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import numpy as np
import matplotlib.pyplot as plt

data = np.loadtxt('frogmuscleT1.txt')

v = data[:,1]
T1 = data[:,0]

plt.plot(v,T1,'o',markersize=4, color='firebrick',label='Frog muscle data points')

ln_T1 = np.log(T1)
ln_v = np.log(v)

n = len(ln_v)
sum_x = np.sum(ln_v)
sum_y = np.sum(ln_T1)
sum_xy = np.sum(ln_v * ln_T1)
sum_x2 = np.sum(ln_v**2)

B = (n * sum_xy - sum_x * sum_y) / (n * sum_x2 - sum_x**2)
ln_A = (sum_y - B * sum_x) / n

A = np.exp(ln_A)

print(f"Fitted equation: T_1 = {A:.2f} * v^{B:.2f}")

A = 208.30
B = 0.38

v_fit = np.linspace(1, 62, 100)
T1_fit = A * v_fit**B
plt.plot(v_fit, T1_fit, label=f'Fit: $T_1 = {A:.2f} \, v^{{{B:.2f}}}$', color='cornflowerblue')

plt.xlabel('Frequency, MHz')
plt.ylabel('T1, ms')
plt.legend(fontsize=12)

plt.savefig("frogmuscleT1.png")