def calc_grad_theta(self, xmins, xmaxs, As_vectorized, BasMats, pts0, dt,
nTimeSteps, nStepsOdeSolver, pts_at_T, grad_per_point,
dim_domain, dim_range, nCs, incs):
if dim_domain != dim_range:
raise ValueError
if pts_at_T is None:
raise ValueError
if len(incs) != dim_domain:
raise ValueError(len(incs), dim_domain)
if As_vectorized.ndim != 2:
raise ValueError(As_vectorized.shape)
if As_vectorized.shape[1] != (dim_domain + 1) * dim_domain:
raise ValueError(As_vectorized.shape,
(dim_domain + 1) * dim_domain)
nPts = pts0.shape[0]
if not isinstance(pts0, CpuGpuArray):
raise TypeError
if not isinstance(pts_at_T, CpuGpuArray):
raise TypeError
# number of threads per block has to be >= than number of cells
# if self.nCells <= 128:
# threadsPerBlock = 128
if self.nCells <= 256:
threadsPerBlock = 256
# threadsPerBlock = 256/4
elif 256 < self.nCells <= 512:
threadsPerBlock = 512
elif 512 < self.nCells <= 625:
threadsPerBlock = 625
elif 512 < self.nCells <= 1024:
threadsPerBlock = 1024
else:
raise NotImplementedError
nBlocks = int(np.ceil(float(nPts) / float(threadsPerBlock)))
if 0:
print '(nPts', nPts
print 'nBlocks', nBlocks
print 'threadsPerBlock = ', threadsPerBlock
print
d = len(BasMats)
if not isinstance(grad_per_point, CpuGpuArray):
raise TypeError
if grad_per_point.shape != (nPts, dim_range, d):
raise ValueError(grad_per_point.shape)
if 1:
nC0, nC1, nC2, inc_x, inc_y, inc_z = self.parse_nCs_and_incs(
dim_domain, incs, nCs)
if dim_domain == dim_range:
calc_gpu = self.calc_grad_theta_gpu
else:
raise NotImplementedError
if 0:
ipshell('hi')
1 / 0
calc_gpu(pts0.gpu,
pts_at_T.gpu,
drv.In(As_vectorized),
BasMats.gpu,
grad_per_point.gpu,
np.int32(d),
self.my_dtype(dt),
np.int32(nTimeSteps),
np.int32(nStepsOdeSolver),
np.int32(nPts),
np.int32(nC0),
np.int32(nC1),
np.int32(nC2),
np.float64(inc_x),
np.float64(inc_y),
np.float64(inc_z),
grid=(nBlocks, 1, 1),
block=(threadsPerBlock, 1, 1))
return grad_per_point
def calc_ll(self, theta):
"""
Computes the ll per measurments.
"""
cpa_space = self.cpa_space
src = self.src
signal = self.signal
params_flow_int = self.params_flow_int
transformed = self.transformed
sigma_signal = self.sigma_signal
ll = self.ll
if src.shape[1] != cpa_space.dim_domain:
raise ValueError(src.shape)
cpa_space.theta2Avees(theta)
cpa_space.update_pat()
cpa_space.calc_T_inv(pts=src, out=transformed, **params_flow_int)
if transformed.shape != src.shape:
raise ValueError(transformed.shape, src.shape)
if 0:
# I think this is irrelevant here.
# (it was relevant for the 1d case)
scale_pts = src.shape[0] # Assuming we normalized src
# to [0,1],
# we need to scale it
# t0 [0,1,..,num_of_samples+1]
transformed.gpu *= scale_pts
if self.interp_type_for_ll == 'gpu_linear':
resampler(pts_gpu=transformed.gpu,
img_gpu=signal.src.gpu,
img_wrapped_gpu=signal.transformed.gpu)
else:
remap_fwd_opencv(pts_inv=transformed,
img=signal.src,
img_wrapped_fwd=signal.transformed,
interp_method=self.interp_type_for_ll)
# if signal.dst.shape[1]>1:
# raise NotImplementedError("Only 1D signals for now")
# plt.figure(17);
# signal.transformed.gpu2cpu()
# if not signal.transformed.cpu.any():
# raise ValueError('wtf')
# plt.subplot(221)
# plt.imshow(signal.src.cpu.reshape(256,-1))
# plt.subplot(222)
# plt.imshow(signal.transformed.cpu.reshape(256,-1))
#
# ipshell('hi')
# 2/0
calc_signal_err_per_sample(signal.transformed.gpu, signal.dst.gpu,
self.signal.err.gpu)
# print np.allclose(signal.transformed.gpu.get()-
# signal.dst.gpu.get(),
# self.signal.err.gpu.get())
# if self.dim_signal != 1:
# raise NotImplementedError
calc_ll_per_sample(ll=ll.gpu,
err=self.signal.err.gpu,
sigma=sigma_signal)
if 0:
res = -0.5 / (sigma_signal**2) * (
(signal.transformed.gpu - signal.dst.gpu)**2).get()
np.allclose(res.ravel(), ll.gpu.get())
ipshell('stop')
1 / 0
# 1/0
# ipshell('stop');
# if any(theta):
# 1/0
def create_cont_constraint_mat_separable(H, v1s, v2s, nSides, nConstraints, nC,
dim_domain, dim_range, tess):
"""
L is the matrix that encodes the constraints of the consistent subspace.
Its null space space is the sought-after consistent subspace
(unless additional constraints are added; e.g., sub-algerba or bdry
conditions).
"""
if dim_domain != 2:
raise ValueError
if dim_range not in [1, 2]:
raise ValueError
nHomoCoo = dim_domain + 1
length_Avee = dim_range * nHomoCoo
L1 = np.zeros((nConstraints / 2, nC * nHomoCoo))
nPtsInSide = 2 # Since, in 2D, the side is always a line joining 2 pts.
# if nSides != nConstraints/(nPtsInSide*dim_domain):
# raise ValueError(nSides,nConstraints)
if nSides != nConstraints / (nPtsInSide * dim_range):
print " print nSides , nConstraints/(nPtsInSide*dim_range):"
print nSides, nConstraints / (nPtsInSide * dim_range)
ipshell('stop')
raise ValueError(nSides, (nConstraints, nPtsInSide, dim_range))
if nSides != H.shape[0]:
raise ValueError(nSides, H.shape)
# M = nPtsInSide*dim_range
M = nPtsInSide
if dim_range == 1:
raise NotImplementedError
for i in range(nSides):
v1 = v1s[i]
v2 = v2s[i]
h = H[i]
a, b = h.nonzero()[0] # idx for the relevant As
# s stands for start
# e stands for end
s1 = a * length_Avee
e1 = s1 + nHomoCoo
s2 = b * length_Avee
e2 = s2 + nHomoCoo
# Constraint 1:
L[i * M, s1:e1] = v1
L[i * M, s2:e2] = -v1
# Constraint 2:
L[i * M + 1, s1:e1] = v2
L[i * M + 1, s2:e2] = -v2
elif dim_range == 2:
for i in range(nSides):
v1 = v1s[i]
v2 = v2s[i]
if np.allclose(v1, v2):
raise ValueError(v1, v2)
h = H[i]
a, b = h.nonzero()[0] # idx for the relevant As
# L1 is acting on columns of the following form:
# [ a_1 b_1 c_1 d_1 a_2 b_2 c_2 d_2 ... a_Nc b_Nc c_Nc d_Nc]
# s stands for start
# e stands for end
s1 = a * nHomoCoo
e1 = s1 + nHomoCoo
s2 = b * nHomoCoo
e2 = s2 + nHomoCoo
try:
# Constraint 1:
row = np.zeros(L1.shape[1])
row[s1:e1] = v1
row[s2:e2] = -v1
# x component
L1[i * M] = row
except:
ipshell('fail')
raise
# Constraint 2:
row = np.zeros(L1.shape[1])
row[s1:e1] = v2
row[s2:e2] = -v2
# x component
L1[i * M + 1] = row
else:
raise ValueError(dim_range)
return L1
def __init__(self,cpa_space,scale_spatial=1.0/10,scale_value=0.001*1,
left_blk_rel_scale=None,
right_vec_scale=None):
# scale_spatial=0.0
if cpa_space.only_local:
raise NotImplementedError('only_local=', cpa_space.only_local)
self.scale_spatial = scale_spatial
self.scale_value = scale_value
if left_blk_rel_scale is None:
raise ValueError("You need to pass this argument. 0.5 may be a good value")
if right_vec_scale is None:
raise ValueError("You need to pass this argument. 0.5 may be a good value")
self.left_blk_rel_scale = left_blk_rel_scale
self.right_vec_scale = right_vec_scale
# Covariance on the joint Lie algebra
self.pa_cov = create_joint_algebra_cov(cpa_space,
scale_spatial=scale_spatial,
scale_value=scale_value,
# scale_value=1.0, %FOR DEBUGGING
left_blk_rel_scale=left_blk_rel_scale,
right_vec_scale=right_vec_scale)
# Covariance on the subspace of that Lie algebra
self.cpa_cov = self.pa_cov_to_cpa_cov(cpa_space,self.pa_cov)
#
# self.cpa_cov_debug = self.pa_cov_to_cpa_cov(cpa_space,self.pa_cov*(10**2))
#
# C=self.cpa_cov
# D=self.cpa_cov_debug
# ipshell('hi')
# 1/0
# computing inverse
if 0:
try:
self.pa_cov_inv = inv(self.pa_cov)
# ipshell("STOP")
except:
ipshell("Failed to invert")
raise
else:
pass
self.cpa_cov_inv = inv(self.cpa_cov)
# if cpa_space.dim_domain==2:
# if cpa_space.tess=='tri':
# nV = len(cpa_space.local_stuff['vert_tess'])
# if nV*2 != cpa_space.d:
# raise ValueError( nV , cpa_space.d)
#
if cpa_space.local_stuff:
A2v = cpa_space.local_stuff.linop_Avees2velTess
B = cpa_space.B
# H = A2v.matmat(B.dot(B.T))
H = A2v.matmat(B).dot(B.T)
# self.velTess_cpa_cov = H.dot(self.pa_cov).dot(H.T)
# self.velTess_cpa_cov_inv = inv(self.velTess_cpa_cov)
self.velTess_cov_byB = H.dot(self.pa_cov).dot(H.T)
try:
self.velTess_cov_byB_inv = inv(self.velTess_cov_byB)
except:
# self.velTess_cov_byB=None
self.velTess_cov_byB_inv=None
if 0:
self.velTess_cov = create_cov_velTess(cpa_space=cpa_space,
scale_spatial=scale_spatial,
scale_value = scale_value)
self.velTess_cov_inv = inv( self.velTess_cov)
def create_verts_and_H_type_II(self,dim_range):
"""
This assummes 3D
H encodes the n'bors info.
