{"id":12555,"date":"2023-09-11T17:15:20","date_gmt":"2023-09-11T17:15:20","guid":{"rendered":"https:\/\/www.digitaldesignjournal.com\/?p=12555"},"modified":"2023-09-15T08:26:46","modified_gmt":"2023-09-15T08:26:46","slug":"python-voigt-profile","status":"publish","type":"post","link":"https:\/\/www.digitaldesignjournal.com\/python-voigt-profile\/","title":{"rendered":"Python voigt Profile [Explained With Examples]"},"content":{"rendered":"\n

A Voigt profile, also known as a Voigt function or Voigt distribution, is a convolution of a Gaussian distribution and a Lorentzian distribution.<\/p>\n\n\n\n

It is often used in spectroscopy and other fields to model spectral lines that exhibit both Gaussian and Lorentzian broadening. <\/p>\n\n\n\n

You can create a Voigt profile in Python using various libraries, but I’ll show you how to do it using the scipy<\/code> library, which provides a built-in function for generating Voigt profiles.<\/p>\n\n\n\n

Here’s an example of how to create a Voigt profile using scipy<\/code>:<\/p>\n\n\n

import<\/span> numpy as<\/span> np\nfrom<\/span> scipy.special import<\/span> wofz\nimport<\/span> matplotlib.pyplot as<\/span> plt\n\ndef<\/span> voigt_profile<\/span>(x, sigma, gamma)<\/span>:<\/span>\n    \"\"\"\n    Calculate the Voigt profile.\n\n    Parameters:\n        x (array-like): The x-values at which to calculate the profile.\n        sigma (float): The Gaussian standard deviation.\n        gamma (float): The Lorentzian full-width at half-maximum.\n\n    Returns:\n        array-like: The Voigt profile values at the specified x-values.\n    \"\"\"<\/span>\n    z = (x + 1j<\/span> * gamma) \/ (sigma * np.sqrt(2<\/span>))\n    v = wofz(z).real \/ (sigma * np.sqrt(2<\/span> * np.pi))\n    return<\/span> v\n\n# Define parameters<\/span>\nx = np.linspace(-5<\/span>, 5<\/span>, 1000<\/span>)  # X-values<\/span>\nsigma = 1.0<\/span>                   # Gaussian standard deviation<\/span>\ngamma = 0.5<\/span>                   # Lorentzian full-width at half-maximum<\/span>\n\n# Calculate the Voigt profile<\/span>\nprofile = voigt_profile(x, sigma, gamma)\n\n# Plot the Voigt profile<\/span>\nplt.plot(x, profile, label='Voigt Profile'<\/span>)\nplt.xlabel('X'<\/span>)\nplt.ylabel('Intensity'<\/span>)\nplt.legend()\nplt.title('Voigt Profile'<\/span>)\nplt.grid(True<\/span>)\nplt.show()<\/code><\/span>Code language:<\/span> Python<\/span> (<\/span>python<\/span>)<\/span><\/small><\/pre>\n\n\n
In this code:<\/p>\n\n\n\n
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  1. We import the necessary libraries, including numpy<\/code> for numerical operations, scipy.special.wofz<\/code> for the Faddeeva function (required for the Voigt profile calculation), and matplotlib<\/code> for plotting.<\/li>\n\n\n\n
  2. We define a voigt_profile<\/code> function that calculates the Voigt profile at a given set of x-values using the formula involving the Faddeeva function.<\/li>\n\n\n\n
  3. We specify the parameters sigma<\/code> (Gaussian standard deviation) and gamma<\/code> (Lorentzian full-width at half-maximum).<\/li>\n\n\n\n
  4. We calculate the Voigt profile for the specified x-values.<\/li>\n\n\n\n
  5. Finally, we plot the Voigt profile using Matplotlib.<\/li>\n<\/ol>\n\n\n\n
