Fitting the tanh function

fit_tanh.py

import pandas as pd
import numpy as np
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt
import sympy as sp
from pandas.plotting import table



# Load your data from the CSV file 
data = pd.read_csv('data.csv')  # file for data as comma seperated values 
print(data.head(10))
# name x and y values from the data correlate that with the values 
x_data = data['Temperature in Celsius'].values  
y_data = data['Energy'].values  

fig, ax = plt.subplots(figsize=(8, 4)) 
ax.axis('off')
table_data = table(ax, data.head(5), loc='center', colWidths=[0.55]*len(data.head(5).columns))

# Save the plot as an image (e.g., PNG)
plt.savefig('table_image.png', bbox_inches='tight')

# Initial Plot
# plt.figure(figsize=(16, 12)) 
# plt.scatter(x_data, y_data, label="Data")
# plt.xlabel("Temperature",fontsize=17)
# plt.ylabel("Energy",fontsize=17)
# plt.title("Temperature vs Energy",fontsize=22)
# plt.show()


#  hyperbolic tangent (tanh) function
def tanh_func(x, a, b, c, d):
    return a * np.tanh(b * (x + c)) + d

# Fit the data to the tanh function
# Set initial guess to apparent inflection point
initial_guess = [1.0, 1.0, 0.0, 0.0]
params, covariance = curve_fit(tanh_func, x_data, y_data, p0=initial_guess)


# Extract the parameters
a, b, c, d = params

# Create a range of x values for the curve change value of "127" to max number or data points i didnt know how to get max size of the data sheet
x_fit = np.linspace(min(x_data), max(x_data), 137)

# Calculate the y values for the fitted curve
y_fit = tanh_func(x_fit, a, b, c, d)

# Plot of the data and the fitted curve
plt.figure(figsize=(16, 12)) 
plt.scatter(x_data, y_data, label="Data")
plt.plot(x_fit, y_fit, label="Tanh Fit", color= "red")
plt.xticks(fontsize=15) 
plt.yticks(fontsize=15)
plt.xlabel("Temperature",fontsize=17)
plt.ylabel("Energy",fontsize=17)
plt.title("Temperature vs Energy",fontsize=22)



# Display the equation
equation = f"y = {a:.2f} * tanh({b:.2f} * x + {c:.2f}) + {d:.2f}"
print("Equation:", equation)


text_x = 8  # x-coordinate
text_y = 16  # y-coordinate

plt.text(text_x, text_y, equation, fontsize=19, color='red',
         bbox={'facecolor': 'white', 'alpha': 0.7, 'edgecolor': 'gray'})


# Define the variables and the function
x = sp.symbols('x')
y = a * sp.tanh(b * (x + c)) + d
print("Initialized Equation.")

# Calculate the second derivative
second_derivative = sp.diff(y, x, 2)
print("Solved Second Derivative.")
sp.pprint(second_derivative)
domain = sp.Interval(-50, 50)
inflection_points = sp.solve(second_derivative, x, domain=domain, simplify=False, rational=False)

print("Solved Inflection points.")
print(inflection_points)
inflection_points_numeric = [point.evalf() for point in inflection_points]

# Print the inflection point(s)
text_x = 8  # x-coordinate
text_y = 8  # y-coordinate
print("Inflection point(s):", inflection_points_numeric)
for inflection_text in inflection_points:
    inflection_text = "Inflection point at x = " + str(inflection_text)
    plt.text(text_x, text_y, inflection_text, fontsize=19, color='red',
             bbox={'facecolor': 'white', 'alpha': 0.7, 'edgecolor': 'gray'})
    text_y -= 2  # Adjust vertical position for the next annotation

# Show the plot
plt.savefig("TempvsEnergyPlot")
plt.show()