"""
if self.type != 'II':
raise ValueError(self.type)
dim_domain=self.dim_domain
nC = self.nC
cells_multiidx=self.cells_multiidx
cells_verts=self.cells_verts_homo_coo
# nCx=self.nCx
# nCy=self.nCy
# nCz=self.nCz
if dim_domain !=3:
raise ValueError(dim_domain)
if dim_range != dim_domain:
raise NotImplementedError(dim_range)
# if dim_range not in (1,dim_domain):
# raise NotImplementedError(dim_range)
nbrs = np.zeros((nC,nC))
mi=cells_multiidx # shorter name
for i in range(nC):
for j in range(nC):
if mi[i] == mi[j]:
continue
else:
# pair = (np.abs(mi[i][0]-mi[j][0]),
# np.abs(mi[i][1]-mi[j][1]))
# if set(pair) == set([0,1]):
# nbrs[i,j]=1
triplet = (np.abs(mi[i][0]-mi[j][0]),
np.abs(mi[i][1]-mi[j][1]),
np.abs(mi[i][2]-mi[j][2]))
triplet=np.asarray(triplet)
if (triplet==0).sum()==2 and (triplet==1).sum()==1:
nbrs[i,j]=1
nSides=nbrs.sum().astype(np.int)/2
# H is larger than we need
# but it was easier to code this way.
# Later we eliminate the unused rows.
H = np.zeros((nC**2,nC))
# H = sparse.lil_matrix((nC**2,nC))
for i in range(nC):
for j in range(nC):
# k is the index of the row in H.
# Most rows won't be used.
k = i*nC + j
if i < j:
continue
nbr = nbrs[i,j]
if nbr:
H[k,i]=-1
H[k,j]=+1
verts1 = []
verts2 = []
verts3 = []
verts4 = []
counter = 0
for h in H:
if h.any():
# if h.nnz:
# Very annoying: I think there is a bug in the sparse matrix object.
# Even after 'todense' it is impossible to flatten it properly.
# h = np.asarray(h.todense().tolist()[0]) # Workaround.
counter+=4
# Find the vertex pair
i = (h==1).nonzero()[0][0]
j = (h==-1).nonzero()[0][0]
# a = mi[i]
# b = mi[j]
vi = cells_verts[i]
vj = cells_verts[j]
vi = self.make_it_hashable(vi)
vj = self.make_it_hashable(vj)
side = set(vi).intersection(vj)
if len(side) != 4: # adjcant boxes share 4 verts
ipshell('oops')
raise ValueError(len(side),side)
try:
v1,v2,v3,v4 = np.asarray(list(side))
except:
ipshell('hi')
raise
verts1.append(v1)
verts2.append(v2)
verts3.append(v3)
verts4.append(v4)
# if a != (1,1):
# continue
# print a, ' is a nbr of ',b
if counter != nSides*4:
raise ValueError(counter,nEdges)
# Every side conntect 4 vertices.
# At every vertex, all components of the velocity must agree.
# nConstraints = nSides*4*dim_domain
nConstraints = nSides*4*dim_range
verts1 = np.asarray(verts1)
verts2 = np.asarray(verts2)
verts3 = np.asarray(verts3)
verts4 = np.asarray(verts4)
H = np.asarray([h for h in H if h.any()])
# H = np.asarray([h for h in H if h.nnz])
#
# ipshell('hi')
# 1/0
return verts1,verts2,verts3,verts4,H,nSides,nConstraints
def calc_ll(self, theta):
"""
Computes the ll per measurments.
"""
cpa_space = self.cpa_space
src = self.src
signal = self.signal
params_flow_int = self.params_flow_int
transformed = self.transformed
sigma_signal = self.sigma_signal
ll = self.ll
if src.shape[1] != cpa_space.dim_domain:
raise ValueError(src.shape)
cpa_space.theta2Avees(theta)
cpa_space.update_pat()
cpa_space.calc_T_inv(pts=src, out=transformed, **params_flow_int)
if transformed.shape != src.shape:
raise ValueError(transformed.shape, src.shape)
if 0:
# I think this is irrelevant here.
# (it was relevant for the 1d case)
scale_pts = src.shape[0] # Assuming we normalized src
# to [0,1],
# we need to scale it
# t0 [0,1,..,num_of_samples+1]
transformed.gpu *= scale_pts
if self.interp_type_for_ll == "gpu_linear":
resampler(pts_gpu=transformed.gpu, img_gpu=signal.src.gpu, img_wrapped_gpu=signal.transformed.gpu)
else:
remap_fwd_opencv(
pts_inv=transformed,
img=signal.src,
img_wrapped_fwd=signal.transformed,
interp_method=self.interp_type_for_ll,
)
# if signal.dst.shape[1]>1:
# raise NotImplementedError("Only 1D signals for now")
# plt.figure(17);
# signal.transformed.gpu2cpu()
# if not signal.transformed.cpu.any():
# raise ValueError('wtf')
# plt.subplot(221)
# plt.imshow(signal.src.cpu.reshape(256,-1))
# plt.subplot(222)
# plt.imshow(signal.transformed.cpu.reshape(256,-1))
#
# ipshell('hi')
# 2/0
calc_signal_err_per_sample(signal.transformed.gpu, signal.dst.gpu, self.signal.err.gpu)
# print np.allclose(signal.transformed.gpu.get()-
# signal.dst.gpu.get(),
# self.signal.err.gpu.get())
# if self.dim_signal != 1:
# raise NotImplementedError
calc_ll_per_sample(ll=ll.gpu, err=self.signal.err.gpu, sigma=sigma_signal)
if 0:
res = -0.5 / (sigma_signal ** 2) * ((signal.transformed.gpu - signal.dst.gpu) ** 2).get()
np.allclose(res.ravel(), ll.gpu.get())
ipshell("stop")
1 / 0
def create_verts_and_H_type_I(self, dim_range, valid_outside):
"""
This assummes 2D
H encodes the n'bors info.
"""
if self.type != 'I':
raise ValueError(self.type)
dim_domain = self.dim_domain
nC = self.nC
cells_multiidx = self.cells_multiidx
cells_verts = self.cells_verts_homo_coo
nCx = self.nCx
nCy = self.nCy
if dim_domain != 2:
raise ValueError(dim_domain)
if dim_range not in (1, 2):
raise NotImplementedError(dim_range)
nbrs = np.zeros((nC, nC), dtype=np.bool)
if valid_outside:
left = np.zeros((nC, nC), np.bool)
right = np.zeros((nC, nC), np.bool)
top = np.zeros((nC, nC), np.bool)
bottom = np.zeros((nC, nC), np.bool)
print 'Encoding continuity constraints.'
print 'If nC is large, this may take some time.'
print 'For a given configuration, however, this is done only once;'
print 'the results computed here will be saved and reused the next time'
print 'you use the same configuration.'
