求解参数数组的 ODE (Python) [英] Solve a ODE for arrays of parameters (Python)

问题描述

*我知道这个问题很简单，但我想知道在 Python 中设置这样一个 for 循环的最佳方法.

*I am aware that this question is quite simple but I would like to know the best way to set up such a for loop in Python.

我已经编写了一个程序来计算和绘制二阶微分方程的解(此代码如下).

I have written a program already to calculate and plot the solution to a 2nd order differential equation (this code is given below).

我想知道对 f 参数数组(因此是 f_array)重复此计算的最佳方法.IE.以便该图显示 20 组数据，这些数据将解决方案作为 t 的函数，每组数据具有不同的 f 值.

I would like to know best methods for repeating this calculation for an array of f parameters (hence f_array). I.e. so that the plot shows 20 sets of data referring to solutions as a function of t each with a different value of f.

为任何想法干杯.

from pylab import *
from scipy.integrate import odeint

#Arrays.
tmax = 100
t = linspace(0, tmax, 4000)
fmax = 100
f_array = linspace(0.0, fmax, 20)

#Parameters
l = 2.5
w0 = 0.75
f = 5.0
gamma = w0 + 0.05
m = 1.0
alpha = 0.15
beta = 2.5

def rhs(c,t):
    c0dot = c[1]
    c1dot = -2*l*c[1] - w0*w0*c[0] + (f/m)*cos((gamma)*t)-alpha*c[0] - beta*c[0]*c[0]*c[0]
    return [c0dot, c1dot]

init_x = 15.0
init_v = 0.0
init_cond = [init_x,init_v]
ces = odeint(rhs, init_cond, t)

s_no = 1
subplot(s_no,1,1)
xlabel("Time, t")
ylabel("Position, x")
grid('on')
plot(t,ces[:,0],'-b')
title("Position x vs. time t for a Duffing oscillator.")
show()

下面的图显示了这个方程的解，该方程关于 f 的单个值，用于 t 值的数组.我想要一种快速的方法来为 f 值数组重复这个图.

Here is a plot showing the solution to this equation regarding a single value of f for an array of t values. I would like a quick way to repeat this plot for an array of f values.

推荐答案

这是一种方法:

修改rhs 以接受第三个参数，即参数f.rhs 的定义应该开始

Modify rhs to accept a third argument, the parameter f. The definition of rhs should begin

def rhs(c, t, f):
    ...

使用 for 循环遍历 f_array.在循环中，使用 args 参数调用 odeint，以便 odeint 给出 f 的值作为第三个参数rhs.将每次调用 odeint 的结果保存在一个列表中.基本上，替换

Iterate over the f_array with a for loop. In the loop, call odeint with the args argument so that odeint gives the value of f as the third argument to rhs. Save the results of each call to odeint in a list. Basically, replace

ces = odeint(rhs, init_cond, t)    

与

solutions = []
for f in f_array:
    ces = odeint(rhs, init_cond, t, args=(f,))
    solutions.append(ces)

对于 f_array 中 f 的每个值，您现在在 solutions 列表中有一个解决方案.

For each value of f in f_array, you now have a solution in the solutions list.

要绘制这些，您可以将 plot 调用放在另一个 for 循环中:

To plot these, you could put your plot call in another for loop:

for ces in solutions:
    plot(t, ces[:, 0], 'b-')

这篇关于求解参数数组的 ODE (Python)的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！