Functions
def	makeKernelBasisList (config, targetFwhmPix=None, referenceFwhmPix=None, basisDegGauss=None, basisSigmaGauss=None, metadata=None)

def	generateAlardLuptonBasisList (config, targetFwhmPix=None, referenceFwhmPix=None, basisDegGauss=None, basisSigmaGauss=None, metadata=None)

Variables
int	sigma2fwhm = 2. * np.sqrt(2. * np.log(2.))

Function Documentation

◆ generateAlardLuptonBasisList()

def lsst.ip.diffim.makeKernelBasisList.generateAlardLuptonBasisList	(	config,
		targetFwhmPix = `None`,
		referenceFwhmPix = `None`,
		basisDegGauss = `None`,
		basisSigmaGauss = `None`,
		metadata = `None`
	)

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`.
basisSigmaGauss : `list` of `int`, optional
Sigmas of each Gaussian basis. If None, defaults to `config.alardSigGauss`.
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.

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

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 ``basisSigmaGauss`` is used. If ``basisSigmaGauss`` is not
provided, then ``config.alardSigGauss`` is used. In both cases, the
length of sigmas must be equal to ``config.alardNGauss``.
- 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

Definition at line 86 of file makeKernelBasisList.py.

                                  basisDegGauss=None, basisSigmaGauss=None, metadata=None):
     """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`.
     basisSigmaGauss : `list` of `int`, optional
         Sigmas of each Gaussian basis. If None, defaults to `config.alardSigGauss`.
     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.
  
     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
  
     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 ``basisSigmaGauss`` is used. If ``basisSigmaGauss`` is not
           provided, then ``config.alardSigGauss`` is used. In both cases, the
           length of sigmas must be equal to ``config.alardNGauss``.
         - 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
     """
  
     if config.kernelBasisSet != "alard-lupton":
         raise RuntimeError("Cannot generate %s basis within generateAlardLuptonBasisList" %
                            config.kernelBasisSet)
  
     kernelSize = config.kernelSize
     fwhmScaling = config.kernelSizeFwhmScaling
     basisNGauss = config.alardNGauss
     basisGaussBeta = config.alardGaussBeta
     basisMinSigma = config.alardMinSig
     if basisDegGauss is None:
         basisDegGauss = config.alardDegGauss
     if basisSigmaGauss is None:
         basisSigmaGauss = config.alardSigGauss
  
     if len(basisDegGauss) != basisNGauss:
         raise ValueError("len(basisDegGauss) != basisNGauss : %d vs %d" % (len(basisDegGauss), basisNGauss))
     if len(basisSigmaGauss) != basisNGauss:
         raise ValueError("len(basisSigmaGauss) != basisNGauss : %d vs %d" %
                          (len(basisSigmaGauss), basisNGauss))
     if (kernelSize % 2) != 1:
         raise ValueError("Only odd-sized Alard-Lupton bases allowed")
  
     logger = Log.getLogger("lsst.ip.diffim.generateAlardLuptonBasisList")
     if (targetFwhmPix is None) or (referenceFwhmPix is None) or (not config.scaleByFwhm):
         logger.info("PSF sigmas are not available or scaling by fwhm disabled, "
                     "falling back to config values")
         if metadata is not None:
             metadata.add("ALBasisNGauss", basisNGauss)
             metadata.add("ALBasisDegGauss", basisDegGauss)
             metadata.add("ALBasisSigGauss", basisSigmaGauss)
             metadata.add("ALKernelSize", kernelSize)
             metadata.add("ALBasisMode", "config")
  
         return diffimLib.makeAlardLuptonBasisList(kernelSize//2, basisNGauss, basisSigmaGauss, basisDegGauss)
  
     targetSigma = targetFwhmPix / sigma2fwhm
     referenceSigma = referenceFwhmPix / sigma2fwhm
     logger.debug("Generating matching bases for sigma %.2f pix -> %.2f pix", targetSigma, referenceSigma)
  
     # Modify the size of Alard Lupton kernels based upon the images FWHM
     #
     # Note the operation is : template.x.kernel = science
     #
     # Assuming the template and science image Psfs are Gaussians with
     # the Fwhm above, Fwhm_T **2 + Fwhm_K **2 = Fwhm_S **2
     #
     if targetSigma == referenceSigma:
         # Leave defaults as-is
         logger.debug("Target and reference psf fwhms are equal, falling back to config values")
         basisMode = "config"
     elif referenceSigma > targetSigma:
         # Normal convolution
  
