나는 Symphy와 함께 Lagrangians에서 ODE를 생성하고 Numpy와 Scipy를 사용하여 수치 적 통합을 수행하는 등 여러 프로세스를 자동화하려고합니다. 끝에 전체 코드.solve()
으로 미분 방정식을 생성의 결과로 나는 다음과 같은 Sympy 식으로 사전을 얻을 : 나는 Scipy에서 odeint()
와 미분 방정식의 시스템을 통합하려는이에서 다음odeint()의 Sympy 표현이 유도 오류를냅니다.
{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)
}
. 이를 위해 def Field(Q,t):
안에있는 사전에서 표현식 (예 : lambdify
)을 추출하여 odeint(Field,Q_0,t_array)
으로 소개해야합니다. 여기에 내가 어려움을 실행하는 곳이다 :
가 처음
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)]
을 시도했지만 그것은이 개 인수 필드를 필요로이
odeint()
에 갈 수 없어, 나는의 선택
arga=()
에 전달하려 나에게 (긴) 오류가 제공
odeint()
:
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.
그래서 나는 본질적으로 동일하지만 루프 않고 시도를
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]
와 (내가 생각하는) 같은 문제가 : 나는 단순히하려고하면
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.
을 :
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]
통합이 잘 작동합니다. 또한 EquX()
이라는 함수를 비슷한 인수로 호출하면 odeint()
안에 들어가므로 제대로 작동합니다.
전체 코드
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
마지막으로 전체 오류 :
---------------------------------------------------------------------------
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 일부 파생 오류가 나는 외부 odeint를 재현하지 못할 odeint() 안에 표시() 정의와 만들어진 함수.