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import sys
if sys.path[0] != "../..":
sys.path.insert(0, "../..")
import unittest
from pyx import mathutils
class PolynomTestCase(unittest.TestCase):
def makePolyRoots(self, *rs):
# creates a polynom with zeros rs
if len(rs) == 1:
return [1, -rs[0]]
cs = self.makePolyRoots(*rs[1:])
return [cim1-rs[0]*ci for cim1, ci in zip(cs+[0], [0]+cs)]
def makePolyNonroots(self, cs, a, b):
# adds a factor ((x-a)**2 + b) to the polynom with coefficients cs
# which can be used (for b > 0) to construct polynoms with complex roots
return [cim2-2*a*cim1+(a*a+b)*ci for cim2, cim1, ci in zip(cs+[0, 0], [0]+cs+[0], [0, 0]+cs)]
def compareRoots(self, found, should):
found.sort()
# we remove degeneracies in found, since we do *not* claim to properly handle degeneracies
i = 1
while len(found) > i:
if found[i] - found[i-1] < 1e-7:
del found[i]
else:
i += 1
self.assertEqual(len(found), len(should))
for r1, r2 in zip(found, should):
self.assertAlmostEqual(r1, r2)
def testConstant(self):
self.compareRoots(mathutils.realpolyroots(1), [])
self.compareRoots(mathutils.realpolyroots(0), [0])
def testLinear(self):
self.compareRoots(mathutils.realpolyroots(0, 1), [])
self.compareRoots(mathutils.realpolyroots(0, 0), [0])
self.compareRoots(mathutils.realpolyroots(1, 1), [-1])
self.compareRoots(mathutils.realpolyroots(2, 0), [0])
self.compareRoots(mathutils.realpolyroots(4, -1), [0.25])
self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(1.7)), [1.7])
self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(-42)), [-42])
def testQuadratic(self):
self.compareRoots(mathutils.realpolyroots(0, 1, 1), [-1])
self.compareRoots(mathutils.realpolyroots(1, -4, 3), [1, 3])
self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(1.7, 2.3)), [1.7, 2.3])
self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(2.3, 1.7)), [1.7, 2.3])
self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(1.7, -2.3)), [-2.3, 1.7])
self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(-2.3, 1.7)), [-2.3, 1.7])
self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(1.7, 1.7)), [1.7])
self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots([1], 1.7, 1)), [])
self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots([1], 1.7, -1)), [0.7, 2.7])
self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots([1], 1.7, -4)), [-0.3, 3.7])
def testCubic(self):
self.compareRoots(mathutils.realpolyroots(0, 0, 0, 1), [])
self.compareRoots(mathutils.realpolyroots(0, 0, 1, 1), [-1])
self.compareRoots(mathutils.realpolyroots(0, 1, -4, 3), [1, 3])
self.compareRoots(mathutils.realpolyroots(1, -9, 23, -15), [1, 3, 5])
self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(1.7, 2.3, 4.2)), [1.7, 2.3, 4.2])
self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(1.7, -2.3, 4.2)), [-2.3, 1.7, 4.2])
self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(1.7, -2.3, -4.2)), [-4.2, -2.3, 1.7])
self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots(self.makePolyRoots(1.7), 2.3, 1)), [1.7])
self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots(self.makePolyRoots(1.7), 2.3, -1)), [1.3, 1.7, 3.3])
self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots(self.makePolyRoots(1.7), 2.3, -4)), [0.3, 1.7, 4.3])
def testQuartic(self):
self.compareRoots(mathutils.realpolyroots(0, 0, 0, 0, 1), [])
self.compareRoots(mathutils.realpolyroots(0, 0, 0, 1, 1), [-1])
self.compareRoots(mathutils.realpolyroots(0, 1, -9, 23, -15), [1, 3, 5])
self.compareRoots(mathutils.realpolyroots(1, -16, 86, -176, 105), [1, 3, 5, 7])
self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(1.7, 2.3, 4.2, 13)), [1.7, 2.3, 4.2, 13])
self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(1.7, -2.3, 4.2, 13)), [-2.3, 1.7, 4.2, 13])
self.compareRoots(mathutils.realpolyroots(*self.makePolyRoots(1.7, -2.3, -4.2, 13)), [-4.2, -2.3, 1.7, 13])
self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots(self.makePolyRoots(1.7, 2.3), 4.2, 1)), [1.7, 2.3])
self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots(self.makePolyRoots(1.7, 2.3), 4.2, -1)), [1.7, 2.3, 3.2, 5.2])
self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots(self.makePolyRoots(1.7, 2.3), 4.2, -4)), [1.7, 2.2, 2.3, 6.2])
self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots(self.makePolyRoots(1.7, -2.3), 4.2, -1)), [-2.3, 1.7, 3.2, 5.2])
self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots(self.makePolyRoots(1.7, -2.3), 4.2, -4)), [-2.3, 1.7, 2.2, 6.2])
self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots(self.makePolyNonroots([1], 1.7, 1), 2.3, 1)), [])
self.compareRoots(mathutils.realpolyroots(*self.makePolyNonroots(self.makePolyNonroots([1], 1.7, 1), 2.3, -1)), [1.3, 3.3])
if __name__ == "__main__":
unittest.main()
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