# TODO: Cython
#
for i in range(nC):
if nC > 200 and i % 200 == 0:
print i, '/', nC
for j in range(nC):
# shorter names
mi = cells_multiidx[i]
mj = cells_multiidx[j]
vi = cells_verts[i]
vj = cells_verts[j]
vi = self.make_it_hashable(vi)
vj = self.make_it_hashable(vj)
shared_verts = set(vi).intersection(vj)
if len(mi) != 3:
raise ValueError
if len(mj) != 3:
raise ValueError
if mi == mj:
# same cell, nothing to do here
continue
elif mi[:-1] == mj[:-1]:
# Same rect boxs, different triangles
s = set([mi[-1], mj[-1]])
if s in [
set([0, 1]),
set([1, 2]),
set([2, 3]),
set([3, 0])
]:
nbrs[i, j] = 1
else:
# different rect boxes
if valid_outside:
# try to deal with the extension
if mi[0] == mj[0] == 0: # leftmost col
if mi[2] == mj[2] == 3: # left triangle
if np.abs(mi[1] - mj[1]) == 1: # adjacent rows
nbrs[i, j] = 1
left[i, j] = True
continue
if mi[0] == mj[0] == nCx - 1: # rightmost col
if mi[2] == mj[2] == 1: # right triangle
if np.abs(mi[1] - mj[1]) == 1: # adjacent rows
nbrs[i, j] = 1
right[i, j] = True
continue
if mi[1] == mj[1] == 0: # uppermost row
if mi[2] == mj[2] == 0: # upper triangle
if np.abs(mi[0] - mj[0]) == 1: # adjacent cols
nbrs[i, j] = 1
top[i, j] = True
continue
if mi[1] == mj[1] == nCy - 1: # lowermost row
if mi[2] == mj[2] == 2: # lower triangle
if np.abs(mi[0] - mj[0]) == 1: # adjacent cols
nbrs[i, j] = 1
bottom[i, j] = True
continue
if set([mi[2], mj[2]]) not in [set([0, 2]), set([1, 3])]:
continue
pair = (mi[0] - mj[0]), (mi[1] - mj[1])
# Recall the order of triangles is
# 0
# 3 1
# 2
# vertical nbr's
if pair == (0, 1) and (mi[2], mj[2]) == (0, 2):
nbrs[i, j] = 1
elif pair == (0, -1) and (mi[2], mj[2]) == (2, 0):
nbrs[i, j] = 1
# horizontal nbr's
elif pair == (1, 0) and (mi[2], mj[2]) == (3, 1):
nbrs[i, j] = 1
elif pair == (-1, 0) and (mi[2], mj[2]) == (1, 3):
nbrs[i, j] = 1
print 'Creating H of size (nC**2,nC)=({},{})'.format(nC**2, nC)
try:
H = np.zeros((nC**2, nC))
except MemoryError:
msg = 'Got MemoryError when trying to call np.zeros((nC**2,nC))'
ipshell(msg)
raise MemoryError('np.zeros((nC**2,nC))', 'nC={}'.format(nC))
# H = sparse.lil_matrix((nC**2,nC))
for i in range(nC):
for j in range(nC):
k = i * nC + j
if i < j:
continue
nbr = nbrs[i, j]
if nbr:
H[k, i] = -1
H[k, j] = +1
# ipshell('save H')
# 1/0
verts1 = []
verts2 = []
k = 0
print 'Extracting the vertices'
for count, h in enumerate(H):
if H.shape[0] > 1000:
if count % 100000 == 0:
print count, '/', H.shape[0]
# ipshell('..')
if h.any():
# if h.nnz:
# ipshell('STOP')
# # Make h dense and flat
# h=np.asarray(h.todense()).ravel()
i = (h == 1).nonzero()[0][0]
j = (h == -1).nonzero()[0][0]
mi = cells_multiidx[i]
mj = cells_multiidx[j]
vi = cells_verts[i]
vj = cells_verts[j]
vi = self.make_it_hashable(vi)
vj = self.make_it_hashable(vj)
shared_verts = set(vi).intersection(vj)
if len(shared_verts) == 0:
continue
if len(shared_verts) == 1:
# single vertex
if any([left[i, j], right[i, j], top[i, j], bottom[i, j]]):
# shared_vert is a set that contains a single tuple.
v_aux = list(shared_verts)[0] # v_aux is a tuple
v_aux = list(
v_aux) # Now v_aux is a list (i.e. mutable)
if left[i, j] or right[i, j]:
v_aux[
0] -= 10 # Create a new vertex with the same y
elif top[i, j] or bottom[i, j]:
v_aux[
1] -= 10 # Create a new vertex with the same x
else:
raise ValueError("WTF?")
v_aux = tuple(v_aux)
shared_verts.add(v_aux) # add it to the set
# ipshell('hello')
# print shared_verts
else:
# We can skip it since the continuity at this vertex
# will be imposed via the edges.
continue
if len(shared_verts) != 2:
ipshell('oops')
raise ValueError(len(shared_verts), shared_verts)
try:
v1, v2 = np.asarray(list(shared_verts))
except:
ipshell('oops2')
raise
k += 2
verts1.append(v1)
verts2.append(v2)
# if a != (1,1):
# continue
# print a, ' is a nbr of ',b
# nEdges=nbrs.sum().astype(np.int)/2
# if k != nEdges*2:
# raise ValueError(k,nEdges)
nEdges = k / 2
# Every edge connects 2 vertices.
# At every vertex, all components of the velocity must agree.
nConstraints = nEdges * 2 * dim_range
verts1 = np.asarray(verts1)
verts2 = np.asarray(verts2)
H = np.asarray([h for h in H if h.any()])
# H = np.asarray([h for h in H if h.nnz])
print 'H is ready'
return verts1, verts2, H, nEdges, nConstraints
def __init__(self,
cpa_space,
scale_spatial=1.0 / 10,
scale_value=0.001 * 1,
left_blk_rel_scale=None,
right_vec_scale=None):
# scale_spatial=0.0
if cpa_space.only_local:
raise NotImplementedError('only_local=', cpa_space.only_local)
self.scale_spatial = scale_spatial
self.scale_value = scale_value
if left_blk_rel_scale is None:
raise ValueError(
"You need to pass this argument. 0.5 may be a good value")
if right_vec_scale is None:
raise ValueError(
"You need to pass this argument. 0.5 may be a good value")
self.left_blk_rel_scale = left_blk_rel_scale
self.right_vec_scale = right_vec_scale
# Covariance on the joint Lie algebra
self.pa_cov = create_joint_algebra_cov(
cpa_space,
scale_spatial=scale_spatial,
scale_value=scale_value,
# scale_value=1.0, %FOR DEBUGGING
left_blk_rel_scale=left_blk_rel_scale,
right_vec_scale=right_vec_scale)
# Covariance on the subspace of that Lie algebra
self.cpa_cov = self.pa_cov_to_cpa_cov(cpa_space, self.pa_cov)
#
# self.cpa_cov_debug = self.pa_cov_to_cpa_cov(cpa_space,self.pa_cov*(10**2))
#
# C=self.cpa_cov
# D=self.cpa_cov_debug
# ipshell('hi')
# 1/0
# computing inverse
if 0:
try:
self.pa_cov_inv = inv(self.pa_cov)
# ipshell("STOP")
except:
ipshell("Failed to invert")
raise
else:
pass
self.cpa_cov_inv = inv(self.cpa_cov)
# if cpa_space.dim_domain==2:
# if cpa_space.tess=='tri':
# nV = len(cpa_space.local_stuff['vert_tess'])
# if nV*2 != cpa_space.d:
# raise ValueError( nV , cpa_space.d)
#
if cpa_space.local_stuff:
A2v = cpa_space.local_stuff.linop_Avees2velTess
B = cpa_space.B
# H = A2v.matmat(B.dot(B.T))
H = A2v.matmat(B).dot(B.T)
# self.velTess_cpa_cov = H.dot(self.pa_cov).dot(H.T)
# self.velTess_cpa_cov_inv = inv(self.velTess_cpa_cov)
self.velTess_cov_byB = H.dot(self.pa_cov).dot(H.T)
try:
self.velTess_cov_byB_inv = inv(self.velTess_cov_byB)
except:
# self.velTess_cov_byB=None
self.velTess_cov_byB_inv = None
if 0:
self.velTess_cov = create_cov_velTess(
cpa_space=cpa_space,
scale_spatial=scale_spatial,
scale_value=scale_value)
self.velTess_cov_inv = inv(self.velTess_cov)
def create_cont_constraint_mat(N, H, verts, nSides, nConstraints, nC,
dim_domain, dim_range, tess):
"""
L is the matrix that encodes the constraints of the consistent subspace.
Its null space space is the sought-after consistent subspace
(unless additional constraints are added; e.g., sub-algerba or bdry
conditions).
"""
if dim_domain != N:
raise ValueError
if dim_range != N:
raise NotImplementedError
nHomoCoo = dim_domain + 1
# length_Avee = dim_domain*nHomoCoo
length_Avee = dim_range * nHomoCoo
L = np.zeros((nConstraints, nC * length_Avee))
#
if tess == 'II':
nPtsInSide = 2**(N - 1)
else:
raise ValueError
# if nSides != nConstraints/(nPtsInSide*dim_domain):
# raise ValueError(nSides,nConstraints)
if nSides != nConstraints / (nPtsInSide * dim_range):
print " print nSides , nConstraints/(nPtsInSide*dim_range):"
print nSides, nConstraints / (nPtsInSide * dim_range)
ipshell('stop')
raise ValueError(nSides, (nConstraints, nPtsInSide, dim_range))
if nSides != H.shape[0]:
raise ValueError(nSides, H.shape)
M = nPtsInSide * dim_range
verts = np.asarray(map(np.asarray, verts))
# verts.shape is (2**(N-1),nSides,N+1))
if verts.shape != (2**(N - 1), nSides, N + 1):
raise ValueError(verts.shape)
if dim_range == N:
# loop over interfaces
for i in range(nSides):
verts_in_this_side = verts[:, i, :]
h = H[i]
a, b = h.nonzero()[0] # idx for the relevant As
# s stands for start
# e stands for end
s1 = a * length_Avee
e1 = s1 + nHomoCoo
s2 = b * length_Avee
e2 = s2 + nHomoCoo
# loop over vertices in this inter-cell interface
for j in range(nPtsInSide):
row = np.zeros(L.shape[1])
row[s1:e1] = verts_in_this_side[j]
row[s2:e2] = -verts_in_this_side[j]
# loop over coordinates in this vertex
for coo in range(N):
L[i * M + j * N + coo] = np.roll(row, coo * nHomoCoo)
else:
raise ValueError(dim_range)
return L
def create_cont_constraint_mat(H, v1s, v2s, v3s, v4s, nSides, nConstraints, nC,
dim_domain, dim_range, tess):
"""
L is the matrix that encodes the constraints of the consistent subspace.
