def events(t, y):
value = [y[0]]
isterminal = [1]
direction = [-1]
return [value, isterminal, direction]
def dydt(t, y):
return [y[1], -9.8]
tstart = 0
tfinal = 30
y0 = [0.0, 20.0]
options = Odeoptions()
options.odeset('Refine', 10)
options.odeset('Events', events)
tout = np.array([tstart])
yout = np.array([[y0[0]], [y0[1]]])
teout = np.array([0])
yeout = np.array([[0], [0]])
ieout = np.array([0])
for i in range(10):
tspan = np.array([tstart, tfinal])
res = ode45(dydt, tspan, y0, options)
nt = len(res.t)
parentdir = os.path.dirname(currentdir)
sys.path.append(parentdir)
from ode45 import ode45
from odeoptions import Odeoptions
def sin(t, y):
dydt = np.cos(t)
return dydt
tspan = [0, 10]
y0 = [0]
myOptions = Odeoptions() #Create an option with default value.
myOptions.odeset('RelTol', 1e-5)
myOptions.odeset('AbsTol', 1e-8)
myOptions.odeset('Refine', 10)
myOptions.odeset('NormControl', True)
myOptions.odeset('MaxStep', 1)
myOptions.odeset('InitialStep', 0.1)
sol = ode45(sin, tspan, y0, myOptions)
#Plot ode45 approx
fig = plt.figure()
plt.title('Ode45 approx')
plt.xlabel('t')
plt.ylabel('y')
plt.plot(sol.t, sol.y[0])
def odearguments(FcnHandlesUsed, solver, ode, tspan, y0, options, extras):
if FcnHandlesUsed:
tspan = np.array(tspan)
if tspan.size < 2:
raise Exception("pyhton:odearguments:tspan.size < 2")
htspan = np.abs(tspan[1] - tspan[0])
tspan = np.array(tspan)
ntspan = tspan.size
t0 = tspan[0]
NEXT = 1 # NEXT entry in tspan
tfinal = tspan[ntspan - 1]
args = extras
y0 = np.array(y0)
neq = len(y0)
# Test that tspan is internally consistent.
if any(np.isnan(tspan)):
raise Exception("pyhton:odearguments:TspanNaNValues")
if t0 == tfinal:
raise Exception("pyhton:odearguments:TspanEndpointsNotDistinct")
if tfinal > t0:
tdir = 1
else:
tdir = -1
if any(tdir * np.diff(tspan) <= 0):
raise Exception("pyhton:odearguments:TspanNotMonotonic")
f0 = feval(ode, t0, y0, args)
if options is None:
options = Odeoptions() #Use default values
if options.MaxStep is None:
options.MaxStep = np.abs(0.1 * (tfinal - t0))
rtol = np.array([options.RelTol])
if (len(rtol) != 1 or rtol <= 0):
raise Exception("pyhton:odearguments:RelTolNotPosScalar")
if rtol < 100 * np.finfo(float).eps:
rtol = 100 * np.finfo(float).eps
atol = options.AbsTol
if isinstance(atol, list):
atol = np.array(atol)
else:
atol = np.array([atol])
if any(atol <= 0):
raise Exception("python:odearguments:AbsTolNotPos")
normcontrol = options.NormControl
if normcontrol:
if len(atol) != 1:
raise Exception("python:odearguments:NonScalarAbsTol")
normy = np.linalg.norm(y0)
else:
if ((len(atol) != 1) and (len(atol) != neq)):
raise Exception("python:odearguments:SizeAbsTol")
normy = None
threshold = atol / rtol
hmax = np.array([options.MaxStep])
if hmax <= 0:
raise Exception("python:odearguments:MaxStepLEzero")
htry = options.InitialStep
if htry is not None:
if htry <= 0:
raise Exception("python:odearguments:InitialStepLEzero")
odeFcn = ode
dataType = 'float64'
return neq, tspan, ntspan, NEXT, t0, tfinal, tdir, y0, f0, args, odeFcn, options, threshold, rtol, normcontrol, normy, hmax, htry, htspan, dataType
