test/unit/test_mathutils.py

   1 import sys
   2 if sys.path[0] != "../..":
   3     sys.path.insert(0, "../..")
   4
   5 import unittest
   6
   7 from pyx import mathutils
   8
   9 class PolynomTestCase(unittest.TestCase):
  10
  11     def makePolyRoots(self, *rs):
  12         # creates a polynom with zeros rs
  13         if len(rs) == 1:
  14             return [1, -rs[0]]
  15         cs = self.makePolyRoots(*rs[1:])
  16         return [cim1-rs[0]*ci for cim1, ci in zip(cs+[0], [0]+cs)]
  17
  18     def makePolyNonroots(self, cs, a, b):
  19         # adds a factor ((x-a)**2 + b) to the polynom with coefficients cs
  20         # which can be used (for b > 0) to construct polynoms with complex roots
  21         return [cim2-2*a*cim1+(a*a+b)*ci for cim2, cim1, ci in zip(cs+[0, 0], [0]+cs+[0], [0, 0]+cs)]
  22
  23     def compareRoots(self, found, should):
  24         found.sort()
  25         # we remove degeneracies in found, since we do *not* claim to properly handle degeneracies
  26         i = 1
  27         while len(found) > i:
  28             if found[i] - found[i-1] < 1e-7:
  29                 del found[i]
  30             else:
  31                 i += 1
  32         self.assertEqual(len(found), len(should))
  33         for r1, r2 in zip(found, should):
  34             self.assertAlmostEqual(r1, r2)
  35
  36     def testConstant(self):
  37         self.compareRoots(mathutils.realpolyroots(1), [])
  38         self.compareRoots(mathutils.realpolyroots(0), [0])
  39
  40     def testLinear(self):
  41         self.compareRoots(mathutils.realpolyroots(0, 1), [])
  42         self.compareRoots(mathutils.realpolyroots(0, 0), [0])
  43         self.compareRoots(mathutils.realpolyroots(1, 1), [-1])
  44         self.compareRoots(mathutils.realpolyroots(2, 0), [0])
  45         self.compareRoots(mathutils.realpolyroots(4, -1), [0.25])
  46         self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(1.7)), [1.7])
  47         self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(-42)), [-42])
  48
  49     def testQuadratic(self):
  50         self.compareRoots(mathutils.realpolyroots(0, 1, 1), [-1])
  51         self.compareRoots(mathutils.realpolyroots(1, -4, 3), [1, 3])
  52         self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(1.7, 2.3)), [1.7, 2.3])
  53         self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(2.3, 1.7)), [1.7, 2.3])
  54         self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(1.7, -2.3)), [-2.3, 1.7])
  55         self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(-2.3, 1.7)), [-2.3, 1.7])
  56         self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(1.7, 1.7)), [1.7])
  57         self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots([1], 1.7, 1)), [])
  58         self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots([1], 1.7, -1)), [0.7, 2.7])
  59         self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots([1], 1.7, -4)), [-0.3, 3.7])
  60
  61     def testCubic(self):
  62         self.compareRoots(mathutils.realpolyroots(0, 0, 0, 1), [])
  63         self.compareRoots(mathutils.realpolyroots(0, 0, 1, 1), [-1])
  64         self.compareRoots(mathutils.realpolyroots(0, 1, -4, 3), [1, 3])
  65         self.compareRoots(mathutils.realpolyroots(1, -9, 23, -15), [1, 3, 5])
  66         self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(1.7, 2.3, 4.2)), [1.7, 2.3, 4.2])
  67         self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(1.7, -2.3, 4.2)), [-2.3, 1.7, 4.2])
  68         self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(1.7, -2.3, -4.2)), [-4.2, -2.3, 1.7])
  69         self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots(self.makePolyRoots(1.7), 2.3, 1)), [1.7])
  70         self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots(self.makePolyRoots(1.7), 2.3, -1)), [1.3, 1.7, 3.3])
  71         self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots(self.makePolyRoots(1.7), 2.3, -4)), [0.3, 1.7, 4.3])
  72
  73     def testQuartic(self):
  74         self.compareRoots(mathutils.realpolyroots(0, 0, 0, 0, 1), [])
  75         self.compareRoots(mathutils.realpolyroots(0, 0, 0, 1, 1), [-1])
  76         self.compareRoots(mathutils.realpolyroots(0, 1, -9, 23, -15), [1, 3, 5])
  77         self.compareRoots(mathutils.realpolyroots(1, -16, 86, -176, 105), [1, 3, 5, 7])
  78         self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(1.7, 2.3, 4.2, 13)), [1.7, 2.3, 4.2, 13])
  79         self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(1.7, -2.3, 4.2, 13)), [-2.3, 1.7, 4.2, 13])
  80         self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(1.7, -2.3, -4.2, 13)), [-4.2, -2.3, 1.7, 13])
  81         self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots(self.makePolyRoots(1.7, 2.3), 4.2, 1)), [1.7, 2.3])
  82         self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots(self.makePolyRoots(1.7, 2.3), 4.2, -1)), [1.7, 2.3, 3.2, 5.2])
  83         self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots(self.makePolyRoots(1.7, 2.3), 4.2, -4)), [1.7, 2.2, 2.3, 6.2])
  84         self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots(self.makePolyRoots(1.7, -2.3), 4.2, -1)), [-2.3, 1.7, 3.2, 5.2])
  85         self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots(self.makePolyRoots(1.7, -2.3), 4.2, -4)), [-2.3, 1.7, 2.2, 6.2])
  86         self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots(self.makePolyNonroots([1], 1.7, 1), 2.3, 1)), [])
  87         self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots(self.makePolyNonroots([1], 1.7, 1), 2.3, -1)), [1.3, 3.3])
  88
  89
  90 if __name__ == "__main__":
  91     unittest.main()