Its null space space is the sought-after consistent subspace
(unless additional constraints are added; e.g., sub-algerba or bdry
conditions).
"""
if dim_domain != 3:
raise ValueError
if dim_range not in [1, 3]:
raise ValueError
nHomoCoo = dim_domain + 1
# length_Avee = dim_domain*nHomoCoo
length_Avee = dim_range * nHomoCoo
L = np.zeros((nConstraints, nC * length_Avee))
#
if tess == 'II':
nPtsInSide = 4
elif tess == 'I':
nPtsInSide = 3
# if nSides != nConstraints/(nPtsInSide*dim_domain):
# raise ValueError(nSides,nConstraints)
if nSides != nConstraints / (nPtsInSide * dim_range):
print " print nSides , nConstraints/(nPtsInSide*dim_range):"
print nSides, nConstraints / (nPtsInSide * dim_range)
ipshell('stop')
raise ValueError(nSides, (nConstraints, nPtsInSide, dim_range))
if nSides != H.shape[0]:
raise ValueError(nSides, H.shape)
M = nPtsInSide * dim_range
if dim_range == 1:
for i in range(nSides):
v1 = v1s[i]
v2 = v2s[i]
v3 = v3s[i]
if tess == 'II':
v4 = v4s[i]
h = H[i]
a, b = h.nonzero()[0] # idx for the relevant As
# s stands for start
# e stands for end
s1 = a * length_Avee
e1 = s1 + nHomoCoo
s2 = b * length_Avee
e2 = s2 + nHomoCoo
# Constraint 1:
L[i * M, s1:e1] = v1
L[i * M, s2:e2] = -v1
# Constraint 2:
# x component
L[i * M + 1, s1:e1] = v2
L[i * M + 1, s2:e2] = -v2
# Constraint 3:
L[i * M + 2, s1:e1] = v3
L[i * M + 2, s2:e2] = -v3
if tess == 'II':
# Constraint 4:
L[i * M + 3, s1:e1] = v4
L[i * M + 3, s2:e2] = -v4
elif dim_range == 3:
for i in range(nSides):
v1 = v1s[i]
v2 = v2s[i]
v3 = v3s[i]
if tess == 'II':
v4 = v4s[i]
if np.allclose(v1, v2):
raise ValueError(v1, v2)
if np.allclose(v1, v3):
raise ValueError(v1, v3)
if np.allclose(v2, v3):
raise ValueError(v2, v3)
if tess == 'II':
if np.allclose(v1, v4):
raise ValueError(v1, v4)
if np.allclose(v2, v4):
raise ValueError(v2, v4)
if np.allclose(v3, v4):
raise ValueError(v3, v4)
h = H[i]
a, b = h.nonzero()[0] # idx for the relevant As
# s stands for start
# e stands for end
s1 = a * length_Avee
e1 = s1 + nHomoCoo
s2 = b * length_Avee
e2 = s2 + nHomoCoo
# Constraint 1:
row = np.zeros(L.shape[1])
row[s1:e1] = v1
row[s2:e2] = -v1
# x component
L[i * M] = row
# y component
L[i * M + 1] = np.roll(row, nHomoCoo)
# z component
L[i * M + 2] = np.roll(row, 2 * nHomoCoo)
# Constraint 2:
row = np.zeros(L.shape[1])
row[s1:e1] = v2
row[s2:e2] = -v2
# x component
L[i * M + 3] = row
# y component
L[i * M + 4] = np.roll(row, nHomoCoo)
# z component
L[i * M + 5] = np.roll(row, nHomoCoo * 2)
# Constraint 3:
row = np.zeros(L.shape[1])
row[s1:e1] = v3
row[s2:e2] = -v3
# x component
L[i * M + 6] = row
# y component
L[i * M + 7] = np.roll(row, nHomoCoo)
# z component
L[i * M + 8] = np.roll(row, 2 * nHomoCoo)
# ipshell('qqq')
# 1/0
if tess == 'II':
# Constraint 4:
row = np.zeros(L.shape[1])
row[s1:e1] = v4
row[s2:e2] = -v4
# x component
L[i * M + 9] = row
# y component
L[i * M + 10] = np.roll(row, nHomoCoo)
# z component
L[i * M + 11] = np.roll(row, 2 * nHomoCoo)
else:
raise ValueError(dim_range)
return L
def create_verts_and_H_type_II(self,
# nC, cells_multiidx, cells_verts,dim_domain,
dim_range):
"""
This assummes 2D
H encodes the n'bors info.
"""
if self.type != 'II':
raise ValueError(self.type)
dim_domain=self.dim_domain
nC = self.nC
cells_multiidx=self.cells_multiidx
cells_verts=self.cells_verts_homo_coo
# nCx=self.nCx
# nCy=self.nCy
if dim_domain !=2:
raise ValueError(dim_domain)
if dim_range not in (1,dim_domain):
raise NotImplementedError(dim_range)
nbrs = np.zeros((nC,nC))
for i in range(nC):
for j in range(nC):
# shorter names
mi = cells_multiidx[i]
mj = cells_multiidx[j]
if mi == mj:
continue
else:
pair = (np.abs(mi[0]-mj[0]),
np.abs(mi[1]-mj[1]))
if set(pair) == set([0,1]):
nbrs[i,j]=1
nEdges=nbrs.sum().astype(np.int)/2
H = np.zeros((nC**2,nC))
# H = sparse.lil_matrix((nC**2,nC))
for i in range(nC):
for j in range(nC):
k = i*nC + j
if i < j:
continue
nbr = nbrs[i,j]
if nbr:
H[k,i]=-1
H[k,j]=+1
# ipshell('hi')
# 1/0
verts1 = []
verts2 = []
k = 0
for h in H:
# ipshell('..')
if h.any():
# if h.nnz:
# Very annoying: I think there is a bug in the sparse matrix object.
# Even after 'todense' it is impossible to flatten it properly.
# h = np.asarray(h.todense().tolist()[0]) # Workaround.
k+=2
i = (h==1).nonzero()[0][0]
j = (h==-1).nonzero()[0][0]
# if set([i,j])==set([6,9]):
# ipshell('debug')
# 1/0
# a = mi
# b = mj
vi = cells_verts[i]
vj = cells_verts[j]
vi = self.make_it_hashable(vi)
vj = self.make_it_hashable(vj)
edge = set(vi).intersection(vj)
if len(edge) != 2:
ipshell('oops')
raise ValueError(len(edge),edge)
try:
v1,v2 = np.asarray(list(edge))
except:
ipshell('oops2')
raise
verts1.append(v1)
verts2.append(v2)
# if a != (1,1):
# continue
# print a, ' is a nbr of ',b
if k != nEdges*2:
raise ValueError(k,nEdges)
# Every edge connects 2 vertices.
# At every vertex, all components of the velocity must agree.
#nConstraints = nEdges*2*dim_domain
nConstraints = nEdges*2*dim_range
verts1 = np.asarray(verts1)
verts2 = np.asarray(verts2)
H = np.asarray([h for h in H if h.any()])
# H = np.asarray([h for h in H if h.nnz])
# ipshell('hi')
# 1/0
return verts1,verts2,H,nEdges,nConstraints
def create_verts_and_H_type_I(self,dim_range,valid_outside):
"""
This assummes 2D
H encodes the n'bors info.
"""
if self.type != 'I':
raise ValueError(self.type)
dim_domain=self.dim_domain
nC = self.nC
cells_multiidx=self.cells_multiidx
cells_verts=self.cells_verts_homo_coo
nCx=self.nCx
nCy=self.nCy
if dim_domain !=2:
raise ValueError(dim_domain)
if dim_range not in (1,2):
raise NotImplementedError(dim_range)
nbrs = np.zeros((nC,nC),dtype=np.bool)
if valid_outside:
left=np.zeros((nC,nC),np.bool)
right=np.zeros((nC,nC),np.bool)
top=np.zeros((nC,nC),np.bool)
bottom=np.zeros((nC,nC),np.bool)
print 'Encoding continuity constraints.'
print 'If nC is large, this may take some time.'
print 'For a given configuration, however, this is done only once;'
print 'the results computed here will be saved and reused the next time'
print 'you use the same configuration.'
