Generate an Alard-Lupton kernel basis list based upon the Config and
the input FWHM of the science and template images.
Parameters
----------
config : `lsst.ip.diffim.PsfMatchConfigAL`
Configuration object for the Alard-Lupton algorithm.
targetFwhmPix : `float`, optional
Fwhm width (pixel) of the template exposure characteristic psf.
This is the _target_ that will be matched to the science exposure.
referenceFwhmPix : `float`, optional
Fwhm width (pixel) of the science exposure characteristic psf.
basisDegGauss : `list` of `int`, optional
Polynomial degree of each Gaussian (sigma) basis. If None, defaults to `config.alardDegGauss`.
metadata : `lsst.daf.base.PropertySet`, optional
If specified, object to collect metadata fields about the kernel basis list.
Returns
-------
basisList : `list` of `lsst.afw.math.kernel.FixedKernel`
List of basis kernels. For each degree value ``n`` in ``config.basisDegGauss`` (n+2)(n+1)/2 kernels
are generated and appended to the list in the order of the polynomial parameter number.
See `lsst.afw.math.polynomialFunction2D` documentation for more details.
Notes
-----
The polynomial functions (``f``) are always evaluated in the -1.0, +1.0 range in both x, y directions,
edge to edge, with ``f(0,0)`` evaluated at the kernel center pixel, ``f(-1.0,-1.0)`` at the kernel
``(0,0)`` pixel. They are not scaled by the sigmas of the Gaussians.
Base Gaussian widths (sigmas in pixels) of the kernels are determined as:
- If not all fwhm parameters are provided or ``config.scaleByFwhm==False``
then ``config.alardNGauss`` and ``config.alardSigGauss`` are used.
- If ``targetFwhmPix<referenceFwhmPix`` (normal convolution):
First sigma ``Sig_K`` is determined to satisfy: ``Sig_reference**2 = Sig_target**2 + Sig_K**2``.
If it's larger than ``config.alardMinSig * config.alardGaussBeta``, make it the
second kernel. Else make it the smallest kernel, unless only 1 kernel is asked for.
- If ``referenceFwhmPix < targetFwhmPix`` (deconvolution):
Define the progression of Gaussians using a
method to derive a deconvolution sum-of-Gaussians from it's
convolution counterpart. [1]_ Only use 3 since the algorithm
assumes 3 components.
Metadata fields
---------------
ALBasisNGauss : `int`
The number of base Gaussians in the AL basis functions.
ALBasisDegGauss : `list` of `int`
Polynomial order of spatial modification of the base Gaussian functions.
ALBasisSigGauss : `list` of `float`
Sigmas in pixels of the base Gaussians.
ALKernelSize : `int`
Kernel stamp size is (ALKernelSize pix, ALKernelSize pix).
ALBasisMode : `str`, either of ``config``, ``convolution``, ``deconvolution``
Indicates whether the config file values, the convolution or deconvolution algorithm
was used to determine the base Gaussian sigmas and the kernel stamp size.
References
----------
.. [1] Ulmer, W.: Inverse problem of linear combinations of Gaussian convolution kernels
(deconvolution) and some applications to proton/photon dosimetry and image
processing. http://iopscience.iop.org/0266-5611/26/8/085002 Equation 40
Raises
------
RuntimeError
- if ``config.kernelBasisSet`` is not equal to "alard-lupton"
ValueError
- if ``config.kernelSize`` is even
- if the number of Gaussians and the number of given
sigma values are not equal or
- if the number of Gaussians and the number of given
polynomial degree values are not equal
Definition at line 82 of file makeKernelBasisList.py.