Added A sample Linear problem that runs!

SimPEG/forward/LinearProblem.py

@@ -0,0 +1,91 @@
+import numpy as np
+from SimPEG.mesh import TensorMesh
+from SimPEG.forward import Problem
+from SimPEG.regularization import Regularization
+from SimPEG.inverse import *
+import matplotlib.pyplot as plt
+
+N = 100
+h = np.ones(N)/N
+M = 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)
+
+
+
+plt.figure(1)
+for i in range(nk):
+    plt.plot(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
+
+# plt.figure(3)
+# plt.plot(d_true,'-o')
+# plt.plot(d_obs,'r-o')
+
+
+
+class LinearProblem(Problem):
+    """docstring for LinearProblem"""
+
+    def dpred(self, m, u=None):
+        return self.G.dot(m)
+
+    def J(self, m, v, u=None):
+        return G.dot(v)
+
+    def Jt(self, m, v, u=None):
+        return G.T.dot(v)
+
+    def modelTransform(self, m):
+        return m
+
+    def modelTransformDeriv(self, m):
+        return sp.eye(m.size)
+
+prob = LinearProblem(M)
+prob.G = G
+prob.dobs = d_obs
+prob.std = np.ones_like(d_obs)*0.1
+
+reg = Regularization(M)
+
+opt = InexactGaussNewton(maxIter=10)
+
+inv = Inversion(prob,reg,opt)
+
+m0 = np.zeros_like(m_true)
+
+mrec = inv.run(m0)
+
+
+plt.figure(2)
+
+plt.plot(M.vectorCCx, m_true, 'b-')
+plt.plot(M.vectorCCx, mrec, 'r-')
+
+
+
+plt.show()

SimPEG/forward/Problem.py

@@ -82,6 +82,17 @@ class Problem(object):
     def dobs(self, value):
         self._dobs = value
 
+    def dpred(self, m, u=None):
+        """
+            Predicted data.
+
+            .. math::
+                d_\\text{pred} = Pu(m)
+        """
+        if u is None:
+            u = self.field(m)
+        return self.P*u
+
     def misfit(self, m, u=None):
         """
             :param numpy.array m: geophysical model
@@ -152,17 +163,6 @@ class Problem(object):
         """
         pass
 
-    def dpred(self, m, u=None):
-        """
-            Predicted data.
-
-            .. math::
-                d_\\text{pred} = Pu(m)
-        """
-        if u is None:
-            u = self.field(m)
-        return self.P*u
-
     def modelTransform(self, m):
         """
             :param numpy.array m: model