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