# TODO: Cython
#
for i in range(nC):
if nC > 200 and i % 200==0:
print i,'/',nC
for j in range(nC):
# shorter names
mi = cells_multiidx[i]
mj = cells_multiidx[j]
vi = cells_verts[i]
vj = cells_verts[j]
vi=self.make_it_hashable(vi)
vj=self.make_it_hashable(vj)
shared_verts = set(vi).intersection(vj)
if len(mi)!=3:
raise ValueError
if len(mj)!=3:
raise ValueError
if mi == mj:
# same cell, nothing to do here
continue
elif mi[:-1]==mj[:-1]:
# Same rect boxs, different triangles
s = set([mi[-1],mj[-1]])
if s in [set([0,1]),set([1,2]),set([2,3]),set([3,0])]:
nbrs[i,j]=1
else:
# different rect boxes
if valid_outside:
# try to deal with the extension
if mi[0]==mj[0]==0: # leftmost col
if mi[2]==mj[2]==3: # left triangle
if np.abs(mi[1]-mj[1])==1: # adjacent rows
nbrs[i,j]=1
left[i,j]=True
continue
if mi[0]==mj[0]==nCx-1: # rightmost col
if mi[2]==mj[2]==1: # right triangle
if np.abs(mi[1]-mj[1])==1: # adjacent rows
nbrs[i,j]=1
right[i,j]=True
continue
if mi[1]==mj[1]==0: # uppermost row
if mi[2]==mj[2]==0: # upper triangle
if np.abs(mi[0]-mj[0])==1: # adjacent cols
nbrs[i,j]=1
top[i,j]=True
continue
if mi[1]==mj[1]==nCy-1: # lowermost row
if mi[2]==mj[2]==2: # lower triangle
if np.abs(mi[0]-mj[0])==1: # adjacent cols
nbrs[i,j]=1
bottom[i,j]=True
continue
if set([mi[2],mj[2]]) not in [set([0,2]),set([1,3])]:
continue
pair = (mi[0]-mj[0]),(mi[1]-mj[1])
# Recall the order of triangles is
# 0
# 3 1
# 2
# vertical nbr's
if pair == (0,1) and (mi[2],mj[2])==(0,2):
nbrs[i,j]=1
elif pair == (0,-1) and (mi[2],mj[2])==(2,0):
nbrs[i,j]=1
# horizontal nbr's
elif pair == (1,0) and (mi[2],mj[2])==(3,1):
nbrs[i,j]=1
elif pair == (-1,0) and (mi[2],mj[2])==(1,3):
nbrs[i,j]=1
print 'Creating H of size (nC**2,nC)=({},{})'.format(nC**2,nC)
try:
H = np.zeros((nC**2,nC))
except MemoryError:
msg='Got MemoryError when trying to call np.zeros((nC**2,nC))'
ipshell(msg)
raise MemoryError('np.zeros((nC**2,nC))','nC={}'.format(nC))
# H = sparse.lil_matrix((nC**2,nC))
for i in range(nC):
for j in range(nC):
k = i*nC + j
if i < j:
continue
nbr = nbrs[i,j]
if nbr:
H[k,i]=-1
H[k,j]=+1
# ipshell('save H')
# 1/0
verts1 = []
verts2 = []
k = 0
print 'Extracting the vertices'
for count,h in enumerate(H):
if H.shape[0]>1000:
if count % 100000 == 0:
print count,'/',H.shape[0]
# ipshell('..')
if h.any():
# if h.nnz:
# ipshell('STOP')
# # Make h dense and flat
# h=np.asarray(h.todense()).ravel()
i = (h==1).nonzero()[0][0]
j = (h==-1).nonzero()[0][0]
mi = cells_multiidx[i]
mj = cells_multiidx[j]
vi = cells_verts[i]
vj = cells_verts[j]
vi=self.make_it_hashable(vi)
vj=self.make_it_hashable(vj)
shared_verts = set(vi).intersection(vj)
if len(shared_verts) ==0:
continue
if len(shared_verts) ==1:
# single vertex
if any([left[i,j],right[i,j],top[i,j],bottom[i,j]]):
# shared_vert is a set that contains a single tuple.
v_aux = list(shared_verts)[0] # v_aux is a tuple
v_aux = list(v_aux) # Now v_aux is a list (i.e. mutable)
if left[i,j] or right[i,j]:
v_aux[0]-=10 # Create a new vertex with the same y
elif top[i,j] or bottom[i,j]:
v_aux[1]-=10 # Create a new vertex with the same x
else:
raise ValueError("WTF?")
v_aux = tuple(v_aux)
shared_verts.add(v_aux) # add it to the set
# ipshell('hello')
# print shared_verts
else:
# We can skip it since the continuity at this vertex
# will be imposed via the edges.
continue
if len(shared_verts) != 2:
ipshell('oops')
raise ValueError(len(shared_verts),shared_verts)
try:
v1,v2 = np.asarray(list(shared_verts))
except:
ipshell('oops2')
raise
k+=2
verts1.append(v1)
verts2.append(v2)
# if a != (1,1):
# continue
# print a, ' is a nbr of ',b
# nEdges=nbrs.sum().astype(np.int)/2
# if k != nEdges*2:
# raise ValueError(k,nEdges)
nEdges = k/2
# Every edge connects 2 vertices.
# At every vertex, all components of the velocity must agree.
nConstraints = nEdges*2*dim_range
verts1 = np.asarray(verts1)
verts2 = np.asarray(verts2)
H = np.asarray([h for h in H if h.any()])
# H = np.asarray([h for h in H if h.nnz])
print 'H is ready'
return verts1,verts2,H,nEdges,nConstraints
def create_verts_and_H_type_II(self,dim_range):
"""
"""
dim_domain = self.dim_domain
nCs = self.nCs
nC = self.nC
cells_multiidx=self.cells_multiidx
cells_verts=self.cells_verts_homo_coo
N = len(nCs)
if dim_domain !=N:
raise ValueError(dim_domain)
nbrs = np.zeros((nC,nC))
mi=cells_multiidx # shorter name
for i in range(nC):
for j in range(nC):
if mi[i] == mi[j]:
continue
else:
t = np.abs(np.asarray(mi[i])-np.asarray(mi[j]))
if (t==0).sum()==N-1 and (t==1).sum()==1:
nbrs[i,j]=1
nSides=nbrs.sum().astype(np.int)/2
# H is larger than we need
# but it was easier to code this way.
# Later we eliminate the unused rows.
H = np.zeros((nC**2,nC))
# H = sparse.lil_matrix((nC**2,nC))
for i in range(nC):
for j in range(nC):
# k is the index of the row in H.
# Most rows won't be used.
k = i*nC + j
if i < j:
continue
nbr = nbrs[i,j]
if nbr:
H[k,i]=-1
H[k,j]=+1
# verts1 = []
# verts2 = []
# verts3 = []
# verts4 = []
verts = [[] for i in range(2**(N-1))]
counter = 0
for h in H:
if h.any():
# if h.nnz:
# Very annoying: I think there is a bug in the sparse matrix object.
# Even after 'todense' it is impossible to flatten it properly.
# h = np.asarray(h.todense().tolist()[0]) # Workaround.
# update: the sparsity issue was because I used arrays
# while the sparse functions want matrices.
counter+=2**(N-1)
# Find the vertex pair
i = (h==1).nonzero()[0][0]
j = (h==-1).nonzero()[0][0]
vi = cells_verts[i]
vj = cells_verts[j]
vi=self.make_it_hashable(vi)
vj=self.make_it_hashable(vj)
side = set(vi).intersection(vj)
if len(side) != 2**(N-1): # adjcant boxes share 2**(N-1) verts
ipshell('oops')
raise ValueError(len(side),side)
_verts = np.asarray(list(side))
# try:
#
# v1,v2,v3,v4 = np.asarray(list(side))
# except:
# ipshell('hi')
# raise
# verts1.append(v1)
# verts2.append(v2)
# verts3.append(v3)
# verts4.append(v4)
for i in range(2**(N-1)):
verts[i].append(_verts[i])
# if a != (1,1):
# continue
# print a, ' is a nbr of ',b
if counter != nSides*2**(N-1):
raise ValueError(counter,nSides)
# Every side conntect 2**(N-1) vertices.
# At every vertex, all components of the velocity must agree.
############## nConstraints = nSides*2**(N-1)*dim_domain
nConstraints = nSides*2**(N-1)*dim_range
#
# verts1 = np.asarray(verts1)
# verts2 = np.asarray(verts2)
# verts3 = np.asarray(verts3)
# verts4 = np.asarray(verts4)
H = np.asarray([h for h in H if h.any()])
# H = np.asarray([h for h in H if h.nnz])
#
return verts,H,nSides,nConstraints
def create_verts_and_H_type_I(self, dim_range, valid_outside):
"""
This assummes 2D
H encodes the n'bors info.
