def test_vangenuchten_k(self):
mesh = Mesh.TensorMesh([50])
hav = Richards.Empirical._vangenuchten_k(mesh)
m = np.random.randn(50)
def wrapper(u):
return hav.transform(u, m), hav.transformDerivU(u, m)
passed = checkDerivative(wrapper, np.random.randn(50), plotIt=False)
self.assertTrue(passed,True)
hav = Richards.Empirical._vangenuchten_k(mesh)
u = np.random.randn(50)
def wrapper(m):
return hav.transform(u, m), hav.transformDerivM(u, m)
passed = checkDerivative(wrapper, np.random.randn(50), plotIt=False)
self.assertTrue(passed,True)
def test_vangenuchten_k(self):
mesh = Mesh.TensorMesh([50])
hav = Richards.Empirical._vangenuchten_k(mesh)
m = np.random.randn(50)
def wrapper(u):
return hav.transform(u, m), hav.transformDerivU(u, m)
passed = checkDerivative(wrapper, np.random.randn(50), plotIt=False)
self.assertTrue(passed,True)
hav = Richards.Empirical._vangenuchten_k(mesh)
u = np.random.randn(50)
def wrapper(m):
return hav.transform(u, m), hav.transformDerivM(u, m)
passed = checkDerivative(wrapper, np.random.randn(50), plotIt=False)
self.assertTrue(passed,True)
def test_Sensitivity_full(self):
mTrue = self.Ks * np.ones(self.M.nC)
J = self.prob.Jfull(mTrue)
derChk = lambda m: [self.survey.dpred(m), J]
print('2D: Testing Richards Derivative FULL')
passed = checkDerivative(derChk, mTrue, num=4, plotIt=False)
self.assertTrue(passed, True)
def test_Sensitivity_full(self):
mTrue = self.Ks * np.ones(self.M.nC)
J = self.prob.Jfull(mTrue)
derChk = lambda m: [self.survey.dpred(m), J]
print "2D: Testing Richards Derivative FULL"
passed = checkDerivative(derChk, mTrue, num=4, plotIt=False)
self.assertTrue(passed, True)
def test_BaseHaverkamp_Theta(self):
mesh = Mesh.TensorMesh([50])
hav = Richards.Empirical._haverkamp_theta(mesh)
m = np.random.randn(50)
def wrapper(u):
return hav.transform(u, m), hav.transformDerivU(u, m)
passed = checkDerivative(wrapper, np.random.randn(50), plotIt=False)
self.assertTrue(passed,True)
def test_BaseHaverkamp_Theta(self):
mesh = Mesh.TensorMesh([50])
hav = Richards.Empirical._haverkamp_theta(mesh)
m = np.random.randn(50)
def wrapper(u):
return hav.transform(u, m), hav.transformDerivU(u, m)
passed = checkDerivative(wrapper, np.random.randn(50), plotIt=False)
self.assertTrue(passed,True)
def test_Sensitivity(self):
mTrue = self.Ks * np.ones(self.M.nC)
derChk = lambda m: [
self.survey.dpred(m), lambda v: self.prob.Jvec(m, v)
]
print('3D: Testing Richards Derivative')
passed = checkDerivative(derChk, mTrue, num=4, plotIt=False)
self.assertTrue(passed, True)
def test_simpleFunction(self):
def simpleFunction(x):
return np.sin(x), lambda xi: sdiag(np.cos(x)) * xi
passed = checkDerivative(simpleFunction,
np.random.randn(5),
plotIt=False)
self.assertTrue(passed, True)
def test_vangenuchten_k(self):
mesh = Mesh.TensorMesh([50])
hav = Richards.Empirical._vangenuchten_k(mesh)
m = np.random.randn(50)
passed = checkDerivative(
lambda u: (hav.transform(u, m), hav.transformDerivU(u, m)),
np.random.randn(50),
plotIt=False)
self.assertTrue(passed, True)
hav = Richards.Empirical._vangenuchten_k(mesh)
u = np.random.randn(50)
passed = checkDerivative(
lambda m: (hav.transform(u, m), hav.transformDerivM(u, m)),
np.random.randn(50),
plotIt=False)
self.assertTrue(passed, True)
def test_vangenuchten_theta_u(self):
mesh = Mesh.TensorMesh([50])
van = Richards.Empirical.Vangenuchten_theta(mesh)
passed = checkDerivative(
lambda u: (van(u), van.derivU(u)),
np.random.randn(50),
plotIt=False
)
self.assertTrue(passed, True)
def test_Richards_getResidual_Newton(self):
self.prob.doNewton = True
m = self.Ks
passed = checkDerivative(
lambda hn1: self.prob.getResidual(m, self.h0, hn1, self.prob.timeSteps[0], self.prob.boundaryConditions),
self.h0,
plotIt=False,
)
self.assertTrue(passed, True)
def test_Richards_getResidual_Newton(self):
self.prob.doNewton = True
m = self.Ks
passed = checkDerivative(lambda hn1: self.prob.getResidual(
m, self.h0, hn1, self.prob.timeSteps[0], self.prob.
