def solve_newton(Ma1, ga, AR, Yp):
Niter = 10
Ma_guess = np.ones((Niter, )) * np.nan
K = cf.mcpTo_APo_from_Ma(Ma1, ga) / AR
Ma_guess[0] = 0.5
if (cf.mcpTo_APo_from_Ma(1., ga) < K *
(1. + Yp * (1. - 1. / cf.Po_P_from_Ma(0., ga)))):
return np.nan
print('beans')
def f(x):
return (K * (1. + Yp * (1. - 1. / cf.Po_P_from_Ma(x, ga))) -
cf.mcpTo_APo_from_Ma(x, ga))
def fp(x):
return (
K * Yp * cf.der_Po_P_from_Ma(x, ga) / cf.Po_P_from_Ma(x, ga)**2. -
cf.der_mcpTo_APo_from_Ma(x, ga))
for n in range(Niter - 1):
Ma_guess[n + 1] = Ma_guess[n] - f(Ma_guess[n]) / fp(Ma_guess[n])
if np.abs(Ma_guess[n + 1] - Ma_guess[n]) < Ma_tol:
# Q_guess = cf.mcpTo_APo_from_Ma(Ma_guess,ga)
# if plot_stuff:
# a.plot(Ma_guess,Q_guess,'ko-')
return Ma_guess[n + 1]
break
return np.nan
def solve_fixed_point(Ma1, ga, AR, Yp):
Niter = 100
Ma_guess = np.ones((Niter, )) * np.nan
# Q_guess = np.ones((Niter,))*np.nan
K = cf.mcpTo_APo_from_Ma(Ma1, ga) / AR
Ma_guess[0] = 0.5
for n in range(Niter - 1):
Ma_guess[n + 1] = (K * (1. + Yp *
(1. - 1. / cf.Po_P_from_Ma(Ma_guess[n], ga))) /
cf.mcpTo_APo_from_Ma(Ma_guess[n], ga) * Ma_guess[n])
if np.abs(Ma_guess[n + 1] - Ma_guess[n]) < Ma_tol:
# print('Fixed point broke at %d' % n)
# if plot_stuff:
# Q_guess = cf.mcpTo_APo_from_Ma(Ma_guess,ga)
# a.plot(Ma_guess,Q_guess,'kx-')
return Ma_guess[n + 1]
break
return np.nan
def fp(x):
return (
K * Yp * cf.der_Po_P_from_Ma(x, ga) / cf.Po_P_from_Ma(x, ga)**2. -
cf.der_mcpTo_APo_from_Ma(x, ga))
def f(x):
return (K * (1. + Yp * (1. - 1. / cf.Po_P_from_Ma(x, ga))) -
cf.mcpTo_APo_from_Ma(x, ga))
# import sympy as sp
# m, g, AR, Yp = sp.symbols('Ma, ga, AR, Yp')
# flowfun = g/sp.sqrt(g-1.)*m*(1.+((g-1.)*m*m)/2.)**((g+1.)/(g-1.)/-2.)
# PR = 1.+Yp*(1.-(1.+((g-1.)*m*m)/2.)**(-g/(g-1.)))
Ma1_in = 0.3
Ma2_in = np.linspace(0., 1., 1000)
AR_in = 0.39
Yp_in = 0.05
ga_in = 1.4
Ma_tol = 0.000001
f, a = plt.subplots()
Q2b = (cf.mcpTo_APo_from_Ma(Ma1_in, ga_in) / AR_in *
(1. + Yp_in * (1. - 1. / cf.Po_P_from_Ma(Ma2_in, ga_in))))
Q2a = cf.mcpTo_APo_from_Ma(Ma2_in, ga_in)
a.plot(Ma2_in, Q2a)
a.plot(Ma2_in, Q2b)
def solve_newton(Ma1, ga, AR, Yp):
Niter = 10
Ma_guess = np.ones((Niter, )) * np.nan
K = cf.mcpTo_APo_from_Ma(Ma1, ga) / AR
Ma_guess[0] = 0.5
if (cf.mcpTo_APo_from_Ma(1., ga) < K *
(1. + Yp * (1. - 1. / cf.Po_P_from_Ma(0., ga)))):
return np.nan
print('beans')