay(points, qhull_options=options)
tri = DT.simplices
keep = np.ones(len(tri), dtype=bool)
for i, t in enumerate(tri):
if abs(np.linalg.det(np.hstack(
(points[t], np.ones([1, N + 1]).T)))) < 1E-15:
keep[i] = False # Point is coplanar, we don't want to keep it
tri = tri[keep]
DT.simplices = tri
return DT
def create_triangulation(self, ures=4, vres=4, lres=1, **kwargs):
"""Compute the triangulation of the volume using scipy's
`delaunay` function
Parameters
----------
ures, vres : int
Specifies the oversampling of the original
volume in u and v directions. For example:
if `ures` = 2, and `self.u` = [0, 1, 2, 3],
then the surface will be resampled at
[0, 0.5, 1, 1.5, 2, 2.5, 3] prior to
plotting.
kwargs : dict
See scipy docs for `scipy.spatial.Delaunay()`
Returns
-------
None
"""
from scipy.spatial import Delaunay
if self.tri is not None:
return self.tri
# Make new u and v values of (possibly) higher resolution
# the original ones.
hru, hrv, hrl = self._resample_uvl(ures, vres, lres)
N = 3
volpts = self.ev(hru, hrv, hrl).reshape(3, -1).T
qhull_options = 'QJ'
tri = Delaunay(volpts, qhull_options=qhull_options)
keep = np.ones(len(tri.simplices), dtype=bool)
for i, t in enumerate(tri.simplices):
if abs(np.linalg.det(np.hstack(
(volpts[t], np.ones([1, N + 1]).T)))) < 1E-12:
keep[i] = False # Point is coplanar, we don't want to keep it
tri.simplices = tri.simplices[keep]
self.tri = tri
return tri
def plot_model_grid():
'''
Plot the grid of models in each metallicity.
Internal use.
'''
grid_kurucz = pd.read_csv('files/grid_points_kurucz.csv')
for m_h in grid_kurucz.groupby('m_h').size().index:
plt.figure(figsize=(13,4))
index = grid_kurucz['m_h'] == m_h
grid_matrix = np.array(grid_kurucz.loc[index, ['Teff', 'logg']])
tri = Delaunay(grid_matrix)
for i in range(len(tri.simplices)-1, -1, -1):
if min(grid_matrix[tri.simplices[i]][:,0]) >= 35000:
teff_gap = 5000
else:
teff_gap = 1500
if np.ptp(grid_matrix[tri.simplices[i]][:,0]) >= teff_gap or np.ptp(grid_matrix[tri.simplices[i]][:,1]) > 0.5:
tri.simplices = np.concatenate([tri.simplices[:i], tri.simplices[i+1:]])
plt.triplot(grid_matrix[:,0], grid_matrix[:,1], tri.simplices, zorder=0, lw=1, color='gray',alpha=0.5)
if m_h < 0.5:
plt.plot([50000, 42500], [5, 5], color='gray', zorder=0, alpha=0.5, lw=1)
elif m_h == 0.5:
plt.plot([45000, 40000], [5, 5], color='gray', zorder=0, alpha=0.5, lw=1)
elif m_h == 1:
plt.plot([40000, 37500], [5, 5], color='gray', zorder=0, alpha=0.5, lw=1)
plt.scatter(grid_kurucz.loc[index & (grid_kurucz['length']==72), 'Teff'], grid_kurucz.loc[index & (grid_kurucz['length']==72), 'logg'], s=5, label='Model length: 72')
plt.scatter(grid_kurucz.loc[index & (grid_kurucz['length']==64), 'Teff'], grid_kurucz.loc[index & (grid_kurucz['length']==64), 'logg'], s=5, c='C3', label='Model length: 64')
plt.legend()
plt.xlim((1175, 52325))
plt.title('[Fe/H] = {:.1f}'.format(m_h))
plt.xlabel(r'$T_\mathrm{{eff}}$'); plt.ylabel('logg')
plt.gca().invert_xaxis(); plt.gca().invert_yaxis()
plt.tight_layout()
plt.savefig('../docs/img/grid_points_kurucz/m_h{:+.1f}.png'.format(m_h), dpi=250)
plt.close()
set(indx for simplex in triang.simplices if x in simplex
for indx in simplex if indx != x))
### remove convex hull for more sensible graph
hull = ConvexHull(points)
delete_indices = []
for tidx in range(tri.simplices.shape[0]):
for hidx in range(hull.simplices.shape[0]):
is_hull = (int(
(tri.simplices[tidx] == hull.simplices[hidx][0]).any()) + int(
(tri.simplices[tidx] == hull.simplices[hidx][1]).any())) == 2
if is_hull:
delete_indices.append(tidx)
delete_indices = sorted(np.sort(delete_indices), reverse=True)
for idx in delete_indices:
tri.simplices = np.delete(tri.simplices, idx, 0)
### write graph file
graphfile = open('./graph.graph', 'w+')
for pidx in range(points.size // 2):
neighbours = find_neighbours(pidx, tri)
if neighbours != []:
graphfile.write("%d : %d %s\n" % (pidx, len(neighbours), ' '.join(
[str(neighbour) for neighbour in neighbours])))
mappingfile = open('./graph.mapping', 'w+')
for pidx in range(points.size // 2):
neighbours = find_neighbours(pidx, tri)
if neighbours != []:
mappingfile.write("(%f , %f) : %d\n" %
(points[pidx][0], points[pidx][1], pidx))
def preprocessingDataReceivers(mesh_file, receivers_file,
out_dir, rank):
''' Preprocess conductivity model associated to a given mesh in Gmsh
format. Here, dofs are defined for edge finite element computations.
:param str mesh_file: mesh file name to be preprocess.
:param str receivers_file: receiver positions file name to be preprocess.
:param str out_dir: path for output.
:param int rank: MPI rank.
:return: None
'''
from scipy.spatial import Delaunay
if rank == 0:
PETSc.Sys.Print(' Receiver positions (receivers.dat)')
# Check if mesh_file exist
success = checkFilePath(mesh_file)
if rank == 0:
if not success:
msg = (' preprocessingDataReceivers(): file ' + mesh_file +
' does not exist.')
raise ValueError(msg)
# Check if receivers_file exist
success = checkFilePath(receivers_file)
if rank == 0:
if not success:
msg = (' preprocessingDataReceivers(): file ' + receivers_file +
' does not exist.')
raise ValueError(msg)
# Read receivers_file
receivers = np.loadtxt(receivers_file)
# Number of receivers
if receivers.ndim == 1:
nReceivers = 1
else:
dim = receivers.shape
nReceivers = dim[0]
# Read nodes
nodes, nNodes = readGmshNodes(mesh_file)
# Build Delaunay triangulation with nodes
tri = Delaunay(nodes)
# Delete unnecesary arrays
del nodes
# Read connectivity
elemsN, nElems = readGmshConnectivity(mesh_file)
# Compute dofs
dofs, _ = computeDofs(elemsN, nElems)
# Overwrite Delaunay structure with mesh_file connectivity
tri.simplices = elemsN.astype(np.int32)
# Delete unnecesary arrays
del elemsN
# Find out which tetrahedral element points are in
recvElems = tri.find_simplex(receivers)
# Determine if all receiver points were found
idx = np.where(recvElems < 0)[0]
# If idx is not empty, there are receivers outside the domain
if idx.size != 0:
PETSc.Sys.Print(' Some receivers are were not located')
PETSc.Sys.Print(' Following ID-receivers will not be taken ' +
'into account: ')
PETSc.Sys.Print(idx)
# Update number of receivers
nReceivers = nReceivers - len(idx)
if nReceivers == 0:
PETSc.Sys.Print(' No receiver has been found. Nothing to do.'