    You can adjust the sigma<\/code> and gamma<\/code> parameters to see how they affect the shape of the Voigt profile.<\/p>\n\n\n\n
    Fitting the data with a voigt function in python<\/h2>\n\n\n\n
    Fitting data with a Voigt function in Python involves a different process than simply creating a Voigt profile. To fit data with a Voigt function, you typically use a curve fitting library like scipy.optimize.curve_fit<\/code> to find the parameters that best describe your data. Here’s an example of how to fit data with a Voigt function using scipy<\/code>:<\/p>\n\n\n
    import<\/span> numpy as<\/span> np\nfrom<\/span> scipy.optimize import<\/span> curve_fit\nimport<\/span> matplotlib.pyplot as<\/span> plt\nfrom<\/span> scipy.special import<\/span> wofz\n\n# Define the Voigt profile function<\/span>\ndef<\/span> voigt_profile<\/span>(x, amplitude, center, sigma, gamma)<\/span>:<\/span>\n    z = ((x - center) + 1j<\/span> * gamma) \/ (sigma * np.sqrt(2<\/span>))\n    v = amplitude * wofz(z).real \/ (sigma * np.sqrt(2<\/span> * np.pi))\n    return<\/span> v\n\n# Generate some synthetic data<\/span>\nx_data = np.linspace(-5<\/span>, 5<\/span>, 100<\/span>)\ny_data = voigt_profile(x_data, amplitude=1.0<\/span>, center=0.0<\/span>, sigma=1.0<\/span>, gamma=0.5<\/span>) + np.random.normal(0<\/span>, 0.05<\/span>, len(x_data))\n\n# Fit the data to the Voigt profile function<\/span>\ninitial_guess = (1.0<\/span>, 0.0<\/span>, 1.0<\/span>, 0.5<\/span>)  # Initial parameter guess<\/span>\nparams, covariance = curve_fit(voigt_profile, x_data, y_data, p0=initial_guess)\n\n# Extract the fitted parameters<\/span>\namplitude_fit, center_fit, sigma_fit, gamma_fit = params\n\n# Plot the original data and the fitted Voigt profile<\/span>\nplt.figure(figsize=(8<\/span>, 6<\/span>))\nplt.plot(x_data, y_data, 'b.'<\/span>, label='Data'<\/span>)\nplt.plot(x_data, voigt_profile(x_data, *params), 'r-'<\/span>, label='Fit'<\/span>)\nplt.xlabel('X'<\/span>)\nplt.ylabel('Intensity'<\/span>)\nplt.legend()\nplt.title('Voigt Function Fit'<\/span>)\nplt.grid(True<\/span>)\nplt.show()\n\n# Print the fitted parameters<\/span>\nprint(\"Amplitude:\"<\/span>, amplitude_fit)\nprint(\"Center:\"<\/span>, center_fit)\nprint(\"Sigma:\"<\/span>, sigma_fit)\nprint(\"Gamma:\"<\/span>, gamma_fit)<\/code><\/span>Code language:<\/span> Python<\/span> (<\/span>python<\/span>)<\/span><\/small><\/pre>\n\n\n
    In this code:<\/p>\n\n\n\n
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    1. We define the voigt_profile<\/code> function as before, which calculates the Voigt profile.<\/li>\n\n\n\n
    2. We generate synthetic data with some added noise.<\/li>\n\n\n\n
    3. We use curve_fit<\/code> from scipy.optimize<\/code> to fit the synthetic data to the Voigt function. We provide an initial guess for the parameters.<\/li>\n\n\n\n
    4. We plot both the original data and the fitted Voigt profile.<\/li>\n\n\n\n
    5. We print the fitted parameters, which represent the amplitude, center, sigma (Gaussian standard deviation), and gamma (Lorentzian full-width at half-maximum) of the Voigt function.<\/li>\n<\/ol>\n\n\n\n
      You can adapt this code to fit your own data by replacing x_data<\/code> and y_data<\/code> with your actual data points. Adjust the initial guess as needed to improve the fit.<\/p>\n\n\n\n
      Read More;<\/strong><\/p>\n\n\n\n