def make_initial_conditions(system, displacement, low):
"""
A FUNCTION THAT CREATES THE INITIAL CONDITIONS FOR THE SEARCH OF THE
COMMUTATION CURVE IN A DETERMINED SYSTEM. TAKES AS INPUT THE SYSTEM THAT
IS GOING TO BE ANALYZED, THE displacement TO THE RIGHT, AND HOW FAR low THE
LINE SEGMENT IS GOING TO GO.
"""
C = sir.CurveSegment(system.sbar, system.imax, 0, system, 1)
C.s = C.s + displacement
s_inter, i_inter = C._curve_sol(low)
C = sir.CurveSegment(system.sbar, system.imax, 0, system, s_inter)
C.s = C.s + displacement
s0 = np.linspace(C.s[-1], 1)
i0 = np.array([i_inter] * len(s0))
s0 = np.concatenate((C.s, s0))
i0 = np.concatenate((C.i, i0))
return s0, i0
def tra(s_c, point, system):
"""
A FUNCTION THAT CALCULATES THE TIME OF THE TRAJECTORY BY A GIVEN
CONMUTATION POINT s.
"""
try:
s_c = s_c[0]
except:
pass
#print("Input is already a float.")
#print("The given conmutation point is: {}".format(s_c))
u0_curve = sir.CurveSegment(point.s0, point.i0, 0, system)
sc, ic = u0_curve._curve_sol(system.imax)
#print("The intersection point is: {}".format(sc))
if s_c >= sc:
#print("I'ma do it with only two thingamajigs.")
Tu = sir.CurveSegment(point.s0, point.i0, 0, system, s_c)
Tu.get_time()
i_c = system._curve(s_c, point.s0, point.i0, 0)
Tc = sir.CurveSegment(s_c, i_c, system.umax, system)
send, iend = Tc.curve_intersection(system.tau)
Tc = sir.CurveSegment(s_c, i_c, system.umax, system, send)
Tc.get_time()
#print("Tu: {}".format(Tu.time))
#print("Tc: {}".format(Tc.time))
#print(Tu.time + Tc.time)
return sir.Trajectory(Tu, Tc)
else:
#print("I'ma have to do it with three thingamajigs.")
Tu = sir.CurveSegment(point.s0, point.i0, 0, system, sc)
Tu.get_time()
Ts = sir.LineSegment(sc, s_c, system)
Ts.get_time()
Tc = sir.CurveSegment(s_c, system.imax, system.umax, system)
send, iend = Tc.curve_intersection(system.tau)
Tc = sir.CurveSegment(s_c, system.imax, system.umax, system, send)
Tc.get_time()
#print("Tu: {}".format(Tu.time))
#print("Ts: {}".format(Ts.time))
#print("Tc: {}".format(Tc.time))
#print(Tu.time + Ts.time + Tc.time)
return sir.Trajectory(Tu, Ts, Tc)
return f
def fun2(x):
f = 1 / (x * fun(x))
return f
#%%
A = Test(0.6)
print(A)
print(A.x)
print(A.get_time(0.6, 0.5))
imax = 0.1
umax = 0.5
gamma = 0.2
beta = 0.5
B = sir.SIR()
B.set_params([imax, umax, gamma, beta], flag="bg")
B._find_tau()
T = B.tau
T.get_time(2, 1)
L = sir.CurveSegment(0.6, 0.08, umax, B, 0.5)
L.get_time(0.6, 0.5)
print(L.time)
i = scipy.integrate.quad(fun2, 0.6, 0.5)
print(-i[0] / ((1 - 0.5) * 0.5))
# SET HOW FAR TO THE RIGHT THE REFERENCE CURVE BASED ON SIR.tau WILL BE MOVED. displacement = 0.001 # SET HOW FAR LOW THE CURVE SIR.tau WILL GO. i_low = 0.0005 #%% # CREATE SYSTEM, SET PARAMETERS, AND FIND CURVES tau, phi ET CETERA. A = sir.SIR() A.set_params([imax, umax, gamma, beta], flag="bg") A._find_curves() # CREATE A CURVE THAT IS A CLONE OF A.tau AND DISPLACE IT TO THE RIGHT BY # displacement UNITS. USE THIS CURVE AND A LINSPACE AT I = i_low TO CREATE ALL # INITIAL CONDITIONS, s0 AND i0. C = sir.CurveSegment(A.sbar, A.imax, 0, A, 1) C.s = C.s + displacement s_inter, i_inter = C._curve_sol(i_low) C = sir.CurveSegment(A.sbar, A.imax, 0, A, s_inter) C.s = C.s + displacement s0 = np.linspace(C.s[-1], 1) i0 = np.array([i_inter] * len(s0)) s0 = np.concatenate((C.s, s0)) i0 = np.concatenate((C.i, i0)) # A PLOT TO SEE IF ALL IS ALRIGHT. fig, ax = plt.subplots() ax.set_xlabel(r"$S$") ax.set_ylabel(r"$I$") ax.set_xlim(A.sbar, 1) ax.set_ylim(0, A.imax * 1.1)
#%% imax = 0.1 umax = 0.5 gamma = 0.2 beta = 0.5 displacement = 0.01 i_low = 0.0005 #%% A = sir.SIR() A.set_params([imax, umax, gamma, beta], flag="bg") C = sir.CurveSegment(A.sbar, A.imax, 0, A, 1) C.s = C.s + displacement s_inter, i_inter = C._curve_sol(i_low) C = sir.CurveSegment(A.sbar, A.imax, 0, A, s_inter) C.s = C.s + displacement s0 = np.linspace(C.s[-1], 1) i0 = np.array([i_inter] * len(s0)) s0 = np.concatenate((C.s, s0)) i0 = np.concatenate((C.i, i0)) fig, ax = plt.subplots() ax.set_xlim(A.sbar, 1) ax.set_ylim(0, A.imax * 1.1) ax.plot(A.tau.s, A.tau.i, "r-") ax.plot(s0, i0, "b-")