         # First Gaussian has the sigma that comes from the convolution
         # of two Gaussians : Sig_S**2 = Sig_T**2 + Sig_K**2
         #
         # If it's larger than basisMinSigma * basisGaussBeta, make it the
         # second kernel.  Else make it the smallest kernel.  Unless
         # only 1 kernel is asked for.
         logger.debug("Reference psf fwhm is the greater, normal convolution mode")
         basisMode = "convolution"
         kernelSigma = np.sqrt(referenceSigma**2 - targetSigma**2)
         if kernelSigma < basisMinSigma:
             kernelSigma = basisMinSigma
  
         basisSigmaGauss = []
         if basisNGauss == 1:
             basisSigmaGauss.append(kernelSigma)
             nAppended = 1
         else:
             if (kernelSigma/basisGaussBeta) > basisMinSigma:
                 basisSigmaGauss.append(kernelSigma/basisGaussBeta)
                 basisSigmaGauss.append(kernelSigma)
                 nAppended = 2
             else:
                 basisSigmaGauss.append(kernelSigma)
                 nAppended = 1
  
         # Any other Gaussians above basisNGauss=1 come from a scaling
         # relationship: Sig_i+1 / Sig_i = basisGaussBeta
         for i in range(nAppended, basisNGauss):
             basisSigmaGauss.append(basisSigmaGauss[-1]*basisGaussBeta)
  
         kernelSize = int(fwhmScaling * basisSigmaGauss[-1])
         kernelSize += 0 if kernelSize%2 else 1  # Make sure it's odd
         kernelSize = min(config.kernelSizeMax, max(kernelSize, config.kernelSizeMin))
  
     else:
         # Deconvolution; Define the progression of Gaussians using a
         # method to derive a deconvolution sum-of-Gaussians from it's
         # convolution counterpart.  Only use 3 since the algorithm
         # assumes 3 components.
         #
         # http://iopscience.iop.org/0266-5611/26/8/085002  Equation 40
  
         # Use specializations for deconvolution
         logger.debug("Target psf fwhm is the greater, deconvolution mode")
         basisMode = "deconvolution"
         basisNGauss = config.alardNGaussDeconv
         basisMinSigma = config.alardMinSigDeconv
  
         kernelSigma = np.sqrt(targetSigma**2 - referenceSigma**2)
         if kernelSigma < basisMinSigma:
             kernelSigma = basisMinSigma
  
         basisSigmaGauss = []
         if (kernelSigma/basisGaussBeta) > basisMinSigma:
             basisSigmaGauss.append(kernelSigma/basisGaussBeta)
             basisSigmaGauss.append(kernelSigma)
             nAppended = 2
         else:
             basisSigmaGauss.append(kernelSigma)
             nAppended = 1
  
         for i in range(nAppended, basisNGauss):
             basisSigmaGauss.append(basisSigmaGauss[-1]*basisGaussBeta)
  
         kernelSize = int(fwhmScaling * basisSigmaGauss[-1])
         kernelSize += 0 if kernelSize%2 else 1  # Make sure it's odd
         kernelSize = min(config.kernelSizeMax, max(kernelSize, config.kernelSizeMin))
  
         # Now build a deconvolution set from these sigmas
         sig0 = basisSigmaGauss[0]
         sig1 = basisSigmaGauss[1]
         sig2 = basisSigmaGauss[2]
         basisSigmaGauss = []
         for n in range(1, 3):
             for j in range(n):
                 sigma2jn = (n - j)*sig1**2
                 sigma2jn += j * sig2**2
                 sigma2jn -= (n + 1)*sig0**2
                 sigmajn = np.sqrt(sigma2jn)
                 basisSigmaGauss.append(sigmajn)
  
         basisSigmaGauss.sort()
         basisNGauss = len(basisSigmaGauss)
         basisDegGauss = [config.alardDegGaussDeconv for x in basisSigmaGauss]
  
     if metadata is not None:
         metadata.add("ALBasisNGauss", basisNGauss)
         metadata.add("ALBasisDegGauss", basisDegGauss)
         metadata.add("ALBasisSigGauss", basisSigmaGauss)
         metadata.add("ALKernelSize", kernelSize)
         metadata.add("ALBasisMode", basisMode)
  
     logger.debug("basisSigmaGauss: %s basisDegGauss: %s",
                  ','.join(['{:.1f}'.format(v) for v in basisSigmaGauss]),
                  ','.join(['{:d}'.format(v) for v in basisDegGauss]))
  
     return diffimLib.makeAlardLuptonBasisList(kernelSize//2, basisNGauss, basisSigmaGauss, basisDegGauss)

◆ makeKernelBasisList()

def lsst.ip.diffim.makeKernelBasisList.makeKernelBasisList	(	config,
		targetFwhmPix = `None`,
		referenceFwhmPix = `None`,
		basisDegGauss = `None`,
		basisSigmaGauss = `None`,
		metadata = `None`
	)

Generate the delta function or Alard-Lupton kernel bases depending on the Config.
Wrapper to call either `lsst.ip.diffim.makeDeltaFunctionBasisList` or
`lsst.ip.diffim.generateAlardLuptonBasisList`.

