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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)) | |