Moved DC and Linear to the examples directory.

SimPEG/examples/DC.py

@@ -0,0 +1,242 @@
+from SimPEG.mesh import TensorMesh
+from SimPEG.forward import Problem, ModelTransforms
+from SimPEG.tests import checkDerivative
+from SimPEG.utils import ModelBuilder, sdiag, mkvc
+from SimPEG import Solver
+import numpy as np
+import scipy.sparse as sp
+
+
+class DCProblem(ModelTransforms.LogModel, Problem):
+    """
+        **DCProblem**
+
+        Geophysical DC resistivity problem.
+
+    """
+    def __init__(self, mesh):
+        Problem.__init__(self, mesh)
+        self.mesh.setCellGradBC('neumann')
+
+    def reshapeFields(self, u):
+        if len(u.shape) == 1:
+            u = u.reshape([-1, self.RHS.shape[1]], order='F')
+        return u
+
+    def createMatrix(self, m):
+        """
+            Makes the matrix A(m) for the DC resistivity problem.
+
+            :param numpy.array m: model
+            :rtype: scipy.csc_matrix
+            :return: A(m)
+
+            .. math::
+                c(m,u) = A(m)u - q = G\\text{sdiag}(M(mT(m)))Du - q = 0
+
+            Where M() is the mass matrix and mT is the model transform.
+        """
+        D = self.mesh.faceDiv
+        G = self.mesh.cellGrad
+        sigma = self.modelTransform(m)
+        Msig = self.mesh.getFaceMass(sigma)
+        A = D*Msig*G
+        return A.tocsc()
+
+    def dpred(self, m, u=None):
+        """
+            Predicted data.
+
+            .. math::
+                d_\\text{pred} = Pu(m)
+        """
+        if u is None:
+            u = self.field(m)
+
+        u = self.reshapeFields(u)
+
+        return mkvc(self.P*u)
+
+    def field(self, m):
+        A = self.createMatrix(m)
+        solve = Solver(A)
+        phi = solve.solve(self.RHS)
+        return mkvc(phi)
+
+    def J(self, m, v, u=None):
+        """
+            :param numpy.array m: model
+            :param numpy.array v: vector to multiply
+            :param numpy.array u: fields
+            :rtype: numpy.array
+            :return: Jv
+
+            .. math::
+                c(m,u) = A(m)u - q = G\\text{sdiag}(M(mT(m)))Du - q = 0
+
+                \\nabla_u (A(m)u - q) = A(m)
+
+                \\nabla_m (A(m)u - q) = G\\text{sdiag}(Du)\\nabla_m(M(mT(m)))
+
+            Where M() is the mass matrix and mT is the model transform.
+
+            .. math::
+                J = - P \left( \\nabla_u c(m, u) \\right)^{-1} \\nabla_m c(m, u)
+
+                J(v) = - P ( A(m)^{-1} ( G\\text{sdiag}(Du)\\nabla_m(M(mT(m))) v ) )
+        """
+        if u is None:
+            u = self.field(m)
+
+        u = self.reshapeFields(u)
+
+        P = self.P
+        D = self.mesh.faceDiv
+        G = self.mesh.cellGrad
+        A = self.createMatrix(m)
+        Av_dm = self.mesh.getFaceMassDeriv()
+        mT_dm = self.modelTransformDeriv(m)
+
+        dCdu = A
+
+        dCdm = np.empty_like(u)
+        for i, ui in enumerate(u.T):  # loop over each column
+            dCdm[:, i] = D * ( sdiag( G * ui ) * ( Av_dm * ( mT_dm * v ) ) )
+
+        solve = Solver(dCdu)
+        Jv = - P * solve.solve(dCdm)
+        return mkvc(Jv)
+
+    def Jt(self, m, v, u=None):
+        """Takes data, turns it into a model..ish"""
+
+        if u is None:
+            u = self.field(m)
+
+        u = self.reshapeFields(u)
+        v = self.reshapeFields(v)
+
+        P = self.P
+        D = self.mesh.faceDiv
+        G = self.mesh.cellGrad
+        A = self.createMatrix(m)
+        Av_dm = self.mesh.getFaceMassDeriv()
+        mT_dm = self.modelTransformDeriv(m)
+
+        dCdu = A.T
+        solve = Solver(dCdu)
+
+        w = solve.solve(P.T*v)
+
+        Jtv = 0
+        for i, ui in enumerate(u.T):  # loop over each column
+            Jtv += sdiag( G * ui ) * ( D.T * w[:,i] )
+
+        Jtv = - mT_dm.T * ( Av_dm.T * Jtv )
+        return Jtv
+
+
+
+def genTxRxmat(nelec, spacelec, surfloc, elecini, mesh):
+    """ Generate projection matrix (Q) and """
+    elecend = 0.5+spacelec*(nelec-1)
+    elecLocR = np.linspace(elecini, elecend, nelec)
+    elecLocT = elecLocR+1
+    nrx = nelec-1
+    ntx = nelec-1
+    q = np.zeros((mesh.nC, ntx))
+    Q = np.zeros((mesh.nC, nrx))
+
+    for i in range(nrx):
+
+        rxind1 = np.argwhere((mesh.gridCC[:,0]==surfloc) & (mesh.gridCC[:,1]==elecLocR[i]))
+        rxind2 = np.argwhere((mesh.gridCC[:,0]==surfloc) & (mesh.gridCC[:,1]==elecLocR[i+1]))
+
+        txind1 = np.argwhere((mesh.gridCC[:,0]==surfloc) & (mesh.gridCC[:,1]==elecLocT[i]))
+        txind2 = np.argwhere((mesh.gridCC[:,0]==surfloc) & (mesh.gridCC[:,1]==elecLocT[i+1]))
+
+        q[txind1,i] = 1
+        q[txind2,i] = -1
+        Q[rxind1,i] = 1
+        Q[rxind2,i] = -1
+
+    Q = sp.csr_matrix(Q)
+    rxmidLoc = (elecLocR[0:nelec-1]+elecLocR[1:nelec])*0.5
+    return q, Q, rxmidLoc
+
+
+
+if __name__ == '__main__':
+
+    from SimPEG.regularization import Regularization
+    from SimPEG import inverse
+    import matplotlib.pyplot as plt
+
+    # Create the mesh
+    h1 = np.ones(20)
+    h2 = np.ones(100)
+    mesh = TensorMesh([h1,h2])
+
+    # Create some parameters for the model
+    sig1 = np.log(1)
+    sig2 = np.log(0.01)
+
+    # Create a synthetic model from a block in a half-space
+    p0 = [5, 10]
+    p1 = [15, 50]
+    condVals = [sig1, sig2]
+    mSynth = ModelBuilder.defineBlockConductivity(p0,p1,mesh.gridCC,condVals)
+    plt.colorbar(mesh.plotImage(mSynth))
+    plt.show()
+
+    # Set up the projection
+    nelec = 50
+    spacelec = 2
+    surfloc = 0.5
+    elecini = 0.5
+    elecend = 0.5+spacelec*(nelec-1)
+    elecLocR = np.linspace(elecini, elecend, nelec)
+    rxmidLoc = (elecLocR[0:nelec-1]+elecLocR[1:nelec])*0.5
+    q, Q, rxmidloc = genTxRxmat(nelec, spacelec, surfloc, elecini, mesh)
+    P = Q.T
+
+    # Create some data
+    problem = DCProblem(mesh)
+    problem.P = P
+    problem.RHS = q
+    dobs, Wd = problem.createSyntheticData(mSynth, std=0.05)
+
+    u = problem.field(mSynth)
+    u = problem.reshapeFields(u)
+    mesh.plotImage(u[:,10])
+    # plt.show()
+
+    # Now set up the problem to do some minimization
+    problem.dobs = dobs
+    problem.std = dobs*0 + 0.05
+    m0 = mesh.gridCC[:,0]*0+sig2
+
+    opt = inverse.InexactGaussNewton(maxIterLS=20, maxIter=10, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6)
+    reg = Regularization(mesh)
+    inv = inverse.Inversion(problem, reg, opt, beta0=1e4)
+
+    # Check Derivative
+    derChk = lambda m: [inv.dataObj(m), inv.dataObjDeriv(m)]
+    checkDerivative(derChk, mSynth)
+
+
+
+    print inv.dataObj(m0)
+    print inv.dataObj(mSynth)
+
+    m = inv.run(m0)
+
+    plt.colorbar(mesh.plotImage(m))
+    print m
+    plt.show()
+
+
+
+
+
+

