numpy - Curve fit exponential growth function in Python

Numpy - Curve fit exponential growth function in Python

To fit an exponential growth function to data using NumPy in Python, you can use the curve_fit function from the scipy.optimize module. Here's how you can do it:

import numpy as np from scipy.optimize import curve_fit import matplotlib.pyplot as plt # Define the exponential growth function def exponential_growth(x, a, b): return a * np.exp(b * x) # Generate some sample data x_data = np.array([0, 1, 2, 3, 4, 5]) y_data = np.array([1, 2, 4, 8, 16, 32]) # Exponential growth data # Fit the exponential growth function to the data params, covariance = curve_fit(exponential_growth, x_data, y_data) # Extract the fitted parameters a_fit, b_fit = params # Plot the original data and the fitted curve plt.scatter(x_data, y_data, label='Data') plt.plot(x_data, exponential_growth(x_data, a_fit, b_fit), label='Fitted curve', color='red') plt.xlabel('X') plt.ylabel('Y') plt.title('Exponential Growth Curve Fit') plt.legend() plt.grid(True) plt.show() print("Fitted parameters:") print("a =", a_fit) print("b =", b_fit)

In this code:

  • We define the exponential growth function exponential_growth(x, a, b) where a and b are parameters to be fitted.
  • We generate some sample data x_data and y_data.
  • We use curve_fit to fit the exponential growth function to the data. This function returns the optimal parameters and the covariance of the parameters.
  • We extract the fitted parameters a_fit and b_fit.
  • We plot the original data and the fitted curve using Matplotlib.
  • Finally, we print the fitted parameters.

Make sure you have the necessary libraries installed (numpy, scipy, matplotlib) before running the code. Adjust the exponential_growth function and the sample data according to your specific data and model.

Examples

  1. Curve Fitting Exponential Growth Function Using numpy in Python

    • Description: Find the best fit exponential growth curve for data points using numpy's curve_fit function in Python.
    • Code:
      import numpy as np from scipy.optimize import curve_fit def exponential_growth_func(x, a, b): return a * np.exp(b * x) # Example data points x_data = np.array([1, 2, 3, 4, 5]) y_data = np.array([2, 5, 13, 32, 80]) params, covariance = curve_fit(exponential_growth_func, x_data, y_data) # Extracting parameters a, b = params

  2. Exponential Growth Curve Fitting with Initial Guesses

    • Description: Perform exponential growth curve fitting with initial guesses for parameters using numpy's curve_fit function in Python.
    • Code:
      # Example data points and initial guesses x_data = np.array([1, 2, 3, 4, 5]) y_data = np.array([2, 5, 13, 32, 80]) initial_guesses = (1.0, 0.1) # Initial guess for (a, b) params, covariance = curve_fit(exponential_growth_func, x_data, y_data, p0=initial_guesses)

  3. Plot Exponential Growth Curve Fit with Matplotlib

    • Description: Plot the exponential growth curve fit along with the original data points using Matplotlib after curve fitting with numpy in Python.
    • Code:
      import matplotlib.pyplot as plt # Plot data points plt.scatter(x_data, y_data, label='Data') # Plot fitted curve x_fit = np.linspace(min(x_data), max(x_data), 100) y_fit = exponential_growth_func(x_fit, *params) plt.plot(x_fit, y_fit, 'r-', label='Exponential Growth Fit') plt.legend() plt.xlabel('X') plt.ylabel('Y') plt.show()

  4. Handling Curve Fitting Errors and Exceptions

    • Description: Handle errors and exceptions that may occur during exponential growth curve fitting using numpy's curve_fit function in Python.
    • Code:
      try: params, covariance = curve_fit(exponential_growth_func, x_data, y_data) except RuntimeError: print("Curve fitting failed. Try with different initial guesses or data.")

  5. Exponential Growth Curve Fitting with Constraints

    • Description: Apply constraints on parameters during exponential growth curve fitting using numpy's curve_fit function in Python.
    • Code:
      # Example constraints: a > 0, b > 0 bounds = ([0, 0], [np.inf, np.inf]) # Lower and upper bounds for parameters params, covariance = curve_fit(exponential_growth_func, x_data, y_data, bounds=bounds)

  6. Exponential Growth Curve Fitting with Weighted Residuals

    • Description: Perform exponential growth curve fitting with weighted residuals using numpy's curve_fit function in Python.
    • Code:
      # Example weights weights = np.array([1, 2, 3, 4, 5]) # Weights for each data point params, covariance = curve_fit(exponential_growth_func, x_data, y_data, sigma=weights)

  7. Exponential Growth Curve Fitting with Logarithmic Transformation

    • Description: Apply a logarithmic transformation to data before performing exponential growth curve fitting in Python using numpy's curve_fit function.
    • Code:
      x_data_log = np.log(x_data) y_data_log = np.log(y_data) params, covariance = curve_fit(exponential_growth_func, x_data_log, y_data_log)

  8. Exponential Growth Curve Fitting with Custom Error Function

    • Description: Define a custom error function to optimize during exponential growth curve fitting in Python using numpy's curve_fit function.
    • Code:
      def custom_error_func(params, x, y): a, b = params y_fit = a * np.exp(b * x) return y - y_fit params, covariance = curve_fit(custom_error_func, x_data, y_data)

  9. Perform Exponential Growth Curve Fitting Using scipy.optimize.minimize

    • Description: Utilize scipy's minimize function for exponential growth curve fitting in Python as an alternative to numpy's curve_fit function.
    • Code:
      from scipy.optimize import minimize # Define objective function def objective(params): a, b = params return np.sum((y_data - a * np.exp(b * x_data)) ** 2) # Initial guess initial_guesses = (1.0, 0.1) # Minimize objective function result = minimize(objective, initial_guesses) # Extract parameters params = result.x

  10. Exponential Growth Curve Fitting with Nonlinear Least Squares

    • Description: Perform exponential growth curve fitting using nonlinear least squares optimization in Python with numpy's curve_fit function.
    • Code:
      from scipy.optimize import least_squares def residual(params, x, y): return y - exponential_growth_func(x, *params) params, _ = least_squares(residual, initial_guesses, args=(x_data, y_data))

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