Merge branch 'feat/sparse-regularization' into patch/sparse-dcip

# Conflicts:
#	SimPEG/Examples/__init__.py
#	SimPEG/Optimization.py

SimPEG/Examples/Inversion_IRLS.py

@@ -0,0 +1,132 @@
+from SimPEG import *
+
+
+def run(N=200, plotIt=True):
+    """
+        Inversion: Linear Problem
+        =========================
+
+        Here we go over the basics of creating a linear problem and inversion.
+
+    """
+
+
+    np.random.seed(1)
+
+    std_noise = 1e-2
+
+    mesh = Mesh.TensorMesh([N])
+
+    m0 = np.ones(mesh.nC) * 1e-4
+    nk = 10
+    jk = np.linspace(1.,nk,nk)
+    p = -2.
+    q = 1.
+
+    g = lambda k: np.exp(p*jk[k]*mesh.vectorCCx)*np.cos(np.pi*q*jk[k]*mesh.vectorCCx)
+
+    G = np.empty((nk, mesh.nC))
+
+    for i in range(nk):
+        G[i,:] = g(i)
+
+    mtrue = np.zeros(mesh.nC)
+    mtrue[mesh.vectorCCx > 0.3] = 1.
+    mtrue[mesh.vectorCCx > 0.45] = -0.5
+    mtrue[mesh.vectorCCx > 0.6] = 0
+
+
+    prob = Problem.LinearProblem(mesh, G)
+    survey = Survey.LinearSurvey()
+    survey.pair(prob)
+    survey.dobs = prob.fields(mtrue) + std_noise * np.random.randn(nk)
+    #survey.makeSyntheticData(mtrue, std=std_noise)
+
+    wd = np.ones(nk) * std_noise
+
+    #print survey.std[0]
+    #M = prob.mesh
+    # Distance weighting
+    wr = np.sum(prob.G**2.,axis=0)**0.5
+    wr = ( wr/np.max(wr) )
+
+    reg = Regularization.Simple(mesh)
+    reg.wght = wr
+
+    dmis = DataMisfit.l2_DataMisfit(survey)
+    dmis.Wd = 1./wd
+
+    opt = Optimization.ProjectedGNCG(maxIter=30,lower=-2.,upper=2., maxIterCG= 20, tolCG = 1e-4)
+    invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
+    invProb.curModel = m0
+
+    beta = Directives.BetaSchedule(coolingFactor=2, coolingRate=1)
+    target = Directives.TargetMisfit()
+
+    betaest = Directives.BetaEstimate_ByEig()
+    inv = Inversion.BaseInversion(invProb, directiveList=[beta, betaest, target])
+
+
+    mrec = inv.run(m0)
+    ml2 = mrec
+    print "Final misfit:" + str(invProb.dmisfit.eval(mrec))
+
+    # Switch regularization to sparse
+    phim = invProb.phi_m_last
+    phid =  invProb.phi_d
+
+    reg = Regularization.Sparse(mesh)
+
+#==============================================================================
+#     fig, axes = plt.subplots(1,2,figsize=(12*1.2,4*1.2))
+#     dmdx = reg.mesh.cellDiffxStencil * mrec
+#     plt.plot(np.sort(dmdx))
+#==============================================================================
+
+    #reg.recModel = mrec
+    reg.wght = np.ones(mesh.nC)
+    reg.mref = np.zeros(mesh.nC)
+    reg.eps_p = 2e-3
+    reg.eps_q = 2e-3
+    reg.norms   = [0., 0., 2., 2.]
+    reg.wght = wr
+
+    opt = Optimization.ProjectedGNCG(maxIter=5 ,lower=-2.,upper=2., maxIterCG= 100, tolCG = 1e-3)
+    invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta = invProb.beta*2.)
+    beta = Directives.BetaSchedule(coolingFactor=1, coolingRate=1)
+    #betaest = Directives.BetaEstimate_ByEig()
+    target = Directives.TargetMisfit()
+    IRLS =Directives.update_IRLS( phi_m_last = phim, phi_d_last = phid )
+
+    inv = Inversion.BaseInversion(invProb, directiveList=[beta,IRLS])
+
+    m0 = mrec
+
+    # Run inversion
+    mrec = inv.run(m0)
+
+    print "Final misfit:" + str(invProb.dmisfit.eval(mrec))
+
+
+    if plotIt:
+        import matplotlib.pyplot as plt
+
+        fig, axes = plt.subplots(1,2,figsize=(12*1.2,4*1.2))
+        for i in range(prob.G.shape[0]):
+            axes[0].plot(prob.G[i,:])
+        axes[0].set_title('Columns of matrix G')
+
+        axes[1].plot(mesh.vectorCCx, mtrue, 'b-')
+        axes[1].plot(mesh.vectorCCx, ml2, 'r-')
+        #axes[1].legend(('True Model', 'Recovered Model'))
+        axes[1].set_ylim(-1.0,1.25)
+
+        axes[1].plot(mesh.vectorCCx, mrec, 'k-',lw = 2)
+        axes[1].legend(('True Model', 'Smooth l2-l2',
+        'Sparse lp:' + str(reg.norms[0]) + ', lqx:' + str(reg.norms[1]) ), fontsize = 12)
+        plt.show()
+
+    return prob, survey, mesh, mrec
+
+if __name__ == '__main__':
+    run()