SimPEG/examples/Linear.py

@@ -0,0 +1,80 @@
+from SimPEG import mesh, forward, inverse, regularization, np
+import matplotlib.pyplot as plt
+
+
+class LinearProblem(forward.Problem):
+    """docstring for LinearProblem"""
+
+    def __init__(self, *args, **kwargs):
+        forward.Problem.__init__(self, *args, **kwargs)
+
+    def dpred(self, m, u=None):
+        return self.G.dot(m)
+
+    def J(self, m, v, u=None):
+        return self.G.dot(v)
+
+    def Jt(self, m, v, u=None):
+        return self.G.T.dot(v)
+
+
+def example(N):
+    h = np.ones(N)/N
+    M = mesh.TensorMesh([h])
+
+    nk = 20
+    jk = np.linspace(1.,20.,nk)
+    p = -0.25
+    q = 0.25
+
+    g = lambda k: np.exp(p*jk[k]*M.vectorCCx)*np.cos(2*np.pi*q*jk[k]*M.vectorCCx)
+
+    G = np.empty((nk, M.nC))
+
+    for i in range(nk):
+        G[i,:] = g(i)
+
+
+    m_true = np.zeros(M.nC)
+    m_true[M.vectorCCx > 0.3] = 1.
+    m_true[M.vectorCCx > 0.45] = -0.5
+    m_true[M.vectorCCx > 0.6] = 0
+
+
+    d_true = G.dot(m_true)
+    noise = 0.1 * np.random.rand(d_true.size)
+
+    d_obs = d_true + noise
+
+    prob = LinearProblem(M)
+    prob.G = G
+    prob.dobs = d_obs
+    prob.std = np.ones_like(d_obs)*0.1
+
+    return prob, m_true
+
+
+if __name__ == '__main__':
+
+    prob, m_true = example(100)
+    M = prob.mesh
+
+    reg = regularization.Regularization(M)
+    opt = inverse.InexactGaussNewton(maxIter=20)
+    inv = inverse.Inversion(prob,reg,opt,beta0=1e-4)
+    m0 = np.zeros_like(m_true)
+
+    mrec = inv.run(m0)
+
+    plt.figure(1)
+    for i in range(prob.G.shape[0]):
+        plt.plot(prob.G[i,:])
+
+    plt.figure(2)
+
+    plt.plot(M.vectorCCx, m_true, 'b-')
+    plt.plot(M.vectorCCx, mrec, 'r-')
+
+
+
+    plt.show()

SimPEG/examples/__init__.py

@@ -0,0 +1,2 @@
+import DC
+import Linear