' Aborting')
exit(-1)
# Remove idx from receivers matrix
receivers = np.delete(receivers, idx, axis=0)
# Create new file with located points coordinates
# Build path to save the file
out_path = out_dir + 'receiversPETGEM.txt'
PETSc.Sys.Print(' Saving file with localized receiver positions ' +
'(receiversPETGEM.txt)')
np.savetxt(out_path, receivers, fmt='%1.8e')
# Allocate space for receives in PETGEM format
numDimensions = 3
nodalOrder = 4
edgeOrder = 6
allocate = numDimensions+nodalOrder*numDimensions+nodalOrder+edgeOrder
tmp = np.zeros((nReceivers, allocate), dtype=np.float)
# Fill tmp matrix with receiver positions, element coordinates and
# nodal indexes
for iReceiver in np.arange(nReceivers):
# If there is one receiver
if nReceivers == 1:
# Get receiver coordinates
coordiReceiver = receivers[0:]
# Get element coordinates (container element)
coordElement = tri.points[tri.simplices[recvElems, :]]
coordElement = coordElement.flatten()
# Get nodal indexes (container element)
nodesElement = tri.simplices[recvElems, :]
# Get element-dofs indices (container element)
dofsElement = dofs[recvElems, :]
# If there are more than one receivers
else:
# Get receiver coordinates
coordiReceiver = receivers[iReceiver, :]
# Get element coordinates (container element)
coordElement = tri.points[tri.simplices[recvElems[iReceiver], :]]
coordElement = coordElement.flatten()
# Get nodal indexes (container element)
nodesElement = tri.simplices[recvElems[iReceiver], :]
# Get element-dofs indices (container element)
dofsElement = dofs[recvElems[iReceiver], :]
# Insert data for iReceiver
tmp[iReceiver, 0:3] = coordiReceiver
tmp[iReceiver, 3:15] = coordElement
tmp[iReceiver, 15:19] = nodesElement
tmp[iReceiver, 19:] = dofsElement
# Delete unnecesary arrays
del tri
del dofs
# Get matrix dimensions
size = tmp.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(size[0], size[1], tmp)
# Delete unnecesary arrays
del tmp
# Verify if OUT_DIR exists
checkIfDirectoryExist(out_dir)
# Build path to save the file
out_path = out_dir + 'receivers.dat'
# Write PETGEM receivers in PETSc format
writeParallelDenseMatrix(out_path, matrix, communicator=PETSc.COMM_SELF)
return nReceivers
def ComputeTriangularMesh(vertices, segments):
from scipy.spatial import Delaunay
from copy import deepcopy
nVertices = len(vertices)
tri = Delaunay(np.array(vertices))
trigs = deepcopy(tri.simplices)
#+++++++++++++++++++++++++++++++++
#compute vertices2simplices list:
vertices2simplices = [[]]*nVertices
cnt = 0
for trig in trigs:
for i in trig:
alist=list(vertices2simplices[i])
alist.append(cnt)
vertices2simplices[i] = alist
cnt += 1 #trig counter
#print(trigs)
#print(vertices2simplices)
#+++++++++++++++++++++++++++++++++
#compute neighbors:
trigNeighbors = 0*trigs #-1 means no neighbor trig!
trigNeighbors[:,:] = -1
#run over all triangles
for i in range(len(trigs)):
for j in range(3):
i0 = trigs[i,j]
i1 = trigs[i,(j+1)%3]
actSeg = [i0, i1]
listTest = vertices2simplices[i0] + vertices2simplices[i1]
for trigIndex in listTest:
if trigIndex < i:
for k in range(3):
t0 = trigs[trigIndex, k]
t1 = trigs[trigIndex, (k+1)%3]
if (i0 == t1) and (i1 == t0): #opposite trig orientation is reversed ...
trigNeighbors[i,j] = trigIndex
trigNeighbors[trigIndex,k] = i
#print("neighbors=", trigNeighbors)
#+++++++++++++++++++++++++++++++++
#compute inside triangles:
trianglesInside = [-1]*len(trigs) #-1 is undefined, 0=outside, 1=inside
for seg in segments: #triangles left to segment are inside
listTest = vertices2simplices[seg[0]] + vertices2simplices[seg[1]]
for trigIndex in listTest:
for k in range(3):
t0 = trigs[trigIndex, k]
t1 = trigs[trigIndex, (k+1)%3]
if (seg[0] == t0) and (seg[1] == t1): #inside triangle
trianglesInside[trigIndex] = 1
elif (seg[0] == t1) and (seg[1] == t0): #outside triangle
trianglesInside[trigIndex] = 0
#print(trianglesInside)
#finally find remaining triangles (usually all triangles are on boundary, so nothing remains):
undefinedTrigs = True
while undefinedTrigs: #iterate as long as there are undefined triangles; usually only few iterations necessary
undefinedTrigs = False
#print("iterate neighbors")
for i in range(len(trigs)):
if trianglesInside[i] == -1: #still undefined
found = False
for j in range(3): #look at all neighbors
tn = trigNeighbors[i, j]
if trianglesInside[tn] != -1:
trianglesInside[i] = trianglesInside[tn]
found = True
if not found:
undefinedTrigs = True
#now create new list of interior triangles
interiorTrigs = []
for i in range(len(trigs)):
if trianglesInside[i] == 1:
interiorTrigs += [list(trigs[i])]
#print("interiorTrigs=",interiorTrigs)
tri.simplices = np.array(interiorTrigs)
return tri
def _make_delaunay_mesh(self, coords, connectivity):
mesh = Delaunay(coords)
mesh.simplices = connectivity.astype(np.int32)
return mesh
def wet_circles(A, B, thetaA, thetaB):
"""Generates a mesh that wets the surface of circles A and B.
Parameters
-------------
A,B : Circle
theta : list
the number of radians that the wet covers and number of the points on
the surface range
"""
vector = B.center - A.center
if vector.x > 0:
angleA = np.arctan(vector.y / vector.x)
angleB = PI + angleA
else:
angleB = np.arctan(vector.y / vector.x)
angleA = PI + angleB
# print(vector)
rA = A.radius
rB = B.radius
points = []
for t in ((np.arange(0, thetaA[1]) / (thetaA[1] - 1) - 0.5) * thetaA[0] +
angleA):
x = rA * np.cos(t) + A.center.x
y = rA * np.sin(t) + A.center.y
points.append([x, y])
mid = len(points)
for t in ((np.arange(0, thetaB[1]) / (thetaB[1] - 1) - 0.5) * thetaB[0] +
angleB):
x = rB * np.cos(t) + B.center.x
y = rB * np.sin(t) + B.center.y
points.append([x, y])
points = np.array(points)
# Triangulate the polygon
tri = Delaunay(points)
# Remove extra triangles
# print(tri.simplices)
mask = np.sum(tri.simplices < mid, 1)
mask = np.logical_and(mask < 3, mask > 0)
tri.simplices = tri.simplices[mask, :]
# print(tri.simplices)
m = Mesh()
for t in tri.simplices:
m.append(
Triangle(
Point([points[t[0], 0], points[t[0], 1]]),
Point([points[t[1], 0], points[t[1], 1]]),
Point([points[t[2], 0], points[t[2], 1]])
)
)
return m
def run(self, setup):
"""Run a preprocessing task.
:param obj setup: inputSetup object.
