def qr_solve_lsq(M, b): Vt = mp.qr_solve(M, b) V = mp.zeros(M.cols,1) for i in range(M.cols): V[i] = Vt[0][i] return V
def __iter__(self):
f = self.f
x0 = self.constraint(self.x0)
norm = self.norm
J = self.J
fx = self._matrix(f(x0))
fxnorm = norm(fx)
cancel = False
x0 = self._matrix(x0)
while not cancel:
# get direction of descent
fxn = -fx
Jx = J(x0)
try:
s = self._Axb(Jx, fxn)
except:
try:
s = mp.qr_solve(Jx, fxn)[0]
except ZeroDivisionError:
cancel = True
break
except TypeError:
cancel = True
break
# damping step size TODO: better strategy (hard task)
l = self._mpfloat('1.0')
x1 = x0 + l * s
damp_iter = 0
while True:
damp_iter += 1
if x1.tolist() == x0.tolist() or damp_iter > self.max_damping:
if self.verbose > 1:
print("Solver: Found stationary point.")
cancel = True
break
x1 = self._matrix(self.constraint(x1))
fx = self._matrix(f(list(x1)))
newnorm = norm(fx)
if newnorm <= fxnorm:
# new x accepted
fxnorm = newnorm
x0 = x1
break
l /= 2.0
x1 = x0 + l * s
yield (x0, fxnorm)
def solve_ss_network(self, T, P):
"""
calculates the steady state concentrations if all A => B + C
reactions are irreversible and the flux from/to the source
configuration is 1.0
"""
A = np.zeros((len(self.isomers), len(self.isomers)))
b = np.zeros(len(self.isomers))
bimolecular = len(self.source) > 1
isomer_spcs = [iso.species[0] for iso in self.isomers]
for rxn in self.net_reactions:
if rxn.reactants[0] in isomer_spcs:
ind = isomer_spcs.index(rxn.reactants[0])
kf = rxn.get_rate_coefficient(T, P)
A[ind, ind] -= kf
else:
ind = None
if rxn.products[0] in isomer_spcs:
ind2 = isomer_spcs.index(rxn.products[0])
kr = rxn.get_rate_coefficient(
T, P) / rxn.get_equilibrium_constant(T)
A[ind2, ind2] -= kr
else:
ind2 = None
if ind is not None and ind2 is not None:
A[ind, ind2] += kr
A[ind2, ind] += kf
if bimolecular:
if rxn.reactants[0] == self.source:
kf = rxn.get_rate_coefficient(T, P)
b[ind2] += kf
elif rxn.products[0] == self.source:
kr = rxn.get_rate_coefficient(
T, P) / rxn.get_equilibrium_constant(T)
b[ind] += kr
if not bimolecular:
ind = isomer_spcs.index(self.source[0])
b[ind] = -1.0 # flux at source
else:
b = -b / b.sum() # 1.0 flux from source
if len(b) == 1:
return np.array([b[0] / A[0, 0]])
con = np.linalg.cond(A)
if np.log10(con) < 15:
c = np.linalg.solve(A, b)
else:
logging.warning(
"Matrix Ill-conditioned, attempting to use Arbitrary Precision Arithmetic"
)
mp.dps = 30 + int(np.log10(con))
Amp = mp.matrix(A.tolist())
bmp = mp.matrix(b.tolist())
try:
c = mp.qr_solve(Amp, bmp)
c = np.array(list(c[0]))
