def get_solver(self, func):
"""
Returns the solver method from odespy package.
Args:
func: function
function with ODE system.
Returns: an instance of odeSolver
"""
if self.solverMethod is solverMethod.LSODA:
solver = odespy.Lsoda(func)
elif self.solverMethod is solverMethod.LSODAR:
solver = odespy.Lsodar(func)
elif self.solverMethod is solverMethod.LSODE:
solver = odespy.Lsode(func)
elif self.solverMethod is solverMethod.HEUN:
solver = odespy.Heun(func)
elif self.solverMethod is solverMethod.EULER:
solver = odespy.Euler(func)
elif self.solverMethod is solverMethod.RK4:
solver = odespy.RK4(func)
elif self.solverMethod is solverMethod.DORMAN_PRINCE:
solver = odespy.DormandPrince(func)
elif self.solverMethod is solverMethod.RKFehlberg:
solver = odespy.RKFehlberg(func)
elif self.solverMethod is solverMethod.Dopri5:
solver = odespy.Dopri5(func)
elif self.solverMethod is solverMethod.Dop853:
solver = odespy.Dop853(func)
elif self.solverMethod is solverMethod.Vode:
solver = odespy.Vode(func)
elif self.solverMethod is solverMethod.AdamsBashforth2:
solver = odespy.AdamsBashforth2(func, method='bdf')
elif self.solverMethod is solverMethod.Radau5:
solver = odespy.Radau5(func)
elif self.solverMethod is solverMethod.AdamsBashMoulton2:
solver = odespy.AdamsBashMoulton2(func)
# update default parameters
solver.nsteps = SolverConfigurations.N_STEPS
solver.atol = SolverConfigurations.ABSOLUTE_TOL
solver.rtol = SolverConfigurations.RELATIVE_TOL
return solver
adams_or_bdf = 'bdf'
import odespy
solvers = [
odespy.AdamsBashMoulton2(problem),
odespy.AdamsBashMoulton3(problem),
odespy.AdamsBashforth2(problem),
odespy.AdamsBashforth3(problem),
odespy.AdamsBashforth4(problem),
odespy.AdaptiveResidual(problem, solver='Euler'),
odespy.Backward2Step(problem),
odespy.BackwardEuler(problem),
odespy.Dop853(problem, rtol=rtol, atol=atol),
odespy.Dopri5(problem, rtol=rtol, atol=atol),
odespy.Euler(problem),
odespy.Heun(problem),
odespy.Leapfrog(problem),
odespy.LeapfrogFiltered(problem),
odespy.MidpointImplicit(problem),
odespy.MidpointIter(problem, max_iter=10, eps_iter=1E-7),
odespy.RK2(problem),
odespy.RK3(problem),
odespy.RK4(problem),
odespy.RKFehlberg(problem, rtol=rtol, atol=atol),
odespy.SymPy_odefun(problem),
odespy.ThetaRule(problem),
odespy.Trapezoidal(problem),
odespy.Vode(problem, rtol=rtol, atol=atol, adams_or_bdf=adams_or_bdf),
]
theta_exact = lambda t: problem.Theta * numpy.cos(sqrt(problem.c) * t)
"""Oscillating pendulum."""
import odespy, numpy
from math import sin, pi, sqrt
c = 1
Theta = pi / 4
def f(u, t):
theta, omega = u
return [omega, -c * sin(theta)]
solver = odespy.Heun(f)
solver.set_initial_condition([Theta, 0])
freq = sqrt(c) # frequency of oscillations when Theta is small
period = 2 * pi / freq # the period of the oscillations
T = 10 * period # final time
N_per_period = 20 # resolution of one period
N = N_per_period * period
time_points = numpy.linspace(0, T, N + 1)
u, t = solver.solve(time_points)
theta = u[:, 0]
omega = u[:, 1]
from matplotlib.pyplot import *
plot(t, theta, 'r-')
savefig('tmppng')
numpy.random.seed(12)
t = self.solver.t
dW = numpy.random.normal(loc=0, scale=1, size=len(t)-1)
dt = t[1:] - t[:-1]
self.N = self.sigma*dW/numpy.sqrt(dt)
x, v = u
N = self.N[self.solver.n]
return [v, N -self.b*v -self.c*x]
from numpy import pi, linspace
from matplotlib.pyplot import *
import odespy
problem = WhiteNoiseOscillator(b=0.1, c=pi**2, sigma=1)
solvers = [odespy.Heun(problem.f), odespy.RK4(problem.f),
odespy.ForwardEuler(problem.f)]
for solver in solvers:
f.connect_solver(solver)
solver.set_initial_condition([0,0]) # start from rest
T = 60 # with c=pi**2, the period is 1
u, t = solver.solve(linspace(0, T, 10001))
x = u[:,0]
plot(t, x)
hold(True)
legend([str(s) for s in solvers])
savefig('tmppng'); savefig('tmp.pdf')
show()