working on getting baker to work in 3D. the code runs, but the numbers are odd. I suspect the rectangular grid, and am going to try a random cloud of points.

.setup

@@ -1,2 +1 @@
 export PATH=$PWD/bin:$PWD/test:$PATH
-export PYTHONPATH=$PWD/lib

bin/driver.py

@@ -6,18 +6,18 @@ from optparse import OptionParser
 import numpy as np
 
 from baker.tools import rms, exact_func
-import grid
+from grid.DD import simple_random_grid, simple_rect_grid
 
 
 def get_mesh(source, destination, use_structured_grid = False):
   mesh_source = None
   mesh_dest   = None
   if use_structured_grid:
-    mesh_source = grid.simple_rect_grid(source, source)
+    mesh_source = simple_rect_grid(source, source)
-    mesh_dest   = grid.simple_rect_grid(destination, destination)
+    mesh_dest   = simple_rect_grid(destination, destination)
   else:
-    mesh_source = grid.simple_random_grid(source)
+    mesh_source = simple_random_grid(source)
-    mesh_dest   = grid.simple_random_grid(destination)
+    mesh_dest   = simple_random_grid(destination)
 
   if not (mesh_dest and mesh_source):
     raise smberror('problem creating mesh objects')
@@ -39,35 +39,33 @@ if __name__ == '__main__':
                     dest="extra",
                     type='int',
                     default = 3,
-                    help = "how many extra points")
+                    help = "how many extra points (%default)")
 
   parser.add_option("-s",
                     "--source-total",
                     dest="source_total",
                     type='int',
                     default = 100,
-                    help = "total number of source points for random,\
+                    help = "total number of source points for random, resolution for structured (%default)")
-                              resolution for structured")
 
   parser.add_option("-d",
                     "--destination-total",
                     dest="destination_total",
                     type='int',
                     default = 100,
-                    help = "total number of destination points,\
+                    help = "total number of destination points, resolution for structured (%default)")
-                             resolution for structured")
 
   parser.add_option("-r",
                     "--structured",
                     action = 'store_true',
                     default = False,
-                    help = "use a structured grid instead of random point cloud")
+                    help = "use a structured grid instead of random point cloud (%default)")
 
   parser.add_option("-v",
                     "--verbose",
                     action = 'store_true',
                     default = False,
-                    help = "verbosity")
+                    help = "verbosity (%default)")
 
   (options, args) = parser.parse_args()
 

bin/grid_regular.py

@@ -1,9 +1,9 @@
-#!/usr/bin/python
+#!/usr/bin/python2.6
 
 import sys
 import pickle
 
-from grid        import simple_rect_grid, simple_random_grid
+from grid.DD     import simple_rect_grid, simple_random_grid
 from baker       import run_baker
 from baker.tools import smberror
 

lib/baker/baker.py

@@ -41,9 +41,14 @@ def get_phis_3D(X, r):
     X -- the destination point (3D)
          X = [0,0,0]
     r -- the four points that make up the tetrahedron (3D)
-         r = [[-1, -1], [0, 2], [1, -1]]
+         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],
+             ]
 
-    this will return [0.333, 0.333, 0.333]
+    this will return [0.25, 0.25, 0.25, 0.25]
   """
 
   # baker: eq 7
@@ -82,7 +87,7 @@ def qlinear(X, R):
   qlin = sum([q_i * phi_i for q_i, phi_i in zip(R.q, phis)])
   return phis, qlin
 
-def qlinear_3D(X, R, q):
+def qlinear_3D(X, R):
   """
     this calculates the linear portion of q from X to r
 
@@ -91,8 +96,8 @@ def qlinear_3D(X, R, q):
     q = CFD quantities of interest at the simplex points(R)
   """
 
-  phis = get_phis_3D(X, R)
+  phis = get_phis_3D(X, R.points)
-  qlin = sum([q_i * phi_i for q_i, phi_i in zip(q, phis)])
+  qlin = sum([q_i * phi_i for q_i, phi_i in zip(R.q, phis)])
   return phis, qlin
 
 def run_baker(X, R, S):
@@ -103,13 +108,11 @@ def run_baker(X, R, S):
          X = [0,0]
 
     R = Simplex
-
     S = extra points
-
   """
 