if any(c <= 0.0):
c, rnorm = opt.nnls(A, b)
c = c.astype(np.float64)
except: # fall back to raw flux analysis rather than solve steady state problem
return None
if np.isnan(c).any():
return None
return c
def lin_solve(mat, vec):
if mode == mode_python:
return np.linalg.solve(mat, vec)
else:
return mpmath.qr_solve(mat, vec)[0]
def _action(self, act=1):
if QSMODE == MODE_MPMATH:
args = {}
if act==0:
self.typeStr = "mpmath_qr_solve_dps"+getArgDesc(mpmath.qr_solve, args)+" DPS"+str(DPS)
self.matrixType = 1
self.indexType = 1
else:
self.coeffVec = mpmath.qr_solve(self.sysMat, self.resVec, **args)
self.printCalStr()
else:
if PYTYPE_COEFF_SOLVE_METHOD == "numpy_solve":
args = {}
if act==0:
self.typeStr = "numpy_solve"+getArgDesc(np.linalg.solve, args)
self.matrixType = 0
self.indexType = 0
else:
self.coeffVec = np.linalg.solve(self.sysMat, self.resVec, **args)
self.printCalStr()
elif PYTYPE_COEFF_SOLVE_METHOD == "numpy_lstsq":
args = {}
if act==0:
self.typeStr = "numpy_lstsq"+getArgDesc(np.linalg.lstsq, args)
self.matrixType = 0
self.indexType = 0
else:
self.coeffVec = np.linalg.lstsq(self.sysMat, self.resVec, **args)[0]
self.printCalStr()
elif PYTYPE_COEFF_SOLVE_METHOD == "numpy_sparse_bicg":
args = {}
if act==0:
self.typeStr = "numpy_sparse_bicg"+getArgDesc(sp_sparse_linalg.bicg, args)
self.matrixType = 0
self.indexType = 1
else:
self.coeffVec = self._sparseRet(sp_sparse_linalg.bicg(self.sysMat, self.resVec, **args))#, tol=1e-05, maxiter=10*len(self.resVec)
elif PYTYPE_COEFF_SOLVE_METHOD == "numpy_sparse_bicgstab":
args = {}
if act==0:
self.typeStr = "numpy_sparse_bicgstab"+getArgDesc(sp_sparse_linalg.bicgstab, args)
self.matrixType = 0
self.indexType = 1
else:
self.coeffVec = self._sparseRet(sp_sparse_linalg.bicgstab(self.sysMat, self.resVec, **args))#, tol=1e-05, maxiter=10*len(self.resVec)
elif PYTYPE_COEFF_SOLVE_METHOD == "numpy_sparse_lgmres":
args = {}
if act==0:
self.typeStr = "numpy_sparse_lgmres"+getArgDesc(sp_sparse_linalg.lgmres, args)
self.matrixType = 0
self.indexType = 1
else:
self.coeffVec = self._sparseRet(sp_sparse_linalg.lgmres(self.sysMat, self.resVec, **args))#, tol=1e-05, maxiter=1000
elif PYTYPE_COEFF_SOLVE_METHOD == "numpy_sparse_minres":
args = {}
if act==0:
self.typeStr = "numpy_sparse_minres"+getArgDesc(sp_sparse_linalg.minres, args)
self.matrixType = 0
self.indexType = 1
else:
self.coeffVec = self._sparseRet(sp_sparse_linalg.minres(self.sysMat, self.resVec, **args))#, tol=1e-05, maxiter=5*self.sysMat.shape[0]
elif PYTYPE_COEFF_SOLVE_METHOD == "numpy_sparse_qmr":
