def test_poisson_residual():
'''Residual for Poisson.'''
ml = MeshLevel1D(j=1)
prob = PsmootherPoisson(testargs)
f = np.array([1.0, 0.5, 0.0, 0.5, 1.0])
w = f.copy()
Fcorrect = -np.array([0.0, 0.5 * ml.h, 4.0, 0.5 * ml.h, 0.0])
assert all(prob.residual(ml, w, ml.ellf(f)) == Fcorrect)
def test_ml_cR():
'''Canonical restriction in MeshLevel1D.'''
ml = MeshLevel1D(j=1)
assert ml.m == 3
assert ml.mcoarser == 1
r = ml.zeros()
r[1:4] = 1.0
assert all(ml.cR(r) == [0.0, 2.0, 0.0])
def test_ml_mR():
'''Monotone restriction in MeshLevel1D.'''
ml = MeshLevel1D(j=2)
assert ml.m == 7
v = np.array([0.0, 1.0, 1.0, 0.5, 0.5, 0.5, 0.5, 1.0, 0.0])
assert all(ml.mR(v) == [0.0, 1.0, 0.5, 1.0, 0.0])
vback = ml.cP(ml.mR(v)) # note cP uses zero boundary values
assert all(vback[2:-2] >= v[2:-2])
assert all(vback[[1, -2]] == [0.5, 0.5])
def test_ml_basics():
'''Basic MeshLevel1D functionality.'''
ml = MeshLevel1D(j=2)
assert ml.m == 7
assert ml.l2norm(ml.zeros()) == 0.0
v = ml.zeros()
assert len(v) == ml.m + 2
assert (ml.l2norm(ml.xx()) - 1.0 / np.sqrt(2.0)) < 1.0e-10
f = np.ones(ml.m + 2)
ellcorrect = ml.h * np.array([0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0])
assert all(ml.ellf(f) == ellcorrect)
def test_pngssia_residual():
'''Residual for SIA.'''
ml = MeshLevel1D(j=1, xmax=1800.0e3) # note [0,xmax] = [0,1800] km
prob = PNsmootherSIA(testargs)
ml.b = ml.zeros() # attach bed elevation to mesh
m = np.array([-1.0, 0.5, 0.5, 0.5, -1.0]) / prob.secpera
s = np.array([0.0, 2500.0, 3100.0, 2500.0,
0.0]) # hand-adjusted so res is small!
res = prob.residual(ml, s, ml.ellf(m))
ml.checklen(res)
assert all(abs(res) < 1.0e-2)
def test_poisson_pgssweep():
'''Projected Gauss-Seidel sweep for Poisson.'''
ml = MeshLevel1D(j=0)
prob = PsmootherPoisson(testargs)
f = np.array([0.0, 1.0, 0.0])
ell = ml.ellf(f)
assert all(ell == ml.h * f)
w = ml.zeros()
assert all(prob.residual(ml, w, ell) == -ml.h * f)
phi = np.array([-2.0, -2.0, -2.0]) # thus unconstrained
prob.smoothersweep(ml, w, ell, phi, forward=True)
assert all(prob.residual(ml, w, ell) == ml.zeros())
def test_ml_hierarchy():
'''For an obstacle phi(x), and defect obstacles generated by monotone
restriction down the hierarchy,
chi_J(x) = phi(x), chi_{j-1}(x) = mR(chi_j(x)),
show that the increments Phi_j(x) = chi_j(x) - chi_{j-1}(x) add up:
phi(x) = sum_{j=0}^J Phi_j(x)
(Interpreting this equation requires canonical prolongation.)
