pyextal.larbed.peaks
====================

.. py:module:: pyextal.larbed.peaks

.. autoapi-nested-parse::

   Least-squares peak fitting used to locate the direct beam on the detector.

   Each model function is a factory: it takes the model parameters and returns a
   callable evaluated on pixel index arrays, which is what
   :func:`scipy.optimize.leastsq` is driven with here.



Functions
---------

.. autoapisummary::

   pyextal.larbed.peaks.gaussian2D
   pyextal.larbed.peaks.gaussian1D
   pyextal.larbed.peaks.lorentzian1D
   pyextal.larbed.peaks.lorentzian2D
   pyextal.larbed.peaks.moments
   pyextal.larbed.peaks.fitPeak2D
   pyextal.larbed.peaks.fitPeak
   pyextal.larbed.peaks.fitPeak2DGauss


Module Contents
---------------

.. py:function:: gaussian2D(height, center_y, center_x, width_x)

   Builds a circular 2D Gaussian.

   :param height: Peak amplitude.
   :type height: float
   :param center_y: Centre along the first axis.
   :type center_y: float
   :param center_x: Centre along the second axis.
   :type center_x: float
   :param width_x: Standard deviation, shared by both axes.
   :type width_x: float

   :returns: ``f(x, y)`` evaluating the Gaussian.
   :rtype: callable


.. py:function:: gaussian1D(height, center, width)

   Builds a 1D Gaussian.

   :param height: Peak amplitude.
   :type height: float
   :param center: Peak centre.
   :type center: float
   :param width: Standard deviation.
   :type width: float

   :returns: ``f(x)`` evaluating the Gaussian.
   :rtype: callable


.. py:function:: lorentzian1D(height, center, width, y0, slope)

   Builds a 1D Lorentzian on a linear background.

   :param height: Peak amplitude.
   :type height: float
   :param center: Peak centre.
   :type center: float
   :param width: Half-width at half-maximum.
   :type width: float
   :param y0: Background offset.
   :type y0: float
   :param slope: Background slope.
   :type slope: float

   :returns: ``f(x)`` evaluating the Lorentzian plus background.
   :rtype: callable


.. py:function:: lorentzian2D(height, center_x, center_y, width_x, a, b, c)

   Builds a circular 2D Lorentzian on a planar background.

   :param height: Peak amplitude.
   :type height: float
   :param center_x: Centre along the second axis.
   :type center_x: float
   :param center_y: Centre along the first axis.
   :type center_y: float
   :param width_x: Half-width at half-maximum.
   :type width_x: float
   :param a: Background gradient along x.
   :type a: float
   :param b: Background gradient along y.
   :type b: float
   :param c: Background offset.
   :type c: float

   :returns: ``f(y, x)`` evaluating the Lorentzian plus background.
   :rtype: callable


.. py:function:: moments(data)

   Estimates Gaussian parameters of a 2D distribution from its moments.

   :param data: 2D image containing a single peak.
   :type data: np.ndarray

   :returns: Two ``(height, centre, width)`` triples, for the second and first
             axes respectively, suitable as a least-squares starting guess.
   :rtype: tuple


.. py:function:: fitPeak2D(data, func)

   Fits a 7-parameter 2D peak model with a planar background.

   :param data: 2D image containing a single peak.
   :type data: np.ndarray
   :param func: Model factory taking 7 parameters, such as
                :func:`lorentzian2D`.
   :type func: callable

   :returns: The fitted parameters.
   :rtype: np.ndarray


.. py:function:: fitPeak(data, func)

   Fits 1D models to the two projections of a 2D peak.

   :param data: 2D image containing a single peak.
   :type data: np.ndarray
   :param func: 1D model factory taking 5 parameters, such as
                :func:`lorentzian1D`.
   :type func: callable

   :returns: ``[xh, xc, xw, yh, yc, yw]`` — amplitude, centre, and width
             for each projection.
   :rtype: np.ndarray


.. py:function:: fitPeak2DGauss(data, func)

   Fits a 4-parameter circular 2D Gaussian.

   :param data: 2D image containing a single peak.
   :type data: np.ndarray
   :param func: Model factory taking 4 parameters, normally
                :func:`gaussian2D`.
   :type func: callable

   :returns: ``[height, center_y, center_x, width_x]``.
   :rtype: np.ndarray