   # calculate values only for the triangle
-  phi, qlin = qlinear (X, R)
+  phi, qlin = qlinear(X, R)
 
   if len(S.points) == 0:
     answer = {
@@ -129,7 +132,13 @@ def run_baker(X, R, S):
     cur_phi, cur_qlin = qlinear(s, R)
     (phi1, phi2, phi3) = cur_phi
 
-    B.append([phi1 * phi2, phi2 * phi3, phi3 * phi1])
+    B.append(
+              [
+                phi1 * phi2,
+                phi2 * phi3,
+                phi3 * phi1,
+              ]
+            )
     w.append(q - cur_qlin)
 
   B = np.array(B)
@@ -161,3 +170,87 @@ def run_baker(X, R, S):
             }
 
   return answer
+
+def run_baker_3D(X, R, S):
+  """
+    This is the main function to call to get an interpolation to X from the input meshes
+
+    X -- the destination point (3D)
+         X = [0,0,0]
+
+    R = Simplex (4 points, contains X)
+    S = extra points (surrounding, in some manner, R and X, but not in R)
+  """
+
+  # calculate values only for the triangle
+  phi, qlin = qlinear_3D(X, R)
+
+  if len(S.points) == 0:
+    answer = {
+               'a': None,
+               'b': None,
+               'c': None,
+               'd': None,
+               'e': None,
+               'f': None,
+               'qlin': qlin,
+               'error': None,
+               'final': None,
+              }
+    return answer
+
+  B = [] # baker eq 9
+  w = [] # baker eq 11
+
+  for (s, q) in zip(S.points, S.q):
+    cur_phi, cur_qlin = qlinear_3D(s, R)
+    (phi1, phi2, phi3, phi4) = cur_phi
+
+    B.append(
+              [
+                phi1 * phi2,
+                phi1 * phi3,
+                phi1 * phi4,
+                phi2 * phi3,
+                phi2 * phi4,
+                phi3 * phi4,
+              ]
+            )
+
+    w.append(q - cur_qlin)
+
+  B = np.array(B)
+  w = np.array(w)
+
+  A = np.dot(B.T, B)
+  b = np.dot(B.T, w)
+
+  # baker solve eq 10
+  try:
+    (a, b, c, d, e, f) = np.linalg.solve(A,b)
+  except:
+    print >> sys.stderr, "warning: run_baker: linear calculation went bad, resorting to np.linalg.pinv"
+    (a, b, c, d, e, f) = np.dot(np.linalg.pinv(A), b)
+
+  error_term =  a * phi[0] * phi[1]\
+              + b * phi[0] * phi[2]\
+              + c * phi[0] * phi[3]\
+              + d * phi[1] * phi[2]\
+              + e * phi[1] * phi[3]\
+              + f * phi[2] * phi[3]
+
+  q_final = qlin + error_term
+
+  answer = {
+             'a': a,
+             'b': b,
+             'c': c,
+             'd': d,
+             'e': e,
+             'f': f,
+             'qlin': qlin,
+             'error': error_term,
+             'final': q_final,
+            }
+
+  return answer

lib/baker/tools.py

@@ -24,3 +24,12 @@ def exact_func(x, y):
     the exact function used from baker's article (for testing)
   """
   return np.power((np.sin(x * np.pi) * np.cos(y * np.pi)), 2)
+
+def exact_func_3D(X):
+  """
+    the exact function (3D) used from baker's article (for testing)
+  """
+  x = X[0]
+  y = X[1]
+  z = X[2]
+  return np.power((np.sin(x * np.pi / 2.0) * np.sin(y * np.pi / 2.0) * np.sin(z * np.pi / 2.0)), 2)

lib/grid/grid.py

@@ -7,49 +7,11 @@ from   collections import defaultdict
 import numpy as np
 import scipy.spatial
 
-from baker        import run_baker, get_phis
+from baker        import run_baker
 from baker.tools  import exact_func, smberror
+from simplex      import face
 from smcqdelaunay import *
 
