def test_hht_basic_2nd_order_spring():
""" Test the hht method for a spring system.
Tests for several values of alpha.
"""
y0 = 3.0
v0 = 2.0
ode = mass_spring_damper(3, 2, 3)
prob = Explicit_Problem(ode, y0)
vals = array([-1.0/3.0,-0.2,-0.1,-0.05,0.0])
for alpha in vals:
hht = HHT(prob, v0, alpha = alpha)
end = 10.0
t, y = hht.simulate(end)
nose.tools.assert_almost_equal(y[-1]/y[-1], ode.explicit(end, v0, y0)/y[-1],places = 1)
def test_hht_basic_2nd_order_damping():
""" Test hht of simple a 2nd order ODE,
ybis(t) = constant* t. Tests for several values of alpha.
"""
f = lambda t: 5.0/3.0* t**3 + 2*t + 3
""" Take off in a rocket at g-acc from 5m above ground, v0 = 10m/s """
def ode_2(t,x,y):
return 10.0 * t
y0 = 3.0
v0 = 2.0
prob = Explicit_Problem(ode_2, y0)
vals = array([-1.0/3.0,-0.2,-0.1,-0.05,0.0])
for alpha in vals:
hht = HHT(prob, v0, alpha = alpha)
end = 10.0
t, y = hht.simulate(end)
nose.tools.assert_almost_equal(y[-1]/y[-1], f(end)/y[-1],places = 1)
def test_against_normal_solvers():
""" Test the HHT method on the damper system and compares the
result against a simulation using LSODAR
"""
end = 10.0
ode = flattened_2nd_order(3, 2, 3)
y0 = 3.0
v0 = 2.0
prob = Explicit_Problem(ode, [y0,v0])
exp_sim = LSODAR(prob)
t, y = exp_sim.simulate(end)
ode = mass_spring_damper(3, 2, 3)
prob = Explicit_Problem(ode, y0)
hht = HHT(prob, v0, alpha = -0.2)
t, y_2 = hht.simulate(end)
nose.tools.assert_almost_equal(y[-1][0]/y[-1][0], y_2[-1]/y[-1][0],places = 1)
def test_pend_hht_against_normal():
""" Test out hht solver againts the pendulum by comparing the result
of a simulation against one done by assimulo"""
import problems as p
from matplotlib.pylab import plot, show, figure
pend = p.Pendulum2nd()
ode = pend.fcn
end = 15
y0 = pend.initial_condition()
prob = Explicit_Problem(ode, y0[0])
hht = HHT(prob, y0[1], alpha=-0.2)
t, y_1 = hht.simulate(end)
ode = pend.fcn_1
prob = Explicit_Problem(ode, y0)
sim = LSODAR(prob)
t, y_3 = sim.simulate(end)
nose.tools.assert_almost_equal(y_3[-1][0]/y_3[-1][0], y_1[-1]/y_3[-1][0],places = 1)
