How to use discretize - 10 common examples

def dotest(MYSOLVER, multi=False, A=None, **solverOpts):
    if A is None:
        h1 = np.ones(10)*100.
        h2 = np.ones(10)*100.
        h3 = np.ones(10)*100.

        h = [h1,h2,h3]

        M = TensorMesh(h)

        D = M.faceDiv
        G = -M.faceDiv.T
        Msig = M.getFaceInnerProduct()
        A = D*Msig*G
        A[-1,-1] *= 1/M.vol[-1] # remove the constant null space from the matrix
    else:
        M = Mesh.TensorMesh([A.shape[0]])

    Ainv = MYSOLVER(A, **solverOpts)
    if multi:
        e = np.ones(M.nC)
    else:
        e = np.ones((M.nC, numRHS))
    rhs = A * e
    x = Ainv * rhs

]

        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)

]

        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)

'tol': tol,
        'maxit': maxit,
        'nu_init': nu_init,
        'nu_pre': nu_pre,
        'nu_coarse': nu_coarse,
        'nu_post': nu_post,
        'clevel': clevel,
        },
    'result': efield.field,
    'hresult': hfield.field,
}

# # # # # # # # # # 3. TensorMesh check # # # # # # # # # #
# Create an advanced grid with discretize.

grid = TensorMesh(
        [[(10, 10, -1.1), (10, 20, 1), (10, 10, 1.1)],
         [(33, 20, 1), (33, 10, 1.5)],
         [20]],
        x0='CN0')

# List of all attributes in emg3d-grid.
all_attr = [
    'hx', 'hy', 'hz', 'vectorNx', 'vectorNy', 'vectorNz', 'vectorCCx', 'nE',
    'vectorCCy', 'vectorCCz', 'nEx', 'nEy', 'nEz', 'nCx', 'nCy', 'nCz', 'vnC',
    'nNx', 'nNy', 'nNz', 'vnN', 'vnEx', 'vnEy', 'vnEz', 'vnE', 'nC', 'nN', 'x0'
]

mesh = {'attr': all_attr}

for attr in all_attr:
    mesh[attr] = getattr(grid, attr)

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_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_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 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_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 _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)