boundaryConditions),
self.h0,
plotIt=False)
self.assertTrue(passed, True)
def test_haverkamp_theta_u(self):
mesh = Mesh.TensorMesh([50])
hav = Richards.Empirical.Haverkamp_theta(mesh)
passed = checkDerivative(
lambda u: (hav(u), hav.derivU(u)),
np.random.randn(50),
plotIt=False
)
self.assertTrue(passed, True)
def _dotest_sensitivity(self):
print('Testing Richards Derivative dim={}'.format(
self.mesh.dim
))
passed = checkDerivative(
lambda m: [self.survey.dpred(m), lambda v: self.prob.Jvec(m, v)],
self.mtrue,
num=4,
plotIt=False
)
self.assertTrue(passed, True)
def _dotest_sensitivity_full(self):
print('Testing Richards Derivative FULL dim={}'.format(
self.mesh.dim
))
J = self.prob.Jfull(self.mtrue)
passed = checkDerivative(
lambda m: [self.survey.dpred(m), J],
self.mtrue,
num=4,
plotIt=False
)
self.assertTrue(passed, True)
def test_haverkamp_k_u(self):
mesh = Mesh.TensorMesh([5])
hav = Richards.Empirical.Haverkamp_k(mesh)
print('Haverkamp_k test u deriv')
passed = checkDerivative(
lambda u: (hav(u), hav.derivU(u)),
np.random.randn(mesh.nC),
plotIt=False
)
self.assertTrue(passed, True)
def _test_deriv(self, x=None, num=4, plotIt=False, **kwargs):
print('Testing {0!s} Deriv'.format(self.__class__.__name__))
if x is None:
if self.nP == '*':
x = np.random.randn(np.random.randint(1e2, high=1e3))
else:
x = np.random.randn(self.nP)
return checkDerivative(lambda m: [self(m), self.deriv(m)],
x,
num=num,
plotIt=plotIt,
**kwargs)
def _test_deriv2(self, x=None, num=4, plotIt=False, **kwargs):
print('Testing {0!s} Deriv2'.format(self.__class__.__name__))
if x is None:
if self.nP == '*':
x = np.random.randn(np.random.randint(1e2, high=1e3))
else:
x = np.random.randn(self.nP)
v = x + 0.1 * np.random.rand(len(x))
return checkDerivative(
lambda m: [self.deriv(m).dot(v),
self.deriv2(m, v=v)],
x,
num=num,
expectedOrder=1,
plotIt=plotIt,
**kwargs)
def test_haverkamp_k_m(self):
mesh = Mesh.TensorMesh([5])
expmap = Maps.IdentityMap(nP=mesh.nC)
wires2 = Maps.Wires(('one', mesh.nC), ('two', mesh.nC))
wires3 = Maps.Wires(
('one', mesh.nC), ('two', mesh.nC), ('three', mesh.nC)
)
opts = [
('Ks',
dict(KsMap=expmap), 1),
('A',
dict(AMap=expmap), 1),
('gamma',
dict(gammaMap=expmap), 1),
('Ks-A',
dict(KsMap=expmap*wires2.one, AMap=expmap*wires2.two), 2),
('Ks-gamma',
dict(KsMap=expmap*wires2.one, gammaMap=expmap*wires2.two), 2),
('A-gamma',
dict(AMap=expmap*wires2.one, gammaMap=expmap*wires2.two), 2),
('Ks-A-gamma', dict(
KsMap=expmap*wires3.one,
AMap=expmap*wires3.two,
gammaMap=expmap*wires3.three), 3),
]
u = np.random.randn(mesh.nC)
for name, opt, nM in opts:
np.random.seed(2)
hav = Richards.Empirical.Haverkamp_k(mesh, **opt)
def fun(m):
hav.model = m
return hav(u), hav.derivM(u)
print('Haverkamp_k test m deriv: ', name)
passed = checkDerivative(
fun,
np.random.randn(mesh.nC * nM),
plotIt=False
)
self.assertTrue(passed, True)
def test_vangenuchten_k_m(self):
mesh = Mesh.TensorMesh([50])
expmap = Maps.ExpMap(nP=mesh.nC)
idnmap = Maps.IdentityMap(nP=mesh.nC)
seeds = {
'Ks': np.random.triangular(
np.log(1e-7), np.log(1e-6), np.log(1e-5), mesh.nC
),
'I': np.random.rand(mesh.nC),
'n': np.random.rand(mesh.nC) + 1,
'alpha': np.random.rand(mesh.nC),
}
opts = [
('Ks',
dict(KsMap=expmap), 1),
('I',
dict(IMap=idnmap), 1),
('n',
dict(nMap=idnmap), 1),
('alpha',
dict(alphaMap=idnmap), 1),
]
u = np.random.randn(mesh.nC)
for name, opt, nM in opts:
van = Richards.Empirical.Vangenuchten_k(mesh, **opt)
x0 = np.concatenate([seeds[n] for n in name.split('-')])
def fun(m):
van.model = m
return van(u), van.derivM(u)
print('Vangenuchten_k test m deriv: ', name)
passed = checkDerivative(
fun,
x0,
plotIt=False
)
self.assertTrue(passed, True)
def _dotest_getResidual(self, newton):
print('Testing richards get residual newton={}, dim={}'.format(
newton,
self.mesh.dim
))
self.prob.do_newton = newton
passed = checkDerivative(
lambda hn1: self.prob.getResidual(
self.mtrue,
self.h0,
hn1,
self.prob.timeSteps[0],
self.prob.boundary_conditions
),
self.h0,
expectedOrder=2 if newton else 1,
plotIt=False
)
self.assertTrue(passed, True)
def test_vangenuchten_theta_m(self):
mesh = Mesh.TensorMesh([50])
idnmap = Maps.IdentityMap(nP=mesh.nC)
seeds = {
'theta_r': np.random.rand(mesh.nC),
'theta_s': np.random.rand(mesh.nC),
'n': np.random.rand(mesh.nC) + 1,
'alpha': np.random.rand(mesh.nC),
}
opts = [
('theta_r',
dict(theta_rMap=idnmap), 1),
('theta_s',
dict(theta_sMap=idnmap), 1),
('n',
dict(nMap=idnmap), 1),
('alpha',
dict(alphaMap=idnmap), 1),
]
u = np.random.randn(mesh.nC)
for name, opt, nM in opts:
van = Richards.Empirical.Vangenuchten_theta(mesh, **opt)
x0 = np.concatenate([seeds[n] for n in name.split('-')])
def fun(m):
van.model = m
return van(u), van.derivM(u)
print('Vangenuchten_theta test m deriv: ', name)
passed = checkDerivative(
fun,
x0,
plotIt=False
)
self.assertTrue(passed, True)
def test_simplePass(self):
def simplePass(x):
return np.sin(x), sdiag(np.cos(x))
passed = checkDerivative(simplePass, np.random.randn(5), plotIt=False)
self.assertTrue(passed, True)
def test_simpleFail(self):
def simpleFail(x):
return np.sin(x), -sdiag(np.cos(x))
passed = checkDerivative(simpleFail, np.random.randn(5), plotIt=False)
self.assertTrue(not passed, True)
def test_simpleFunction(self):
def simpleFunction(x):
return np.sin(x), lambda xi: sdiag(np.cos(x))*xi
passed = checkDerivative(simpleFunction, np.random.randn(5), plotIt=False)
self.assertTrue(passed, True)
def test_Sensitivity(self):
mTrue = self.Ks * np.ones(self.M.nC)
derChk = lambda m: [self.survey.dpred(m), lambda v: self.prob.Jvec(m, v)]
print "3D: Testing Richards Derivative"
passed = checkDerivative(derChk, mTrue, num=4, plotIt=False)
self.assertTrue(passed, True)
