def multipole_to_local(self,
level_start_target_or_target_parent_box_nrs,
target_or_target_parent_boxes,
starts, lists, mpole_exps):
tree = self.tree
local_exps = self.local_expansion_zeros()
rscale = 1
from pyfmmlib import h2dmploc_vec
for itgt_box, tgt_ibox in enumerate(target_or_target_parent_boxes):
start, end = starts[itgt_box:itgt_box+2]
tgt_center = tree.box_centers[:, tgt_ibox]
#print tgt_ibox, "<-", lists[start:end]
tgt_loc = 0
for src_ibox in lists[start:end]:
src_center = tree.box_centers[:, src_ibox]
tgt_loc = tgt_loc + h2dmploc_vec(
self.helmholtz_k,
rscale, src_center, mpole_exps[src_ibox],
rscale, tgt_center, self.nterms)[:, 0]
local_exps[tgt_ibox] += tgt_loc
return local_exps
def multipole_to_local(self, target_or_target_parent_boxes, starts, lists,
mpole_exps):
tree = self.tree
local_exps = self.local_expansion_zeros()
rscale = 1
from pyfmmlib import h2dmploc_vec
for itgt_box, tgt_ibox in enumerate(target_or_target_parent_boxes):
start, end = starts[itgt_box:itgt_box + 2]
tgt_center = tree.box_centers[:, tgt_ibox]
#print tgt_ibox, "<-", lists[start:end]
tgt_loc = 0
for src_ibox in lists[start:end]:
src_center = tree.box_centers[:, src_ibox]
tgt_loc = tgt_loc + h2dmploc_vec(
self.helmholtz_k, rscale, src_center, mpole_exps[src_ibox],
rscale, tgt_center, self.nterms)[:, 0]
local_exps[tgt_ibox] += tgt_loc
return local_exps
def test_translations():
nterms = 15
zk = 3
rscale = 1
n = 40
# centered at the origin, extent [-.5,.5]
sources = np.random.uniform(size=(n, 2)) - 0.5
charges = np.random.uniform(size=n)
targets_center = np.array([10, 0])
targets = np.random.uniform(size=(n, 2)) - 0.5 + targets_center
from pyfmmlib import (h2dformmp, h2dmpmp_vec, h2dmploc_vec, h2dlocloc_vec,
h2dtaeval_vec, hpotgrad2dall_vec, h2dmpeval_vec)
ref_value, _, _ = hpotgrad2dall_vec(ifgrad=False,
ifhess=False,
sources=sources.T,
charge=charges,
targets=targets.T,
zk=zk)
# {{{ multipole 1
mp1_center = np.array([0, 0])
ier, mp1 = h2dformmp(zk, rscale, sources.T, charges, mp1_center, nterms)
assert ier == 0
mp1_value, _, _ = h2dmpeval_vec(zk,
rscale,
mp1_center,
mp1,
ztarg=targets.T,
ifgrad=False,
ifhess=False)
assert la.norm(mp1_value - ref_value) / la.norm(ref_value) < 1e-12
# }}}
# {{{ multipole 2
mp2_center = np.array([2, 0])
mp2 = h2dmpmp_vec(zk, rscale, mp1_center, mp1, rscale, mp2_center, nterms)
mp2_value, _, _ = h2dmpeval_vec(zk,
rscale,
mp2_center,
mp2,
ztarg=targets.T,
ifgrad=False,
ifhess=False)
assert la.norm(mp2_value - ref_value) / la.norm(ref_value) < 3e-5
# }}}
# {{{ local 1
loc1_center = targets_center - np.array([1, 0])
loc1 = h2dmploc_vec(zk, rscale, mp2_center, mp2, rscale, loc1_center,
nterms)
loc1_value, _, _ = h2dtaeval_vec(zk,
rscale,
loc1_center,
loc1,
ztarg=targets.T,
ifgrad=False,
ifhess=False)
assert la.norm(loc1_value - ref_value) / la.norm(ref_value) < 3e-5
# }}}
# {{{ local 2
loc2_center = targets_center
loc2 = h2dlocloc_vec(zk, rscale, loc1_center, loc1, rscale, loc2_center,
nterms)
loc2_value, _, _ = h2dtaeval_vec(zk,
rscale,
loc2_center,
loc2,
ztarg=targets.T,
ifgrad=False,
ifhess=False)
assert la.norm(loc2_value - ref_value) / la.norm(ref_value) < 1e-4
def test_translations():
nterms = 15
zk = 3
rscale = 1
n = 40
# centered at the origin, extent [-.5,.5]
sources = np.random.uniform(size=(n, 2)) - 0.5
charges = np.random.uniform(size=n)
targets_center = np.array([10, 0])
targets = np.random.uniform(size=(n, 2)) - 0.5 + targets_center
from pyfmmlib import (h2dformmp, h2dmpmp_vec, h2dmploc_vec,
h2dlocloc_vec, h2dtaeval_vec, hpotgrad2dall_vec, h2dmpeval_vec)
ref_value, _, _ = hpotgrad2dall_vec(ifgrad=False, ifhess=False,
sources=sources.T, charge=charges,
targets=targets.T, zk=zk)
# {{{ multipole 1
mp1_center = np.array([0, 0])
ier, mp1 = h2dformmp(zk, rscale, sources.T, charges, mp1_center, nterms)
assert ier == 0
mp1_value, _, _ = h2dmpeval_vec(zk, rscale, mp1_center, mp1, ztarg=targets.T,
ifgrad=False, ifhess=False)
assert la.norm(mp1_value - ref_value) / la.norm(ref_value) < 1e-12
# }}}
# {{{ multipole 2
mp2_center = np.array([2, 0])
mp2 = h2dmpmp_vec(zk, rscale, mp1_center, mp1, rscale, mp2_center, nterms)
mp2_value, _, _ = h2dmpeval_vec(zk, rscale, mp2_center, mp2, ztarg=targets.T,
ifgrad=False, ifhess=False)
assert la.norm(mp2_value - ref_value) / la.norm(ref_value) < 3e-5
# }}}
# {{{ local 1
loc1_center = targets_center - np.array([1, 0])
loc1 = h2dmploc_vec(zk, rscale, mp2_center, mp2, rscale, loc1_center, nterms)
loc1_value, _, _ = h2dtaeval_vec(zk, rscale, loc1_center, loc1,
ztarg=targets.T, ifgrad=False, ifhess=False)
assert la.norm(loc1_value - ref_value) / la.norm(ref_value) < 3e-5
# }}}
# {{{ local 2
loc2_center = targets_center
loc2 = h2dlocloc_vec(zk, rscale, loc1_center, loc1, rscale, loc2_center, nterms)
loc2_value, _, _ = h2dtaeval_vec(zk, rscale, loc2_center, loc2, ztarg=targets.T,
ifgrad=False, ifhess=False)
assert la.norm(loc2_value - ref_value) / la.norm(ref_value) < 1e-4