Question

我有几个相关的功能，因为它们非常复杂和庞大，我不想用精确的数学代码为你烦恼。我尽力缩短计算时间来证明这一点。您可以在第一个函数中选择任何5x5 Hermitian矩阵。以下是代码摘要：

from numpy import linalg as LA
import numpy as np
import scipy as sp

def matrix(x, alpha, beta):
    mat = #Some 5x5 matrix which depend on the parameters x, alpha, beta.
    return np.sort(LA.eigvals(mat)) #it returns an array with 5 elements.

def integrand(x, alpha, beta):
    #Some mathematical calculation which uses the function above, it returns a scalar. 
    h = 0.0000000001;
    #The routine below is for taking the derivative with respect to beta
    mm = np.imag(matrix(x,alpha,beta + 1j*h))/h
    return (mm[0]**2 + mm[2]**2)

def integrate(alpha, beta):
    return quad(integrand,0,600, args = (alpha,beta))[0]-1

y0 = 1.5    
beta = 2

fsolve(integrate,y0,args = (beta))

fsolve给了我很多错误，它们都是一样的：

TypeError: ufunc 'isfinite' not supported for the input types, and the inputs could not be safely coerced to any supported types according to the casting rule ''safe''

错误是由于某些功能给出了NaN。

/usr/local/anaconda/lib/python2.7/site-packages/numpy/linalg/linalg.pyc in _assertFinite(*arrays)
214 def _assertFinite(*arrays):
215     for a in arrays:
--> 216         if not (isfinite(a).all()):
217             raise LinAlgError("Array must not contain infs or NaNs")
218 

TypeError: ufunc 'isfinite' not supported for the input types, and the inputs could not be safely coerced to any supported types according to the casting rule ''safe''

我猜这是由于数据类型的数量不够。我怀疑这是由于集成功能的最后一行：

quad(...)[0]-1

我是Python世界的新手，非常感谢任何帮助或解决方法。有没有办法在整个计算过程中设置数据类型？

编辑简化代码：

from scipy.integrate import quad
from numpy import linalg as LA
import numpy as np
from pylab import *

from scipy.integrate import odeint
from scipy.integrate import ode
from scipy.optimize import fsolve


#This routine is for the matrix, and the routine returns the eigenvalues
def matrix(r, theta, delta1, delta2):

    mat = np.array([[r**2-1,r*np.cos(theta),0,delta1],[r*np.cos(theta),r**2 - 1, -delta1,0],[0,-delta2,-r**2+1,-r*np.cos(theta)],[delta2,0,-r*np.cos(theta),-r**2+1]])

    return np.sort(LA.eigvals(mat))[2:4]

#This routine takes the derivatives of eigenvalues with respect to the parameter delta. I set delta1 = delta2.
def deriv(r, theta, delta):

    h = 0.00000000001

    return np.imag(matrix(r, theta, delta, delta+h*1j))/h

#This is the integrand that we need to integrate over r and theta
def integrand(theta,r, beta, delta):

    ee = matrix(r, theta, delta, delta)

    dd = deriv(r, theta, delta)

    return (np.tanh(0.5*beta*ee[0])*dd[0]+np.tanh(0.5*beta*ee[1])*dd[1])*r*r*np.sin(theta)

#Just integrate over theta
def polarint(y,r,beta,delta):

    return quad(integrand,0,np.pi,args = (r,beta,delta))[0]

#Instead of integrating directly over r, solve the differential equation.
#Lambda is the range of r.
def givesclen(delta, beta, lam):
    y0 = 0
    t_out = np.linspace(0, lam, 2500);
    rt = odeint(polarint,y0,t_out,args=(beta,delta))
    temp = (rt[-1]/delta)/(4*np.pi**2)-t_out[-1]/(2*np.pi**2)
    return temp[0]

#The goal is to find the delta; given sl, lam, beta
#Such that the result of the integration is equal to sl
def equationgap(delta, beta, lam,sl):
    return givesclen(delta, beta, lam)*4*np.pi - sl

#Test if the equationgap works, the result should be close to zero!
equationgap(.5,40,500,.1744)

#Now use the fsolve function should find the delta to be .5!
beta = 50
lam = 600
sl = 0.174
mu = 1
fsolve(equationgap,.6,args = (beta, lam, sl))

scipy中的fsolve TypeError错误

0 个答案: