def test_line_derivative(self):
# using AlmostEqual for floating point error
gamma = ComplexLine(0, 1)
self.assertAlmostEqual(gamma.derivative(0), 1)
self.assertAlmostEqual(gamma.derivative(0.5), 1)
self.assertAlmostEqual(gamma.derivative(0.75), 1)
self.assertAlmostEqual(gamma.derivative(0), 1)
gamma = ComplexLine(-1.j, 1.j)
self.assertAlmostEqual(gamma.derivative(0), 2.j)
self.assertAlmostEqual(gamma.derivative(0.5), 2.j)
self.assertAlmostEqual(gamma.derivative(0.75), 2.j)
self.assertAlmostEqual(gamma.derivative(1), 2.j)
def test_line_derivative(self):
# using AlmostEqual for floating point error
gamma = ComplexLine(0, 1)
self.assertAlmostEqual(gamma.derivative(0), 1)
self.assertAlmostEqual(gamma.derivative(0.5), 1)
self.assertAlmostEqual(gamma.derivative(0.75), 1)
self.assertAlmostEqual(gamma.derivative(0), 1)
gamma = ComplexLine(-1.j, 1.j)
self.assertAlmostEqual(gamma.derivative(0), 2.j)
self.assertAlmostEqual(gamma.derivative(0.5), 2.j)
self.assertAlmostEqual(gamma.derivative(0.75), 2.j)
self.assertAlmostEqual(gamma.derivative(1), 2.j)
def test_simple_composite(self):
gammax1 = ComplexLine(4, 1)
gamma1 = RiemannSurfacePathSmale(self.X1, gammax1, [-2, 2])
gammax2 = ComplexArc(1, 0, 0, pi)
gamma2 = RiemannSurfacePathSmale(self.X1, gammax2, [-1, 1])
gamma = gamma1 + gamma2
nu = lambda x, y: y
nu_gamma = gamma.parameterize(nu)
val = nu_gamma(0.0)
test = gammax1.derivative(0.0) * (-2)
self.assertAlmostEqual(val, test)
val = nu_gamma(0.25)
test = gammax1.derivative(0.5) * (-sqrt(2.5))
self.assertAlmostEqual(val, test)
eps = 1e-12
val = nu_gamma(0.5 - eps)
test = gammax1.derivative(1.0 - eps / 2) * (-1)
self.assertAlmostEqual(val, test)
val = nu_gamma(0.5)
test = gammax2.derivative(0.0) * (-1)
self.assertAlmostEqual(val, test)
val = nu_gamma(0.5 + eps)
test = gammax2.derivative(eps / 2) * (-1)
self.assertAlmostEqual(val, test)
val = nu_gamma(0.75)
test = gammax2.derivative(0.5) * (-sqrt(1.j))
self.assertAlmostEqual(val, test)
val = nu_gamma(1.0)
test = gammax2.derivative(1.0) * (-1.j)
self.assertAlmostEqual(val, test)
def test_simple_composite(self):
gammax1 = ComplexLine(4,1)
gamma1 = RiemannSurfacePathSmale(self.X1, gammax1, [-2,2])
gammax2 = ComplexArc(1,0,0,pi)
gamma2 = RiemannSurfacePathSmale(self.X1, gammax2, [-1,1])
gamma = gamma1 + gamma2
nu = lambda x,y: y
nu_gamma = gamma.parameterize(nu)
val = nu_gamma(0.0)
test = gammax1.derivative(0.0)*(-2)
self.assertAlmostEqual(val, test)
val = nu_gamma(0.25)
test = gammax1.derivative(0.5)*(-sqrt(2.5))
self.assertAlmostEqual(val, test)
eps = 1e-12
val = nu_gamma(0.5-eps)
test = gammax1.derivative(1.0-eps/2)*(-1)
self.assertAlmostEqual(val, test)
val = nu_gamma(0.5)
test = gammax2.derivative(0.0)*(-1)
self.assertAlmostEqual(val, test)
val = nu_gamma(0.5+eps)
test = gammax2.derivative(eps/2)*(-1)
self.assertAlmostEqual(val, test)
val = nu_gamma(0.75)
test = gammax2.derivative(0.5)*(-sqrt(1.j))
self.assertAlmostEqual(val, test)
val = nu_gamma(1.0)
test = gammax2.derivative(1.0)*(-1.j)
self.assertAlmostEqual(val, test)
