I'm trying to fit a curve to a differential equation. For the sake of simplicity, I'm just doing the logistic equation here. I wrote the code below but I get an error shown below it. I'm not quite sure what I'm doing wrong.
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.
@hpaulj has pointed out the problem with the shape of the return value from logistic_solution and shown that fixing that eliminates the error that you reported.
There is, however, another problem in the code. The problem does not generate an error, but it does result in an incorrect solution to your test problem (the logistic differential equation). By default, odeint expects the t argument of the function that computes the differential equations to be the second argument. Either change the order of the first two arguments of logistic_de, or add the argument tfirst=True to your call of odeint. The second option is a bit nicer, because it will allow you to use logistic_de with scipy.integrate.solve_ivp if you decide to try that function instead of odeint.