args = {}
if act==0:
self.typeStr = "numpy_sparse_qmr"+getArgDesc(sp_sparse_linalg.qmr, args)
self.matrixType = 0
self.indexType = 1
else:
self.coeffVec = self._sparseRet(sp_sparse_linalg.qmr(self.sysMat, self.resVec, **args))#, tol=1e-05, maxiter=10*len(self.resVec)
elif PYTYPE_COEFF_SOLVE_METHOD == "numpy_qr":
args_qr = {}
args_s = {}
if act==0:
self.typeStr = "numpy_qr"+getArgDesc(np.linalg.qr, args_qr)+",numpy_solve"+getArgDesc(np.linalg.solve, args_s)
self.matrixType = 0
self.indexType = 0
else:
Q,R = np.linalg.qr(self.sysMat, **args_qr)
y = np.dot(Q.T,self.resVec)
self.coeffVec = np.linalg.solve(R,y, **args_s)
self.printCalStr()
def solve_SS_network(self, T, P):
"""
calculates the steady state concentrations if all A => B + C
reactions are irreversible and the flux from/to the source
configuration is 1.0
"""
A = np.zeros((len(self.isomers), len(self.isomers)))
b = np.zeros(len(self.isomers))
bimolecular = len(self.source) > 1
isomerSpcs = [iso.species[0] for iso in self.isomers]
for rxn in self.pathReactions:
if rxn.reactants[0] in isomerSpcs:
ind = isomerSpcs.index(rxn.reactants[0])
kf = rxn.getRateCoefficient(T, P)
A[ind, ind] -= kf
else:
ind = None
if rxn.products[0] in isomerSpcs:
ind2 = isomerSpcs.index(rxn.products[0])
kr = rxn.getRateCoefficient(T,
P) / rxn.getEquilibriumConstant(T)
A[ind2, ind2] -= kr
else:
ind2 = None
if ind and ind2:
A[ind, ind2] += kr
A[ind2, ind] += kf
if bimolecular:
if rxn.reactants[0].species == self.source:
kf = rxn.getRateCoefficient(T, P)
b[ind2] += kf
elif rxn.products[0].species == self.source:
kr = rxn.getRateCoefficient(
T, P) / rxn.getEquilibriumConstant(T)
b[ind] += kr
if not bimolecular:
ind = isomerSpcs.index(self.source[0])
b[ind] = -1.0 #flux at source
else:
b = -b / b.sum() #1.0 flux from source
if len(b) == 1:
return np.array([b[0] / A[0, 0]])
con = np.linalg.cond(
A
) #this matrix can be very ill-conditioned so we enhance precision accordingly
mp.dps = 30 + int(np.log10(con))
Amp = mp.matrix(A.tolist())
bmp = mp.matrix(b.tolist())
c = mp.qr_solve(Amp, bmp)
c = np.array(list(c[0]))
if any(c <= 0.0):
c, rnorm = opt.nnls(A, b)
c = c.astype(np.float64)
return c
def Bound(U,B,sol,eig,dic,order,condB = "harm pot",condU = 'Inviscid'):
lso = len(sol)
for s in range(len(sol)):
globals() ['C'+str(s)] = Symbol('C'+str(s))
#################################
### Inviscid solution : ###
### lso=3 --> 1 boundary ###
### lso=6 --> 2 boundaries ###
#################################
nn = n.xreplace(dic).doit()
