了解scipy.integrate，odeint包装器odeintw

Question

我正在尝试解决一个由4个PDE组成的耦合非线性系统，代码如下：

import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from odeintw import odeintw

# constants
global rH, L, q, p, Q, mu
rH = 1.0 ; L = 1.0 ; p = 2.0 ; q  = 1.0 ; Q = 1.71 ; mu = Q*rH/L**2 

def dfunc(G, kx, ky, w, r): 

 try: 
    z = 1.0/(rH - r)

 except ZeroDivisionError:
 print "Trying to divide zero"

 phi = mu*( 1.0 - rH/r) 
 fr = 1.0 - (rH/r)**3 
 scale = L**2 * np.sqrt(fr) / r**2 + 0j

 vp = (w + q*phi)/(np.sqrt(fr)) + p*mu*rH/r + 0j 
 vn = (w + q*phi)/(np.sqrt(fr)) - p*mu*rH/r + 0j

 # G11 -> G1, G12 -> G2, G21 -> G3, G22 -> G4 

 G1, G2, G3, G4 = G

 G11 = (vp - kx + (vn + kx)*G1**2 - ky*G1*G2 - ky*G1*G3 
 + (vp-kx)*G2*G3 ) 
 G12 = (ky + (vn + kx)*G1*G2 - ky*G2**2 - ky*G1*G4 
 + (vp-kx)*G2*G4 ) 
 G21 = (ky + (vn + kx)*G1*G3 - ky*G1*G4 - ky*G3**2 
 + (vp-kx)*G3*G4 ) 
 G22 = (vn + kx + (vn + kx)*G2*G3 - ky*G2*G4 - ky*G2*G3
 + (vp-kx)*G4**2 ) 

 return np.multiply(scale, np.array([ G11, G12, G21, G22 ]))

 # jaccobian

def jac(G, kx, ky, w, r):

 G1, G2, G3, G4 = G

 jac = np.array([  
   [2(vn+kx)*G1 - ky*(G2+G3), -ky*G1 + (vp-kx)*G3, -ky*G1+(vp-kx)*G2, 0   ],
   [(vn+kx)*G2-ky*G4, (vn+kx)*G1-2*ky*G2+(vp-kx)*G4, 0, -ky*G1+(vp-kx)*G2 ],
   [(vn+kx)*G3-ky*G4, 0, (vn+kx)*G1-2*ky*G3+(vp-kx)*G4, -ky*G1+(vp-kx)*G3 ],  
   [0, (vn+kx)*G3-ky*(G4+G3), (vn+kx)*G2-ky*G2, -ky*G2+2*(vp-kx)*G4 ]
   ]) 

 return np.multiply(scale, jac)

# Initial value
Gir = np.array([ 1.0j, 0, 0, 1.0j ])
r = np.arange(rH + 0.1, 1000*rH, 1) 

kx = 0
ky = 0
w = 0.0001 + 0.0000001j 

G, infodict = odeintw(dfunc, Gir, r, args=(kx,ky,w), Dfun=jac, full_output=True )

print 'final', np.size(G), G

但是，它会给出以下错误，并且不会真正从初始点移动：

lsoda--  warning..internal t (=r1) and h (=r2) are
   such that in the machine, t + h = t on the next step  
   (h = step size). solver will continue anyway
  In above,  R1 =   .1100000000000E+01   R2 =   .3569471009368E-22

最终的解决方案G是一个3996大小的数组，请帮助我理解这一点。谢谢!

Answer 1

在函数dfunc和jac中，第二个参数必须是自变量。在您的示例中，自变量是r，因此应该开始定义

def dfunc(G, r, kx, ky, w):

和

def jac(G, r, kx, ky, w):