def solve(init_a, init_b, power, solver='scipy'):
x = sp.symbols('x:2', real=True)
p = sp.Symbol('p', real=True, negative=False, integer=True)
f = [x[0] + (x[0] - x[1])**p/2 - 1,
(x[1] - x[0])**p/2 + x[1]]
neqsys = SymbolicSys(x, f, [p])
return neqsys.solve([init_a, init_b], [power], solver=solver)
def main(conc=7e-3, pH=2.0, beta_a=-2.774, beta_b=-2.81):
# Fe³⁺ + H₂O = FeOH²⁺ + H⁺ α₁ = log10(β₁) = -2.774
# y 1 z 10**-pH
#
# 10**-pH * z / y = 10**α₁ (1)
#
# 2 Fe³⁺ + 2H₂O = Fe₂OH₂⁴⁺ + 2H⁺ α₂ = log10(β₂) = -2.81
# y 1 x 10**-pH
#
# x*10**-2*pH / y**2 = 10**α₂ (2)
#
# Total amount of Fe:
# conc = [Fe³⁺] + [FeOH²⁺] + 2[Fe₂OH₂⁴⁺]
# conc = y + z + 2*x (3)
symbs = x, y, z = sympy.symbols('x y z')
eq1 = 10**-pH * z / y - 10**beta_a
eq2 = x*10**(-2*pH) / y**2 - 10**beta_b
eq3 = y + z + 2*x - conc
print([eq1, eq2, eq3])
neqsys = SymbolicSys(symbs, [eq1, eq2, eq3])
xout, sol = neqsys.solve([conc/3, conc/3, conc/3])
print(dict(zip('Fe2(OH)2+4 Fe3+ FeOH+2'.split(), xout)))
# Simplified treatment:
neqsys2 = SymbolicSys([x, y], [eq2, 2*x + y - conc])
xout, sol = neqsys2.solve([conc/2, conc/2])
print(dict(zip('Fe2(OH)2+4 Fe3+'.split(), xout)))
def main(init_conc='1e-7,1e-7,1e-7,1,55.5',
lnKa=-21.28,
lnKw=-36.25,
savetxt='None',
verbose=False,
rref=False,
charge=False,
solver='scipy'):
# H+, OH- NH4+, NH3, H2O
iHp, iOHm, iNH4p, iNH3, iH2O = init_conc = map(float, init_conc.split(','))
lHp, lOHm, lNH4p, lNH3, lH2O = x = sp.symarray('x', 5)
Hp, OHm, NH4p, NH3, H2O = map(sp.exp, x)
# lHp + lOHm - lH2O - lnKw,
# lHp + lNH3 - lNH4p - lnKa,
coeffs = [[1, 1, 0, 0, -1], [1, 0, -1, 1, 0]]
vals = [lnKw, lnKa]
lp = linear_exprs(coeffs, x, vals, rref=rref)
f = lp + [
Hp + OHm + 4 * NH4p + 3 * NH3 + 2 * H2O -
(iHp + iOHm + 4 * iNH4p + 3 * iNH3 + 2 * iH2O), # H
NH4p + NH3 - (iNH4p + iNH3), # N
OHm + H2O - (iOHm + iH2O)
]
if charge:
f += [Hp - OHm + NH4p - (iHp - iOHm + iNH4p)]
neqsys = SymbolicSys(x, f)
x, sol = neqsys.solve([0] * 5, solver=solver)
if verbose:
print(np.exp(x), sol)
else:
print(np.exp(x))
assert sol.success
def main(init_conc='1e-7,1e-7,1e-7,1,55.5',
lnKa=-21.28, lnKw=-36.25,
savetxt='None', verbose=False,
rref=False, charge=False, solver='scipy'):
# H+, OH- NH4+, NH3, H2O
iHp, iOHm, iNH4p, iNH3, iH2O = init_conc = map(float, init_conc.split(','))
lHp, lOHm, lNH4p, lNH3, lH2O = x = sp.symarray('x', 5)
Hp, OHm, NH4p, NH3, H2O = map(sp.exp, x)
# lHp + lOHm - lH2O - lnKw,
# lHp + lNH3 - lNH4p - lnKa,
coeffs = [[1, 1, 0, 0, -1], [1, 0, -1, 1, 0]]
vals = [lnKw, lnKa]
lp = linear_exprs(coeffs, x, vals, rref=rref)
f = lp + [
Hp + OHm + 4*NH4p + 3*NH3 + 2*H2O - (
iHp + iOHm + 4*iNH4p + 3*iNH3 + 2*iH2O), # H
NH4p + NH3 - (iNH4p + iNH3), # N
OHm + H2O - (iOHm + iH2O)
]
if charge:
f += [Hp - OHm + NH4p - (iHp - iOHm + iNH4p)]
neqsys = SymbolicSys(x, f)
x, sol = neqsys.solve([0]*5, solver=solver)
if verbose:
print(np.exp(x), sol)
else:
print(np.exp(x))
assert sol.success
def _SymbolicSys_from_NumSys(