-class face(object):
-  def __init__(self, name):
-    self.name      = name
-    self.verts     = []
-    self.neighbors = []
-
-  def add_vert(self, v):
-    """
-       v should be an index into grid.points
-    """
-    self.verts.append(v)
-
-  def add_neighbor(self, n):
-    """
-       reference to another face object
-    """
-    self.neighbors.append(n)
-
-  def contains(self, X, grid):
-    R    = [grid.points[i] for i in self.verts]
-
-    phis = get_phis(X, R)
-
-    r = True
-    if [i for i in phis if i < 0.0]:
-      r = False
-    return r
-
-  def __str__(self):
-    neighbors = [i.name for i in self.neighbors]
-    return '%s: verts: %s neighbors: [%s]' %\
-           (
-             self.name,
-             self.verts,
-             ", ".join(neighbors)
-           )
-
-
-
 
 
 class grid(object):
@@ -97,7 +59,7 @@ class grid(object):
       R is a grid object that is the (a) containing simplex around point X
       S is S_j from baker's paper : some points from all point that are not the simplex
     """
-    (dist, indicies) = self.tree.query(X, 3 + extra_points)
+    (dist, indicies) = self.tree.query(X, simplex_size + extra_points)
 
 
     # get the containing simplex
@@ -152,7 +114,7 @@ class grid(object):
     try:
       (R, S) = self.get_simplex_and_nearest_points(X)
       answer = run_baker(X, R, S)
-    except smberror as e:
+    except smberror, e:
       print "caught error: %s, trying with connectivity-based mesh" % e
       (R, S) = self.get_points_conn(X)
       answer = run_baker(X, R, S)
@@ -199,27 +161,6 @@ class grid(object):
 
     #   self.facets_for_point[int(point[1:])] = [i for i in neighboring_facets.split() if i in self.faces]
 
-  def for_qhull_generator(self):
-    """
-      this returns a generator that should be fed into qdelaunay
-    """
-
-    yield '2';
-    yield '%d' % len(self.points)
-
-    for p in self.points:
-      yield "%f %f" % (p[0], p[1])
-
-  def for_qhull(self):
-    """
-      this returns a single string that should be fed into qdelaunay
-    """
-    r  = '2\n'
-    r += '%d\n' % len(self.points)
-    for p in self.points:
-      r += "%f %f\n" % (p[0], p[1])
-    return r
-
   def __str__(self):
     r = ''
     assert( len(self.points) == len(self.q) )
@@ -233,49 +174,7 @@ class grid(object):
         r += "%s\n" % v
     return r
 
-class simple_rect_grid(grid):
-  def __init__(self, xres = 5, yres = 5):
-    xmin = -1.0
-    xmax =  1.0
-    xspan = xmax - xmin
-    xdel = xspan / float(xres - 1)
 
-    ymin = -1.0
-    ymay =  1.0
-    yspan = ymay - ymin
-    ydel = yspan / float(yres - 1)
-
-
-    points = []
-    q      = []
-    for x in xrange(xres):
-      cur_x = xmin + (x * xdel)
-      for y in xrange(yres):
-        cur_y = ymin + (y * ydel)
-        points.append([cur_x, cur_y])
-        q.append(exact_func(cur_x, cur_y))
-    grid.__init__(self, points, q)
-    self.construct_connectivity()
-
-
-
-class simple_random_grid(simple_rect_grid):
-  def __init__(self, num_points = 10):
-    points = []
-    q = []
-
-    r = np.random
-
-    for i in xrange(num_points):
-      cur_x = r.rand()
-      cur_y = r.rand()
-
-      points.append([cur_x, cur_y])
-      q.append(exact_func(cur_x, cur_y))
-    grid.__init__(self, points, q)
-
-    self.points = np.array(self.points)
-    self.q      = np.array(self.q)
 
 
 if __name__ == '__main__':

setup.py

@@ -4,7 +4,7 @@ use_setuptools()
 from setuptools import setup, find_packages
 
 setup(
-        name             = 'bakinterp',
+        name             = 'interpolosion',
         version          = '0.01',
         package_dir      = {'':'lib'},
         packages         = find_packages('lib'),

test/baker.test.py

@@ -10,7 +10,6 @@ import scipy.spatial
 class TestSequenceFunctions(unittest.TestCase):
   def setUp(self):
     self.l = [[-1, 1], [-1, 0], [-1, 1], [0, -1], [0, 0], [0, 1], [1, -1], [1, 0], [1, 1]]
-    self.approx_fmt = "%0.6f"
     self.all_points = [
                         [ 0, 0], # 0
                         [ 1, 0], # 1
@@ -37,9 +36,9 @@ class TestSequenceFunctions(unittest.TestCase):
     r = [[-1, -1], [0, 2], [1, -1]]
 
     result = baker.get_phis(X, r)
-    result = [self.approx_fmt % i for i in result]
+    result = [round(i, 5) for i in result]
 
