使用python odeint scipy求解一系列ode时拆分状态向量

Question

我将我的代码从Matlab转换为Python，并停留在如何拆分状态向量，以便结果返回两个解决方案的问题上。对于两个初始条件，我有一个向量和一个值，我希望最终结果是一个矩阵和一个向量。

我尝试以与解决方案（soln = [dfdt，dcdt]）相同的方式加入初始条件（y0 = [c_pt_0，x_0]）（如下代码所示）。我还尝试了在matlab中使用的类似方法，该方法将初始条件连接到一个数组中，然后对结果进行拆包，但我认为问题出在维度上。

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<p class="results"></p><div class="green">That's all folks!</div></p>

跟踪： ValueError：设置具有序列的数组元素。

非常感谢您的帮助。

编辑：添加了MATLAB代码

这是我想要转换为状态向量被分割的python的MATLAB代码。我有三个文件（一个主文件，f函数和参数）。请原谅任何手掌编码错误，但即使如此，我也非常感谢任何建议。

modified_model.m：

#Basic imports
import numpy as np
import pylab
import matplotlib. pyplot as plt
import scipy
from scipy.integrate import odeint
import matplotlib.pyplot as plt

# define parameters
pi = 3.14159265 
V_m = 9.09
m_V__M_Pt = 1e6/195.084    
rho = 21.45
R0 = 10**(-8.19)
k_d = 10**(-13)
k_r = 10**(-5)
S = 0.314   #distribution parameter
M = 0.944   #distribution parameter

## geometry
# Finite Volume Method with equidistant elements
r_max = 30.1e-9                     #maximum value
n = 301                             #number of elements of FVM
dr = r_max/n                        #length of elements, equidistant
ini_r = np.linspace(5e-10,r_max,n+1)    #boundaries of elements
mid_r = ini_r[0:n]+dr/2             #center of elements

## initial conditions
#initial distribution
x0 = 1/(S*np.sqrt(2*pi)*mid_r*1e9)*np.exp((-(np.log(mid_r*1e9)-M)**2)/(2*S**2))
c_pt_0 = 0
y0 = [x0, c_pt_0]

MN_0 = scipy.trapz(np.power(mid_r, 3)*x0,
                        x=mid_r)    # initial mass
M_0 = 4/3*pi*rho*MN_0

def f(y, t):
    r = y[0]
    c_pt = y[1]

    #materials balance
    drdt = V_m * k_r * c_pt * np.exp(-R0/ mid_r) - V_m * k_d * np.exp(R0/ mid_r)
    dmdt = 4*pi*rho*mid_r**2*drdt
    dMdt = np.trapz(r*dmdt, x=mid_r)

    dcdt = m_V__M_Pt*(-dMdt)/M_0
    dfdt = -(np.gradient(r*drdt, dr))

    soln = [dfdt, dcdt]
    return soln

#------------------------------------------------------
#define timespace
time = np.linspace(0, 30, 500)

#solve ode system
sln_1 = odeint (f , y0 , time,
    rtol = 1e-3, atol = 1e-5)

pylab.plot(mid_r, sln_1[1,:], color = 'r', marker = 'o')
pylab.plot(mid_r, sln_1[-1,:], color = 'b', marker = 'o')
plt.show()

f.m

function modified_model

% import parameters
p = cycling_parameters;

% initial conditions
c_pt_0 = 0;
y0 = [p.x0; c_pt_0];

% call integrator 
options_ODE=odeset('Stats','on', 'RelTol',1e-3,'AbsTol',1e-5);
[~, y] = ode15s(@(t,y) f(t, y, p), p.time, y0, options_ODE);

%% Post processing
% split state vector
r       = y(:,1:p.n);
c_Pt = y(:,p.n+1);

%% Plot results 

figure
hold on;
plot(p.r_m, r(1,:));
plot(p.r_m, r(end,:));
xlabel({'size'},'FontSize',15)
ylabel({'counts'},'FontSize',15)

和参数文件：cycling_parameters.m

function soln = f(~, y, p)

%split state vector
r = y(1:p.n);
c_pt = y(p.n+1);

