humbertovarona / pCurveFit

Find the best function that fits a time series

pCurveFit

Find the best function that fits a time series

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Release date

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Programming language

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Installation

pip install numpy
pip install matplotlib
pip install scipy

Requirements

import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

Functions list

1. fit_time_series Fit a time series to the best-fitting mathematical equation

Arguments:

time: Array of time values.

data: Array of corresponding data values.

Returns: The best-fitting function best_func, optimal parameters best_params, and covariance matrix cov_matrix.

2. jacobian Compute the Jacobian matrix of a given function

Arguments:

func: Function for which to calculate the Jacobian.

x: Array of input values.

params: Additional parameters required by the function.

Returns: array: Jacobian matrix jac.

3. compute_bias Compute the bias between the predicted values and the actual data.

Arguments:

data: Function for which to calculate the Jacobian.

predicted: Array of predicted values.

Returns: float value (Bias value).

4. compute_rmse Compute the Root Mean Squared Error (RMSE) between the predicted values and the actual data.

Arguments:

data: Function for which to calculate the Jacobian.

predicted: Array of predicted values.

Returns: float value (RMSE value).

5. compute_scatter_index Compute the scatter index between the predicted values and the actual data.

Arguments:

data: Function for which to calculate the Jacobian.

predicted: Array of predicted values.

Returns: float value (Scatter index value).

6. compute_r_squared Compute the coefficient of determination (R-squared) between the predicted values and the actual data.

Arguments:

data: Function for which to calculate the Jacobian.

predicted: Array of predicted values.

Returns: float value (R-squared value).

7. plot_data_and_fit Plot the original data along with the best-fitting function.

Arguments:

time: Array of time values.

data: Array of corresponding data values.

func: The best-fitting function.

params: The optimal parameters.

Returns: none.

8. read_data Read the data from a file with columns separated by commas.

Arguments:

filename: Path to the data file (including filename).

Returns: Time values time and data values as numpy arrays variables.

9. format_equation_with_coefficients Formats the best-fit equation with substituted coefficients as a string.

Arguments:

best_func: The best-fitting function.

best_params: The optimal parameters.

Returns: equation_with_coefficients: The formatted equation with substituted coefficients (string).

Usage examples

Sample 1

time = np.array([1, 1.5, 2, 3, 4, 5])
data = np.array([1.5, 3, 8, 20, 48, 120])
best_func, best_params, cov_matrix = fit_time_series(time, data)

predicted_data = best_func(time, *best_params)

bias = calculate_bias(data, predicted_data)
rmse = calculate_rmse(data, predicted_data)
scatter_index = calculate_scatter_index(data, predicted_data)
r_squared = calculate_r_squared(data, predicted_data)

print("Bias:", bias)
print("RMSE:", rmse)
print("Scatter Index:", scatter_index)
print("R-squared:", r_squared)

plot_data_and_fit(time, data, best_func, best_params)

Sample 2

filename = 'data.csv'
time, data = read_data(filename)

# Select column 3 from 'data.csv' (var3)
var3 = data[:, 2]
best_func, best_params, cov_matrix = fit_time_series(time, var3)

print("Best-fitting function:", best_func.__name__)
print("Optimal parameters:", best_params)
print("Covariance matrix:", cov_matrix)

predicted_data = best_func(time, *best_params)

bias = calculate_bias(var3, predicted_data)
rmse = calculate_rmse(var3, predicted_data)
scatter_index = calculate_scatter_index(var3, predicted_data)
r_squared = calculate_r_squared(var3, predicted_data)

print("Bias:", bias)
print("RMSE:", rmse)
print("Scatter Index:", scatter_index)
print("R-squared:", r_squared)

plot_data_and_fit(time, var3, best_func, best_params)

equation_string = format_equation_with_coefficients(best_func, best_params)
print(equation_string)