"""
if self.type != 'I':
raise ValueError(self.type)
dim_domain = self.dim_domain
nC = self.nC
cells_multiidx = self.cells_multiidx
cells_verts = self.cells_verts_homo_coo
nCx = self.nCx
nCy = self.nCy
nCz = self.nCz
if valid_outside:
raise NotImplementedError('dim_domain =', dim_domain,
'valid_outside =', valid_outside)
if dim_domain != 3:
raise ValueError(dim_domain)
nbrs = np.zeros((nC, nC))
mi = cells_multiidx # shorter name
for i in range(nC):
for j in range(nC):
# shorter names
mi = cells_multiidx[i]
mj = cells_multiidx[j]
# tetrahedron index within the box
ti = mi[-1]
tj = mj[-1]
if len(mi) != 4:
raise ValueError(len(mi))
if len(mj) != 4:
raise ValueError(len(mj))
vi = cells_verts[i]
vj = cells_verts[j]
vi = self.make_it_hashable(vi)
vj = self.make_it_hashable(vj)
if mi == mj:
continue
elif mi[:-1] == mj[:-1]:
# Same rect boxs, different tetrahedra
if ti == 0 or tj == 0:
if tj == ti:
raise ValueError
else:
nbrs[i, j] = 1
else:
# Different boxes
if len(set(vi).intersection(vj)) == 3:
nbrs[i, j] = 1
nSides = nbrs.sum().astype(np.int) / 2
# H is larger than we need
# but it was easier to code this way.
# Later we eliminate the unused rows.
H = np.zeros((nC**2, nC))
# H = sparse.lil_matrix((nC**2,nC))
for i in range(nC):
for j in range(nC):
# k is the index of the row in H.
# Most rows won't be used.
k = i * nC + j
if i < j:
continue
nbr = nbrs[i, j]
if nbr:
H[k, i] = -1
H[k, j] = +1
verts1 = []
verts2 = []
verts3 = []
verts4 = []
counter = 0
for h in H:
if h.any():
# if h.nnz:
# Very annoying: I think there is a bug in the sparse matrix object.
# Even after 'todense' it is impossible to flatten it properly.
# h = np.asarray(h.todense().tolist()[0]) # Workaround.
# Find the vertex pair
i = (h == 1).nonzero()[0][0]
j = (h == -1).nonzero()[0][0]
mi = cells_multiidx[i] # for debugging
mj = cells_multiidx[j] # for debugging
ti = mi[-1]
tj = mj[-1]
# a = mi
# b = mj
vi = cells_verts[i]
vj = cells_verts[j]
vi = self.make_it_hashable(vi)
vj = self.make_it_hashable(vj)
side = set(vi).intersection(vj)
len_side = len(side)
if len_side == 3:
v1, v2, v3 = np.asarray(list(side))
v4 = None
verts1.append(v1)
verts2.append(v2)
verts3.append(v3)
verts4.append(v4)
elif len_side == 2:
if ti == 0 and tj == 0:
# That's ok. Can ignore it:
# these should be the two "Central" tetrahedra
# of two adjacent cell.
continue
else:
raise ValueError
elif len_side == 1:
continue
# I thinkg this should be ok.
# I don't have time now to check this happens only when
# it should... TODO
else:
print('len(side) = ', len(side))
ipshell('wtf')
raise ValueError(len(side), side)
counter += len_side
# if a != (1,1):
# continue
# print a, ' is a nbr of ',b
# Every side connects 3 vertices.
nPtsInSide = 3
if counter != nSides * nPtsInSide:
ipshell('WTF')
raise ValueError(counter, nSides)
# At every vertex, all components of the velocity must agree.
nConstraints = nSides * nPtsInSide * dim_range
verts1 = np.asarray(verts1)
verts2 = np.asarray(verts2)
verts3 = np.asarray(verts3)
verts4 = np.asarray(verts4)
H = np.asarray([h for h in H if h.any()])
# H = np.asarray([h for h in H if h.nnz])
#
# ipshell('hi')
# 1/0
return verts1, verts2, verts3, verts4, H, nSides, nConstraints
def create_verts_and_H_type_II(
self,
# nC, cells_multiidx, cells_verts,dim_domain,
dim_range):
"""
This assummes 2D
H encodes the n'bors info.
"""
if self.type != 'II':
raise ValueError(self.type)
dim_domain = self.dim_domain
nC = self.nC
cells_multiidx = self.cells_multiidx
cells_verts = self.cells_verts_homo_coo
# nCx=self.nCx
# nCy=self.nCy
if dim_domain != 2:
raise ValueError(dim_domain)
if dim_range not in (1, dim_domain):
raise NotImplementedError(dim_range)
nbrs = np.zeros((nC, nC))
for i in range(nC):
for j in range(nC):
# shorter names
mi = cells_multiidx[i]
mj = cells_multiidx[j]
if mi == mj:
continue
else:
pair = (np.abs(mi[0] - mj[0]), np.abs(mi[1] - mj[1]))
if set(pair) == set([0, 1]):
nbrs[i, j] = 1
nEdges = nbrs.sum().astype(np.int) / 2
H = np.zeros((nC**2, nC))
# H = sparse.lil_matrix((nC**2,nC))
for i in range(nC):
for j in range(nC):
k = i * nC + j
if i < j:
continue
nbr = nbrs[i, j]
if nbr:
H[k, i] = -1
H[k, j] = +1
# ipshell('hi')
# 1/0
verts1 = []
verts2 = []
k = 0
for h in H:
# ipshell('..')
if h.any():
# if h.nnz:
# Very annoying: I think there is a bug in the sparse matrix object.
# Even after 'todense' it is impossible to flatten it properly.
# h = np.asarray(h.todense().tolist()[0]) # Workaround.
k += 2
i = (h == 1).nonzero()[0][0]
j = (h == -1).nonzero()[0][0]
# if set([i,j])==set([6,9]):
# ipshell('debug')
# 1/0
# a = mi
# b = mj
vi = cells_verts[i]
vj = cells_verts[j]
vi = self.make_it_hashable(vi)
vj = self.make_it_hashable(vj)
edge = set(vi).intersection(vj)
if len(edge) != 2:
ipshell('oops')
raise ValueError(len(edge), edge)
try:
v1, v2 = np.asarray(list(edge))
except:
ipshell('oops2')
raise
verts1.append(v1)
verts2.append(v2)
# if a != (1,1):
# continue
# print a, ' is a nbr of ',b
if k != nEdges * 2:
raise ValueError(k, nEdges)
# Every edge connects 2 vertices.
# At every vertex, all components of the velocity must agree.
#nConstraints = nEdges*2*dim_domain
nConstraints = nEdges * 2 * dim_range
verts1 = np.asarray(verts1)
verts2 = np.asarray(verts2)
H = np.asarray([h for h in H if h.any()])
# H = np.asarray([h for h in H if h.nnz])
# ipshell('hi')
# 1/0
return verts1, verts2, H, nEdges, nConstraints
def create_verts_and_H_type_II(self, dim_range):
"""
This assummes 3D
H encodes the n'bors info.
"""
if self.type != 'II':
raise ValueError(self.type)
dim_domain = self.dim_domain
nC = self.nC
cells_multiidx = self.cells_multiidx
cells_verts = self.cells_verts_homo_coo
# nCx=self.nCx
# nCy=self.nCy
# nCz=self.nCz
if dim_domain != 3:
raise ValueError(dim_domain)
if dim_range != dim_domain:
raise NotImplementedError(dim_range)
# if dim_range not in (1,dim_domain):
# raise NotImplementedError(dim_range)
nbrs = np.zeros((nC, nC))
mi = cells_multiidx # shorter name
for i in range(nC):
for j in range(nC):
if mi[i] == mi[j]:
continue
else:
# pair = (np.abs(mi[i][0]-mi[j][0]),
# np.abs(mi[i][1]-mi[j][1]))
# if set(pair) == set([0,1]):
# nbrs[i,j]=1
triplet = (np.abs(mi[i][0] - mi[j][0]),
np.abs(mi[i][1] - mi[j][1]),
np.abs(mi[i][2] - mi[j][2]))
triplet = np.asarray(triplet)
if (triplet == 0).sum() == 2 and (triplet == 1).sum() == 1:
nbrs[i, j] = 1
nSides = nbrs.sum().astype(np.int) / 2
# H is larger than we need
# but it was easier to code this way.
# Later we eliminate the unused rows.
H = np.zeros((nC**2, nC))
# H = sparse.lil_matrix((nC**2,nC))
for i in range(nC):
for j in range(nC):
# k is the index of the row in H.
# Most rows won't be used.
k = i * nC + j
if i < j:
continue
nbr = nbrs[i, j]
if nbr:
H[k, i] = -1
H[k, j] = +1
verts1 = []
verts2 = []
verts3 = []
verts4 = []
counter = 0
for h in H:
if h.any():
# if h.nnz:
# Very annoying: I think there is a bug in the sparse matrix object.
# Even after 'todense' it is impossible to flatten it properly.
# h = np.asarray(h.todense().tolist()[0]) # Workaround.
counter += 4
# Find the vertex pair
i = (h == 1).nonzero()[0][0]
j = (h == -1).nonzero()[0][0]
# a = mi[i]
# b = mi[j]
vi = cells_verts[i]
vj = cells_verts[j]
vi = self.make_it_hashable(vi)
vj = self.make_it_hashable(vj)
side = set(vi).intersection(vj)
if len(side) != 4: # adjcant boxes share 4 verts
ipshell('oops')
raise ValueError(len(side), side)
try:
v1, v2, v3, v4 = np.asarray(list(side))
except:
ipshell('hi')
raise
verts1.append(v1)
verts2.append(v2)
verts3.append(v3)
verts4.append(v4)
# if a != (1,1):
# continue
# print a, ' is a nbr of ',b
if counter != nSides * 4:
raise ValueError(counter, nEdges)
# Every side conntect 4 vertices.
# At every vertex, all components of the velocity must agree.
# nConstraints = nSides*4*dim_domain
nConstraints = nSides * 4 * dim_range
verts1 = np.asarray(verts1)
verts2 = np.asarray(verts2)
verts3 = np.asarray(verts3)
verts4 = np.asarray(verts4)
H = np.asarray([h for h in H if h.any()])
# H = np.asarray([h for h in H if h.nnz])
#
# ipshell('hi')
# 1/0
return verts1, verts2, verts3, verts4, H, nSides, nConstraints
def create_cont_constraint_mat(H,v1s,v2s,v3s,v4s,nSides,nConstraints,nC,
dim_domain,dim_range,tess):
"""
L is the matrix that encodes the constraints of the consistent subspace.
