def xtest_assembler2d():
# setup discretisation
# --------------------
# setup PU
bbox = Box([[0, 1], [0, 1]])
tree = nTree(bbox=bbox)
# tree.refine(refines)
tree.refine(refines)
pu = PU(tree, weighttype='bspline3', scaling=scaling)
if plot_patches:
pu.tree.plot2d()
# setup monomial basis
basis = MonomialBasis(maxdegree, 2)
basisset = BasisSet(basis)
# setup dof manager
ids = [id for id in tree.leafs()]
dof = DofManager(ids, basisset)
# setup quadrature
quad = TensorQuadrature()
# setup assembler
asm = Assembler(tree, pu, basisset, dof, quad)
# assemble problem
# ----------------
N = dof.dim()
logger.info("system has dimension " + str(N))
print "PROBLEM SIZE %i" % N
A = lil_matrix((N, N))
b = np.zeros(N)
PDE = ReactionDiffusion(basedegree=maxdegree, D=1, r=1)
asm.assemble(A, b, lhs=PDE.lhs, rhs=PDE.rhs, symmetric=True)
# solve system
# ------------
A = A.tocsr()
x = spsolve(A, b)
# x = bicg(A, b)
# print A.todense()
# print b
# print x
# print x.shape
# plot solution
if plot_solution:
puf = PUFunction(x, tree, pu, basisset, dof)
Plotter.plot(lambda x: puf(x, gradient=False), 2, [[0, 1], [0, 1]], resolution=1 / 3, vectorized=False)
def test_monomials():
print "\n" + "*"*50
print "TEST MONOMIALS"
print "*"*50
# 1d
# ==================
degree = 2
B1 = MonomialBasis(degree, 1)
idx = B1.idx
N = 5
x = np.linspace(0, 1, N)
y = np.zeros_like(x)
Dy = np.zeros_like(x)
print "==== 1d for", x
for i in range(B1.dim):
print "\tbasis", i, str(idx[i])
B1(x, i, gradient=False, y=y)
B1(x, i, gradient=True, y=Dy)
print "\ty =", y, "\tDy =", Dy
if False and with_plot:
Plotter.plot(lambda x:B1(x, i, gradient=False), 1, [0, 1], resolution=1 / 50)
#2d
# ==================
degree = 2
B2 = MonomialBasis(degree, 2)
idx2 = B2.idx
x2 = np.array([[cx, 1] for cx in x])
# x2v = x2.view()
# x2v.shape = x2.shape[0] * x2.shape[1]
# print "X2", x2v
y2 = np.zeros_like(x2[:, 0])
Dy2 = np.zeros_like(x2)
print "==== 2d for", x2
for i in range(B2.dim):
print "\tbasis", i, str(idx2[i])
B2(x2, i, gradient=False, y=y2)
B2(x2, i, gradient=True, y=Dy2)
print "\ty2 =", y2
print "\tDy2 =", Dy2
if with_plot:
Plotter.plot(lambda x:B2(x, i, gradient=False), 2, [[0, 1], [0, 1]], resolution=1 / 50)
def test_pu():
print "\n" + "*"*50
print "TEST PU"
print "*"*50
# 1d
# ==================
if False:
print "======== 1d ========="
bbox = Box([[0, 1]])
tree = nTree(bbox=bbox)
pu = PU(tree, weighttype='bspline3', scaling=1.8)
pu.tree.refine(2)
for id in pu.indices:
print "\t", id, ":", pu.get_node(id)
for id in pu.indices:
node = pu.get_node(id)
cn = node.center
print "\n", node
neighbours = pu.get_neighbours(id)
active_neighbours = pu.get_active_neighbours(id, cn)
print "\tneighbours", neighbours
print "\tactive neighbours", active_neighbours
pu.prepare_neighbours(id)
y = pu(cn, gradient=False)
print "\tcenter f(", cn, ") =", y
Dy = pu(cn, gradient=True)
print "\tcenter Df(", cn, ") =", Dy
if with_plot:
# pu.prepare_neighbours(id, onlyself=True)
Plotter.plot(lambda x:pu(x, gradient=False), 1, [-1 / 4, 5 / 4], resolution=1 / 50)
# 2d
# ==================
if True:
print "======== 2d ========="
bbox = Box([[0, 1], [0, 1]])
tree = nTree(bbox=bbox)
pu = PU(tree, weighttype='bspline3', scaling=1.8)
pu.tree.refine(2)
for id in pu.indices:
print "\t", id, ":", pu.get_node(id)
if with_plot:
pc = 0
for id in pu.indices:
node = pu.get_node(id)
cn = node.center
print "\n", node
neighbours = pu.get_neighbours(id)
active_neighbours = pu.get_active_neighbours(id, cn)
print "\tneighbours", neighbours
print "\tactive neighbours", active_neighbours
pu.prepare_neighbours(id)
y = pu(cn, gradient=False)
print "\tcenter f(", cn, ") =", y
Dy = pu(cn, gradient=True)
print "\tcenter Df(", cn, ") =", Dy
if with_plot:
# pu.prepare_neighbours(id, onlyself=True)
if pc <= 5: # don't plot too many functions...
pc += 1
Plotter.plot(lambda x:pu(x, gradient=False, only_weight=False), 2, [[-1 / 4, 5 / 4], [-1 / 4, 5 / 4]], resolution=1 / 50)