From c8868177731b70bda818bc3d10d7858bdb87530d Mon Sep 17 00:00:00 2001
From: seogi_macbook <sgkang09@github.com>
Date: Mon, 14 Sep 2015 13:06:51 -0700
Subject: [PATCH 1/2] Fix bug in CircMap

Add PolyMap for 2D, and test
---
 SimPEG/Maps.py | 61 +++++++++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 60 insertions(+), 1 deletion(-)

diff --git a/SimPEG/Maps.py b/SimPEG/Maps.py
index 6dca13dd..0380447e 100644
--- a/SimPEG/Maps.py
+++ b/SimPEG/Maps.py
@@ -696,4 +696,63 @@ class CircleMap(IdentityMap):
         g3 = a*(-X + x)*(-sig1 + sig2)/(np.pi*(a**2*(-r + np.sqrt((X - x)**2 + (Y - y)**2))**2 + 1)*np.sqrt((X - x)**2 + (Y - y)**2))
         g4 = a*(-Y + y)*(-sig1 + sig2)/(np.pi*(a**2*(-r + np.sqrt((X - x)**2 + (Y - y)**2))**2 + 1)*np.sqrt((X - x)**2 + (Y - y)**2))
         g5 = -a*(-sig1 + sig2)/(np.pi*(a**2*(-r + np.sqrt((X - x)**2 + (Y - y)**2))**2 + 1))
-        return np.c_[g1,g2,g3,g4,g5]
+        return sp.csr_matrix(np.c_[g1,g2,g3,g4,g5])
+
+
+class PolyMap(IdentityMap):
+
+    """PolyMap
+
+        Parameterize the model space using a polynomials in a wholespace.
+
+        ..math::
+            
+            y = \mathbf{V} c
+
+        Define the model as:
+
+        ..math::
+
+            m = [\sigma_1, \sigma_2, c]
+
+    """
+    def __init__(self, mesh, order, logSigma=True):
+        assert mesh.dim == 2, "Working for a 2D mesh only right now. But it isn't that hard to change.. :)"
+        IdentityMap.__init__(self, mesh)
+        self.logSigma = logSigma
+        self.order = order
+    
+    slope = 1e4
+
+    @property
+    def nP(self):
+        return self.order+3
+
+    def _transform(self, m):
+        alpha = self.slope
+        sig1,sig2 = m[0],m[1]
+        c = m[2:]
+        if self.logSigma:
+            sig1, sig2 = np.exp(sig1), np.exp(sig2)
+        X = self.mesh.gridCC[:,0]
+        Y = self.mesh.gridCC[:,1]
+        f = polynomial.polyval(X, c) - Y
+        return sig1+(sig2-sig1)*(np.arctan(alpha*f)/np.pi+0.5)
+    
+    def deriv(self, m):
+        alpha = self.slope
+        sig1,sig2, c = m[0],m[1],m[2:]
+        if self.logSigma:
+            sig1, sig2 = np.exp(sig1), np.exp(sig2)
+        X = self.mesh.gridCC[:,0]
+        Y = self.mesh.gridCC[:,1]
+        f = polynomial.polyval(X, c) - Y
+        V = polynomial.polyvander(X, len(c)-1)        
+        if self.logSigma:
+            g1 = -(np.arctan(alpha*f)/np.pi + 0.5)*sig1 + sig1
+            g2 = (np.arctan(alpha*f)/np.pi + 0.5)*sig2
+        else:
+            g1 = -(np.arctan(alpha*f)/np.pi + 0.5) + 1.0
+            g2 = (np.arctan(alpha*f)/np.pi + 0.5)
+        g3 = Utils.sdiag(alpha*(sig2-sig1)/(1.+(alpha*f)**2)/np.pi)*V
+        return sp.csr_matrix(np.c_[g1,g2,g3])    

From f726a27269054d3b7d02fb7ce337abc8eaba7b5e Mon Sep 17 00:00:00 2001
From: seogi_macbook <sgkang09@github.com>
Date: Mon, 14 Sep 2015 21:25:15 -0700
Subject: [PATCH 2/2] Fix target misfit

---
 SimPEG/Directives.py | 2 +-
 SimPEG/Maps.py       | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/SimPEG/Directives.py b/SimPEG/Directives.py
index 3ec9e96e..48d7abcf 100644
--- a/SimPEG/Directives.py
+++ b/SimPEG/Directives.py
@@ -149,7 +149,7 @@ class TargetMisfit(InversionDirective):
     @property
     def target(self):
         if getattr(self, '_target', None) is None:
-            self._target = self.survey.nD
+            self._target = self.survey.nD*0.5
         return self._target
     @target.setter
     def target(self, val):
diff --git a/SimPEG/Maps.py b/SimPEG/Maps.py
index 0380447e..ae6411fd 100644
--- a/SimPEG/Maps.py
+++ b/SimPEG/Maps.py
@@ -1,7 +1,7 @@
 import Utils, numpy as np, scipy.sparse as sp
 from Tests import checkDerivative
 from PropMaps import PropMap, Property
-
+from numpy.polynomial import polynomial
 
 class IdentityMap(object):
     """