def epsilon_family(
limited_srm,
par_dict,
control_start_values,
times,
func_dict,
epsilons
):
z=Symbol('z')
eps=Symbol('eps')
u_z_exp=half_saturation(z,eps)
bm=BastinModel(limited_srm,u_z_exp,z)
fig=plt.figure()
ax1=fig.add_subplot(1,1,1)
ax1.set_title("control u for different values of epsilon")
for eps_val in epsilons:
par_dict[eps]=eps_val
bmr=BastinModelRun(
bm,
par_dict,
control_start_values,
times,
func_dict
)
phi_num=bmr.phi_num((z,))
soln=bmr.solve()
z_sol=soln[:,3]
pe('bm.u_expr',locals())
u=phi_num(z_sol)
ax1.plot(times,u)
ax1.legend(loc=3)
fig.savefig(my_func_name()+'.pdf')
def epsilon_family_2(limited_srm, par_dict, start_values, times, func_dict, zs,
epsilons):
z = Symbol('z')
eps = Symbol('eps')
z0 = Symbol('z0')
u_z_exp = half_saturation(z, eps)
bm = BastinModel(limited_srm, u_z_exp, z)
fig = plt.figure()
ax1 = fig.add_subplot(1, 1, 1)
ax1.set_title("control u for different values of epsilon")
for z0_val in zs:
for eps_val in epsilons:
control_start_values = np.array(list(start_values) + [z0_val])
par_dict[eps] = eps_val
par_dict[z0] = z0_val,
bmr = BastinModelRun(bm, par_dict, control_start_values, times,
func_dict)
phi_num = bmr.phi_num((z, ))
soln = bmr.solve()
z_sol = soln[:, 3]
pe('bm.u_expr', locals())
u = phi_num(z_sol)
ax1.plot(times,
u,
label="eps:" + str(eps_val) + ",z0=" + str(z0_val))
ax1.legend(loc=3)
fig.savefig(my_func_name() + '.pdf')
def deceleration_family(limited_srm, par_dict, start_values, times, func_dict,
zs, alphas):
z = Symbol('z')
z_max = Symbol('z_max')
alph = Symbol('alph')
u_z_exp = deceleration(z, z_max, alph)
bm = BastinModel(limited_srm, u_z_exp, z)
fig = plt.figure()
ax1 = fig.add_subplot(1, 1, 1)
ax1.set_title(
"control u with deceleration limiter for different values of alph")
for z_max_val in zs:
for alpha_val in alphas:
control_start_values = np.array(list(start_values) + [z_max_val])
par_dict[z_max] = z_max_val
par_dict[alph] = alpha_val
bmr = BastinModelRun(bm, par_dict, control_start_values, times,
func_dict)
phi_num = bmr.phi_num((z, ))
soln = bmr.solve()
z_sol = soln[:, 3]
pe('bm.u_expr', locals())
u = phi_num(z_sol)
ax1.plot(times,
u,
label="alph:" + str(alpha_val) + ",z_max=" +
str(z_max_val))
ax1.legend(loc=3)
fig.savefig(my_func_name() + '.pdf')
def continiuous_integral(t, Phi_func):
# We compute the integral of the continious function
# With an integration rule that
#print(phi_vals)
def rhs(tau, X):
# although we do not need X we have to provide a
# righthandside suitable for solve_ivp
return np.matmul(Phi_func(t, tau), u_num(tau)).flatten()
#pe('integrand_vals',locals())
ys = solve_ivp(rhs, y0=np.zeros(nr_pools), t_span=(t_0, t)).y
pe('ys.shape', locals())
val = ys[:, -1].reshape(nr_pools, 1)
#pe('val',locals())
return val
def cubic_family(
limited_srm,
par_dict,
start_values,
times,
func_dict,
zs
):
z=Symbol('z')
z_max=Symbol('z_max')
u_z_exp=cubic(z,z_max)
bm=BastinModel(limited_srm,u_z_exp,z)
fig=plt.figure()
ax1=fig.add_subplot(1,1,1)
#ax1.set_title("control u for different values of z_max")
for z_max_val in zs:
control_start_values=np.array(list(start_values)+[z_max_val])
par_dict[z_max]=z_max_val
bmr=BastinModelRun(
bm,
par_dict,
control_start_values,
times,
func_dict
)
phi_num=bmr.phi_num((z,))
soln=bmr.solve()
z_sol=soln[:,3]
pe('bm.u_expr',locals())
u=phi_num(z_sol)
ax1.plot(times,u,label="$z_{max}$="+str(z_max_val))
ax1.set_ylabel('$u(t)$ (unitless)')
ax1.set_xlabel('Time (years)')
ax1.legend(loc=3)
fig.savefig(my_func_name()+'.pdf')