def test_simple_line_dxds(self):
gammax = ComplexLine(1, 3) # dx/ds = 2
gamma = RiemannSurfacePathSmale(self.X1, gammax, [-1, 1])
nu = lambda x, y: y
nu_gamma = gamma.parameterize(nu)
val = nu_gamma(0.0)
self.assertAlmostEqual(val, -2)
val = nu_gamma(0.5)
self.assertAlmostEqual(val, -2 * sqrt(2.0))
val = nu_gamma(1.0)
self.assertAlmostEqual(val, -2 * sqrt(3.0))
def test_simple_line_smale(self):
gammax = ComplexLine(1, 2)
gamma = RiemannSurfacePathSmale(self.X1, gammax, [-1, 1])
nu = lambda x, y: y
nu_gamma = gamma.parameterize(nu)
val = nu_gamma(0.0)
self.assertAlmostEqual(val, -1)
val = nu_gamma(0.5)
self.assertAlmostEqual(val, -sqrt(1.5))
val = nu_gamma(1.0)
self.assertAlmostEqual(val, -sqrt(2.0))
def test_simple_line_dxds(self):
gammax = ComplexLine(1,3) # dx/ds = 2
gamma = RiemannSurfacePathSmale(self.X1, gammax, [-1,1])
nu = lambda x,y: y
nu_gamma = gamma.parameterize(nu)
val = nu_gamma(0.0)
self.assertAlmostEqual(val, -2)
val = nu_gamma(0.5)
self.assertAlmostEqual(val, -2*sqrt(2.0))
val = nu_gamma(1.0)
self.assertAlmostEqual(val, -2*sqrt(3.0))
def test_simple_line_smale(self):
gammax = ComplexLine(1,2)
gamma = RiemannSurfacePathSmale(self.X1, gammax, [-1,1])
nu = lambda x,y: y
nu_gamma = gamma.parameterize(nu)
val = nu_gamma(0.0)
self.assertAlmostEqual(val, -1)
val = nu_gamma(0.5)
self.assertAlmostEqual(val, -sqrt(1.5))
val = nu_gamma(1.0)
self.assertAlmostEqual(val, -sqrt(2.0))
def test_simple_arc(self):
gammax = ComplexArc(1, 0, 0, pi)
gamma = RiemannSurfacePathSmale(self.X1, gammax, [-1, 1])
nu = lambda x, y: y
nu_gamma = gamma.parameterize(nu)
val = nu_gamma(0.0)
test = gammax.derivative(0.0) * (-1)
self.assertAlmostEqual(val, test)
val = nu_gamma(0.5)
test = gammax.derivative(0.5) * (-sqrt(1.j))
self.assertAlmostEqual(val, test)
val = nu_gamma(1.0)
test = gammax.derivative(1.0) * (-1.j)
self.assertAlmostEqual(val, test)
def test_simple_arc(self):
gammax = ComplexArc(1,0,0,pi)
gamma = RiemannSurfacePathSmale(self.X1, gammax, [-1,1])
nu = lambda x,y: y
nu_gamma = gamma.parameterize(nu)
val = nu_gamma(0.0)
test = gammax.derivative(0.0)*(-1)
self.assertAlmostEqual(val, test)
val = nu_gamma(0.5)
test = gammax.derivative(0.5)*(-sqrt(1.j))
self.assertAlmostEqual(val, test)
val = nu_gamma(1.0)
test = gammax.derivative(1.0)*(-1.j)
self.assertAlmostEqual(val, test)
