Display issue of fitted curve: cannot solve coarseness

Question

Despite having a working script for curve fitting using the lmfit library, I am not able to solve a display issue. Indeed, having only 5 dependent values, the resulting graph is rather coarse.

Before switching to lmfit , I was using curve_fit and could solve the display issue by simply using np.linspace and plot the optimized values resulting from the fit procedure. Then, I was displaying the "real" values through plt.errorbar . With lmfit , the above solution yields a mismatch error, since it recognizes the "fake" independent variables and launches a mismatch type error.

My full script is the following:

import lmfit as lf
from lmfit import Model, Parameters
import numpy as np
import matplotlib.pyplot as plt
from math import atan


def on_res(omega_eff, thetas, R2avg=5, k_ex=0.1, phi_ex=500):
    return R2avg*(np.sin(thetas))**2 + ((np.sin(thetas))**2)*(phi_ex*k_ex/(k_ex**2 + omega_eff**2))

model = Model(on_res,independent_vars=['omega_eff','thetas'])
params = model.make_params(R2avg=5, k_ex=0.01, phi_ex=1500)


carrier = 6146.53
O_1 = 5846
spin_locks = (1000, 2000, 3000, 4000, 5000) 
delta_omega = (O_1 - carrier)

omega_eff1 = ((delta_omega**2) + (spin_locks[0]**2))**0.5
omega_eff2 = ((delta_omega**2) + (spin_locks[1]**2))**0.5
omega_eff3 = ((delta_omega**2) + (spin_locks[2]**2))**0.5
omega_eff4 = ((delta_omega**2) + (spin_locks[3]**2))**0.5
omega_eff5 = ((delta_omega**2) + (spin_locks[4]**2))**0.5

theta_rad1 = atan(spin_locks[0]/delta_omega)
theta_rad2 = atan(spin_locks[1]/delta_omega)
theta_rad3 = atan(spin_locks[2]/delta_omega)
theta_rad4 = atan(spin_locks[3]/delta_omega)
theta_rad5 = atan(spin_locks[4]/delta_omega)

x = (omega_eff1/1000, omega_eff2/1000, omega_eff3/1000, omega_eff4/1000, omega_eff5/1000)# , omega_eff6/1000)# , omega_eff7/1000)
theta = (theta_rad1, theta_rad2, theta_rad3, theta_rad4, theta_rad5)
R1rho_vals = (7.9328, 6.2642, 6.0005, 5.9972, 5.988)
e = (0.2, 0.2, 0.2, 0.2, 0.2)

new_x = np.linspace(0, 6, 1000)
omega_eff = np.array(x, dtype=float)
thetas = np.array(theta, dtype=float)
R1rho_vals = np.array(R1rho_vals, dtype=float)
error = np.array(e, dtype=float)
R2avg = []
k_ex = []
phi_ex = []

result = model.fit(R1rho_vals, params, weights=1/error, thetas=thetas, omega_eff=omega_eff, method = "emcee", steps = 1000)

print(result.fit_report())

plt.errorbar(x, R1rho_vals, yerr = error, fmt = ".k", markersize = 8, capsize = 3)
plt.plot(new_x, result.best_fit)
plt.show()

As you can see running it, it launches the mismatch shape error message. Changing the plt.plot line to plt.plot(x, result.best_fit) yields the graph correctly, but displaying a very coarse profile (as one would expect, having only 5 points on the x-axis).

Are you aware of any way to solve this? Checking the documentation, I noticed the examples provided all plot the results via the actual independent variables values, since they have enough experimental values.

Answer 1

您需要使用自变量的新值重新评估ModelResult：

plt.plot(new_x, result.eval(omega_eff=new_x/1000., thetas=thetas))