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- #from mpmath.calculus import ODE_step_euler, ODE_step_rk4, odeint, arange
- from mpmath import odefun, cos, sin, mpf, sinc, mp
- '''
- solvers = [ODE_step_euler, ODE_step_rk4]
- def test_ode1():
- """
- Let's solve:
- x'' + w**2 * x = 0
- i.e. x1 = x, x2 = x1':
- x1' = x2
- x2' = -x1
- """
- def derivs((x1, x2), t):
- return x2, -x1
- for solver in solvers:
- t = arange(0, 3.1415926, 0.005)
- sol = odeint(derivs, (0., 1.), t, solver)
- x1 = [a[0] for a in sol]
- x2 = [a[1] for a in sol]
- # the result is x1 = sin(t), x2 = cos(t)
- # let's just check the end points for t = pi
- assert abs(x1[-1]) < 1e-2
- assert abs(x2[-1] - (-1)) < 1e-2
- def test_ode2():
- """
- Let's solve:
- x' - x = 0
- i.e. x = exp(x)
- """
- def derivs((x), t):
- return x
- for solver in solvers:
- t = arange(0, 1, 1e-3)
- sol = odeint(derivs, (1.,), t, solver)
- x = [a[0] for a in sol]
- # the result is x = exp(t)
- # let's just check the end point for t = 1, i.e. x = e
- assert abs(x[-1] - 2.718281828) < 1e-2
- '''
- def test_odefun_rational():
- mp.dps = 15
- # A rational function
- f = lambda t: 1/(1+mpf(t)**2)
- g = odefun(lambda x, y: [-2*x*y[0]**2], 0, [f(0)])
- assert f(2).ae(g(2)[0])
- def test_odefun_sinc_large():
- mp.dps = 15
- # Sinc function; test for large x
- f = sinc
- g = odefun(lambda x, y: [(cos(x)-y[0])/x], 1, [f(1)], tol=0.01, degree=5)
- assert abs(f(100) - g(100)[0])/f(100) < 0.01
- def test_odefun_harmonic():
- mp.dps = 15
- # Harmonic oscillator
- f = odefun(lambda x, y: [-y[1], y[0]], 0, [1, 0])
- for x in [0, 1, 2.5, 8, 3.7]: # we go back to 3.7 to check caching
- c, s = f(x)
- assert c.ae(cos(x))
- assert s.ae(sin(x))
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