/usr/lib/python2.7/dist-packages/mpmath/tests/test_ode.py is in python-mpmath 0.19-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 | #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))
|