Parameters
----------
config : `lsst.ip.diffim.PsfMatchConfigAL`
    Configuration object.
targetFwhmPix : `float`, optional
    Passed on to `lsst.ip.diffim.generateAlardLuptonBasisList`.
    Not used for delta function basis sets.
referenceFwhmPix : `float`, optional
    Passed on to `lsst.ip.diffim.generateAlardLuptonBasisList`.
    Not used for delta function basis sets.
basisDegGauss : `list` of `int`, optional
    Passed on to `lsst.ip.diffim.generateAlardLuptonBasisList`.
    Not used for delta function basis sets.
basisSigmaGauss : `list` of `int`, optional
    Passed on to `lsst.ip.diffim.generateAlardLuptonBasisList`.
    Not used for delta function basis sets.
metadata : `lsst.daf.base.PropertySet`, optional
    Passed on to `lsst.ip.diffim.generateAlardLuptonBasisList`.
    Not used for delta function basis sets.

Returns
-------
basisList: `list` of `lsst.afw.math.kernel.FixedKernel`
    List of basis kernels.

Notes
-----
See `lsst.ip.diffim.generateAlardLuptonBasisList` and
`lsst.ip.diffim.makeDeltaFunctionBasisList` for more information.

Raises
------
ValueError
    If ``config.kernelBasisSet`` has an invalid value (not "alard-lupton" or "delta-function").

Definition at line 32 of file makeKernelBasisList.py.

                         basisDegGauss=None, basisSigmaGauss=None, metadata=None):
     """Generate the delta function or Alard-Lupton kernel bases depending on the Config.
     Wrapper to call either `lsst.ip.diffim.makeDeltaFunctionBasisList` or
     `lsst.ip.diffim.generateAlardLuptonBasisList`.
  
     Parameters
     ----------
     config : `lsst.ip.diffim.PsfMatchConfigAL`
         Configuration object.
     targetFwhmPix : `float`, optional
         Passed on to `lsst.ip.diffim.generateAlardLuptonBasisList`.
         Not used for delta function basis sets.
     referenceFwhmPix : `float`, optional
         Passed on to `lsst.ip.diffim.generateAlardLuptonBasisList`.
         Not used for delta function basis sets.
     basisDegGauss : `list` of `int`, optional
         Passed on to `lsst.ip.diffim.generateAlardLuptonBasisList`.
         Not used for delta function basis sets.
     basisSigmaGauss : `list` of `int`, optional
         Passed on to `lsst.ip.diffim.generateAlardLuptonBasisList`.
         Not used for delta function basis sets.
     metadata : `lsst.daf.base.PropertySet`, optional
         Passed on to `lsst.ip.diffim.generateAlardLuptonBasisList`.
         Not used for delta function basis sets.
  
     Returns
     -------
     basisList: `list` of `lsst.afw.math.kernel.FixedKernel`
         List of basis kernels.
  
     Notes
     -----
     See `lsst.ip.diffim.generateAlardLuptonBasisList` and
     `lsst.ip.diffim.makeDeltaFunctionBasisList` for more information.
  
     Raises
     ------
     ValueError
         If ``config.kernelBasisSet`` has an invalid value (not "alard-lupton" or "delta-function").
     """
     if config.kernelBasisSet == "alard-lupton":
         return generateAlardLuptonBasisList(config, targetFwhmPix=targetFwhmPix,
                                             referenceFwhmPix=referenceFwhmPix,
                                             basisDegGauss=basisDegGauss,
                                             basisSigmaGauss=basisSigmaGauss,
                                             metadata=metadata)
     elif config.kernelBasisSet == "delta-function":
         kernelSize = config.kernelSize
         return diffimLib.makeDeltaFunctionBasisList(kernelSize, kernelSize)
     else:
         raise ValueError("Cannot generate %s basis set" % (config.kernelBasisSet))
  
  

Variable Documentation

◆ sigma2fwhm

int lsst.ip.diffim.makeKernelBasisList.sigma2fwhm = 2. * np.sqrt(2. * np.log(2.))

Definition at line 29 of file makeKernelBasisList.py.

Functions

Variables

Function Documentation

◆ generateAlardLuptonBasisList()

◆ makeKernelBasisList()

Variable Documentation

◆ sigma2fwhm