% materials balance
drdt = p.Vm_Pt.*p.k_rdp.*c_pt.*exp(-p.R0./p.r_m) - p.Vm_Pt.*p.k_dis.*exp(p.R0./p.r_m);
dmdt = 4*pi*p.rho*p.r_m.^2.*drdt; 
dMdt = trapz(p.r_m, r.*dmdt);
dcdt = p.I_V*p.m_V__M_Pt*(-dMdt)/p.M_0;
dfdt = - gradient(r.*drdt,p.dr);

soln = [dfdt; dcdt];

Answer 1

查看完这两个代码后，问题在于odeint求解器仅接受一维数组输入，而您的y0为[int，array（300，）]，而odeint无法使用该数组。但是，您可以将y0合并为一维数组，然后将其拆分为要积分的函数以进行计算，然后重新组合为输出。这是一个工作代码：

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

class P:
    def __init__(self, S, M):
        self.M = 195.084
        self.rho = 21.45
        self.m_V__M_Pt = (1*10**6)/self.M
        self.Vm_Pt = 9.09
        self.R0_log = -8.1963
        self.k_dis_log = -13
        self.k_rdp_log = -11
        self.R0 = 10**(self.R0_log)
        self.k_dis = 10**(self.k_dis_log)
        self.k_rdp = 10**(self.k_rdp_log)
        self.r_max = 10.1*10**(-9)
        self.n = 301
        self.dr = self.r_max / self.n
        self.r = np.linspace(5*10**(-10), self.r_max, self.n)
        self.r_m = self.r[0:self.n+1]+self.dr/2
        self.x0 = self.compute_x0(S, M)
        self.r_squared = np.power(self.r_m, 2)
        self.r_cubed = np.power(self.r_m, 3)
        self.MN_0 = np.trapz(self.r_m, np.multiply(self.r_cubed, self.x0))
        self.M_0 = (4 / 3)* np.pi * self.rho * self.MN_0
        self.I_V = 1

    def compute_x0(self, S, M):
        p1 = np.multiply(2, np.power(S, 2))
        p2 = np.multiply(S, np.sqrt(np.multiply(2, np.pi)))
        p3 = np.log(self.r_m*1*10**(9)) - M
        p4 = np.multiply(p2, self.r_m*10**(9))
        p5 = np.power(-p3, 2)
        p6 = np.multiply(p4, np.exp(np.divide(p5,p1)))
        p7 = np.divide(1, p6)
        return p7

def cycling_parameters():
    S = 0.314
    M = 0.944
    p = P(S, M)
    return p

def f(y, t):
    p = cycling_parameters()
    c_pt = y[0]
    r = np.delete(y, 0)
    p1 = np.multiply(p.Vm_Pt, p.k_rdp)
    p2 = np.multiply(p1, c_pt)
    p3 = np.multiply(p.Vm_Pt, p.k_dis)
    drdt = np.multiply(p2, np.exp(np.divide(-p.R0, p.r_m))) - np.multiply(p3, np.exp(np.divide(p.R0, p.r_m)))
    dmdt = np.multiply(4*np.pi*p.rho*np.power(p.r_m, 2), drdt)
    p4 = np.multiply(r, dmdt)
    dMdt = np.trapz(p.r_m, p4)
    dcdt = p.I_V*p.m_V__M_Pt*(-dMdt)/p.M_0
    p5 = np.multiply(r, drdt)
    dfdt = - np.gradient(p5,p.dr)
    ans = np.insert(dfdt, 0, dcdt)
    return ans

def modified_model():
    p = cycling_parameters()
    c_pt_0 = 0
    y0 = np.insert(p.x0, 0, c_pt_0)
    t = np.linspace(0, 30, 500)
    ans = odeint(f, y0, t, rtol = 1e-3, atol = 1e-5)

    r = ans[:, 1:p.n+1]
    c_Pt = ans[:, 0]
    print(r)
    print(c_Pt)
    plt.plot(p.r_m, r[0, :], color='r', linewidth=0.5)
    plt.plot(p.r_m, r[r.shape[0]-1, :], color='b', linewidth=0.5)
    plt.show()

if __name__ == '__main__':
    modified_model()

Python图（此脚本输出的内容）：

原始Matlab图：