:return: None
"""
# ---------------------------------------------------------------
# Initialization
# ---------------------------------------------------------------
# Start timer
Timers()["Preprocessing"].start()
# Parameters shortcut (for code legibility)
model = setup.model
output = setup.output
# Obtain the MPI environment
parEnv = MPIEnvironment()
# ---------------------------------------------------------------
# Import mesh file (gmsh format)
# ---------------------------------------------------------------
# Read nodes
nodes, _ = readGmshNodes(model.mesh_file)
# Read connectivity
elemsN, nElems = readGmshConnectivity(model.mesh_file)
# ---------------------------------------------------------------
# Preprocessing nodal coordinates
# ---------------------------------------------------------------
Print.master(' Nodal coordinates')
# Build coordinates in PETGEM format where each row
# represent the xyz coordinates of the 4 tetrahedral element
num_dimensions = 3
num_nodes_per_element = 4
data = np.array((nodes[elemsN[:], :]), dtype=np.float)
data = data.reshape(nElems, num_dimensions*num_nodes_per_element)
# Get matrix dimensions
size = data.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(size[0], size[1], data)
# Build path to save the file
out_path = output.directory_scratch + '/nodes.dat'
if parEnv.rank == 0:
# Write PETGEM nodes in PETSc format
writeParallelDenseMatrix(out_path, matrix, communicator=PETSc.COMM_SELF)
# ---------------------------------------------------------------
# Preprocessing mesh connectivity
# ---------------------------------------------------------------
Print.master(' Mesh connectivity')
# Get matrix dimensions
size = elemsN.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(size[0], size[1], elemsN)
# Build path to save the file
out_path = output.directory_scratch + '/meshConnectivity.dat'
if parEnv.rank == 0:
# Write PETGEM connectivity in PETSc format
writeParallelDenseMatrix(out_path, matrix, communicator=PETSc.COMM_SELF)
# ---------------------------------------------------------------
# Preprocessing edges connectivity
# ---------------------------------------------------------------
Print.master(' Edges connectivity')
# Compute edges
elemsE, edgesNodes = computeEdges(elemsN, nElems)
nEdges = edgesNodes.shape[0]
# Get matrix dimensions
size = elemsE.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(size[0], size[1], elemsE)
# Build path to save the file
out_path = output.directory_scratch + '/edges.dat'
if parEnv.rank == 0:
# Write PETGEM edges in PETSc format
writeParallelDenseMatrix(out_path, matrix, communicator=PETSc.COMM_SELF)
# Reshape edgesNodes and save
num_nodes_per_edge = 2
num_edges_per_element = 6
data = np.array((edgesNodes[elemsE[:], :]), dtype=np.float)
data = data.reshape(nElems, num_nodes_per_edge*num_edges_per_element)
# Get matrix dimensions
size = data.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(size[0], size[1], data)
# Build path to save the file
out_path = output.directory_scratch + '/edgesNodes.dat'
if parEnv.rank == 0:
# Write PETGEM edgesNodes in PETSc format
writeParallelDenseMatrix(out_path, matrix, communicator=PETSc.COMM_SELF)
# ---------------------------------------------------------------
# Preprocessing faces connectivity
# ---------------------------------------------------------------
Print.master(' Faces connectivity')
# Compute faces
elemsF, facesN = computeFaces(elemsN, nElems)
nFaces = facesN.shape[0]
# Get matrix dimensions
size = elemsF.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(size[0], size[1], elemsF)
# Build path to save the file
out_path = output.directory_scratch + '/faces.dat'
if parEnv.rank == 0:
# Write PETGEM edges in PETSc format
writeParallelDenseMatrix(out_path, matrix, communicator=PETSc.COMM_SELF)
# ---------------------------------------------------------------
# Preprocessing faces-edges connectivity
# ---------------------------------------------------------------
Print.master(' Faces-edges connectivity')
N = invConnectivity(elemsF, nFaces)
if nElems != 1:
N = np.delete(N, 0, axis=1)
# Allocate
facesE = np.zeros((nFaces, 3), dtype=np.int)
# Compute edges list for each face
for i in np.arange(nFaces):
iEle = N[i, 0]
edgesEle = elemsE[iEle,:]
facesEle = elemsF[iEle,:]
kFace = np.where(facesEle == i)[0]
if kFace == 0: # Face 1
facesE[facesEle[kFace],:] = [edgesEle[0], edgesEle[1], edgesEle[2]]
elif kFace == 1: # Face 2
facesE[facesEle[kFace],:] = [edgesEle[0], edgesEle[4], edgesEle[3]]
elif kFace == 2: # Face 3
facesE[facesEle[kFace],:] = [edgesEle[1], edgesEle[5], edgesEle[4]]
elif kFace == 3: # Face 4
facesE[facesEle[kFace],:] = [edgesEle[2], edgesEle[5], edgesEle[3]]
num_faces_per_element = 4
num_edges_per_face = 3
data = np.array((facesE[elemsF[:], :]), dtype=np.float)
data = data.reshape(nElems, num_faces_per_element*num_edges_per_face)
# Get matrix dimensions
size = data.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(size[0], size[1], data)
# Build path to save the file
out_path = output.directory_scratch + '/facesEdges.dat'
if parEnv.rank == 0:
# Write PETGEM edges in PETSc format
writeParallelDenseMatrix(out_path, matrix, communicator=PETSc.COMM_SELF)
# ---------------------------------------------------------------
# Preprocessing dofs connectivity
# ---------------------------------------------------------------
Print.master(' DOFs connectivity')
# Compute degrees of freedom connectivity
dofs, dof_edges, dof_faces, _, total_num_dofs = computeConnectivityDOFS(elemsE,elemsF,model.basis_order)
# Get matrix dimensions
size = dofs.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(size[0], size[1], dofs)
# Build path to save the file
out_path = output.directory_scratch + '/dofs.dat'
if parEnv.rank == 0:
# Write PETGEM edges in PETSc format
writeParallelDenseMatrix(out_path, matrix, communicator=PETSc.COMM_SELF)
# ---------------------------------------------------------------
# Preprocessing boundaries
# ---------------------------------------------------------------
Print.master(' Boundaries')
# Compute boundary faces
bFacesN, bFaces = computeBoundaryFaces(elemsF, facesN)
# Compute boundary edges
bEdges = computeBoundaryEdges(edgesNodes, bFacesN)
# Compute dofs on boundaries
_, indx_boundary_dofs = computeBoundaries(dofs, dof_edges, dof_faces, bEdges, bFaces, model.basis_order);
# Build PETSc structures
vector = createSequentialVectorWithArray(indx_boundary_dofs)
# Build path to save the file
out_path = output.directory_scratch + '/boundaries.dat'
if parEnv.rank == 0:
# Write PETGEM nodes in PETSc format
writePetscVector(out_path, vector, communicator=PETSc.COMM_SELF)
# ---------------------------------------------------------------
# Preprocessing sigma model
# ---------------------------------------------------------------
Print.master(' Conductivity model')
# Read element's tag
elemsS, nElems = readGmshPhysicalGroups(model.mesh_file)
# Build conductivity arrays
conductivityModel = np.zeros((nElems, 2), dtype=np.float)
for i in np.arange(nElems):
# Set horizontal sigma
conductivityModel[i, 0] = model.sigma_horizontal[np.int(elemsS[i])]
# Set vertical sigma
conductivityModel[i, 1] = model.sigma_vertical[np.int(elemsS[i])]
# Get matrix dimensions
size = conductivityModel.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(size[0], size[1], conductivityModel)
# Build path to save the file
out_path = output.directory_scratch + '/conductivityModel.dat'
if parEnv.rank == 0:
# Write PETGEM edges in PETSc format
writeParallelDenseMatrix(out_path, matrix, communicator=PETSc.COMM_SELF)
# ---------------------------------------------------------------
# Preprocessing receivers
# ---------------------------------------------------------------
Print.master(' Receivers')
# Open receivers_file
fileID = h5py.File(model.receivers_file, 'r')
# Read receivers
receivers = fileID.get('data')[()]
# Number of receivers
if receivers.ndim == 1:
nReceivers = 1
else:
dim = receivers.shape
nReceivers = dim[0]
# Build Delaunay triangulation with nodes
tri = Delaunay(nodes)
# Overwrite Delaunay structure with mesh_file connectivity and points
tri.simplices = elemsN.astype(np.int32)
tri.vertices = elemsN.astype(np.int32)
# Find out which tetrahedral element points are in
recvElems = tri.find_simplex(receivers, bruteforce=True, tol=1.e-12)
# Find out which tetrahedral element source point is in
srcElem = tri.find_simplex(model.src_position, bruteforce=True, tol=1.e-12)
# Determine if all receiver points were found
idx = np.where(np.logical_or(recvElems>nElems, recvElems<0))[0]
# If idx is not empty, there are receivers outside the domain
if idx.size != 0:
Print.master(' The following receivers were not located and will not be taken into account ' + str(idx))
# Update number of receivers
nReceivers = nReceivers - len(idx)
if nReceivers == 0:
Print.master(' No receiver has been found. Nothing to do. Aborting')
exit(-1)
# Remove idx from receivers matrix
receivers = np.delete(receivers, idx, axis=0)
# Remove idx from recvElems
recvElems = np.delete(recvElems, idx, axis=0)
# If srcElem is empty, source not located
if srcElem == 0:
Print.master(' Source no located in the computational domain. Please, improve the mesh quality')
exit(-1)
# Compute number of dofs per element
num_dof_in_element = np.int(model.basis_order*(model.basis_order+2)*(model.basis_order+3)/2)
# Allocate
data_receiver = np.zeros((nReceivers, 53+num_dof_in_element), dtype=np.float)
# Fill tmp matrix with receiver positions, element coordinates and
# nodal indexes
for i in np.arange(nReceivers):
# If there is one receiver
if nReceivers == 1:
# Get index of tetrahedral element (receiver container)
iEle = recvElems
# Get dofs of element container
dofsElement = dofs[iEle]
# If there are more than one receivers
else:
# Get index of tetrahedral element (receiver container)
iEle = recvElems[i]
# Get dofs of element container
dofsElement = dofs[iEle, :]
# Get indexes of nodes for iand insert
nodesReceiver = elemsN[iEle, :]
data_receiver[i, 0:4] = nodesReceiver
# Get nodes coordinates for i and insert
coordEle = nodes[nodesReceiver, :]
coordEle = coordEle.flatten()
data_receiver[i, 4:16] = coordEle
# Get indexes of faces for i and insert
facesReceiver = elemsF[iEle, :]
data_receiver[i, 16:20] = facesReceiver
# Get edges indexes for faces in i and insert
edgesReceiver = facesE[facesReceiver, :]
edgesReceiver = edgesReceiver.flatten()
data_receiver[i, 20:32] = edgesReceiver
# Get indexes of edges for i and insert
edgesReceiver = elemsE[iEle, :]
data_receiver[i, 32:38] = edgesReceiver
# Get node indexes for edges in i and insert
edgesNodesReceiver = edgesNodes[edgesReceiver, :]
edgesNodesReceiver = edgesNodesReceiver.flatten()
data_receiver[i, 38:50] = edgesNodesReceiver
# Get receiver coordinates
coordReceiver = receivers[i,: ]
data_receiver[i, 50:53] = coordReceiver
# Get dofs for srcElem and insert
dofsReceiver = dofsElement
data_receiver[i, 53::] = dofsReceiver
# Get matrix dimensions
size = data_receiver.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(size[0], size[1], data_receiver)
# Build path to save the file
out_path = output.directory_scratch + '/receivers.dat'
if parEnv.rank == 0:
# Write PETGEM receivers in PETSc format
writeParallelDenseMatrix(out_path, matrix, communicator=PETSc.COMM_SELF)
# Compute number of dofs per element
num_dof_in_element = np.int(model.basis_order*(model.basis_order+2)*(model.basis_order+3)/2)
# Build data for source insertion
vector = np.zeros(50+num_dof_in_element, dtype=np.float)
# Get indexes of nodes for srcElem and insert
nodesSource = elemsN[srcElem, :]
vector[0:4] = nodesSource
# Get nodes coordinates for srcElem and insert
coordSource = nodes[nodesSource, :]
coordSource = coordSource.flatten()
vector[4:16] = coordSource
# Get indexes of faces for srcElem and insert
facesSource = elemsF[srcElem, :]
vector[16:20] = facesSource
# Get edges indexes for faces in srcElem and insert
edgesFace = facesE[facesSource, :]
edgesFace = edgesFace.flatten()
vector[20:32] = edgesFace
# Get indexes of edges for srcElem and insert
edgesSource = elemsE[srcElem, :]
vector[32:38] = edgesSource
# Get node indexes for edges in srcElem and insert
edgesNodesSource = edgesNodes[edgesSource, :]
edgesNodesSource = edgesNodesSource.flatten()
vector[38:50] = edgesNodesSource
# Get dofs for srcElem and insert
dofsSource = dofs[srcElem,:]
vector[50::] = dofsSource
# Build PETSc structures
vector = createSequentialVectorWithArray(vector)
# Build path to save the file
out_path = output.directory_scratch + '/source.dat'
if parEnv.rank == 0:
# Write PETGEM nodes in PETSc format
writePetscVector(out_path, vector, communicator=PETSc.COMM_SELF)
# ---------------------------------------------------------------
# Sparsity pattern
# ---------------------------------------------------------------
# Setup valence for each basis order (adding a small percentage to keep safe)
valence = np.array([50, 200, 400, 800, 1400, 2500])
# Build nnz pattern for each row
nnz = np.full((total_num_dofs), valence[model.basis_order-1], dtype=np.int)
# Build PETSc structures
vector = createSequentialVectorWithArray(nnz)
# Build path to save the file
out_path = output.directory_scratch + '/nnz.dat'
if parEnv.rank == 0:
# Write PETGEM nodes in PETSc format
writePetscVector(out_path, vector, communicator=PETSc.COMM_SELF)
# ---------------------------------------------------------------
# Print mesh statistics
# ---------------------------------------------------------------
Print.master(' ')
Print.master(' Mesh statistics')
Print.master(' Number of elements: {0:12}'.format(str(nElems)))
Print.master(' Number of faces: {0:12}'.format(str(nFaces)))
Print.master(' Number of edges: {0:12}'.format(str(nEdges)))
Print.master(' Number of dofs: {0:12}'.format(str(total_num_dofs)))
Print.master(' Number of boundaries: {0:12}'.format(str(len(indx_boundary_dofs))))
# ---------------------------------------------------------------
# Print data model
# ---------------------------------------------------------------
Print.master(' ')
Print.master(' Model data')
Print.master(' Number of materials: {0:12}'.format(str(np.max(elemsS)+1)))
Print.master(' Vector basis order: {0:12}'.format(str(model.basis_order)))
Print.master(' Frequency (Hz): {0:12}'.format(str(model.frequency)))
Print.master(' Source position (xyz): {0:12}'.format(str(model.src_position)))
Print.master(' Source azimuth: {0:12}'.format(str(model.src_azimuth)))
Print.master(' Source dip: {0:12}'.format(str(model.src_dip)))
Print.master(' Source current: {0:12}'.format(str(model.src_current)))
Print.master(' Source length: {0:12}'.format(str(model.src_length)))
Print.master(' Sigma horizontal: {0:12}'.format(str(model.sigma_horizontal)))
Print.master(' Sigma vertical: {0:12}'.format(str(model.sigma_vertical)))
Print.master(' Number of receivers: {0:12}'.format(str(nReceivers)))
# Apply barrier for MPI tasks alignement
parEnv.comm.barrier()
# Stop timer
Timers()["Preprocessing"].stop()
b = points_3d[simple[1]]
c = points_3d[simple[2]]
mesh.add_facet((a, b, c))
# print(a, b, c)
for simple in tri.simplices[mask]:
a1 = [points_3d[simple[0]][0], points_3d[simple[0]][1], points_3d[simple[0]][2]]
a1[2] = zscale * zmin + args.base
b1 = [points_3d[simple[1]][0], points_3d[simple[1]][1], points_3d[simple[1]][2]]
b1[2] = zscale * zmin + args.base
c1 = [points_3d[simple[2]][0], points_3d[simple[2]][1], points_3d[simple[2]][2]]
c1[2] = zscale * zmin + args.base
mesh.add_facet((a1, b1, c1))
# print(a1, b1, c1)
tri.simplices = tri.simplices[mask]
ch = ConcaveHull()
ch.loadpoints(points_2d)
ch.calculatehull()
hull_points = np.vstack(ch.boundary.exterior.coords.xy).T.tolist()
# print(hull_points[:2])
points_2d = points_2d.tolist()
# print(points_2d[:2])
for i, hp in enumerate(hull_points):
if i == len(hull_points)-1:
continue
# print(hp)
ind = points_2d.index(hp)
# ---------------------------------------------------------------
# Preprocessing receivers
# ---------------------------------------------------------------
Print.master(' Receivers')
# Setup receivers
receivers = np.vstack((inline, broadside))
# Number of receivers
nReceivers = receivers.shape[0]
# Build Delaunay triangulation with nodes
tri = Delaunay(nodes)
# Overwrite Delaunay structure with mesh_file connectivity and points
tri.simplices = elemsN.astype(np.int32)
tri.vertices = elemsN.astype(np.int32)
# Find out which tetrahedral element points are in
recvElems = tri.find_simplex(receivers, bruteforce=True, tol=1.e-12)
# Determine if all receiver points were found
idx = np.where(np.logical_or(recvElems > nElems, recvElems < 0))[0]
# If idx is not empty, there are receivers outside the domain
if idx.size != 0:
Print.master(
' The following receivers were not located and will not be taken into account '
+ str(idx))
# Update number of receivers
nReceivers = nReceivers - len(idx)
x_res = 141.7/512
y_res = x_res
z_res = .8
res_arr = np.array([x_res, y_res, z_res])
x_pix = 512
y_pix = x_pix
z_pix = 151
mesh = meshio.read('ProcessedMSHs/Gel4I.msh')
points_pix = mesh.points/res_arr
mins = np.floor(points_pix.min(0)).astype(int)
maxs = np.ceil(points_pix.max(0)).astype(int)
test_points = np.array(np.meshgrid(np.arange(mins[0], maxs[0]+1),
np.arange(mins[1], maxs[1]+1),
np.arange(mins[2], maxs[2]+1))).T.reshape(-1,3)
tri = Delaunay(points_pix)
tri.simplices = mesh.cells['triangle'].astype(np.int32)
output = np.asarray([tri.find_simplex(point) for point in test_points])
ind = np.argwhere(output>=0).flatten()
inside_points = test_points[ind]
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(inside_points[:, 0], inside_points[:, 1], inside_points[:, 2], s=3, c='g')
plt.show()
def run(self, inputSetup):
"""Run a preprocessing task.
:param obj inputSetup: inputSetup object.
:return: None
"""
# ---------------------------------------------------------------
# Obtain the MPI environment
# ---------------------------------------------------------------
parEnv = MPIEnvironment()
# Start timer
Timers()["Preprocessing"].start()
# ---------------------------------------------------------------
# Preprocessing (sequential task)
# ---------------------------------------------------------------
if (parEnv.rank == 0):
# Parameters shortcut (for code legibility)
model = inputSetup.model
run = inputSetup.run
output = inputSetup.output
out_dir = output.get('directory_scratch')
# Compute number of dofs per element
basis_order = run.get('nord')
num_dof_in_element = np.int(basis_order * (basis_order + 2) *
(basis_order + 3) / 2)
if (model.get('mode') == 'csem'):
mode = 'csem'
elif (model.get('mode') == 'mt'):
mode = 'mt'
# Get data model
data_model = model.get(mode)
# ---------------------------------------------------------------
# Import mesh file
# ---------------------------------------------------------------
mesh_file = model.get('mesh')
# Import mesh
mesh = meshio.read(mesh_file)
# Number of elements
size = mesh.cells[0][1][:].shape
nElems = size[0]
# ---------------------------------------------------------------
# Preprocessing nodal coordinates
# ---------------------------------------------------------------
Print.master(' Nodal coordinates')
# Build coordinates in PETGEM format where each row
# represent the xyz coordinates of the 4 tetrahedral element
num_dimensions = 3
num_nodes_per_element = 4
data = mesh.points[mesh.cells[0][1][:], :]
data = data.reshape(nElems, num_dimensions * num_nodes_per_element)
# Get matrix dimensions
size = data.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(
size[0], size[1], data)
# Build path to save the file
out_path = out_dir + '/nodes.dat'
# Write PETGEM nodes in PETSc format
writeParallelDenseMatrix(out_path,
matrix,
communicator=PETSc.COMM_SELF)
# Remove temporal matrix
del matrix
# ---------------------------------------------------------------
# Preprocessing mesh connectivity
# ---------------------------------------------------------------
Print.master(' Mesh connectivity')
# Get matrix dimensions
size = mesh.cells[0][1][:].shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(
size[0], size[1], mesh.cells[0][1][:])
# Build path to save the file
out_path = out_dir + '/meshConnectivity.dat'
# Write PETGEM connectivity in PETSc format
writeParallelDenseMatrix(out_path,
matrix,
communicator=PETSc.COMM_SELF)
# Remove temporal matrix
del matrix
# ---------------------------------------------------------------
# Preprocessing edges connectivity
# ---------------------------------------------------------------
Print.master(' Edges connectivity')
# Compute edges
elemsE, edgesNodes = computeEdges(mesh.cells[0][1][:], nElems)
nEdges = edgesNodes.shape[0]
# Get matrix dimensions
size = elemsE.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(
size[0], size[1], elemsE)
# Build path to save the file
out_path = out_dir + '/edges.dat'
# Write PETGEM edges in PETSc format
writeParallelDenseMatrix(out_path,
matrix,
communicator=PETSc.COMM_SELF)
# Remove temporal matrix
del matrix
# Reshape edgesNodes and save
num_nodes_per_edge = 2
num_edges_per_element = 6
data = np.array((edgesNodes[elemsE[:], :]), dtype=np.float)
data = data.reshape(nElems,
num_nodes_per_edge * num_edges_per_element)
# Get matrix dimensions
size = data.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(
size[0], size[1], data)
# Build path to save the file
out_path = out_dir + '/edgesNodes.dat'
# Write PETGEM edgesNodes in PETSc format
writeParallelDenseMatrix(out_path,
matrix,
communicator=PETSc.COMM_SELF)
# Remove temporal matrix
del matrix
# ---------------------------------------------------------------
# Preprocessing faces connectivity
# ---------------------------------------------------------------
Print.master(' Faces connectivity')
# Compute faces
elemsF, facesN = computeFaces(mesh.cells[0][1][:], nElems)
nFaces = facesN.shape[0]
# Get matrix dimensions
size = elemsF.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(
size[0], size[1], elemsF)
# Build path to save the file
out_path = out_dir + '/faces.dat'
# Write PETGEM edges in PETSc format
writeParallelDenseMatrix(out_path,
matrix,
communicator=PETSc.COMM_SELF)
# Remove temporal matrix
del matrix
# ---------------------------------------------------------------
# Preprocessing faces-edges connectivity
# ---------------------------------------------------------------
Print.master(' Faces-edges connectivity')
facesE = computeFacesEdges(elemsF, elemsE, nFaces, nElems)
num_faces_per_element = 4
num_edges_per_face = 3
data = np.array((facesE[elemsF[:], :]), dtype=np.float)
data = data.reshape(nElems,
num_faces_per_element * num_edges_per_face)
# Get matrix dimensions
size = data.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(
size[0], size[1], data)
# Build path to save the file
out_path = out_dir + '/facesEdges.dat'
# Write PETGEM edges in PETSc format
writeParallelDenseMatrix(out_path,
matrix,
communicator=PETSc.COMM_SELF)
del matrix
# ---------------------------------------------------------------
# Preprocessing dofs connectivity
# ---------------------------------------------------------------
Print.master(' DOFs connectivity')
# Compute degrees of freedom connectivity
basis_order = run.get('nord')
dofs, dof_edges, dof_faces, _, total_num_dofs = computeConnectivityDOFS(
elemsE, elemsF, basis_order)
# Get matrix dimensions
size = dofs.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(
size[0], size[1], dofs)
# Build path to save the file
out_path = out_dir + '/dofs.dat'
# Write PETGEM edges in PETSc format
writeParallelDenseMatrix(out_path,
matrix,
communicator=PETSc.COMM_SELF)
del matrix
# ---------------------------------------------------------------
# Preprocessing sigma model
# ---------------------------------------------------------------
Print.master(' Conductivity model')
i_model = data_model.get('sigma')
if (run.get('conductivity_from_file')):
# Open sigma file
sigma_file = i_model.get('file')
fileID = h5py.File(sigma_file, 'r')
# Read sigma file
conductivityModel = fileID.get('data')[()]
else:
# Get physical groups
elemsS = mesh.cell_data['gmsh:physical'][0]
elemsS -= np.int(1) # 0-based indexing
# Get horizontal sigma
horizontal_sigma = i_model.get('horizontal')
vertical_sigma = i_model.get('vertical')
# Allocate conductivity array
conductivityModel = np.zeros((nElems, 2), dtype=np.float)
for i in np.arange(nElems):
# Set horizontal sigma
conductivityModel[i,
0] = horizontal_sigma[np.int(elemsS[i])]
# Set vertical sigma
conductivityModel[i, 1] = vertical_sigma[np.int(elemsS[i])]
# Get matrix dimensions
size = conductivityModel.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(
size[0], size[1], conductivityModel)
# Build path to save the file
out_path = out_dir + '/conductivityModel.dat'
# Write PETGEM edges in PETSc format
writeParallelDenseMatrix(out_path,
matrix,
communicator=PETSc.COMM_SELF)
del matrix
# ---------------------------------------------------------------
# Preprocessing boundaries
# ---------------------------------------------------------------
Print.master(' Boundaries')
# Compute boundary faces
bFacesN, bFaces, nbFaces = computeBoundaryFaces(elemsF, facesN)
# Build array with boundary dofs for csem mode (dirichlet BC)
if (mode == 'csem'):
# Compute boundary edges
bEdges = computeBoundaryEdges(edgesNodes, bFacesN)
# Compute dofs on boundaries
_, indx_boundary_dofs = computeBoundaries(
dofs, dof_edges, dof_faces, bEdges, bFaces, basis_order)
# Build PETSc structures
vector = createSequentialVectorWithArray(indx_boundary_dofs)
# Build path to save the file
out_path = out_dir + '/boundaries.dat'
# Write PETGEM nodes in PETSc format
writePetscVector(out_path,
vector,
communicator=PETSc.COMM_SELF)
del vector
elif (mode == 'mt'):
# Compute to what plane the boundary face belongs
planeFace = computeFacePlane(mesh.points, bFaces, bFacesN)
# Compute boundary elements
bElems, numbElems = computeBoundaryElements(
elemsF, bFaces, nFaces)
if (nbFaces != numbElems):
Print.master(
' Number of boundary faces is not consistent.')
exit(-1)
# Allocate
data_boundaries = np.zeros((nbFaces, 53 + num_dof_in_element),
dtype=np.float)
# Fill tmp matrix with data for boundary faces
for i in np.arange(nbFaces):
# Get index of tetrahedral element (boundary element)
iEle = bElems[i]
# Get dofs of element container
dofsElement = dofs[iEle, :]
# Get indexes of nodes for i-boundary element and insert
nodesBoundaryElement = mesh.cells[0][1][iEle, :]
data_boundaries[i, 0:4] = nodesBoundaryElement
# Get nodes coordinates for i-boundary element and insert
coordEle = mesh.points[nodesBoundaryElement, :]
coordEle = coordEle.flatten()
data_boundaries[i, 4:16] = coordEle
# Get indexes of faces for i-boundary element and insert
facesBoundaryElement = elemsF[iEle, :]
data_boundaries[i, 16:20] = facesBoundaryElement
# Get edges indexes for faces in i-boundary element and insert
edgesBoundaryFace = facesE[facesBoundaryElement, :]
edgesBoundaryFace = edgesBoundaryFace.flatten()
data_boundaries[i, 20:32] = edgesBoundaryFace
# Get indexes of edges for i-boundary and insert
edgesBoundaryElement = elemsE[iEle, :]
data_boundaries[i, 32:38] = edgesBoundaryElement
# Get node indexes for edges in i-boundary and insert
edgesNodesBoundaryElement = edgesNodes[
edgesBoundaryElement, :]
edgesNodesBoundaryElement = edgesNodesBoundaryElement.flatten(
)
data_boundaries[i, 38:50] = edgesNodesBoundaryElement
# Get plane face
ifacetype = planeFace[i]
data_boundaries[i, 50] = ifacetype
# Get global face index
localFaceIndex = bFaces[i]
data_boundaries[i, 51] = localFaceIndex
# Get sigma value
sigmaEle = conductivityModel[iEle, 0]
data_boundaries[i, 52] = sigmaEle
# Get dofs for boundary element and insert
dofsBoundaryElement = dofsElement
data_boundaries[i, 53::] = dofsBoundaryElement
# Get matrix dimensions
size = data_boundaries.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(
size[0], size[1], data_boundaries)
# Build path to save the file
out_path = out_dir + '/boundaryElements.dat'
# Write PETGEM receivers in PETSc format
writeParallelDenseMatrix(out_path,
matrix,
communicator=PETSc.COMM_SELF)
del matrix
del data_boundaries
# ---------------------------------------------------------------
# Preprocessing receivers
# ---------------------------------------------------------------
Print.master(' Receivers')
# Open receivers_file
receivers_file = model.get('receivers')
fileID = h5py.File(receivers_file, 'r')
# Read receivers
receivers = fileID.get('data')[()]
# Number of receivers
if receivers.ndim == 1:
nReceivers = 1
else:
dim = receivers.shape
nReceivers = dim[0]
# Find out which tetrahedral element source point is in (only for csem mode)
if (mode == 'csem'):
# Allocate vector to save source data
data_source = np.zeros(50 + num_dof_in_element, dtype=np.float)
i_model = data_model.get('source')
# Get source position
i_source_position = np.asarray(i_model.get('position'),
dtype=np.float)
# Build Delaunay triangulation with nodes
tri = Delaunay(mesh.points)
# Overwrite Delaunay structure with mesh_file connectivity and points
tri.simplices = mesh.cells[0][1][:].astype(np.int32)
tri.vertices = mesh.cells[0][1][:].astype(np.int32)
srcElem = tri.find_simplex(i_source_position,
bruteforce=True,
tol=1.e-12)
# If srcElem=-1, source not located
if srcElem < 0:
Print.master(
' Source no located in the computational domain. Please, verify source position or improve the mesh quality.'
)
exit(-1)
# Build data for source insertion
# Get indexes of nodes for srcElem and insert
nodesSource = mesh.cells[0][1][srcElem, :]
data_source[0:4] = nodesSource
# Get nodes coordinates for srcElem and insert
coordSource = mesh.points[nodesSource, :]
coordSource = coordSource.flatten()
data_source[4:16] = coordSource
# Get indexes of faces for srcElem and insert
facesSource = elemsF[srcElem, :]
data_source[16:20] = facesSource
# Get edges indexes for faces in srcElem and insert
edgesFace = facesE[facesSource, :]
edgesFace = edgesFace.flatten()
data_source[20:32] = edgesFace
# Get indexes of edges for srcElem and insert
edgesSource = elemsE[srcElem, :]
data_source[32:38] = edgesSource
# Get node indexes for edges in srcElem and insert
edgesNodesSource = edgesNodes[edgesSource, :]
edgesNodesSource = edgesNodesSource.flatten()
data_source[38:50] = edgesNodesSource
# Get dofs for srcElem and insert
dofsSource = dofs[srcElem, :]
data_source[50::] = dofsSource
# Get matrix dimensions
size = data_source.shape
# Build PETSc structures
vector = createSequentialVectorWithArray(data_source)
# Build path to save the file
out_path = out_dir + '/source.dat'
# Write PETGEM nodes in PETSc format
writePetscVector(out_path,
vector,
communicator=PETSc.COMM_SELF)
del vector
# ---------------------------------------------------------------
# Sparsity pattern
# ---------------------------------------------------------------
# Setup valence for each basis order (adding a small percentage to keep safe)
valence = np.array([50, 200, 400, 800, 1400, 2500])
# Build nnz pattern for each row
nnz = np.full((total_num_dofs),
valence[basis_order - 1],
dtype=np.int)
# Build PETSc structures
vector = createSequentialVectorWithArray(nnz)
# Build path to save the file
out_path = out_dir + '/nnz.dat'
# Write PETGEM nodes in PETSc format
writePetscVector(out_path, vector, communicator=PETSc.COMM_SELF)
# ---------------------------------------------------------------
# Print mesh statistics
# ---------------------------------------------------------------
Print.master(' ')
Print.master(' Mesh statistics')
Print.master(' Mesh file: {0:12}'.format(
str(model.get('mesh'))))
Print.master(' Number of elements: {0:12}'.format(
str(nElems)))
Print.master(' Number of faces: {0:12}'.format(
str(nFaces)))
Print.master(' Number of edges: {0:12}'.format(
str(nEdges)))
Print.master(' Number of dofs: {0:12}'.format(
str(total_num_dofs)))
if (mode == 'csem'):
Print.master(' Number of boundaries: {0:12}'.format(
str(len(indx_boundary_dofs))))
# ---------------------------------------------------------------
# Print data model
# ---------------------------------------------------------------
Print.master(' ')
Print.master(' Model data')
Print.master(' Modeling mode: {0:12}'.format(str(mode)))
i_sigma = data_model.get('sigma')
if (run.get('conductivity_from_file')):
Print.master(' Conductivity file: {0:12}'.format(
i_sigma.get('file')))
else:
Print.master(' Horizontal conductivity: {0:12}'.format(
str(i_sigma.get('horizontal'))))
Print.master(' Vertical conductivity: {0:12}'.format(
str(i_sigma.get('vertical'))))
if (mode == 'csem'):
i_source = data_model.get('source')
Print.master(' Source:')
Print.master(' - Frequency (Hz): {0:12}'.format(
str(i_source.get('frequency'))))
Print.master(' - Position (xyz): {0:12}'.format(
str(i_source.get('position'))))
Print.master(' - Azimuth: {0:12}'.format(
str(i_source.get('azimuth'))))
Print.master(' - Dip: {0:12}'.format(
str(i_source.get('dip'))))
Print.master(' - Current: {0:12}'.format(
str(i_source.get('current'))))
Print.master(' - Length: {0:12}'.format(
str(i_source.get('length'))))
else:
Print.master(' Frequency (Hz): {0:12}'.format(
str(data_model.get('frequency'))))
Print.master(' Polarization: {0:12}'.format(
str(data_model.get('polarization'))))
Print.master(' Vector basis order: {0:12}'.format(
str(basis_order)))
Print.master(' Receivers file: {0:12}'.format(
str(model.get('receivers'))))
Print.master(' Number of receivers: {0:12}'.format(
str(nReceivers)))
Print.master(' VTK output: {0:12}'.format(
str(output.get('vtk'))))
Print.master(' Cuda support: {0:12}'.format(
str(run.get('cuda'))))
Print.master(' Output directory: {0:12}'.format(
str(output.get('directory'))))
Print.master(' Scratch directory: {0:12}'.format(
str(output.get('directory_scratch'))))
# Stop timer
Timers()["Preprocessing"].stop()
# Apply barrier for MPI tasks alignement
parEnv.comm.barrier()
return
def create_alpha_mask(points,
distance_limit,
resolution_x=1000,
resolution_y=1000,
visualization=True):
"""
Creates interpolation grid, then masks over the alpha shape spanned up by points and defined by distance_limit.
@params:
points - Required : points spanning up alpha shape
distance_limit - Required : distance threshold for removing Delaunay simplices
resolution_x - Optional : resolution for grid in x, default is 1000
resolution_y - Optional : resolution for grid in y, default is 1000
visualization - Optional : boolean for visualizing result, default is False
Returns:
grid_mask : An array containing 1 for cells inside, and 0 for cells outside
"""
import numpy as np
from scipy.spatial import Delaunay
from matplotlib.collections import LineCollection
import matplotlib.path as mplPath
#----------------------------------------------------------------------
# Create Grid
#----------------------------------------------------------------------
# Create meshgrid
xi = np.transpose(
np.linspace(min(points[:, 0]), max(points[:, 0]), resolution_x))
yi = np.transpose(
np.linspace(min(points[:, 1]), max(points[:, 1]), resolution_y))
X, Y = np.meshgrid(xi, yi)
# Reshape into vector
gridpoints_x = np.reshape(X, resolution_x * resolution_y)
gridpoints_y = np.reshape(Y, resolution_x * resolution_y)
# Combine into gridpoints array
gridpoints = np.transpose(np.asarray((gridpoints_x, gridpoints_y)))
#----------------------------------------------------------------------
# Create Alpha Shape
#----------------------------------------------------------------------
# Start Delaunay triangulation
tri = Delaunay(points)
# Auxiliary function for plotting, if required
if visualization == True:
import matplotlib.pyplot as plt
edges = set()
edge_points = []
def add_edge(i, j):
"""Add a line between the i-th and j-th points, if not in the list already"""
if (i, j) in edges or (j, i) in edges:
# already added
return
edges.add((i, j))
edge_points.append(points[[i, j]])
# Remove simplices outside of distance_limit
simplex_flag = np.zeros(len(tri.simplices[:, 0])) # Flags bad simplices
counter = 0
for ia, ib, ic in tri.vertices:
# ia, ib, ic = indices of corner points of the triangle
if np.sqrt((points[ia,0]-points[ib,0])**2+(points[ia,1]-points[ib,1])**2) < distance_limit and \
np.sqrt((points[ia,0]-points[ic,0])**2+(points[ia,1]-points[ic,1])**2) < distance_limit and \
np.sqrt((points[ib,0]-points[ic,0])**2+(points[ib,1]-points[ic,1])**2) < distance_limit:
# do nothing
simplex_flag[counter] = 0
else:
# simplex has at least one side larger than threshold, flag it
simplex_flag[counter] = 1
counter += 1
tri.simplices = tri.simplices[simplex_flag == 0, :] # Remove bad simplices
tri.vertices = tri.vertices[simplex_flag == 0, :] # Remove bad simplices
# Visualize, if requested
if visualization == True:
# Mark all remaining simplices
for ia, ib, ic in tri.vertices:
add_edge(ia, ib)
add_edge(ib, ic)
add_edge(ic, ia)
# Draw them
lines = LineCollection(edge_points)
plt.figure()
plt.gca().add_collection(lines)
plt.plot(points[:, 0], points[:, 1], 'o')
#----------------------------------------------------------------------
# Mask over Alpha Shape
#----------------------------------------------------------------------
# Prepare point flag
flag_gridpoints = np.zeros(len(gridpoints[:, 0]), dtype=np.int)
# Evaluate gridpoints
for sim in range(len(tri.simplices[:, 0])):
# Print progress bar
cv = sim
mv = len(tri.simplices[:, 0]) - 1
print('\r%s |%s| %s%% %s' %
('Masking: ', '\033[33m' + '█' * int(50 * cv // mv) + '-' *
(50 - int(50 * cv // mv)) + '\033[0m',
("{0:." + str(1) + "f}").format(100 *
(cv / float(mv))), ' Complete'),
end='\r')
# Create simplex path
bbPath = mplPath.Path(
np.array([
points[tri.simplices[sim, 0], :], points[tri.simplices[sim,
1], :],
points[tri.simplices[sim, 2], :], points[tri.simplices[sim,
0], :]
]))
# Flag points that are inside this simplex
for gridpts in range(len(gridpoints[:, 0])):
if flag_gridpoints[
gridpts] == 0: # only process points not already allocated
if bbPath.contains_point(
(gridpoints[gridpts, 0], gridpoints[gridpts, 1])) == True:
flag_gridpoints[gridpts] = 1
# Plot, if required
if visualization == True:
plt.scatter(gridpoints[flag_gridpoints == 1, 0],
gridpoints[flag_gridpoints == 1, 1],
color='g')
plt.scatter(gridpoints[flag_gridpoints == 0, 0],
gridpoints[flag_gridpoints == 0, 1],
color='r')
# Reshape flag_gridpoints into a 2D array
global grid_mask
grid_mask = np.reshape(flag_gridpoints, (resolution_y, resolution_x))
# Return result
return grid_mask
def morph_face(src_face, src_pts, tgt_pts, tgt_width, tgt_height):
src_y, src_x, _ = src_face.shape
if not src_x == tgt_width and not src_y == tgt_height:
adjusted_face = cv2.resize(src_face, (tgt_width, tgt_height), interpolation = cv2.INTER_NEAREST)
adjusted_pts = np.copy(src_pts)
adjusted_pts[:, 0] = adjusted_pts[:, 0] * float(tgt_width) / float(src_x)
adjusted_pts[:, 1] = adjusted_pts[:, 1] * float(tgt_height) / float(src_y)
adjusted_pts = np.rint(adjusted_pts).astype(dtype=int)
else:
adjusted_face = np.copy(src_face)
adjusted_pts = np.copy(src_pts)
s_pts = np.append(adjusted_pts, [[0, 0], [tgt_width - 1, 0], [tgt_width - 1, tgt_height - 1], [0, tgt_height - 1]], axis=0)
t_pts = np.append(tgt_pts, [[0, 0], [tgt_width - 1, 0], [tgt_width - 1, tgt_height - 1], [0, tgt_height - 1]], axis=0)
avg_shape = (s_pts + t_pts) / 2.0
tri = Delaunay(avg_shape)
src_tri = Delaunay(s_pts)
src_tri.simplices = tri.simplices.copy()
tgt_tri = Delaunay(t_pts)
tgt_tri.simplices = tri.simplices.copy()
morphed_face = np.empty(shape=(tgt_height, tgt_width, 3))
src_mat = []
for t in tri.simplices:
p1 = src_tri.points[t[0]]
p2 = src_tri.points[t[1]]
p3 = src_tri.points[t[2]]
A = np.matrix([[p1[0], p2[0], p3[0]], [p1[1], p2[1], p3[1]], [1, 1, 1]])
src_mat.append(A)
tri_mat = []
for t in tri.simplices:
p1 = tgt_tri.points[t[0]]
p2 = tgt_tri.points[t[1]]
p3 = tgt_tri.points[t[2]]
A = np.matrix([[p1[0], p2[0], p3[0]], [p1[1], p2[1], p3[1]], [1, 1, 1]])
tri_mat.append((A, A.I))
y = np.arange(0, tgt_height)
x = np.arange(0, tgt_width)
points = np.array(list(itertools.product(x, y)))
one_column = np.ones(points.shape[0])[np.newaxis].T
points_homo = np.transpose(np.hstack((points, one_column)), axes=(1, 0))
inTri = Delaunay.find_simplex(tgt_tri, points, bruteforce=True)
count = 0
for t in tri.simplices:
indices = np.where(inTri == count)[0]
tri_bary = np.dot(tri_mat[count][1], np.take(points_homo, indices=indices, axis=1))
src_pixels = np.array(np.rint(np.dot(src_mat[count], tri_bary)[0:2,:]).astype(dtype=int).T)
tgt_pixels = np.take(points, indices=indices, axis=0)
morphed_face[tgt_pixels[:, 1], tgt_pixels[:, 0]] = adjusted_face[src_pixels[:, 1], src_pixels[:, 0]]
count = count + 1
# plt.imshow(morphed_face)
# plt.show()
# misc.imsave("morphed_face.png", morphed_face)
return morphed_face
# morph_face(np.asarray(Image.open("./Faces/Marq.png")), np.asarray(Image.open("./Faces/Marq.png")), np.loadtxt("./Faces/Marq.csv"), np.loadtxt("./Faces/Smile.csv"), 1000, 667)
def fieldInterpolator(solution_vector, nodes, elemsN, elemsE, edgesN, elemsF,
facesE, dof_connectivity, points, inputSetup):
"""Interpolate electromagnetic field for a set of 3D points.
:param ndarray-petsc solution_vector: vector field to be interpolated
:param ndarray nodes: nodal coordinates
:param ndarray elemsN: elements-node connectivity with dimensions = (number_elements, 4)
:param ndarray elemsE: elements-edge connectivity with dimensions = (number_elements, 6)
:param ndarray edgesN: edge-node connectivity with dimensions = (number_edges, 2)
:param ndarray elemsF: element-faces connectivity with dimensions = (number_elements, 4)
:param ndarray facesE: face-edges connectivity with dimensions = (number_faces, 3)
:param ndarray dof_connectivity: local/global dofs list for elements, dofs index on edges, dofs index on faces, dofs index on volumes, total number of dofs
:param ndarray points: point coordinates
:param obj inputSetup: inputSetup object.
:return: electromagnetic fields for a set of 3D points
:rtype: ndarray and int
"""
# ---------------------------------------------------------------
# Initialization
# ---------------------------------------------------------------
# Parameters shortcut (for code legibility)
model = inputSetup.model
run = inputSetup.run
basis_order = run.get('nord')
if (model.get('mode') == 'csem'):
mode = 'csem'
data_model = model.get(mode) # Get data model
frequency = data_model.get('source').get('frequency')
elif (model.get('mode') == 'mt'):
mode = 'mt'
data_model = model.get(mode) # Get data model
frequency = data_model.get('frequency')
omega = frequency * 2. * np.pi
mu = 4. * np.pi * 1e-7
Const = np.sqrt(-1. + 0.j) * omega * mu
# Number of elements
size = elemsN.shape
nElems = size[0]
# Number of nodes
#size = nodes.shape
#nNodes = size[0]
# Num dof per element
num_dof_in_element = np.int(basis_order * (basis_order + 2) *
(basis_order + 3) / 2)
# Number of points
if points.ndim == 1:
nPoints = 1
else:
dim = points.shape
nPoints = dim[0]
# Find where receivers are located
tri = Delaunay(nodes)
# Overwrite Delaunay structure with mesh_file connectivity and points
tri.simplices = elemsN.astype(np.int32)
tri.vertices = elemsN.astype(np.int32)
# Find out which tetrahedral element points are in
points_in_elements = tri.find_simplex(points, bruteforce=True, tol=1.e-12)
# Determine if all points were found
idx = np.where(
np.logical_or(points_in_elements > nElems, points_in_elements < 0))[0]
# If idx is not empty, there are points outside the domain
if idx.size != 0:
Print.master(
' The following receivers were not located and will not be taken into account '
+ str(idx))
# Update number of receivers
nPoints = nPoints - len(idx)
if nPoints == 0:
Print.master(
' No point has been found. Nothing to do. Aborting')
exit(-1)
# Remove idx from points matrix
points = np.delete(points, idx, axis=0)
# Remove idx from points_in_elements
points_in_elements = np.delete(points_in_elements, idx, axis=0)
indx_ele = points_in_elements
# Allocate array
fields = np.zeros((nPoints, 6), dtype=np.complex)
# Interpolate electromagnetic field for all points
for i in np.arange(nPoints):
# Get element index
iEle = indx_ele[i]
# Get dofs of element container
dofsEle = dof_connectivity[iEle, :]
# Get receiver coordinates
coordPoints = points[i, :]
# Get indexes of nodes for iEle
nodesEle = elemsN[iEle, :]
# Get nodes coordinates for iEle
coordEle = nodes[nodesEle, :]
# Get indexes of faces for iEle
facesEle = elemsF[iEle, :]
# Get edges indexes for faces
edgesFace = facesE[facesEle, :]
# Get indexes of edges for iEle
edgesEle = elemsE[iEle, :]
# Get node indexes for edges in i and insert
edgesNodesEle = edgesN[edgesEle, :]
# Compute jacobian for iEle
jacobian, invjacobian = computeJacobian(coordEle)
# Compute global orientation for iEle
edge_orientation, face_orientation = computeElementOrientation(
edgesEle, nodesEle, edgesNodesEle, edgesFace)
# Transform xyz source position to XiEtaZeta coordinates (reference tetrahedral element)
XiEtaZeta = tetrahedronXYZToXiEtaZeta(coordEle, coordPoints)
# Compute basis for i
basis, curl_basis = computeBasisFunctions(edge_orientation,
face_orientation, jacobian,
invjacobian, basis_order,
XiEtaZeta)
# Get global dofs from x vector
realField = np.real(
solution_vector.getValues(dofsEle.astype(PETSc.IntType)))
imagField = np.imag(
solution_vector.getValues(dofsEle.astype(PETSc.IntType)))
for j in np.arange(num_dof_in_element):
# Exyz[k] = Exyz[k] + real_part*basis + imag_part*basis
fields[i, 0] += realField[j] * basis[0, j] + np.sqrt(
-1. + 0.j) * imagField[j] * basis[0, j]
fields[i, 1] += realField[j] * basis[1, j] + np.sqrt(
-1. + 0.j) * imagField[j] * basis[1, j]
fields[i, 2] += realField[j] * basis[2, j] + np.sqrt(
-1. + 0.j) * imagField[j] * basis[2, j]
# Hxyz[k] = Hxyz[k] + real_part*curl_basis + imag_part*curl_basis
fields[i, 3] += realField[j] * curl_basis[0, j] + np.sqrt(
-1. + 0.j) * imagField[j] * curl_basis[0, j]
fields[i, 4] += realField[j] * curl_basis[1, j] + np.sqrt(
-1. + 0.j) * imagField[j] * curl_basis[1, j]
fields[i, 5] += realField[j] * curl_basis[2, j] + np.sqrt(
-1. + 0.j) * imagField[j] * curl_basis[2, j]
# Following Maxwell equations, apply constant factor to compute magnetic field
fields[:, 3::] /= Const
return fields