def get_stuff_for_the_local_version(cpa_space):
if cpa_space.tess not in ['I','II']:
raise ValueError(cpa_space.tess)
# compute_maps = cpa_space.dim_domain > 1 or cpa_space.tess == 'I'
compute_maps = cpa_space.dim_domain==1 or cpa_space.tess == 'I'
if not compute_maps:
return None
nC = cpa_space.nC
nHomoCoo = cpa_space.nHomoCoo
lengthAvee = cpa_space.lengthAvee
dim_domain = cpa_space.dim_domain
dim_range = cpa_space.dim_range
b = Bunch()
cells_verts_homo_coo = cpa_space.tessellation.cells_verts_homo_coo
if compute_maps:
X = np.zeros((nC,lengthAvee,lengthAvee))
Xinv = np.zeros_like(X)
if dim_domain == 1:
for (x,xinv,(vrt0,vrt1)) in zip(X,Xinv,cells_verts_homo_coo):
x[0,:2]=vrt0
x[1,:2]=vrt1
xinv[:]=inv(x)
elif dim_domain == 2:
for (x,xinv,(vrt0,vrt1,vrt2)) in zip(X,Xinv,cells_verts_homo_coo):
x[0,:3]=x[1,3:]=vrt0
x[2,:3]=x[3,3:]=vrt1
x[4,:3]=x[5,3:]=vrt2
xinv[:]=inv(x)
elif dim_domain == 3:
for (x,xinv,(vrt0,vrt1,vrt2,vrt3)) in zip(X,Xinv,cells_verts_homo_coo):
x[0,:4]=x[1,4:8]=x[2,8:]=vrt0
x[3,:4]=x[4,4:8]=x[5,8:]=vrt1
x[6,:4]=x[7,4:8]=x[8,8:]=vrt2
x[9,:4]=x[10,4:8]=x[11,8:]=vrt3
xinv[:]=inv(x)
else:
raise NotImplementedError(dim_domain)
vert_tess = []
vert_tess_one_cell = []
ind_into_vert_tess = np.zeros((nC,nHomoCoo),np.int)
for c,cell_verts in enumerate(cells_verts_homo_coo):
for j,v in enumerate(cell_verts):
t = tuple(v.tolist())
if t not in vert_tess:
vert_tess.append(t)
# c is the cell index
# j is the index of this vertex within that cell
vert_tess_one_cell.append((c,j))
ind_into_vert_tess[c,j]=vert_tess.index(t)
vert_tess = np.asarray(vert_tess)
vert_tess_one_cell = np.asarray(vert_tess_one_cell)
b.vert_tess = vert_tess
b.ind_into_vert_tess = ind_into_vert_tess
b.Xinv = Xinv
b.X = X
"""
Build a sparse matrix H such that
Avees = H times velTess
The values of H, which is sparse, are dictated by vertTess.
H.shape = (lengthAvee*nC,len(vert_tess)*dim_range)
"""
H = np.zeros((lengthAvee*nC,len(vert_tess)*dim_range))
for c in range(nC):
ind = ind_into_vert_tess[c]
ind_all_coo = np.zeros((len(ind),dim_range),np.int)
for coo in range(dim_range):
ind_all_coo[:,coo]=ind*dim_range+coo
H[c*lengthAvee:(c+1)*lengthAvee,ind_all_coo.ravel()]=Xinv[c]
#
"""
Build a sparse matrix H such that
velTess = G times Avees
G.shape = (len(vert_tess)*dim_range,lengthAvee*nC)
"""
G = np.zeros((len(vert_tess)*dim_range,lengthAvee*nC))
for i in range(vert_tess.shape[0]):
# c is the cell index
# j is the index of this vertex within this cell
c,j = vert_tess_one_cell[i]
for coo in range(dim_range):
G[i*dim_range+coo,lengthAvee*c:lengthAvee*(c+1)]=X[c][j*dim_range+coo]
# ipshell('hi')
H = lil_matrix(H)
G = lil_matrix(G)
b._mat_velTess2Avees = H
b._mat_Avees2velTess = G
#
if 1:
def mv1(v):
return H.dot(v)
def mv2(v):
return G.dot(v)
def rmv1(v):
return H.T.dot(v)
def rmv2(v):
return G.T.dot(v)
def mm1(V):
return H.dot(V)
def mm2(V):
return G.dot(V)
_H = ssl.LinearOperator(H.shape,matvec=mv1,
rmatvec=rmv1,
matmat=mm1)
_G = ssl.LinearOperator(lil_matrix(G).shape,matvec=mv2,
rmatvec=rmv2,
matmat=mm2)
b.linop_velTess2Avees = _H
b.linop_Avees2velTess = _G
return b
