Question

我有一组数据，我试图使用scipy的leastsq函数来适应ODE模型。我的ODE有参数beta和gamma，所以它看起来像这样：

# dS/dt = -betaSI
# dI/dt = betaSI - gammaI
# dR/dt = gammaI
# with y0 = y(t=0) = (S(0),I(0),R(0))

我的想法是找到beta和gamma，以便我的ODE系统的数值积分最接近数据。如果我知道初始条件y0中的所有点，我可以使用leastsq做到这一点。

现在，我正在尝试做同样的事情，但现在传递y0的一个条目作为额外参数。这是Python和我停止沟通的地方...... 我做了一个函数，所以现在我传递给leastsq的参数的第一个条目是我的变量R的初始条件。我收到以下消息：

*Traceback (most recent call last):
  File "/Users/Laura/Dropbox/SHIV/shivmodels/test.py", line 73, in <module>
    p1,success = optimize.leastsq(errfunc, initguess, args=(simpleSIR,[y0[0]],[Tx],[mydata]))
  File "/Library/Frameworks/Python.framework/Versions/7.2/lib/python2.7/site-packages/scipy/optimize/minpack.py", line 283, in leastsq
    gtol, maxfev, epsfcn, factor, diag)
TypeError: array cannot be safely cast to required type*

这是我的代码。对于这个例子来说，它需要更多的参与，因为实际上我想要使用7个参数来适应另一个ode，并希望一次适合多个数据集。但是我想在这里发布更简单的内容......任何帮助都将非常感谢！非常感谢你！

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

#define the time span for the ODE integration:
Tx = np.arange(0,50,1)
num_points = len(Tx)

#define a simple ODE to fit:
def simpleSIR(y,t,params):
    dydt0 = -params[0]*y[0]*y[1]
    dydt1 = params[0]*y[0]*y[1] - params[1]*y[1]
    dydt2 = params[1]*y[1]
    dydt = [dydt0,dydt1,dydt2]
    return dydt


#generate noisy data:
y0 = [1000.,1.,0.]
beta = 12*0.06/1000.0
gamma = 0.25
myparam = [beta,gamma]
sir = odeint(simpleSIR, y0, Tx, (myparam,))

mydata0 = sir[:,0] + 0.05*(-1)**(np.random.randint(num_points,size=num_points))*sir[:,0]
mydata1 = sir[:,1] + 0.05*(-1)**(np.random.randint(num_points,size=num_points))*sir[:,1]
mydata2 = sir[:,2] + 0.05*(-1)**(np.random.randint(num_points,size=num_points))*sir[:,2]
mydata = np.array([mydata0,mydata1,mydata2]).transpose()


#define a function that will run the ode and fit it, the reason I am doing this
#is because I will use several ODE's to see which one fits the data the best.
def fitfunc(myfun,y0,Tx,params):
    myfit = odeint(myfun, y0, Tx, args=(params,))
    return myfit

#define a function that will measure the error between the fit and the real data:
def errfunc(params,myfun,y0,Tx,y):
    """
    INPUTS:
    params are the parameters for the ODE
    myfun is the function to be integrated by odeint
    y0 vector of initial conditions, so that y(t0) = y0
    Tx is the vector over which integration occurs, since I have several data sets and each 
    one has its own vector of time points, Tx is a list of arrays.
    y is the data, it is a list of arrays since I want to fit to multiple data sets at once
    """
    res = []
    for i in range(len(y)):
        V0 = params[0][i]
        myparams = params[1:]
        initCond = np.zeros([3,])
        initCond[:2] = y0[i]
        initCond[2] = V0
        myfit = fitfunc(myfun,initCond,Tx[i],myparams)
        res.append(myfit[:,0] - y[i][:,0])
        res.append(myfit[:,1] - y[i][:,1])
        res.append(myfit[1:,2] - y[i][1:,2])
    #end for
    all_residuals = np.hstack(res).ravel()
    return all_residuals
#end errfunc


#example of the problem:

V0 = [0]
params = [V0,beta,gamma]  
y0 = [1000,1]

#this is just to test that my errfunc does work well.
errfunc(params,simpleSIR,[y0],[Tx],[mydata])
initguess = [V0,0.5,0.5]

p1,success = optimize.leastsq(errfunc, initguess, args=(simpleSIR,[y0[0]],[Tx],[mydata]))

Answer 1

问题在于变量initguess。函数optimize.leastsq具有以下调用签名：

http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.leastsq.html

它的第二个参数x0必须是一个数组。你的清单

initguess = [v0,0.5,0.5]

无法转换为数组，因为v0是列表而不是int或float。因此，当您尝试将initguess从列表转换为leastsq函数中的数组时，会出现错误。

我会从

调整变量参数

def errfunc(params,myfun,y0,Tx,y):

这样它就是一维阵列。将前几个条目设为v0的值，然后将beta和gamma附加到该值。

当初始条件作为参数传递时，使用python leastsq拟合ODE会产生强制转换错误

1 个答案: