:py:mod:`aces.beamset.airyfitter`
=================================

.. py:module:: aces.beamset.airyfitter

.. autoapi-nested-parse::

   ===========
   airyfitter
   ===========
   .. codeauthor:: Dvid McConnell

   Derived from gaussfitter by Adam Ginsburg <adam.g.ginsburg@gmail.com> 3/17/08
   Latest version available at <https://github.com/keflavich/gaussfitter>, where
   it was moved from google code on January 30, 2014



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


Functions
~~~~~~~~~

.. autoapisummary::

   aces.beamset.airyfitter.moments
   aces.beamset.airyfitter.airy
   aces.beamset.airyfitter.airy_sq
   aces.beamset.airyfitter.twodairy
   aces.beamset.airyfitter.airyfit



.. py:function:: moments(data, circle, rotate, vheight, estimator=median, angle_guess=45.0, **kwargs)

   Returns (height, amplitude, x, y, width_x, width_y, rotation angle)
   the parameters of a 2D airy pattern by calculating its
   moments.  Depending on the input parameters, will only output
   a subset of the above.
   If using masked arrays, pass estimator=np.ma.median


.. py:function:: airy(x)


.. py:function:: airy_sq(x)


.. py:function:: twodairy(inpars, circle=False, rotate=True, vheight=True, shape=None)

   Returns a 2d airy pattern of the form:
   x' = np.cos(rota) * x - np.sin(rota) * y
   y' = np.sin(rota) * x + np.cos(rota) * y
   (rota should be in degrees)
   g = b + a * airy (sqrt((x' - xc)/xw)**2 + ((y' - yc)/yw)**2 ))
   inpars = [b,a,center_x,center_y,width_x,width_y,rota]
   (b is background height, a is peak amplitude)
   where x and y are the input parameters of the returned function,
   and all other parameters are specified by this function
   However, the above values are passed by list.  The list should be:
   inpars = (height,amplitude,center_x,center_y,width_x,width_y,rota)
   You can choose to ignore / neglect some of the above input parameters using
   the following options:

   Parameters
   ----------
   circle : bool
       default is an elliptical airy (different x, y widths), but can
       reduce the input by one parameter if it's a circular airy pattern
   rotate : bool
       default allows rotation of the pattern ellipse.  Can
       remove last parameter by setting rotate=0
   vheight : bool
       default allows a variable height-above-zero, i.e. an
       additive constant for the function.  Can remove first
       parameter by setting this to 0
   shape : tuple
       if shape is set (to a 2-parameter list) then returns an image with the
       airy pattern defined by inpars


.. py:function:: airyfit(data, err=None, params=(), autoderiv=True, return_error=False, circle=False, fixed=np.repeat(False, 7), limitedmin=[False, False, False, False, True, True, True], limitedmax=[False, False, False, False, False, False, True], usemoment=np.array([], dtype='bool'), minpars=np.repeat(0, 7), maxpars=[0, 0, 0, 0, 0, 0, 180], rotate=True, vheight=True, quiet=True, returnmp=False, returnfitimage=False, **kwargs)

   Airy pattern fitter with the ability to fit a variety of different forms of
   2-dimensional airy pattern.

   Parameters
   ----------
   data : `numpy.ndarray`
       2-dimensional data array
   err : `numpy.ndarray` or None
       error array with same size as data array.  Defaults to 1 everywhere.
   params : (height, amplitude, x, y, width_x, width_y, rota)
       Initial input parameters for airy pattern.  If not input, these
       will be determined from the moments of the system, assuming no rotation
   autoderiv : bool
       Use the autoderiv provided in the lmder.f function (the alternative is
       to us an analytic derivative with lmdif.f: this method is less robust)
   return_error : bool
       Default is to return only the airy parameters.
       If ``True``, return fit params & fit error
   returnfitimage : bool
       returns (best fit params,best fit image)
   returnmp : bool
       returns the full mpfit struct
   circle : bool
       The default is to fit an elliptical airy pattern (different x, y widths),
       but the input is reduced by one parameter if it's a circular pattern.
   rotate : bool
       Allow rotation of the ellipse.  Can remove
       last parameter of input & fit by setting rotate=False.
       Angle should be specified in degrees.
   vheight : bool
       Allows a variable height-above-zero, i.e. an additive constant
       background for the function.  Can remove the first fitter
       parameter by setting this to ``False``
   usemoment : `numpy.ndarray`, dtype='bool'
       Array to choose which parameters to use a moment estimation for.  Other
       parameters will be taken from params.
   Returns
   -------
   (params, [parerr], [fitimage]) | (mpfit, [fitimage])
   parameters : list
       The default output is a set of parameters with the same shape
       as the input parameters
   fitimage : `numpy.ndarray`
       If returnfitimage==True, the last return will be a 2D array holding the
       best-fit model
   mpfit : `mpfit` object
       If ``returnmp==True`` returns a `mpfit` object. This object contains a
       `covar` attribute which is the 7x7 covariance array generated by the
       mpfit class in the `mpfit_custom.py` module. It contains a `param`
       attribute that contains a list of the best fit parameters in the same
       order as the optional input parameter `params`.