U = (U.xreplace(makedic(veigen(eig,sol),order))).xreplace({U0:1})
B = (B.xreplace(makedic(veigen(eig,sol),order)))
if (condB == "harm pot"):
bchx,bchy,bchz = symbols("bchx,bchy,bchz")
bcc =surfcond((bchx*C.i +bchy*C.j + bchz*C.k)*ansatz - gradient(psi),dic).doit()
sob = list(linsolve([bcc&C.i,bcc&C.j,bcc&C.k],(bchx,bchy,bchz)))[0]
bbc = sob[0]*C.i + sob[1]*C.j + sob[2]*C.k
bb = B.xreplace(makedic(veigen(eig,sol),order)) - (bbc*ansatz)
Eq_b= surfcond(bb,dic)
Eq_bx = Eq_b&C.i; Eq_by = Eq_b&C.j; Eq_bz = Eq_b&C.k
if params.Bound_nb ==2:
bchx2,bchy2,bchz2 = symbols("bchx2,bchy2,bchz2")
bcc2 =surfcond_2((bchx2*C.i +bchy2*C.j +bchz2*C.k)*ansatz - gradient(psi_2b),dic)
sob2 = list(linsolve([bcc2&C.i,bcc2&C.j,bcc2&C.k],(bchx2,bchy2,bchz2)))[0]
bbc2 = sob2[0]*C.i + sob2[1]*C.j + sob2[2]*C.k
bb2 = B.xreplace(makedic(veigen(eig,sol),order)) - (bbc2*ansatz)
Eq_b2= surfcond_2(bb2,dic)
Eq_b2x = Eq_b2&C.i; Eq_b2y = Eq_b2&C.j; Eq_b2z = Eq_b2&C.k
if (condB == "thick"):
bchx,bchy,bchz,eta = symbols("bchx,bchy,bchz,eta")
kz_t = -sqrt(-kxl**2-kyl**2-I*omega/qRmm)
# kz_t = I*1e12
B_mant = (bchx*C.i +bchy*C.j + bchz*C.k)*ansatz.xreplace({kz:kz_t})
eq_ind = (surfcond((diff(B_mant,t)-qRmm*laplacian(B_mant)-diff(B,t) +qRm*laplacian(B) - curl(U.cross(B))).xreplace({kz:kz_t}),dic).xreplace(dic))
eq_E = (qRm*curl(B)-U.cross(B)-qRmm*curl(B_mant))
eq_Et = surfcond(((nn).cross(eq_E)).xreplace({kz:kz_t}),dic)
eq_B = surfcond(((B_mant.dot(nn)-B.dot(nn))).xreplace({kz:kz_t}),dic)
un = (U.dot(nn))
Eq_n1= surfcond((un).xreplace({kz:kz_t}),dic).xreplace(dic)
TEq = [(taylor(eq,order,dic)).xreplace({x:0,y:0,t:0}) for eq in [Eq_n1,eq_ind&C.i,eq_ind&C.j,eq_ind&C.k,eq_Et.dot(tx),eq_Et.dot(ty)]]
Mat, res = linear_eq_to_matrix(TEq,(C0,C1,C2,bchx,bchy,bchz))
U = (U.xreplace(makedic(veigen(eig,sol),order))).xreplace({U0:1})
un = U.dot(nn)
Eq_n1= surfcond(un,dic).xreplace(dic)
if condU == "Inviscid":
if params.Bound_nb ==2:
nn2 = n2.xreplace(dic).doit()
un2 = U.dot(nn2)
Eq_n2= surfcond_2(un2,dic)
TEq = [(taylor(eq,order,dic)).xreplace({x:0,y:0,t:0}) for eq in [Eq_n1,Eq_n2,Eq_bx,Eq_by,Eq_bz,Eq_b2x,Eq_b2y,Eq_b2z]]
Mat, res = linear_eq_to_matrix(TEq,(C0,C1,C2,C3,C4,C5,Symbol("psi"+str(order)),Symbol("psi"+str(order)+"_2b")))
elif params.Bound_nb ==1:
TEq = [(taylor(eq,order,dic)).xreplace({x:0,y:0,t:0}) for eq in [Eq_n1,Eq_bx,Eq_by,Eq_bz]]
Mat, res = linear_eq_to_matrix(TEq,(C0,C1,C2,Symbol("psi"+str(order))))
elif condU == 'noslip':
if params.Bound_nb ==1:
U = (U.xreplace(makedic(veigen(eig,sol),order)))
ut1 = U.dot(tx)
ut2 = U.dot(ty)
Eq_BU1= surfcond(ut1,dic)
Eq_BU2 = surfcond(ut2,dic)
TEq = [(taylor(eq,order,dic)).xreplace({x:0,y:0,t:0}) for eq in [Eq_n1,Eq_BU1,Eq_BU2,Eq_bx,Eq_by,Eq_bz]]
Mat, res = linear_eq_to_matrix(TEq,(C0,C1,C2,C3,C4,Symbol("psi"+str(order))))
elif params.Bound_nb ==2:
un1 = U.dot(tx2)
un2 = U.dot(ty2)
Eq2_BU1= surfcond_2(un1,dic)
Eq2_BU2 = surfcond_2(un2,dic)
TEq = [(taylor(eq,order,dic)).xreplace({x:0,y:0,t:0}) for eq in [Eq_n1,Eq_n2,Eq_BU1,Eq_BU2,Eq2_BU1,Eq2_BU2,Eq_bx,Eq_by,Eq_bz,Eq_b2x,Eq_b2y,Eq_b2z]]
Mat, res = linear_eq_to_matrix(TEq,(C0,C1,C2,C3,C4,C5,C6,C7,C8,C9,Symbol("psi"+str(order)),Symbol("psi"+str(order)+"_2b")))
elif condU == 'stressfree':
if params.Bound_nb ==1:
eu = strain(U)*nn
eu1 = eu*tx
eu2 = eu*ty
Eq_BU1 = surfcond(eu1,dic,realtopo =False)
Eq_BU2 = surfcond(eu2,dic,realtopo =False)
TEq = [(taylor(eq,order,dic)).xreplace({x:0,y:0,t:0}) for eq in [Eq_n1,Eq_BU1,Eq_BU2,Eq_bx,Eq_by,Eq_bz]]
Mat, res = linear_eq_to_matrix(TEq,(C0,C1,C2,C3,C4,Symbol("psi"+str(order))))
elif params.Bound_nb ==2:
eu = strain(U)*nn2
eu1 = eu*tx2
eu2 = eu*ty2
Eq2_BU1 = surfcond2(eu1,dic,realtopo =False)
Eq2_BU2 = surfcond2(eu2,dic,realtopo =False)
TEq = [(taylor(eq,order,dic)).xreplace({x:0,y:0,t:0}) for eq in [Eq_n1,Eq_n2,Eq_BU1,Eq_BU2,Eq2_BU1,Eq2_BU2,Eq_bx,Eq_by,Eq_bz,Eq_b2x,Eq_b2y,Eq_b2z]]
Mat, res = linear_eq_to_matrix(TEq,(C0,C1,C2,C3,C4,C5,C6,C7,C8,C9,Symbol("psi"+str(order)),Symbol("psi"+str(order)+"_2b")))
Mat = Mat.evalf(mp.mp.dps)
res = res.evalf(mp.mp.dps)
Mat = mpmathM(Mat)
res = mpmathM(res)
try:
abc = mp.qr_solve(Mat,res)[0]
except:
abc = mp.lu_solve(Mat,res)
mantle =0 #In progress ...
solans = zeros(7,1)
for l in range(lso):
solans = solans + abc[l]*Matrix(eig[l])*(ansatz).xreplace({kz:sol[l]})
solans = solans.xreplace(dic)
return(abc,solans,mantle)
coe = lambda x: x.coeff(ex)
rmep = (rmec).applyfunc(coe)
nwkz = simplify((log(ex).expand(force=True)/I).xreplace({x:0,y:0,t:0,z:1}))
Mp = simplify(M.xreplace({kz:nwkz}))
rmep = subs_k(rmep,i,Bound_nb)
Mp = subs_k(Mp,i,Bound_nb)
with mp.workdps(int(mp.mp.dps*2)):
Mp = mpmathM(Mp)
rmep = mpmathM(rmep)
try:
soluchap = mp.qr_solve(Mp,rmep)[0]
except:
soluchap = mp.lu_solve(Mp,rmep)
print('QR decomposition failed LU used')
sop = Matrix(soluchap)*ex
so_part = so_part+sop
with mp.workdps(int(mp.mp.dps*2)):
so_part = so_part.xreplace({**dico0,**dico1})
Usopart = so_part[0]*C.i + so_part[1]*C.j + so_part[2]*C.k
Bsopart = so_part[4]*C.i + so_part[5]*C.j + so_part[6]*C.k
psopart = so_part[3]
Ubnd = U + e**i*Usopart