def findStencilsOnStencilSets(self, level, bdyfcn=bdyfcn_null):
from time import time
print "icpm preparartion: diff"
st = time()
Lextend = self.Lextend[level]
Levolve = self.Levolve[level]
#Lghost = self.Lghost[level]
G = self.Grids[level]
for n in Levolve:
n.diffpts = []
gi = n.gridIndex
for offsets in self.DiffStencil:
gii = gi + offsets
nn = G[tuple(gii)]
#mm = Lextend.index(nn)
# Previous works but is quadratic (this is significant
# in practice). Instead we find the indices just
# after we build the stencils and cache them.
mm = nn.IndexInLextend
n.diffpts.append(mm)
print " time=" + str(time() - st)
print "icpm preparartion: interp"
st = time()
for n in Lextend:
n.interppts = []
cpbaseptI = n.cpbaseptI
Xgrid = G[tuple(cpbaseptI)].gridpt
res = bdyfcn(n.whichBdy)
if res == 'dirichlet_2nd_order':
n.interpweights = -buildInterpWeights(Xgrid, n.cp, n.dx,
PAR_EXTSTENWIDTH)
elif res == 'dirichlet_1st_order':
# TODO: why bother with temp? Just numpy.zeros?
temp = buildInterpWeights(Xgrid, n.cp, n.dx, PAR_EXTSTENWIDTH)
n.interpweights = [0] * len(temp)
else:
# includes "neumann_1st_order" and "neumann_2nd_order"
n.interpweights = buildInterpWeights(Xgrid, n.cp, n.dx,
PAR_EXTSTENWIDTH)
#gi = n.gridIndex
for offsets in self.InterpStencil:
# TODO: not right: find basept, UPDATE: this is
# basept, should be correct now
gii = cpbaseptI + offsets
nn = G[tuple(gii)]
#mm = Levolve.index(nn)
# Previous works but is quadratic, see above in the
# diff code. Levolve and Lextend have the same
# indices so we use index in extend here
mm = nn.IndexInLextend
n.interppts.append(mm)
print " time=" + str(time() - st)
def findStencilsOnStencilSets(self, level, bdyfcn=bdyfcn_null):
from time import time
print "icpm preparartion: diff"
st = time()
Lextend = self.Lextend[level]
Levolve = self.Levolve[level]
#Lghost = self.Lghost[level]
G = self.Grids[level]
for n in Levolve:
n.diffpts = []
gi = n.gridIndex
for offsets in self.DiffStencil:
gii = gi + offsets
nn = G[tuple(gii)]
#mm = Lextend.index(nn)
# Previous works but is quadratic (this is significant
# in practice). Instead we find the indices just
# after we build the stencils and cache them.
mm = nn.IndexInLextend
n.diffpts.append(mm)
print " time=" + str(time()-st)
print "icpm preparartion: interp"
st = time()
for n in Lextend:
n.interppts = []
cpbaseptI = n.cpbaseptI
Xgrid = G[tuple(cpbaseptI)].gridpt
res = bdyfcn(n.whichBdy)
if res == 'dirichlet_2nd_order':
n.interpweights = -buildInterpWeights(Xgrid, n.cp, n.dx, PAR_EXTSTENWIDTH)
elif res == 'dirichlet_1st_order':
# TODO: why bother with temp? Just numpy.zeros?
temp = buildInterpWeights(Xgrid, n.cp, n.dx, PAR_EXTSTENWIDTH)
n.interpweights = [0]*len(temp)
else:
# includes "neumann_1st_order" and "neumann_2nd_order"
n.interpweights = buildInterpWeights(Xgrid, n.cp, n.dx, PAR_EXTSTENWIDTH)
#gi = n.gridIndex
for offsets in self.InterpStencil:
# TODO: not right: find basept, UPDATE: this is
# basept, should be correct now
gii = cpbaseptI + offsets
nn = G[tuple(gii)]
#mm = Levolve.index(nn)
# Previous works but is quadratic, see above in the
# diff code. Levolve and Lextend have the same
# indices so we use index in extend here
mm = nn.IndexInLextend
n.interppts.append(mm)
print " time=" + str(time()-st)
def buildExtensionMatrix(g, xy, degreep=3):
r"""
Generate the matrix E
Notes:
In the diff op case, the weights are fixed, here they depend on
which node we're at.
"""
from math import ceil,log10
from scipy.sparse import coo_matrix
from time import time
from numpy import zeros, isscalar
# TODO: dim hardcoded to 2 in some places in this function
dim = xy.shape[1]
dx = g.dx
if (isscalar(dx)):
mytype = type(dx)
else:
mytype = type(dx[0])
relpt = a((g.x1d[0], g.y1d[0]))
#stencilsize = len(Levolve[0].interppts)
stencilsize = (degreep+1)**dim
progout = 10 ** (ceil(log10(len(g.band)))-1)
print "building E"
st=time()
# make empty lists the sparse matrix
# TODO: is it faster to use numpy arrays here?
ii = []; jj = []; aij = []
# how many points to interpolate
N = xy.shape[0]
# TODO: order here must match code elsewhere: this is a very bad idea
stencil = zeros( (stencilsize,dim) , dtype=int)
c = 0
for j in range(0,degreep+1):
for i in range(0,degreep+1):
stencil[c][0] = i
stencil[c][1] = j
c = c+1
# can do all of them at once
#bpij = findGridInterpBasePt(xy, dx, relpt, degreep)
for c in range(0, N):
if c % progout == 0: print " E row " + str(c)
x = xy[c]
bpij = findGridInterpBasePt(x, dx, relpt, degreep)
bpx = relpt + bpij * dx
interpweights = buildInterpWeights(bpx, x, dx, degreep+1)
interppts = g.sub2ind(bpij + stencil)
ii.extend([c]*stencilsize)
jj.extend(interppts)
aij.extend(interpweights)
#TODO: does this work with float96?
E = coo_matrix( (aij,(ii,jj)), shape=(len(g.band),g.nx*g.ny), dtype=mytype )
# TODO: return this info as well:
from numpy import unique
band2 = unique(jj)
print (len(jj),len(band2),len(g.band))
print " E row " + str(len(g.band))
print "elapsed time = " + str(time() - st)
#return E.tocsr()
#E2 = E.tocsr()
#EE = E2[:,band2]
return (E.tocsr(), band2)
