def findStencilSetsSlower(self, level, extraPts=[]):
"""Find the stencil sets [Macdonald & Ruuth 2008]"""
from time import time
global PAR_EXTSTENP
print "finding stencil sets at level " + str(level)
st = time()
#F = self.Lists[level]
G = self.Grids[level]
# find the the CP, then find the points in the extsten
# surrouding it, mark each of them
relpt = self.basicPt
# first, make them all false
for n in G.values():
n.isEvolvePt = False
n.isExtendPt = False
# now, follow the algorithm in [MR2008]
for n in G.values():
cp = n.cp
basept = findGridInterpBasePt(cp,n.dx,relpt,PAR_EXTSTENP)
n.cpbaseptI = basept
for offset in self.InterpStencil:
gridindex = basept + offset
# for each extrapt, find pts in the extsten and mark them
#try:
G[tuple(gridindex)].isEvolvePt = True
#except (KeyError):
# raise NameError('not enough points in grid')
for off2 in self.DiffStencil:
gridind2 = basept + offset + off2
# try:
G[tuple(gridind2)].isExtendPt = True
# except (KeyError):
# raise NameError('not enough points in grid')
print "found stencil sets in time = " + str(time() - st)
def findStencilSetsSlower(self, level, extraPts=[]):
"""Find the stencil sets [Macdonald & Ruuth 2008]"""
from time import time
global PAR_EXTSTENP
print "finding stencil sets at level " + str(level)
st = time()
#F = self.Lists[level]
G = self.Grids[level]
# find the the CP, then find the points in the extsten
# surrouding it, mark each of them
relpt = self.basicPt
# first, make them all false
for n in G.values():
n.isEvolvePt = False
n.isExtendPt = False
# now, follow the algorithm in [MR2008]
for n in G.values():
cp = n.cp
basept = findGridInterpBasePt(cp, n.dx, relpt, PAR_EXTSTENP)
n.cpbaseptI = basept
for offset in self.InterpStencil:
gridindex = basept + offset
# for each extrapt, find pts in the extsten and mark them
#try:
G[tuple(gridindex)].isEvolvePt = True
#except (KeyError):
# raise NameError('not enough points in grid')
for off2 in self.DiffStencil:
gridind2 = basept + offset + off2
# try:
G[tuple(gridind2)].isExtendPt = True
# except (KeyError):
# raise NameError('not enough points in grid')
print "found stencil sets in time = " + str(time() - st)
def findStencilSetsFaster(self, level, extraPts=[]):
"""
Find the stencil sets [Macdonald & Ruuth 2008]. Here we use a
faster version: mark the CP base points in the grid. Then
just iterate over those in a separate loop
"""
from time import time
global PAR_EXTSTENP
print "Finding stencil sets at level " + str(level)
st = time()
#F = self.Lists[level]
G = self.Grids[level]
# find the the CP, then find the points in the extsten
# surrouding it, mark each of them
relpt = self.basicPt
# first, make them all false
for n in G.values():
n.isEvolvePt = False
n.isExtendPt = False
n.isCPBasePt = False
# essentially the algorithm in [MR2008], but here we mark each
# CP Base Point and then iterate over those in a separate
# loop. I confirmed it gives the same thing as the slower
# version and much faster
for n in G.values():
cp = n.cp
basept = findGridInterpBasePt(cp,n.dx,relpt,PAR_EXTSTENP)
n.cpbaseptI = basept
try:
G[tuple(basept)].isCPBasePt = True
except KeyError:
print basept,relpt,basept*n.dx+relpt
print n.dx
print n,n.cp
G[tuple(basept)]
pass #?
for n in G.values():
if n.isCPBasePt == True:
basept = n.gridIndex
for offset in self.InterpStencil:
gridindex = basept + offset
try:
G[tuple(gridindex)].isEvolvePt = True
except (KeyError):
print basept,offset,gridindex
G[tuple(basept)]
pass #?
for off2 in self.DiffStencil:
gridind2 = basept + offset + off2
G[tuple(gridind2)].isExtendPt = True
print "Found stencil sets in time = " + str(time() - st)
def findStencilSetsFaster(self, level, extraPts=[]):
"""
Find the stencil sets [Macdonald & Ruuth 2008]. Here we use a
faster version: mark the CP base points in the grid. Then
just iterate over those in a separate loop
"""
from time import time
global PAR_EXTSTENP
print "Finding stencil sets at level " + str(level)
st = time()
#F = self.Lists[level]
G = self.Grids[level]
# find the the CP, then find the points in the extsten
# surrouding it, mark each of them
relpt = self.basicPt
# first, make them all false
for n in G.values():
n.isEvolvePt = False
n.isExtendPt = False
n.isCPBasePt = False
# essentially the algorithm in [MR2008], but here we mark each
# CP Base Point and then iterate over those in a separate
# loop. I confirmed it gives the same thing as the slower
# version and much faster
for n in G.values():
cp = n.cp
basept = findGridInterpBasePt(cp, n.dx, relpt, PAR_EXTSTENP)
n.cpbaseptI = basept
try:
G[tuple(basept)].isCPBasePt = True
except KeyError:
print basept, relpt, basept * n.dx + relpt
print n.dx
print n, n.cp
G[tuple(basept)]
pass #?
for n in G.values():
if n.isCPBasePt == True:
basept = n.gridIndex
for offset in self.InterpStencil:
gridindex = basept + offset
try:
G[tuple(gridindex)].isEvolvePt = True
except (KeyError):
print basept, offset, gridindex
G[tuple(basept)]
pass #?
for off2 in self.DiffStencil:
gridind2 = basept + offset + off2
G[tuple(gridind2)].isExtendPt = True
print "Found stencil sets in 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)
