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python - 使用 scipy 拟合微分方程，得到“对象对于所需数组来说太深”

问题描述

我正在尝试将曲线拟合到微分方程。为了简单起见，我只是在这里做逻辑方程。我写了下面的代码，但我得到下面显示的错误。我不太确定我做错了什么。

import numpy as np
import pandas as pd
import scipy.optimize as optim
from scipy.integrate import odeint

df_yeast = pd.DataFrame({'cd': [9.6, 18.3, 29., 47.2, 71.1, 119.1, 174.6, 257.3, 350.7, 441., 513.3, 559.7, 594.8, 629.4, 640.8, 651.1, 655.9, 659.6], 'td': np.arange(18)})

N0 = 1
parsic = [5, 2]

def logistic_de(t, N, r, K):
    return r*N*(1 - N/K)

def logistic_solution(t, r, K):
    return odeint(logistic_de, N0, t, (r, K))

params, _ = optim.curve_fit(logistic_solution, df_yeast['td'], df_yeast['cd'], p0=parsic);

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
ValueError: object too deep for desired array

---------------------------------------------------------------------------
error                                     Traceback (most recent call last)
<ipython-input-94-2a5a467cfa43> in <module>
----> 1 params, _ = optim.curve_fit(logistic_solution, df_yeast['td'], df_yeast['cd'], p0=parsic);

~/SageMath/local/lib/python3.9/site-packages/scipy/optimize/minpack.py in curve_fit(f, xdata, ydata, p0, sigma, absolute_sigma, check_finite, bounds, method, jac, **kwargs)
    782         # Remove full_output from kwargs, otherwise we're passing it in twice.
    783         return_full = kwargs.pop('full_output', False)
--> 784         res = leastsq(func, p0, Dfun=jac, full_output=1, **kwargs)
    785         popt, pcov, infodict, errmsg, ier = res
    786         ysize = len(infodict['fvec'])

~/SageMath/local/lib/python3.9/site-packages/scipy/optimize/minpack.py in leastsq(func, x0, args, Dfun, full_output, col_deriv, ftol, xtol, gtol, maxfev, epsfcn, factor, diag)
    420         if maxfev == 0:
    421             maxfev = 200*(n + 1)
--> 422         retval = _minpack._lmdif(func, x0, args, full_output, ftol, xtol,
    423                                  gtol, maxfev, epsfcn, factor, diag)
    424     else:

error: Result from function call is not a proper array of floats.

标签： pythonscipydifferential-equations

解决方案

@hpaulj 指出了返回值形状的问题，logistic_solution并表明修复可以消除您报告的错误。

但是，代码中还有另一个问题。该问题不会产生错误，但会导致您的测试问题（逻辑微分方程）的解不正确。默认情况下，odeint期望t计算微分方程的函数的参数是第二个参数。要么更改前两个参数的顺序，要么logistic_de将参数添加tfirst=True到您的调用中odeint。第二个选项更好一些，因为如果您决定尝试使用该功能而logistic_de不是.scipy.integrate.solve_ivpodeint

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