def rhs(self, b, idx2, pu, basis2, quad, intbox, boundary):
import time
geomdim = intbox.dim
f = self._f
g = self._g
# get quadrature points for pu
tx, w = quad.transformed(intbox, self._quaddegree)
tx = np.array([np.array(cx) for cx in tx]) # convert lists to arrays
# get patch reference points for basis
txv = tx.view()
txv.shape = m.prod(tx.shape)
px = np.zeros_like(tx)
pxv = px.view()
pxv.shape = txv.shape
affine_map_inverse(geomdim, pu._bbox[0:geomdim], txv, pxv)
# reuse result vectors
# _b1 = self._b1
# _Db1 = self._Db1
_b2 = self._b2
_Db2 = self._Db2
# evaluate pu
puf = pu(tx, gradient=False)
for bid2, k in enumerate(range(idx2, idx2 + basis2.dim)):
# evaluate basis2
b2 = basis2(px, bid2, gradient=False, y=_b2[:, 0])
# compute source rhs
val = m.mult(f(tx), puf, b2)
# add to rhs vector
# print "LHS (", k, "):", b[k], "+=", sum(w * val)
b[k] += sum(m.mult(w, val))
# evaluate boundary integrals
if boundary:
# print "BOUNDARY quad"
for bndbox, normal in boundary:
# print normal, bndbox
if self._isNeumannBC(bndbox):
# get surface quadrature points for pu
txb, wb = quad.transformed(bndbox, self._quaddegree)
txb = np.array([np.array(cx) for cx in txb]) # convert lists to arrays
# get patch reference points for basis
txbv = txb.view()
txbv.shape = m.prod(txb.shape)
pxb = np.zeros_like(txb)
pxbv = pxb.view()
pxbv.shape = txbv.shape
affine_map_inverse(geomdim, pu._bbox[0:geomdim], txbv, pxbv)
# evaluate boundary terms
pufb = pu(txb, gradient=False, Noffset=tx.shape[0])
b2b = basis2(pxb, bid2, gradient=False)
gb = g(txb)
# add to rhs vector
valb = m.inner(gb, [normal] * len(txb)) * m.mult(pufb, b2b)
# print "LHS-BC (", k, "):", b[k], "+=", sum(wb * valb)
b[k] += sum(m.mult(wb, valb))
def lhs(self, A, idx1, idx2, pu, basis1, basis2, quad, intbox, boundary):
import time
geomdim = intbox.dim
T = [time.time()] # === 1 ===
# NOTE/TODO: the quadrature degree should depend on the weight function, the basis degree, coefficients and the equation
D = self._D
r = self._r
# get quadrature points for pu
tx, w = quad.transformed(intbox, self._quaddegree)
tx = np.array([np.array(cx) for cx in tx]) # convert lists to arrays
N = len(tx)
# print "QUADDEGREE", self._quaddegree, N
# get patch reference points for basis
txv = tx.view()
txv.shape = m.prod(tx.shape)
px = np.zeros_like(tx)
pxv = px.view()
pxv.shape = txv.shape
affine_map_inverse(geomdim, pu._bbox[0:geomdim], txv, pxv)
T.append(time.time()) # === 2 ===
if self._hs < tx.shape[0]:
self._init_helpers(tx.shape[0])
# reuse result vectors
_b1 = self._b1.view()
_Db1 = self._Db1.view()
_b2 = self._b2.view()
_Db2 = self._Db2.view()
# evaluate pu
puf = pu(tx, gradient=False)
pufd = ml.repmat(puf, geomdim, 1)
pufd = pufd.T
T.append(time.time()) # === 3 ===
Dpuf = pu(tx, gradient=True)
T.append(time.time()) # === 4 ===
dT = [T[i + 1] - T[i] for i in range(len(T) - 1)]
print "TIMINGS A: ", dT, "with", N, "quadrature points for dim", geomdim
T = [time.time()]
for bid1, j in enumerate(range(idx1, idx1 + basis1.dim)):
# evaluate basis1
T = [time.time()] # === 1 ===
b1 = basis1(px, bid1, gradient=False, y=_b1[:, 0])
b1d = ml.repmat(b1, geomdim, 1)
b1d = b1d.T
Db1 = basis1(px, bid1, gradient=True, y=_Db1)
T.append(time.time())
# dT = [T[i + 1] - T[i] for i in range(len(T) - 1)]
# print "TIMINGS B: ", dT
T = [time.time()]
for bid2, k in enumerate(range(idx2, idx2 + basis2.dim)):
# evaluate basis2
T = [time.time()] # === 1 ===
b2 = basis2(px, bid2, gradient=False, y=_b2[:, 0])
b2d = ml.repmat(b2, geomdim, 1)
b2d = b2d.T
Db2 = basis2(px, bid2, gradient=True, y=_Db2)
T.append(time.time()) # === 2 ===
# # debug---
print "px", px.shape, px
print "puf", puf.shape, puf
print "Dpuf", Dpuf.shape, Dpuf
print "b1", b1.shape, b1
print "b2", b2.shape, b2
print "Db1", Db1.shape, Db1
print "Db2", Db2.shape, Db2
# # ---debug
# prepare discretisation parts
T.append(time.time()) # === 3 ===
pub1 = puf * b1
pub2 = puf * b2
T.append(time.time()) # === 4 ===
Dpub1 = m.mult(Dpuf, b1d) + m.mult(pufd, Db1)
Dpub2 = m.mult(Dpuf, b2d) + m.mult(pufd, Db2)
T.append(time.time()) # === 5 ===
# operator matrix with diffusion and reaction
val = D * m.inner(Dpub1, Dpub2) + r * m.mult(pub1, pub2)
T.append(time.time()) # === 6 ===
# print "LHS (", j, k, "):", A[j, k], "+=", sum(w * val)
# add to matrix
print "\\\\\\\\\\\\\\"
print pub1.shape
print m.mult(puf, b1)
print Dpub1.shape
print m.mult(Dpuf, b1d)
print "//////////////"
print "ooooooooooooooooooooooooooooooooooo"
print len(w)
print val.shape
print "1", w
print "2", val
print "3", m.mult(w, val)
print "4", sum(m.mult(w, val))
print "ooooooooooooooooooooooooooooooooooo"
raise Exception()
A[j, k] += sum(m.mult(w, val))
if idx1 != idx2: # symmetric operator
A[k, j] += sum(m.mult(w, val))
T.append(time.time()) # === 7 ===