Its null space space is the sought-after consistent subspace
(unless additional constraints are added; e.g., sub-algerba or bdry
conditions).
"""
if dim_domain != 3:
raise ValueError
if dim_range not in [1,3]:
raise ValueError
nHomoCoo=dim_domain+1
# length_Avee = dim_domain*nHomoCoo
length_Avee = dim_range*nHomoCoo
L = np.zeros((nConstraints,nC*length_Avee))
#
if tess=='II':
nPtsInSide = 4
elif tess=='I':
nPtsInSide = 3
# if nSides != nConstraints/(nPtsInSide*dim_domain):
# raise ValueError(nSides,nConstraints)
if nSides != nConstraints/(nPtsInSide*dim_range):
print " print nSides , nConstraints/(nPtsInSide*dim_range):"
print nSides , nConstraints/(nPtsInSide*dim_range)
ipshell('stop')
raise ValueError( nSides , (nConstraints,nPtsInSide,dim_range))
if nSides != H.shape[0]:
raise ValueError(nSides,H.shape)
M = nPtsInSide*dim_range
if dim_range == 1:
for i in range(nSides):
v1 = v1s[i]
v2 = v2s[i]
v3 = v3s[i]
if tess=='II':
v4 = v4s[i]
h = H[i]
a,b = h.nonzero()[0] # idx for the relevant As
# s stands for start
# e stands for end
s1 = a*length_Avee
e1 = s1+nHomoCoo
s2 = b*length_Avee
e2 = s2+nHomoCoo
# Constraint 1:
L[i*M,s1:e1]= v1
L[i*M,s2:e2]= -v1
# Constraint 2:
# x component
L[i*M+1,s1:e1]= v2
L[i*M+1,s2:e2]= -v2
# Constraint 3:
L[i*M+2,s1:e1]= v3
L[i*M+2,s2:e2]= -v3
if tess=='II':
# Constraint 4:
L[i*M+3,s1:e1]= v4
L[i*M+3,s2:e2]= -v4
elif dim_range==3:
for i in range(nSides):
v1 = v1s[i]
v2 = v2s[i]
v3 = v3s[i]
if tess=='II':
v4 = v4s[i]
if np.allclose(v1,v2):
raise ValueError(v1,v2)
if np.allclose(v1,v3):
raise ValueError(v1,v3)
if np.allclose(v2,v3):
raise ValueError(v2,v3)
if tess=='II':
if np.allclose(v1,v4):
raise ValueError(v1,v4)
if np.allclose(v2,v4):
raise ValueError(v2,v4)
if np.allclose(v3,v4):
raise ValueError(v3,v4)
h = H[i]
a,b = h.nonzero()[0] # idx for the relevant As
# s stands for start
# e stands for end
s1 = a*length_Avee
e1 = s1+nHomoCoo
s2 = b*length_Avee
e2 = s2+nHomoCoo
# Constraint 1:
row = np.zeros(L.shape[1])
row[s1:e1]=v1
row[s2:e2]=-v1
# x component
L[i*M]=row
# y component
L[i*M+1]=np.roll(row,nHomoCoo)
# z component
L[i*M+2]=np.roll(row,2*nHomoCoo)
# Constraint 2:
row = np.zeros(L.shape[1])
row[s1:e1]=v2
row[s2:e2]=-v2
# x component
L[i*M+3]=row
# y component
L[i*M+4]=np.roll(row,nHomoCoo)
# z component
L[i*M+5]=np.roll(row,nHomoCoo*2)
# Constraint 3:
row = np.zeros(L.shape[1])
row[s1:e1]=v3
row[s2:e2]=-v3
# x component
L[i*M+6]=row
# y component
L[i*M+7]=np.roll(row,nHomoCoo)
# z component
L[i*M+8]=np.roll(row,2*nHomoCoo)
# ipshell('qqq')
# 1/0
if tess=='II':
# Constraint 4:
row = np.zeros(L.shape[1])
row[s1:e1]=v4
row[s2:e2]=-v4
# x component
L[i*M+9]=row
# y component
L[i*M+10]=np.roll(row,nHomoCoo)
# z component
L[i*M+11]=np.roll(row,2*nHomoCoo)
else:
raise ValueError(dim_range)
return L
def create_verts_and_H_type_I(self,dim_range,valid_outside):
"""
This assummes 2D
H encodes the n'bors info.
"""
if self.type != 'I':
raise ValueError(self.type)
dim_domain=self.dim_domain
nC = self.nC
cells_multiidx=self.cells_multiidx
cells_verts=self.cells_verts_homo_coo
nCx=self.nCx
nCy=self.nCy
nCz=self.nCz
if valid_outside:
raise NotImplementedError('dim_domain =',dim_domain,
'valid_outside =',valid_outside)
if dim_domain !=3:
raise ValueError(dim_domain)
nbrs = np.zeros((nC,nC))
mi=cells_multiidx # shorter name
for i in range(nC):
for j in range(nC):
# shorter names
mi = cells_multiidx[i]
mj = cells_multiidx[j]
# tetrahedron index within the box
ti = mi[-1]
tj = mj[-1]
if len(mi)!=4:
raise ValueError(len(mi))
if len(mj)!=4:
raise ValueError(len(mj))
vi = cells_verts[i]
vj = cells_verts[j]
vi=self.make_it_hashable(vi)
vj=self.make_it_hashable(vj)
if mi == mj:
continue
elif mi[:-1]==mj[:-1]:
# Same rect boxs, different tetrahedra
if ti==0 or tj==0:
if tj==ti:
raise ValueError
else:
nbrs[i,j]=1
else:
# Different boxes
if len(set(vi).intersection(vj))==3:
nbrs[i,j]=1
nSides=nbrs.sum().astype(np.int)/2
# H is larger than we need
# but it was easier to code this way.
# Later we eliminate the unused rows.
H = np.zeros((nC**2,nC))
# H = sparse.lil_matrix((nC**2,nC))
for i in range(nC):
for j in range(nC):
# k is the index of the row in H.
# Most rows won't be used.
k = i*nC + j
if i < j:
continue
nbr = nbrs[i,j]
if nbr:
H[k,i]=-1
H[k,j]=+1
verts1 = []
verts2 = []
verts3 = []
verts4 = []
counter = 0
for h in H:
if h.any():
# if h.nnz:
# Very annoying: I think there is a bug in the sparse matrix object.
# Even after 'todense' it is impossible to flatten it properly.
# h = np.asarray(h.todense().tolist()[0]) # Workaround.
# Find the vertex pair
i = (h==1).nonzero()[0][0]
j = (h==-1).nonzero()[0][0]
mi = cells_multiidx[i] # for debugging
mj = cells_multiidx[j] # for debugging
ti = mi[-1]
tj = mj[-1]
# a = mi
# b = mj
vi = cells_verts[i]
vj = cells_verts[j]
vi=self.make_it_hashable(vi)
vj=self.make_it_hashable(vj)
side = set(vi).intersection(vj)
len_side = len(side)
if len_side == 3:
v1,v2,v3 = np.asarray(list(side))
v4=None
verts1.append(v1)
verts2.append(v2)
verts3.append(v3)
verts4.append(v4)
elif len_side==2:
if ti == 0 and tj == 0:
# That's ok. Can ignore it:
# these should be the two "Central" tetrahedra
# of two adjacent cell.
continue
else:
raise ValueError
elif len_side == 1:
continue
# I thinkg this should be ok.
# I don't have time now to check this happens only when
# it should... TODO
else:
print ('len(side) = ',len(side))
ipshell('wtf')
raise ValueError(len(side),side)
counter+=len_side
# if a != (1,1):
# continue
# print a, ' is a nbr of ',b
# Every side connects 3 vertices.
nPtsInSide = 3
if counter != nSides*nPtsInSide:
ipshell('WTF')
raise ValueError(counter,nSides)
# At every vertex, all components of the velocity must agree.
nConstraints = nSides*nPtsInSide*dim_range
verts1 = np.asarray(verts1)
verts2 = np.asarray(verts2)
verts3 = np.asarray(verts3)
verts4 = np.asarray(verts4)
H = np.asarray([h for h in H if h.any()])
# H = np.asarray([h for h in H if h.nnz])
#
# ipshell('hi')
# 1/0
return verts1,verts2,verts3,verts4,H,nSides,nConstraints
def calc_grad_theta(self, xmins, xmaxs,
As_vectorized,
BasMats,
pts0,dt,nTimeSteps,
nStepsOdeSolver,pts_at_T,
grad_per_point,
dim_domain,dim_range,
nCs,
incs):
if dim_domain != dim_range:
raise ValueError
if pts_at_T is None:
raise ValueError
if len(incs)!=dim_domain:
raise ValueError(len(incs),dim_domain)
if As_vectorized.ndim != 2:
raise ValueError(As_vectorized.shape)
if As_vectorized.shape[1]!= (dim_domain+1)*dim_domain:
raise ValueError(As_vectorized.shape,(dim_domain+1)*dim_domain)
nPts = pts0.shape[0]
if not isinstance(pts0,CpuGpuArray):
raise TypeError
if not isinstance(pts_at_T,CpuGpuArray):
raise TypeError
# number of threads per block has to be >= than number of cells
# if self.nCells <= 128:
# threadsPerBlock = 128
if self.nCells <= 256:
threadsPerBlock = 256
# threadsPerBlock = 256/4
elif 256<self.nCells<=512:
threadsPerBlock = 512
elif 512<self.nCells<=625:
threadsPerBlock=625
elif 512<self.nCells<=1024:
threadsPerBlock = 1024
else:
raise NotImplementedError
nBlocks = int(np.ceil(float(nPts) / float(threadsPerBlock)))
if 0:
print '(nPts',nPts
print 'nBlocks',nBlocks
print 'threadsPerBlock = ',threadsPerBlock
print
d = len(BasMats)
if not isinstance(grad_per_point,CpuGpuArray):
raise TypeError
if grad_per_point.shape != (nPts,dim_range,d):
raise ValueError(grad_per_point.shape)
if 1:
nC0,nC1,nC2,inc_x,inc_y,inc_z = self.parse_nCs_and_incs(dim_domain,incs,nCs)
if dim_domain == dim_range:
calc_gpu=self.calc_grad_theta_gpu
else:
raise NotImplementedError
if 0:
ipshell('hi')
1/0
calc_gpu(
pts0.gpu,
pts_at_T.gpu,
drv.In(As_vectorized),
BasMats.gpu,
grad_per_point.gpu,
np.int32(d),
self.my_dtype(dt),
np.int32(nTimeSteps),
np.int32(nStepsOdeSolver),
np.int32(nPts),
np.int32(nC0),
np.int32(nC1),
np.int32(nC2),
np.float64(inc_x),
np.float64(inc_y),
np.float64(inc_z),
grid=(nBlocks,1,1),
block=(threadsPerBlock,1,1)
)
return grad_per_point
def create_cont_constraint_mat_separable(H,v1s,v2s,v3s,v4s,nSides,nConstraints,nC,
dim_domain,dim_range,tess):
"""
L is the matrix that encodes the constraints of the consistent subspace.
Its null space space is the sought-after consistent subspace
(unless additional constraints are added; e.g., sub-algerba or bdry
conditions).
"""
if dim_domain != 3:
raise ValueError
if dim_range not in [1,3]:
raise ValueError
nHomoCoo=dim_domain+1
length_Avee = dim_range*nHomoCoo
L1 = np.zeros((nConstraints/3,nC*nHomoCoo))
#
if tess=='II':
nPtsInSide = 4
elif tess=='I':
nPtsInSide = 3
# if nSides != nConstraints/(nPtsInSide*dim_domain):
# raise ValueError(nSides,nConstraints)
if nSides != nConstraints/(nPtsInSide*dim_range):
print " print nSides , nConstraints/(nPtsInSide*dim_range):"
print nSides , nConstraints/(nPtsInSide*dim_range)
ipshell('stop')
raise ValueError( nSides , (nConstraints,nPtsInSide,dim_range))
if nSides != H.shape[0]:
raise ValueError(nSides,H.shape)
# M = nPtsInSide*dim_range
M = nPtsInSide
if dim_range == 1:
raise NotImplementedError
for i in range(nSides):
v1 = v1s[i]
v2 = v2s[i]
v3 = v3s[i]
if tess=='II':
v4 = v4s[i]
h = H[i]
a,b = h.nonzero()[0] # idx for the relevant As
# s stands for start
# e stands for end
s1 = a*length_Avee
e1 = s1+nHomoCoo
s2 = b*length_Avee
e2 = s2+nHomoCoo
# Constraint 1:
L[i*M,s1:e1]= v1
L[i*M,s2:e2]= -v1
# Constraint 2:
L[i*M+1,s1:e1]= v2
L[i*M+1,s2:e2]= -v2
# Constraint 3:
L[i*M+2,s1:e1]= v3
L[i*M+2,s2:e2]= -v3
if tess=='II':
# Constraint 4:
L[i*M+3,s1:e1]= v4
L[i*M+3,s2:e2]= -v4
elif dim_range==3:
for i in range(nSides):
v1 = v1s[i]
v2 = v2s[i]
v3 = v3s[i]
if tess=='II':
v4 = v4s[i]
if np.allclose(v1,v2):
raise ValueError(v1,v2)
if np.allclose(v1,v3):
raise ValueError(v1,v3)
if np.allclose(v2,v3):
raise ValueError(v2,v3)
if tess=='II':
if np.allclose(v1,v4):
raise ValueError(v1,v4)
if np.allclose(v2,v4):
raise ValueError(v2,v4)
if np.allclose(v3,v4):
raise ValueError(v3,v4)
h = H[i]
a,b = h.nonzero()[0] # idx for the relevant As
# L1 is acting on columns of the following form:
# [ a_1 b_1 c_1 d_1 a_2 b_2 c_2 d_2 ... a_Nc b_Nc c_Nc d_Nc]
# s stands for start
# e stands for end
s1 = a*nHomoCoo
e1 = s1+nHomoCoo
s2 = b*nHomoCoo
e2 = s2+nHomoCoo
try:
# Constraint 1:
row = np.zeros(L1.shape[1])
row[s1:e1]=v1
row[s2:e2]=-v1
# x component
L1[i*M]=row
except:
ipshell('fail')
raise
# Constraint 2:
row = np.zeros(L1.shape[1])
row[s1:e1]=v2
row[s2:e2]=-v2
# x component
L1[i*M+1]=row
# Constraint 3:
row = np.zeros(L1.shape[1])
row[s1:e1]=v3
row[s2:e2]=-v3
# x component
L1[i*M+2]=row
if tess=='II':
# Constraint 4:
row = np.zeros(L1.shape[1])
row[s1:e1]=v4
row[s2:e2]=-v4
# x component
L1[i*M+3]=row
else:
raise ValueError(dim_range)
return L1
def create_cont_constraint_mat(N,H,verts,nSides,nConstraints,nC,
dim_domain,dim_range,tess):
"""
L is the matrix that encodes the constraints of the consistent subspace.
Its null space space is the sought-after consistent subspace
(unless additional constraints are added; e.g., sub-algerba or bdry
conditions).
"""
if dim_domain != N:
raise ValueError
if dim_range != N:
raise NotImplementedError
nHomoCoo=dim_domain+1
# length_Avee = dim_domain*nHomoCoo
length_Avee = dim_range*nHomoCoo
L = np.zeros((nConstraints,nC*length_Avee))
#
if tess=='II':
nPtsInSide = 2**(N-1)
else:
raise ValueError
# if nSides != nConstraints/(nPtsInSide*dim_domain):
# raise ValueError(nSides,nConstraints)
if nSides != nConstraints/(nPtsInSide*dim_range):
print " print nSides , nConstraints/(nPtsInSide*dim_range):"
print nSides , nConstraints/(nPtsInSide*dim_range)
ipshell('stop')
raise ValueError( nSides , (nConstraints,nPtsInSide,dim_range))
if nSides != H.shape[0]:
raise ValueError(nSides,H.shape)
M = nPtsInSide*dim_range
verts = np.asarray(map(np.asarray,verts))
# verts.shape is (2**(N-1),nSides,N+1))
if verts.shape != (2**(N-1),nSides,N+1):
raise ValueError(verts.shape)
if dim_range==N:
# loop over interfaces
for i in range(nSides):
verts_in_this_side = verts[:,i,:]
h = H[i]
a,b = h.nonzero()[0] # idx for the relevant As
# s stands for start
# e stands for end
s1 = a*length_Avee
e1 = s1+nHomoCoo
s2 = b*length_Avee
e2 = s2+nHomoCoo
# loop over vertices in this inter-cell interface
for j in range(nPtsInSide):
row = np.zeros(L.shape[1])
row[s1:e1]=verts_in_this_side[j]
row[s2:e2]=-verts_in_this_side[j]
# loop over coordinates in this vertex
for coo in range(N):
L[i*M+j*N+coo]=np.roll(row,coo*nHomoCoo)
else:
raise ValueError(dim_range)
return L