See bottom equation on page 16 of Graeser & Kornhuber (2009).'''
ml1 = MeshLevel1D(j=1)
ml2 = MeshLevel1D(j=2)
assert ml2.m == 7
phi = np.array([0.0, 1.0, 2.0, 1.0, 1.0, 1.0, 0.0, 1.0, 0.0]) # zero b.c.
assert len(phi) == ml2.m + 2
chi2 = phi
chi1 = ml2.mR(chi2)
chi0 = ml1.mR(chi1)
assert all(chi1 == [0.0, 2.0, 1.0, 1.0, 0.0])
assert all(chi0 == [0.0, 2.0, 0.0])
Psi0 = ml2.cP(ml1.cP(chi0))
Psi1 = ml2.cP(chi1 - ml1.cP(chi0))
Psi2 = chi2 - ml2.cP(chi1)
assert all(Psi0 + Psi1 + Psi2 == phi)
def test_sia_exact():
'''Exact solution for SIA.'''
ml = MeshLevel1D(j=2, xmax=1800.0e3) # note [0,xmax] = [0,1800] km
#ml = MeshLevel1D(j=7, xmax=1800.0e3) # note [0,xmax] = [0,1800] km
prob = PNsmootherSIA(testargs)
assert prob.exact_available()
x = ml.xx()
b = prob.phi(x)
m = prob.source(x)
s = prob.exact(x)
assert all(b == 0.0) # check flat bed
assert max(s) == prob.buelerH0 # check height
assert max(x[s > 0.0]) - prob.xc < prob.buelerL # check margin pos
assert min(m) < 0.0 # check mass balance
assert max(m) > 0.0 # changes sign
def test_pngssia_smoothersweep():
'''Smoother for SIA.'''
ml = MeshLevel1D(j=1, xmax=1800.0e3) # note [0,xmax] = [0,1800] km
prob = PNsmootherSIA(testargs)
ml.b = ml.zeros() # attach bed elevation to mesh
ml.g = ml.zeros() # attach fixed portion of soluiton to mesh
m = np.array([-1.0, 0.5, 0.5, 0.5, -1.0]) / prob.secpera
s = np.array([0.0, 2500.0, 3100.0, 2500.0,
0.0]) # hand-adjusted so res is small!
ell = ml.ellf(m)
res = prob.residual(ml, s, ell)
prob.smoothersweep(ml, s, ell, ml.b)
prob.smoothersweep(ml, s, ell, ml.b)
prob.smoothersweep(ml, s, ell, ml.b)
newres = prob.residual(ml, s, ell)
assert ml.l2norm(newres) < ml.l2norm(res)
def test_ml_injectP():
'''Prolongation of linear functionals by injection in MeshLevel1D.'''
ml = MeshLevel1D(j=2)
ell = np.array([0.0, 1.0, 2.0, 3.0, 0.0])
assert all(
ml.injectP(ell) == [0.0, 0.0, 1.0, 0.0, 2.0, 0.0, 3.0, 0.0, 0.0])
def test_ml_iR():
'''Restriction of vectors (functions) by injection in MeshLevel1D.'''
ml = MeshLevel1D(j=2)
v = np.array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 0.0])
assert all(ml.iR(v) == [0.0, 2.0, 4.0, 6.0, 0.0])
def test_ml_cP():
'''Canonical prolongation in MeshLevel1D.'''
ml = MeshLevel1D(j=1)
v = np.array([0.0, 1.0, 0.0])
assert all(ml.cP(v) == [0.0, 0.5, 1.0, 0.5, 0.0])
'combination of -ni and -random is not implemented')
# determine correct interval
L = 1.0
if args.problem == 'poisson' and args.poissoncase == 'pde2':
L = 10.0
elif args.problem == 'sia':
L = args.siaintervallength
# hierarchy is a list of MeshLevel1D with indices [0,..,levels-1]
assert args.jcoarse >= 0
assert args.J >= args.jcoarse
levels = args.J - args.jcoarse + 1
hierarchy = [None] * (levels) # list [None,...,None]
for j in range(levels):
hierarchy[j] = MeshLevel1D(j=j + args.jcoarse, xmax=L)
# set up obstacle problem with smoother (class SmootherObstacleProblem)
if args.problem == 'poisson':
obsprob = PsmootherPoisson(args)
elif args.problem == 'plap':
obsprob = PNsmootherPLap(args)
elif args.problem == 'sia':
obsprob = PNsmootherSIA(args)
# more usage help
if args.monitorerr and not obsprob.exact_available():
print(
'usage ERROR: -monitorerr but exact solution and error not available')
sys.exit(5)