math

Utility math functions which can be shared between Tasks.

Functions:

Name	Description
gaussian	Calculate a 1D Gaussian distirbution.
sigma_to_fwhm	Convert the standard deviation of a Gaussian to Full Width at Half Maximum (FWHM).

gaussian(x_vals, amp, x0, sigma, bkgnd)

1D Gaussian distribution with specified parameters.

Parameters:

Name	Type	Description	Default
x_vals	NDArray[float64]	Values over which to calculate the distribution.	required
amp	float	Amplitude of the distribution.	required
x0	float	Center (mean) of the distribution	required
sigma	float	Standard deviation of the distribution.	required
bkgnd	float | NDArray[float64]	Background/noise. Constant offset (float) or an array of offsets of the same length as x_vals.	required

Returns:

Name	Type	Description
distribution	NDArray[float64]	Calculated Gaussian distribution based on given parameters. Same shape as x_vals.

Source code in lute/tasks/math.py

def gaussian(
    x_vals: npt.NDArray[np.float64], amp: float, x0: float, sigma: float, bkgnd: float
) -> npt.NDArray[np.float64]:
    """1D Gaussian distribution with specified parameters.

    Args:
        x_vals (npt.NDArray[np.float64]): Values over which to calculate the
            distribution.

        amp (float): Amplitude of the distribution.

        x0 (float): Center (mean) of the distribution

        sigma (float): Standard deviation of the distribution.

        bkgnd (float | npt.NDArray[np.float64]): Background/noise. Constant
            offset (float) or an array of offsets of the same length as `x_vals`.

    Returns:
        distribution (npt.NDArray[np.float64]): Calculated Gaussian distribution
            based on given parameters. Same shape as x_vals.
    """
    numerator = -((x_vals - x0) ** 2)
    return amp * np.exp(numerator / (2 * sigma**2)) + bkgnd

sigma_to_fwhm(sigma)

Convert the standard deviation of a Gaussian to Full Width Half Max.

Parameters:

Name	Type	Description	Default
sigma	float	Standard deviation of a Gaussian.	required

Returns:

Name	Type	Description
fhwm	float	Full width at half max of a Gaussian.

Source code in lute/tasks/math.py

def sigma_to_fwhm(sigma: float) -> float:
    """Convert the standard deviation of a Gaussian to Full Width Half Max.

    Args:
        sigma (float): Standard deviation of a Gaussian.

    Returns:
        fhwm (float): Full width at half max of a Gaussian.
    """
    constant: float = (8 * np.log(2)) ** 0.5
    return sigma * constant