#Add parent folder to the path. Code taken from https://codeolives.com/2020/01/10/python-reference-module-in-parent-directory/
import os, sys
currentdir = os.path.dirname(os.path.realpath(__file__))
parentdir = os.path.dirname(currentdir)
sys.path.append(parentdir)
from odeoptions import Odeoptions
from ode45 import ode45
def odefcn(x, y):
epsilon = 1e-2
return ((1 - x) * y - y**2) / epsilon
epsilon = 1e-6
y0 = [1]
xspan = [0, 2]
options = Odeoptions()
options.odeset('NonNegative', [0])
res = ode45(odefcn, xspan, y0, options)
fig = plt.figure()
plt.title('The knee problem')
plt.xlabel('x')
plt.ylabel('y')
plt.plot(res.t, res.y[0], label='Non-negativity')
plt.show()
precision_mean = np.zeros([nbr_Input, nbr_test])
#### INPUT 1
INPUT = 0
tspan = [
0.74414985, 3.5823718, 6.42059375, 9.2588157, 12.09703764, 14.93525959,
17.77348154, 20.61170349, 23.44992544, 26.28814739, 29.12636934,
31.96459129
]
y0_1 = [4.53897499]
y0_2 = [1.20051259, 1.17666892]
y0_3 = [0.45052893, 7.03086018, -1.50526611]
A = -2.83009697
B = -4.97673659
C = -3.50342477
opts = Odeoptions()
precision_mean[INPUT, :] = compute_tests(tspan, y0_1, y0_2, y0_3, opts, A, B,
C)
#### INPUT 2
INPUT = INPUT + 1
tspan = [
1.69850555, 4.63711663, 7.57572772, 10.5143388, 13.45294988, 16.39156097,
19.33017205, 22.26878314, 25.20739422, 28.1460053, 31.08461639,
34.02322747, 36.96183856, 39.90044964, 42.83906072, 45.77767181,
48.71628289
]
y0_1 = [-6.38784938]
y0_2 = [1.60628946, 1.18921585]
y0_3 = [-7.09018137, 4.81021195, -7.82701511]
A = 2.25480317
M[0, 0] = 1
M[1, 1] = m1 + m2
M[1, 5] = -m2 * L * np.sin(y[4])
M[2, 2] = 1
M[3, 3] = m1 + m2
M[3, 5] = m2 * L * np.cos(y[4])
M[4, 4] = 1
M[5, 1] = -L * np.sin(y[4])
M[5, 3] = L * np.cos(y[4])
M[5, 5] = L**2
return M
tspan = np.linspace(0, 4, 25)
y0 = [0, 4, 2, 20, -np.pi / 2, 2]
options = Odeoptions()
options.odeset('Mass', mass)
res = ode45(dydt, tspan, y0, options)
#Plot ode45 approx
fig = plt.figure()
plt.title('A thrown baton problem with mass matrix M(t,y)')
plt.xlabel('x')
plt.ylabel('y')
for j in range(len(res.t)):
theta = res.y[4, j]
X = res.y[0, j]
Y = res.y[2, j]
xvals = np.array([X, X + L * np.cos(theta)])
((y[0] - mustar) / r23),
-2 * y[2] + y[1] - mustar * (y[1] / r13) - mu * (y[1] / r23)
])
def events(t, y):
y0 = np.array([1.2, 0, 0, -1.04935750983031990726])
dDSQdt = 2 * np.dot((y[0:2] - y0[0:2]), y[2:4])
value = np.array([dDSQdt, dDSQdt])
isterminal = np.array([1, 0]) # stop at local minimum
direction = np.array([1, -1]) # [local minimum, local maximum]
return [value, isterminal, direction]
y0 = [1.2, 0, 0, -1.04935750983031990726]
tspan = [0, 7]
options = Odeoptions()
options.odeset('Events', events)
options.odeset('RelTol', 1e-5)
options.odeset('AbsTol', 1e-4)
res = ode45(dydt, tspan, y0, options)
#PLOT
fig = plt.figure()
plt.title('Restricted three body problem')
plt.xlabel('x(t)')
plt.ylabel('y(t)')
plt.plot(res.y[0], res.y[1])
plt.plot(res.ye[0], res.ye[1], 'ro')
plt.show()