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我試圖自動化幾個進程，比如使用Sympy從拉格朗日生成ODE並使用Numpy和Scipy對它們進行數值整合。 最後的完整代碼。與solve()產生的常微分方程的結果我得到一個字典，Sympy表達式如下所示：odeint（）中的Sympy表達式給出了派生錯誤
{Derivative(lambda1(t), t): (y(t) + 1)/(x(t)*y(t)),
Derivative(z(t), t): x(t),
Derivative(x(t), t): y(t)*z(t),
Derivative(y(t), t): -x(t)*z(t)
}
odeint()從SciPy的整合
然後。爲此，我需要從def Field(Q,t):內的字典中提取表達式（例如lambdify），以引入odeint(Field,Q_0,t_array)。這裏就是我困難運行：
我第一次嘗試
def Equ2(nQ,t,Q,Field):
x1,y1,z1,lamb1 = nQ
dQ =[]
for f in Q:
dQ.append(lambdify(Q, Field[f.diff(t)],'numpy')(x1,y1,z1,lamb1))
return dQ[0:len(nQ)]
但因爲它需要的字段2點的參數也不能去odeint()，我試圖將它傳遞的可選arga=()odeint()，給我（長）錯誤：
ValueError Traceback (most recent call last)
<ipython-input-20-63f086b8a252> in Equ2(nQ, t, Q, Field)
20 dQ =[]
21 for f in Q:
---> 22 dQ.append(lambdify(Q, Field[f.diff(t)],'numpy')(x1,y1,z1,lamb1))
23 return dQ[0:len(Q)-1]
[...]
ValueError:
Can't calculate 1st derivative wrt 14.0430379424125.
所以，我想基本上是相同的，但沒有循環，
def Equ1(nQ,t):
x1,y1,z1,lamb1 = nQ
dx = lambdify((x,y,z,lam[0]), field[x.diff(t)],'numpy')(x1,y1,z1,lamb1)
dy = lambdify((x,y,z,lam[0]), field[y.diff(t)],'numpy')(x1,y1,z1,lamb1)
dz = lambdify((x,y,z,lam[0]), field[z.diff(t)],'numpy')(x1,y1,z1,lamb1)
dlam = lambdify((x,y,z,lam[0]), field[lam[0].diff(t)],'numpy')(x1,y1,z1,lamb1)
return [dx,dy,dz]
，並有（我認爲）同樣的問題：
ValueError Traceback (most recent call last)
<ipython-input-20-63f086b8a252> in Equ1(nQ, t)
9 def Equ1(nQ,t):
10 x1,y1,z1,lamb1 = nQ
---> 11 dx = lambdify((x,y,z,lam[0]), field[x.diff(t)],'numpy')(x1,y1,z1,lamb1)
12 dy = lambdify((x,y,z,lam[0]), field[y.diff(t)],'numpy')(x1,y1,z1,lamb1)
13 dz = lambdify((x,y,z,lam[0]), field[z.diff(t)],'numpy')(x1,y1,z1,lamb1)
[...]
ValueError:
Can't calculate 1st derivative wrt 17.6326726993661.
如果我試圖簡單地說：
def Equ0(nQ,t):
x,y,z,lamb = nQ
dx = y*z
dy = -x*z
dz = x
dlam = (y+1.)/(x*y)
return [dx,dy,dz]
整合工作得很好。另外，如果我用類似的參數調用EquX()函數，它將在odeint()之內使用，它們工作得很好。
全碼
from sympy import *
from sympy.physics.mechanics import dynamicsymbols
from numpy import linspace, sin, cos
from scipy.integrate import odeint
t = Symbol('t')
x = Function('x')(t)
y = Function('y')(t)
z = Function('z')(t)
lam = dynamicsymbols('lambda1:{0}'.format(5))
f = x.diff(t)- y*z
eq = Matrix([x.diff(t) - lam[0].diff(t)*y*x*z+z,
y.diff(t) +x*z,
z.diff(t)-x
])
field = solve(list(eq)+[f],[x.diff(t),y.diff(t),z.diff(t),lam[0].diff(t)])
def Equ0(nQ,t):
x,y,z,lamb = nQ
dx = y*z
dy = -x*z
dz = x
dlam = (y+1.)/(x*y)
return [dx,dy,dz]
def Equ1(nQ,t):
x1,y1,z1,lamb1 = nQ
dx = lambdify((x,y,z,lam[0]), field[x.diff(t)],'numpy')(x1,y1,z1,lamb1)
dy = lambdify((x,y,z,lam[0]), field[y.diff(t)],'numpy')(x1,y1,z1,lamb1)
dz = lambdify((x,y,z,lam[0]), field[z.diff(t)],'numpy')(x1,y1,z1,lamb1)
dlam = lambdify((x,y,z,lam[0]), field[lam[0].diff(t)],'numpy')(x1,y1,z1,lamb1)
return [dx,dy,dz]
def Equ2(nQ,t,Q,Field):
x1,y1,z1,lamb1 = nQ
dQ =[]
for f in Q:
dQ.append(lambdify(Q, Field[f.diff(t)],'numpy')(x1,y1,z1,lamb1))
return dQ[0:len(Q)-1]
q = [x,y,z,lam[0]]
nq = [1,2,3,4]
time=linspace(0,10,10)
### This line works just fine:
print Equ0(nq,t), Equ1(nq,t), Equ2(nq,t,q,field) #They give the same output
sol0 = odeint(Equ0,nq,time)
sol1 = odeint(Equ1,nq,time) #Errors here
sol2 = odeint(Equ2,nq,time,args=(q,field)) #And here
最後完整的錯誤：
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-20-63f086b8a252> in Equ1(nQ, t)
9 def Equ1(nQ,t):
10 x1,y1,z1,lamb1 = nQ
---> 11 dx = lambdify((x,y,z,lam[0]), field[x.diff(t)],'numpy')(x1,y1,z1,lamb1)
12 dy = lambdify((x,y,z,lam[0]), field[y.diff(t)],'numpy')(x1,y1,z1,lamb1)
13 dz = lambdify((x,y,z,lam[0]), field[z.diff(t)],'numpy')(x1,y1,z1,lamb1)
/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc in diff(self, *symbols, **assumptions)
2864 new_symbols = list(map(sympify, symbols)) # e.g. x, 2, y, z---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-20-63f086b8a252> in Equ1(nQ, t)
9 def Equ1(nQ,t):
10 x1,y1,z1,lamb1 = nQ
---> 11 dx = lambdify((x,y,z,lam[0]), field[x.diff(t)],'numpy')(x1,y1,z1,lamb1)
12 dy = lambdify((x,y,z,lam[0]), field[y.diff(t)],'numpy')(x1,y1,z1,lamb1)
13 dz = lambdify((x,y,z,lam[0]), field[z.diff(t)],'numpy')(x1,y1,z1,lamb1)
/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc in diff(self, *symbols, **assumptions)
2864 new_symbols = list(map(sympify, symbols)) # e.g. x, 2, y, z
2865 assumptions.setdefault("evaluate", True)
---> 2866 return Derivative(self, *new_symbols, **assumptions)
2867
2868 ###########################################################################
/usr/local/lib/python2.7/dist-packages/sympy/core/function.pyc in __new__(cls, expr, *variables, **assumptions)
1068 ordinal = 'st' if last_digit == 1 else 'nd' if last_digit == 2 else 'rd' if last_digit == 3 else 'th'
1069 raise ValueError(filldedent('''
---> 1070 Can\'t calculate %s%s derivative wrt %s.''' % (count, ordinal, v)))
1071
1072 if all_zero and not count == 0:
ValueError:
Can't calculate 1st derivative wrt 0.0.
2865 assumptions.setdefault("evaluate", True)
---> 2866 return Derivative(self, *new_symbols, **assumptions)
2867
2868 ###########################################################################
/usr/local/lib/python2.7/dist-packages/sympy/core/function.pyc in __new__(cls, expr, *variables, **assumptions)
1068 ordinal = 'st' if last_digit == 1 else 'nd' if last_digit == 2 else 'rd' if last_digit == 3 else 'th'
1069 raise ValueError(filldedent('''
---> 1070 Can\'t calculate %s%s derivative wrt %s.''' % (count, ordinal, v)))
1071
1072 if all_zero and not count == 0:
ValueError:
Can't calculate 1st derivative wrt 0.0.
TL; DR出現內部odeint（），我不能重現外odeint一些推導錯誤（）自定義製作功能。