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)