Update directives

Add IRLS example

SimPEG/Examples/Inversion_IRLS.py

@@ -1,7 +1,7 @@
 from SimPEG import *
 
 
-def run(N=100, plotIt=True):
+def run(N=200, plotIt=True):
     """
         Inversion: Linear Problem
         =========================
@@ -9,39 +9,21 @@ def run(N=100, plotIt=True):
         Here we go over the basics of creating a linear problem and inversion.
 
     """
-
-    class LinearSurvey(Survey.BaseSurvey):
-        def projectFields(self, u):
-            return u
-
-    class LinearProblem(Problem.BaseProblem):
-
-        surveyPair = LinearSurvey
-
-        def __init__(self, mesh, G, **kwargs):
-            Problem.BaseProblem.__init__(self, mesh, **kwargs)
-            self.G = G
-
-        def fields(self, m, u=None):
-            return self.G.dot(m)
-
-        def Jvec(self, m, v, u=None):
-            return self.G.dot(v)
-
-        def Jtvec(self, m, v, u=None):
-            return self.G.T.dot(v)
-
-
+    
+    
     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.
 
-    nk = 20
-    jk = np.linspace(1.,20.,nk)
-    p = -0.25
-    q = 0.25
-
-    g = lambda k: np.exp(p*jk[k]*mesh.vectorCCx)*np.cos(2*np.pi*q*jk[k]*mesh.vectorCCx)
+    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))
 
@@ -52,25 +34,43 @@ def run(N=100, plotIt=True):
     mtrue[mesh.vectorCCx > 0.3] = 1.
     mtrue[mesh.vectorCCx > 0.45] = -0.5
     mtrue[mesh.vectorCCx > 0.6] = 0
+  
 
-    prob = LinearProblem(mesh, G)
-    survey = LinearSurvey()
+    prob = Problem.LinearProblem(mesh, G)
+    survey = Survey.LinearSurvey()
     survey.pair(prob)
-    survey.makeSyntheticData(mtrue, std=0.01)
-
-    M = prob.mesh
-
-    reg = Regularization.Tikhonov(mesh)
+    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) )**0
+    
+    reg = Regularization.Simple(mesh)
+    reg.wght = wr
+    
     dmis = DataMisfit.l2_DataMisfit(survey)
-    opt = Optimization.ProjectedGNCG(maxIter=20,lower=-1.,upper=1., maxIterCG= 20, tolCG = 1e-3)
+    dmis.Wd = 1./wd
+    
+    opt = Optimization.ProjectedGNCG(maxIter=30,lower=-2.,upper=2., maxIterCG= 20, tolCG = 1e-4)
     invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
-    beta = Directives.BetaSchedule()
+    invProb.curModel = m0
+    
+    beta = Directives.BetaSchedule(coolingFactor=2, coolingRate=1)
+    target = Directives.TargetMisfit()
+
     betaest = Directives.BetaEstimate_ByEig()
-    inv = Inversion.BaseInversion(invProb, directiveList=[beta, betaest])
-    m0 = np.zeros_like(survey.mtrue)
+    inv = Inversion.BaseInversion(invProb, directiveList=[beta, betaest, target])
+    
 
     mrec = inv.run(m0)
-
+    
+    print "Final misfit:" + str(invProb.dmisfit.eval(mrec)) 
+    
     if plotIt:
         import matplotlib.pyplot as plt
 
@@ -78,12 +78,54 @@ def run(N=100, plotIt=True):
         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(M.vectorCCx, survey.mtrue, 'b-')
-        axes[1].plot(M.vectorCCx, mrec, 'r-')
-        axes[1].legend(('True Model', 'Recovered Model'))
+        
+        axes[1].plot(mesh.vectorCCx, mtrue, 'b-')
+        axes[1].plot(mesh.vectorCCx, mrec, 'r-')
+        #axes[1].legend(('True Model', 'Recovered Model'))
+        axes[1].set_ylim(-1.0,1.25)
         plt.show()
+        
+    # 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=10 ,lower=-2.,upper=2., maxIterCG= 200, 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:
+        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)
+        
     return prob, survey, mesh, mrec
 
 if __name__ == '__main__':