def J_f_total_v(phiPS_a_v, HP, u, phiPS_ori, f0=0):
phiori = phiPS_ori[0]
phisori = phiPS_ori[1]
phia = phiPS_a_v[0]
phisa = phiPS_a_v[1]
v = phiPS_a_v[2]
phib = (phiori - v * phia) / (1 - v)
phisb = (phisori - v * phisa) / (1 - v)
#print(phia ,phisa, phib,phisb, v)
xeffa = tt.x_eff(HP, phia, phisa, u)
fa = tt.f_eng(HP, phia, phisa, u, x=xeffa)
dfa, dfsa = tt.df_eng(HP, phia, phisa, u, x=xeffa)
xeffb = tt.x_eff(HP, phib, phisb, u)
fb = tt.f_eng(HP, phib, phisb, u, x=xeffb)
dfb, dfsb = tt.df_eng(HP, phib, phisb, u, x=xeffb)
J = np.empty(3)
J[0] = v * (dfa - dfb)
J[1] = v * (dfsa - dfsb)
J[2] = fa - fb + (phib - phia) * dfb + (phisb - phisa) * dfsb
return invT * J
def Eng_all(phi_all, u, HP, phis, phi0, f0):
phi1 = phi_all[0]
phi2 = phi_all[1]
v = (phi2 - phi0) / (phi2 - phi1)
f1 = tt.f_eng(HP, phi1, phis, u)
f2 = tt.f_eng(HP, phi2, phis, u)
fall = invT * (v * f1 + (1 - v) * f2 - f0)
#print(phi_all, fall)
return fall
def f_total_v(phiPS_a_v, HP, u, phiPS_ori, f0):
phiori = phiPS_ori[0]
phisori = phiPS_ori[1]
phia = phiPS_a_v[0]
phisa = phiPS_a_v[1]
v = phiPS_a_v[2]
phib = (phiori - v * phia) / (1 - v)
phisb = (phisori - v * phisa) / (1 - v)
fa = tt.f_eng(HP, phia, phisa, u)
fb = tt.f_eng(HP, phib, phisb, u)
#print(phia ,phisa, phib,phisb, v)
return invT * (v * fa + (1 - v) * fb - f0)
def J_Eng_all(phi_all, u, HP, phis, phi0, f0):
phi1 = phi_all[0]
phi2 = phi_all[1]
v = (phi2 - phi0) / (phi2 - phi1)
xeff1 = tt.x_eff(HP, phi1, phis, u) if tt.useleff else 1
f1 = tt.f_eng(HP, phi1, phis, u, x=xeff1)
df1 = tt.df_eng(HP, phi1, phis, u, x=xeff1)[0]
xeff2 = tt.x_eff(HP, phi2, phis, u) if tt.useleff else 1
f2 = tt.f_eng(HP, phi2, phis, u, x=xeff2)
df2 = tt.df_eng(HP, phi2, phis, u, x=xeff2)[0]
J = np.empty(2)
J[0] = v * ((f1 - f2) / (phi2 - phi1) + df1)
J[1] = (1 - v) * ((f1 - f2) / (phi2 - phi1) + df2)
#print(J)
return invT * J
def ps_bi_solve( HP, u, phiPS_ori ,r_vini, useJ ):
err = phi_min_calc
phiori = phiPS_ori[0]
phisori = phiPS_ori[1]
f0 = tt.f_eng(HP, phiori, phisori, u)
phi_ini = [phiori*0.5, phisori*0.95 ]
vini = [r_vini*vmin(phi_ini, phiPS_ori)]
inis = phi_ini + vini
#print(inis)
cons_all = ( {'type':'ineq', 'fun': lambda x: x[0]-err }, \
{'type':'ineq', 'fun': lambda x: 1-x[0]-err }, \
{'type':'ineq', 'fun': lambda x: x[1]-err }, \
{'type':'ineq', 'fun': lambda x: 1-x[1]-err }, \
{'type':'ineq', 'fun': lambda x: 1-x[0]-x[1]-err }, \
{'type':'ineq', 'fun': lambda x: x[2]-err }, \
{'type':'ineq', 'fun': lambda x: vmin(x,phiPS_ori)-x[2]-err } \
)
if useJ:
result = sco.minimize( f_total_v, inis,\
args = (HP, u, phiPS_ori, f0), \
method = 'SLSQP', \
jac = J_f_total_v, \
constraints = cons_all, \
tol = err/100, \
options={'ftol': err, 'eps': err} )
else:
result = sco.minimize( f_total_v, inis,\
args = (HP, u, phiPS_ori, f0), \
method = 'COBYLA',
constraints = cons_all, \
tol = err/100 )
#print(result.x)
phia = result.x[0]
phisa = result.x[1]
v = result.x[2]
phib = (phiori-v*phia)/(1-v)
phisb = (phisori-v*phisa)/(1-v)
if phia > phib:
t1, t2 = phib, phisb
phib, phisb = phia, phisa
phia, phisa = t1, t2
v = 1-v
return [phia, phisa, phib, phisb, v]
def ps_bi_solve(HP, phis, u, phi_sps, phi_ori=None):
err = phi_min_calc
phi_max = (1 - 2 * phis) / (1 + HP['pc']) - err
sps1, sps2 = phi_sps
phi_all_ini = [sps1 * 0.9, sps2 * 1.1]
if phi_ori == None:
phi_ori = (sps1 + sps2) / 2
f_ori = tt.f_eng(HP, phi_ori, 0, u)
result = sco.minimize( Eng_all, phi_all_ini, \
args = (u, HP, phis, phi_ori, f_ori), \
method = 'L-BFGS-B', \
jac = J_Eng_all, \
bounds = ((err,sps1-err), (sps2+err,phi_max)), \
options={'ftol':1e-20, 'gtol':1e-20, 'eps':1e-20} )
bi1 = min(result.x)
bi2 = max(result.x)
return bi1, bi2
