screamlab.functions module

Provides general-purpose utility functions used across various models.

Functions are independent and stateless, designed to be reusable throughout the codebase.

screamlab.functions.voigt_profile(x, center, sigma, gamma, amplitude)

Compute the Voigt profile, a convolution of a Gaussian and Lorentzian function.

Parameters:

  • x – Array of x values.

  • center – Center of the peak.

  • sigma – Standard deviation of the Gaussian component.

  • gamma – Half-width at half-maximum (HWHM) of the Lorentzian component.

  • amplitude – Peak amplitude.

Returns:

Voigt profile evaluated at x.

screamlab.functions.gauss_profile(x, center, sigma, amplitude)

Compute a Gaussian profile.

Parameters:

  • x – Array of x values.

  • center – Center of the peak.

  • sigma – Standard deviation of the Gaussian distribution.

  • amplitude – Peak amplitude.

Returns:

Gaussian profile evaluated at x.

screamlab.functions.lorentz_profile(x, center, gamma, amplitude)

Compute a Lorentzian profile.

Parameters:

  • x – Array of x values.

  • center – Center of the peak.

  • gamma – Half-width at half-maximum (HWHM) of the Lorentzian function.

  • amplitude – Peak amplitude.

Returns:

Lorentzian profile evaluated at x.

screamlab.functions.fwhm_gaussian(sigma)

Compute the Full Width at Half Maximum (FWHM) of a Gaussian function.

It is calculated using the formula:

FWHM = 2 * sqrt(2 * ln(2)) * sigma

Parameters:

sigma (float) – The standard deviation of the Gaussian function.

Returns:

The full width at half maximum (FWHM) of the Gaussian.

Return type:

float

screamlab.functions.fwhm_lorentzian(gamma)

Compute the Full Width at Half Maximum (FWHM) of a Lorentzian function.

For a Lorentzian distribution, the FWHM is:

FWHM = 2 * gamma

Parameters:

gamma (float) – The half-width at half-maximum (HWHM) parameter of the Lorentzian function.

Returns:

The full width at half maximum (FWHM) of the Lorentzian.

Return type:

float

screamlab.functions.fwhm_voigt(sigma, gamma)

Compute the full width at half maximum (FWHM) of a Voigt profile.

The Voigt profile is a convolution of a Gaussian and a Lorentzian function:

FWHM ≈ 0.5346 * (2 * gamma) + sqrt(0.2166 * (2 * gamma)^2 + 4 * ln(2) * sigma^2)

Parameters:

  • sigma (float) – Standard deviation of the Gaussian component.

  • gamma (float) – Half-width at half-maximum (HWHM) of the Lorentzian component.

Returns:

The approximate FWHM of the Voigt profile.

Return type:

float

screamlab.functions.calc_exponential(time_vals, param)

Compute values of an exponential growth function over time.

The function models the equation:

I(t) = A * (1 - exp(-t / tf))

where:

  • I(t) : The output value at time t

  • A : Amplitude (maximum value the function approaches)

  • tf : Time constant (controls the rate of growth)

Returns:

list

Return type:

Exponential profile evaluated at t.

screamlab.functions.calc_stretched_exponential(time_vals, param)

Compute values of a stretched exponential growth function over time.

The function models the equation:

I(t) = A * (1 - exp(-t / tf)^beta)

where:

  • I(t) : The output value at time t

  • A : Amplitude (maximum value the function approaches)

  • tf : Time constant (controls the rate of growth)

  • beta : stretching exponent

Returns:

list

Return type:

Stretched exponential profile evaluated at t.

screamlab.functions.calc_stretchedexpdecay(time_vals, param)

Compute values of a stretched exponential decay function over time.

The function models the equation:

I(t) = Af * exp((-t / tf)^beta)

where:

  • I(t) : The output value at time t

  • A : Amplitude (maximum value the function approaches)

  • tf : Time constant (controls the rate of growth)

  • beta : stretching exponent

Returns:

list

Return type:

Stretched exponential profile evaluated at t.

screamlab.functions.calc_biexpdecay(time_vals, param)

Compute values of a biexponential decay function over time.