-    right_answer = [self.approx_fmt % i for i in [1/3.0, 1/3.0, 1/3.0]]
+    right_answer = [round(i, 5) for i in [1/3.0, 1/3.0, 1/3.0]]
 
     for a,b in zip(result, right_answer):
       self.assertEqual(a,b)
@@ -78,13 +77,13 @@ class TestSequenceFunctions(unittest.TestCase):
                            self.q[size_of_simplex:size_of_simplex + extra_points])
 
     answer = baker.run_baker(self.X, R, S)
-    a = self.approx_fmt % answer['a']
+    a = round(answer['a'], 5)
-    b = self.approx_fmt % answer['b']
+    b = round(answer['b'], 5)
-    c = self.approx_fmt % answer['c']
+    c = round(answer['c'], 5)
 
     self.assertEqual(a, c)
-    self.assertEqual(c, self.approx_fmt % 0.00)
+    self.assertEqual(c, round(0.00 , 5))
-    self.assertEqual(b, self.approx_fmt % (1/3.0))
+    self.assertEqual(b, round(1/3.0, 5))
 
   def testRunBaker_2(self):
     size_of_simplex = 3
@@ -98,12 +97,12 @@ class TestSequenceFunctions(unittest.TestCase):
 
     answer = baker.run_baker(self.X, R, S)
 
-    a = self.approx_fmt % answer['a']
+    a = round(answer['a'], 5)
-    b = self.approx_fmt % answer['b']
+    b = round(answer['b'], 5)
-    c = self.approx_fmt % answer['c']
+    c = round(answer['c'], 5)
 
     self.assertEqual(a, c)
-    self.assertEqual(c, self.approx_fmt % float(2/3.0))
+    self.assertEqual(c, round(float(2/3.0), 5))
 
   def testRunBaker_3(self):
     size_of_simplex = 3
@@ -116,13 +115,13 @@ class TestSequenceFunctions(unittest.TestCase):
                            self.q[size_of_simplex:size_of_simplex + extra_points])
 
     answer = baker.run_baker(self.X, R, S)
-    a = self.approx_fmt % answer['a']
+    a = round(answer['a'], 5)
-    b = self.approx_fmt % answer['b']
+    b = round(answer['b'], 5)
-    c = self.approx_fmt % answer['c']
+    c = round(answer['c'], 5)
 
-    self.assertEqual(a, self.approx_fmt % float(13/14.0))
+    self.assertEqual(a, round(float(13/14.0), 5))
-    self.assertEqual(b, self.approx_fmt % float(2 / 7.0))
+    self.assertEqual(b, round(float(2 / 7.0), 5))
-    self.assertEqual(c, self.approx_fmt % float(15/14.0))
+    self.assertEqual(c, round(float(15/14.0), 5))
 
   def testRunBaker_4(self):
     size_of_simplex = 3
@@ -135,13 +134,13 @@ class TestSequenceFunctions(unittest.TestCase):
                            self.q[size_of_simplex:size_of_simplex + extra_points])
 
     answer = baker.run_baker(self.X, R, S)
-    a = self.approx_fmt % answer['a']
+    a = round(answer['a'], 5)
-    b = self.approx_fmt % answer['b']
+    b = round(answer['b'], 5)
-    c = self.approx_fmt % answer['c']
+    c = round(answer['c'], 5)
 
-    self.assertEqual(a, self.approx_fmt % float(48/53.0))
+    self.assertEqual(a, round(float(48/53.0), 5))
-    self.assertEqual(b, self.approx_fmt % float(15/53.0))
+    self.assertEqual(b, round(float(15/53.0), 5))
-    self.assertEqual(c, self.approx_fmt % float(54/53.0))
+    self.assertEqual(c, round(float(54/53.0), 5))
 
 if __name__ == '__main__':
   suite = unittest.TestLoader().loadTestsFromTestCase(TestSequenceFunctions)