Source Code for Module pyvision.vector.Polynomial

  1  # PyVision License 
  2  # 
  3  # Copyright (c) 2006-2008 David S. Bolme 
  4  # All rights reserved. 
  5  # 
  6  # Redistribution and use in source and binary forms, with or without 
  7  # modification, are permitted provided that the following conditions 
  8  # are met: 
  9  #  
 10  # 1. Redistributions of source code must retain the above copyright 
 11  # notice, this list of conditions and the following disclaimer. 
 12  #  
 13  # 2. Redistributions in binary form must reproduce the above copyright 
 14  # notice, this list of conditions and the following disclaimer in the 
 15  # documentation and/or other materials provided with the distribution. 
 16  #  
 17  # 3. Neither name of copyright holders nor the names of its contributors 
 18  # may be used to endorse or promote products derived from this software 
 19  # without specific prior written permission. 
 20  #  
 21  #  
 22  # THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 
 23  # ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 
 24  # LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR 
 25  # A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR 
 26  # CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, 
 27  # EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 
 28  # PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR 
 29  # PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF 
 30  # LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING 
 31  # NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 
 32  # SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 
 33   
 34  from pyvision.vector.VectorClassifier import VectorClassifier,TYPE_REGRESSION 
 35  from numpy import array,dot 
 36  from numpy.linalg import lstsq 
 37   
 38 -class Polynomial2D(VectorClassifier): 
 39 -    def __init__(self,order=2,**kwargs): 
 40          #FIXME: DOcument this code 
 41          ''' 
 42          This class fits a polynomial to a function of 2 variables. 
 43          ''' 
 44          self.order = order 
 45          self.x = None 
 46          VectorClassifier.__init__(self,TYPE_REGRESSION,**kwargs) 
 47           
 48           
 49 -    def trainClassifer(self,labels,vectors,ilog=None): 
 50          ''' 
 51          Train the polynomial.  Do not call this function 
 52          manually, instead call the train function on the super 
 53          class. 
 54          ''' 
 55          #build matrix 
 56          matrix = [] 
 57          for each in vectors: 
 58              if len(each) != 2: 
 59                  raise ValueError("ERROR: Vector length=%d.  Polynomial2D only predicts for vectors of length 2."%len(each)) 
 60              x,y = each 
 61              matrix.append(self.buildRow(x,y)) 
 62           
 63          matrix = array(matrix) 
 64          labels = array(labels) 
 65           
 66          x,resids,rank,s = lstsq(matrix,labels) 
 67           
 68          self.x = x 
 69          self.resids = resids 
 70          self.rank = rank 
 71          self.s = s 
 72           
 73          if rank != matrix.shape[1]: 
 74              print "WARNING: Polynomial is not fully constrained." 
 75           
 76                   
 77   
 78 -    def buildRow(self,x,y): 
 79          ''' 
 80          Method for private use only. 
 81          ''' 
 82          row = [1.0] 
 83          for o in range(1,self.order+1): 
 84              for i in range(o+1): 
 85                  row.append(float(x)**i*float(y)**(o-i)) 
 86          return row 
 87   
 88 -    def predictValue(self,data,ilog=None): 
 89          ''' 
 90          Method for private use only.  Call super class predict. 
 91          ''' 
 92          if len(data) != 2: 
 93              raise ValueError("Polynomial2D only predicts for vectors of length 2.") 
 94   
 95          x,y = data 
 96          return dot(self.x , self.buildRow(x,y)) 
 97   
 98  import unittest 
 99   
100 -class _PolyTest(unittest.TestCase): 
101 -    def test_buildrow(self): 
102          poly = Polynomial2D(order=3) 
103          row = array(poly.buildRow(2,2)) 
104          error = row-array([1.0,2.0,2.0,4.0,4.0,4.0,8.0,8.0,8.0,8.0]) 
105          sse = (error*error).sum() 
106          self.assert_(sse < 0.001) 
107   
108          row = array(poly.buildRow(2,1)) 
109          error = row-array([1.0,1.0,2.0,1.0,2.0,4.0,1.0,2.0,4.0,8.0]) 
110          sse = (error*error).sum() 
111          self.assert_(sse < 0.001) 
112   
113          row = array(poly.buildRow(1,2)) 
114          error = row-array([1.0,2.0,1.0,4.0,2.0,1.0,8.0,4.0,2.0,1.0]) 
115          sse = (error*error).sum() 
116          self.assert_(sse < 0.001) 
117   
118 -    def test_train(self): 
119          poly = Polynomial2D(order=2) 
120          for x in range(-8,9): 
121              for y in range(-8,9): 
122                  val = -5 + 3*y + 2*x - 4*y*y + 2*y*x+ x*x 
123                  poly.addTraining(val,[x,y]) 
124          poly.train() 
125          for x in range(-8,9): 
126              for y in range(-8,9): 
127                  val  = -5 + 3*y + 2*x - 4*y*y + 2*y*x+ x*x 
128                  pred = poly.predict([x,y]) 
129                  self.assert_(abs(val - pred) < 0.0001) 
130