exponential decay with scipy just gives step function

问题

I'm trying to do an exponential fit with a set of data:

import matplotlib.pyplot as plt
import numpy as np
import scipy.optimize as opt


def func(x, a, b, c):
    return a * np.exp(x / -b) + c


epr_data = np.loadtxt('T2_text', skiprows=1)

time = epr_data[:, 1]
intensity = epr_data[:, 2]


optimizedParameters, pcov = opt.curve_fit(func, time, intensity)
print(optimizedParameters)
plt.plot(time, intensity, func(time, *optimizedParameters), label="fit")

plt.show()

but i just get this step function and these parameters:

[1.88476367e+05 1.00000000e+00 6.49563230e+03]

the plot with "fit"

as well as this error message:

OptimizeWarning: Covariance of the parameters could not be estimated
  warnings.warn('Covariance of the parameters could not be estimated'

EDIT:

https://pastebin.com/GTTGf0ed

i want to plot the time and first row with intensity

the graph after your suggestion

edit 2:

import matplotlib.pyplot as plt
import numpy as np
import scipy.optimize as opt


def func(x, a, b, c):
    return a * np.exp(x / -b) + c


epr_data = np.loadtxt('T2_text', skiprows=1)

time = epr_data[:, 1]
intensity = epr_data[:, 2]

c0 = np.mean(intensity[-10:])
a0 = intensity[0]-c0
th = time[np.searchsorted(-intensity+c0, -0.5*a0)]
b0 = th / np.log(2)

optimizedParameters, pcov = opt.curve_fit(func, time, intensity, p0=(a0, b0, c0))
print(optimizedParameters)
plt.plot(time, intensity, label='data')
plt.plot(time, func(time, *optimizedParameters), label="fit")
plt.legend()

plt.show()

回答1:

First, fix your plot function call. To plot two curves with one call, you have to give the x and y values for each curve:

plt.plot(time, intensity, time, func(time, *optimizedParameters), label="fit")

For labeling, it might be simpler to call plot twice:

plt.plot(time, intensity, label="data")
plt.plot(time, func(time, *optimizedParameters), label="fit")

It would be easier to address the warning generated by curve_fit if we had your data. Experience shows, however, that it is most likely that the default initial guess of the parameters used by curve_fit (which is all 1s) is just a really bad guess.

Try helping curve_fit by giving it a better starting point for its numerical optimization routine. The following bit of code shows how you can compute rough guesses for a, b and c. Pass these to curve_fit with the argument p0=(a0, b0, c0).

# Assume that the time series is long enough that the tail
# has flattened out to approximately random noise around c.
c0 = np.mean(intensity[-10:])

# This assumes time[0] is 0.
a0 = intensity[0] - c0

# Rough guess of the half-life.
th = time[np.searchsorted(-intensity+c0, -0.5*a0)]
b0 = th / np.log(2)

来源：https://stackoverflow.com/questions/65671927/exponential-decay-with-scipy-just-gives-step-function