rtol = 1e-5
tspan = [t0, tf]
delays = [tau]
def h(t):
return [(-1)**(np.floor(-5 * t))]
jumps = sorted([-k * (1 / 5) for k in range(1, 6)])
tspan = [t0, tf]
sol = solve_dde(fun,
tspan,
delays,
y0,
h,
method='RK23',
jumps=jumps,
atol=atol,
rtol=rtol)
sol45 = solve_dde(fun,
tspan,
delays,
y0,
h,
method='RK45',
jumps=jumps,
atol=atol,
rtol=rtol)
t = sol.t
tf = 10.0
atol = 1e-10
rtol = 1e-5
tspan = [t0, tf]
delays = [tau]
def h(t):
return [1]
sol = solve_dde(fun,
tspan,
delays,
y0,
h,
method='RK23',
tracked_stages=None,
atol=atol,
rtol=rtol)
t = sol.t
y = sol.y[0, :]
yp = sol.yp[0, :]
#jit cdde
f = [-y_jit(0, t_jit - tau)]
DDE = jitcdde(f)
DDE.set_integration_parameters(atol=atol, rtol=rtol)
DDE.constant_past(y0)
DDE.step_on_discontinuities()
data = []
tf = 40
tau1 = 1.
tau10 = 10.
y0 = [5., .1, 1.0]
delays = [tau1, tau10]
tspan = [t0, tf]
zeros = [zero_y0, zero_y1, zero_y2]
atol = 1e-10
rtol = 1e-5
sol23 = solve_dde(fun,
tspan,
delays,
y0,
y0,
method='RK23',
events=zeros,
atol=atol,
rtol=rtol)
t = sol23.t
y0 = sol23.y[0, :]
y1 = sol23.y[1, :]
y2 = sol23.y[2, :]
y0_e = sol23.y_events[0][:, 0]
y1_e = sol23.y_events[1][:, 1]
y2_e = sol23.y_events[2][:, 2]
import scipy.io as spio
beta = 0.25
gamma = 0.1
args = (beta, gamma)
atol = 1e-10
rtol = 1e-5
tspan = [t0, tf]
delays = [tau]
y0 = [1.0]
def h(t):
return [1.]
sol23 = solve_dde(fun, tspan, delays, y0, h, method='RK23', args=args, atol=atol, rtol=rtol)
t = sol23.t
y = sol23.y[0,:]
yp = sol23.yp[0,:]
sol45 = solve_dde(fun, tspan, delays, y0, h, method='RK45', args=args, atol=atol, rtol=rtol)
t45 = sol45.t
y45 = sol45.y[0,:]
yp45 = sol45.yp[0,:]
# jitcdde
f = [ beta * y_jit(0,t_jit-tau) / (1 + y_jit(0,t_jit-tau)**n) - gamma*y_jit(0) ]
DDE = jitcdde(f)
DDE.set_integration_parameters(atol=atol, rtol=rtol)
DDE.constant_past([1.0])
DDE.step_on_discontinuities()
def ev(t, y, Z):
return y[0]
ev.terminal = True
ev.direction = -1
delays = []
sol = solve_dde(fun,
tspan,
delays,
y0,
y0,
method='RK23',
events=ev,
dense_output=True,
atol=atol,
rtol=rtol)
t = sol.t
y_0 = sol.y[0, :]
y_1 = sol.y[1, :]
t_ = np.linspace(0, t[-1])
y1_interp = sol.sol(t_)[1, :]
y0_interp = sol.sol(t_)[0, :]
plt.figure()
plt.plot(t_ivp, y_1_ivp, 'o', label='solve_ivp y1')
plt.plot(t, y_1, 'k', label='solve_dde y1')
plt.plot(t_ivp, y_0_ivp, 'o', label='solve_ivp y0')
tau = 0.74
y0 = [19.001]
h = [19.0]
t0 = 0.0
tf = 40.0
atol = 1e-8
rtol = 1e-8
tspan = [t0, tf]
delays = [tau]
sol = solve_dde(fun,
tspan,
delays,
y0,
h,
method='RK23',
atol=atol,
rtol=rtol,
dense_output=True)
t = sol.t
y = sol.y[0, :]
yp = sol.yp[0, :]
t_m = 5.5
y0_ = sol.sol(t_m)
sol_re = solve_dde(fun, [t_m, tf],
delays,
y0_,
sol,
method='RK23',
finalEvent.terminal = True
def hitGround(t, y, Z):
return y[0]
hitGround.direction = 0 # % All events have to be reported
hitGround.terminal = True
events = [finalEvent, hitGround]
sol23 = solve_dde(fun,
tspan,
delays,
y0,
y0,
method='RK23',
atol=atol,
rtol=rtol,
events=events)
print(
"\nKind of Event: solve_dde dde23 reference DDE_SOLVER"
)
# ref values of matlab dde23 example script
ref = [4.516757065, 9.751053145, 11.670393497]
# computed values from matlab dde23 with same atol & rtol
mat = [4.5167708185, 9.7511043904, 11.6703836720]
# from DDE_SOLVER fortran routine example : Example 4.4.5: Events and Change Routine
f90 = [4.5167570861630821, 9.7510847727976273, 11.670385883524640]
e = 0
return [-10.0]
y0 = 1.0
jumps = [1.]
tf = 2.0
tspan = [0.0, tf]
delays = []
rtol = 1e-5
atol = 1e-10
sol23 = solve_dde(fun,
tspan,
delays, [y0], [y0],
method='RK23',
atol=atol,
rtol=rtol)
sol23_j = solve_dde(
fun,
tspan,
delays,
[y0],
[y0], #tracked_stages=0,
method='RK23',
jumps=jumps,
atol=atol,
rtol=rtol)
print('nfev of f without jumps option : %s' % (sol23.nfev))
print('nfev of f wit jumps option : %s' % (sol23_j.nfev))
args = (tau, N_D, delta, P)
atol = 1e-10
rtol = 1e-5
tspan = [t0, tf]
delays = [tau]
y0 = [100]
jumps = [tau]
sol = solve_dde(fun,
tspan,
delays,
y0,
y0,
method='RK23',
args=args,
jumps=jumps,
atol=atol,
rtol=rtol)
t = sol.t
y = sol.y[0, :]
yp = sol.yp[0, :]
plt.figure()
plt.plot(y, yp, label='solve_dde')
plt.xlabel('y')
plt.ylabel('yp')
plt.legend()
plt.savefig('figures/gurney/phase')