The function models the equation:

I(t) = Af * exp(-t / tf)) + As * exp(-t / ts))

where:

  • I(t) : The output value at time t

  • Af, As: Amplitudes (maximum value the function approaches)

  • tf, ts: Time constants (controls the rate of growth)

Returns:

list

Return type:

Biexponential profile evaluated at t.

screamlab.functions.calc_expdecay(time_vals, param)

Compute values of an exponential growth function over time.

The function models the equation:

I(t) = A * exp(-t / t)

where:

  • I(t) : The output value at time t

  • A : Amplitude (maximum value the function approaches)

  • t : Time constant (controls the rate of decay)

Returns:

list

Return type:

Exponential profile evaluated at t.

screamlab.functions.calc_expdecaywithoffset(time_vals, param)

Compute values of an exponential growth function over time.

The function models the equation:

I(t) = A * exp(-t / t) + I0

where:

  • I(t) : The output value at time t

  • A : Amplitude (maximum value the function approaches)

  • t : Time constant (controls the rate of decay)

Returns:

list

Return type:

Exponential profile evaluated at t.

screamlab.functions.calc_biexponential(time_vals, param)

Compute values of a biexponential growth function over time.

The function models the equation:

I(t) = Af * (1 - exp(-t / tf)) + As * (1 - exp(-t / ts))

where:

  • I(t) : The output value at time t

  • Af, As: Amplitudes (maximum value the function approaches)

  • tf, ts: Time constants (controls the rate of growth)

Returns:

list

Return type:

Biexponential profile evaluated at t.

screamlab.functions.calc_exponential_with_offset(time_vals, param)

Compute values of an exponential growth function with time offset over time.

The function models the equation:

I(t) = Af * (1 - exp(-(t-t0) / tf))

where:

  • I(t) : The output value at time t

  • Af : Amplitudes (maximum value the function approaches)

  • tf : Time constants (controls the rate of growth)

  • t0 : Time offset

Returns:

list

Return type:

Exponential profile with time offset evaluated at t.

screamlab.functions.calc_biexponential_with_offset(time_vals, param)

Compute values of a biexponential growth function with time offset over time.

The function models the equation:

I(t) = Af * (1 - exp(-(t - t0) / tf)) + As * (1 - exp(-(t - t0) / ts))

where:

  • I(t) : The output value at time t

  • Af, As: Amplitudes (maximum value the function approaches)

  • tf, ts: Time constants (controls the rate of growth)

  • t0 : Time offset

Returns:

list

Return type:

Biexponential profile with time offset evaluated at t.

screamlab.functions.generate_spectra_param_dict_global(params)

Generate a dictionary of spectral parameters from a list of parameter names.

Parameters:

params – Dictionary of parameter names and values.

Returns:

Dictionary of structured parameter values.

screamlab.functions.generate_spectra_param_dict_individual(params)

Generate a dictionary of spectral parameters from a list of parameter names.

Parameters:

params – Dictionary of parameter names and values.

Returns:

Dictionary of structured parameter values.

screamlab.functions.calc_peak(x_axis, simspec, val)

Simulates spectra based on given parameters.

screamlab.functions.format_mapping()

Maps each buildup function type to its parameter names.

screamlab.functions.buildup_header()

Returns a list of headers for the buildup analysis table.

screamlab.functions.spectrum_fit_header()

Returns a list of headers for the spectrum fitting results table.

screamlab.functions.return_func_map()

Returns a dictionary mapping function types to their corresponding fitting functions.

screamlab.functions.generate_subspec(spectrum, subspec)

Extract a subspectrum of a spectrum based on a given x-axis range.

Returns:

A tuple containing two arrays: The sliced x- and y-axis values specified range.

Return type:

tuple of ndarray