polish for inclusion into thesis

interp/baker/__init__.py

@@ -11,37 +11,35 @@ log = logging.getLogger('interp')
 
 def get_phis(X, R):
   """
-    The get_phis function is used to get barycentric coordonites for a point on
-    a triangle or tetrahedron:
-
+    The get_phis function is used to get barycentric coordonites for a
+    point on a triangle or tetrahedron. This is equation (*\ref{eq:qlinarea}*)
 
     in 2D:
 
-    X -- the destination point (2D)
-         X = [0,0]
-    r -- the three points that make up the containing triangular simplex (2D)
-         r = [[-1, -1], [0, 2], [1, -1]]
+    X - the destination point (2D)
+        X = [0,0]
+    R - the three points that make up the 2-D triangular simplex
+        R = [[-1, -1], [0, 2], [1, -1]]
 
     this will return [0.333, 0.333, 0.333]
 
 
     in 3D:
 
-    X -- the destination point (3D)
-         X = [0,0,0]
-    R -- the four points that make up the containing simplex, tetrahedron (3D)
-         R = [
-               [0.0, 0.0, 1.0],
-               [0.94280904333606508, 0.0, -0.3333333283722672],
-               [-0.47140452166803232, 0.81649658244673617, -0.3333333283722672],
-               [-0.47140452166803298, -0.81649658244673584, -0.3333333283722672],
-             ]
+    X - the destination point (3D)
+        X = [0,0,0]
+    R - the four points that make up the 3-D simplex (tetrahedron)
+        R = [
+           [ 0.0000,  0.0000,  1.0000],
+           [ 0.9428,  0.0000, -0.3333],
+           [-0.4714,  0.8165, -0.3333],
+           [-0.4714, -0.8165, -0.3333],
+         ]
 
     this will return [0.25, 0.25, 0.25, 0.25]
   """
 
-  # baker: eq 7
-  # TODO: perhaps also test len(R[0])  .. ?
+  # equations (*\ref{eq:lin3d}*) and (*\ref{eq:lin2d}*)
   if len(X) == 2:
     log.debug("running 2D")
     A = np.array([
@@ -85,7 +83,7 @@ def qlinear(X, R):
   """
     this calculates the linear portion of q from R to X
 
-    also, this is baker eq 3
+    This is equation (*\ref{eq:qlinbasis}*)
 
     X = destination point
     R = a inter.grid object; must have R.points and R.q
@@ -100,9 +98,12 @@ def qlinear(X, R):
   return phis, qlin
 
 def get_error(phi, R, S, order = 2):
-  #TODO: change the equation names in the comments
-  B = [] # baker eq 9
-  w = [] # baker eq 11
+  """
+    Calculate the error approximation terms, returning the unknowns
+    a,b, and c in equation (*\ref{eq:quadratic2d}*).
+  """
+  B = [] # equation ((*\ref{eq:B2d}*)
+  w = [] # equation ((*\ref{eq:w}*)
 
   cur_pattern  = pattern(len(phi), order)
   log.info("pattern: %s" % cur_pattern)
@@ -150,8 +151,7 @@ def run_baker(X, R, S, order=2):
     This is the main function to call to get an interpolation to X from the
     input meshes
 
-    X -- the destination point (2D)
-         X = [0,0]
+    X -- the destination point
 
     R = Simplex
     S = extra points
@@ -190,9 +190,7 @@ def run_baker(X, R, S, order=2):
 
 def memoize(f):
   """
-    for more information on what I'm doing here,
-    please read:
-
+    for more information on what I'm doing here, please read:
     http://en.wikipedia.org/wiki/Memoize
   """
   cache = {}