self, NS, conds, rref_equil, rref_preserv, new_eq_params=True
):
from pyneqsys.symbolic import SymbolicSys
import sympy as sp
ns = NS(
self,
backend=sp,
rref_equil=rref_equil,
rref_preserv=rref_preserv,
precipitates=conds,
new_eq_params=new_eq_params,
)
symb_kw = {}
if ns.pre_processor is not None:
symb_kw["pre_processors"] = [ns.pre_processor]
if ns.post_processor is not None:
symb_kw["post_processors"] = [ns.post_processor]
if ns.internal_x0_cb is not None:
symb_kw["internal_x0_cb"] = ns.internal_x0_cb
return SymbolicSys.from_callback(
ns.f,
self.ns,
nparams=self.ns + (self.nr if new_eq_params else 0),
**symb_kw
)
def main(conc=7e-3, pH=2.0, beta_a=-2.774, beta_b=-2.81):
# Fe³⁺ + H₂O = FeOH²⁺ + H⁺ α₁ = log10(β₁) = -2.774
# y 1 z 10**-pH
#
# 10**-pH * z / y = 10**α₁ (1)
#
# 2 Fe³⁺ + 2H₂O = Fe₂OH₂⁴⁺ + 2H⁺ α₂ = log10(β₂) = -2.81
# y 1 x 10**-pH
#
# x*10**-2*pH / y**2 = 10**α₂ (2)
#
# Total amount of Fe:
# conc = [Fe³⁺] + [FeOH²⁺] + 2[Fe₂OH₂⁴⁺]
# conc = y + z + 2*x (3)
symbs = x, y, z = sympy.symbols('x y z')
eq1 = 10**-pH * z / y - 10**beta_a
eq2 = x * 10**(-2 * pH) / y**2 - 10**beta_b
eq3 = y + z + 2 * x - conc
print([eq1, eq2, eq3])
neqsys = SymbolicSys(symbs, [eq1, eq2, eq3])
xout, sol = neqsys.solve([conc / 3, conc / 3, conc / 3])
print(dict(zip('Fe2(OH)2+4 Fe3+ FeOH+2'.split(), xout)))
# Simplified treatment:
neqsys2 = SymbolicSys([x, y], [eq2, 2 * x + y - conc])
xout, sol = neqsys2.solve([conc / 2, conc / 2])
print(dict(zip('Fe2(OH)2+4 Fe3+'.split(), xout)))
def _SymbolicSys_from_NumSys(self, NS, conds, rref_equil, rref_preserv):
from pyneqsys.symbolic import SymbolicSys
import sympy as sp
ns = NS(self, backend=sp, rref_equil=rref_equil,
rref_preserv=rref_preserv, precipitates=conds)
symb_kw = {}
if ns.pre_processor is not None:
symb_kw['pre_processors'] = [ns.pre_processor]
if ns.post_processor is not None:
symb_kw['post_processors'] = [ns.post_processor]
if ns.internal_x0_cb is not None:
symb_kw['internal_x0_cb'] = ns.internal_x0_cb
return SymbolicSys.from_callback(
ns.f, self.ns, nparams=self.ns + self.nr, **symb_kw)
def _SymbolicSys_from_NumSys(self, NS, conds, rref_equil, rref_preserv):
from pyneqsys.symbolic import SymbolicSys
import sympy as sp
ns = NS(self, backend=sp, rref_equil=rref_equil,
rref_preserv=rref_preserv, precipitates=conds)
symb_kw = {}
if ns.pre_processor is not None:
symb_kw['pre_processors'] = [ns.pre_processor]
if ns.post_processor is not None:
symb_kw['post_processors'] = [ns.post_processor]
if ns.internal_x0_cb is not None:
symb_kw['internal_x0_cb'] = ns.internal_x0_cb
return SymbolicSys.from_callback(
ns.f, self.ns, nparams=self.ns + self.nr, **symb_kw)
def solve(init_a, init_b, power, solver='scipy'):
x = sp.symbols('x:2', real=True)
p = sp.Symbol('p', real=True, negative=False, integer=True)
f = [x[0] + (x[0] - x[1])**p / 2 - 1, (x[1] - x[0])**p / 2 + x[1]]
neqsys = SymbolicSys(x, f, [p])
return neqsys.solve([init_a, init_b], [power], solver=solver)
