CalcKSBMoments

For each galaxy in a galaxy set, this module measures the moments as defined in Kaiser Squires & Broadhurst 1995 (both quadrapole and elliptical), weighted by a given function. Once these moments have been computed, an estimate for the shear bias is computed, as are the average ellipticity and angle for the set.

The centroid about which the moments are taken can be given in a number of ways. The default behaviour is to measure the centroid using the zeroth moment. If the keyword FixCentroid is set, the center of the image is used. If the keyword TrueCentroid is set, the values from the data stream, usually generated by MakeGalSet, will be used.

The quadrapole moments are defined as Q_ij=sum(f(x,y)*w(x,y)*i*j)/sum(f(x,y)*w(x,y)) where f(x,y) is the input image and w(x,y) is the weight function and i,j are {x,y}.

The elliptical moments are then e1=(Q_xx-Q_yy)/(Q_xx+Q_yy) and e2=(2*Q_xy)/(Qxx+Q_yy).

The shear bias term, gamma, is given by gamma_i=|e_i|/2 where i={1,2}.

Parameters

Name	Type	Description
FixCentroid	keyword	Fix centroid to center of image.
TrueCentroid	keyword	Use the centroid supplied in the data stream.
WeightModel	string	"Constant" or "Gaussian". The weight model to use when calculating the moments. Either a constant weight or a circular gaussian.
Sigma	double	If using a Gaussian weight model, this is the sigma parameter in units of pixels.
Window	int	Units of pixels. Calculate moments on square domain of side Window instead of entire image. Overridden if larger than either image dimension. If centroid is too close to the edge, smaller, rectangular domains are summed over instead of offset squares.
Verbose	keyword	If present, output messages to screen for debugging purposes.

Inputs

Name	Type	Description
GalSet/Width	int	Width of each image in pixels.
GalSet/Height	int	Height on each image in pixels.
GalSet/BiasedCount	int	Number of biased images in galaxy set.
GalSet/BiasedImages	double*	Array of pixel values of biased images.
GalSet/BiasedCentX	double*	If TrueCentroid is set, an array of the "true" x-coordinate of the galaxy centroid for each image.
GalSet/BiasedCentY	double*	If TrueCentroid is set, an array of the "true" y-coordinate of the galaxy centroid for each image.
GalSet/UnbiasedCount	int	Number of biased images in galaxy set.
GalSet/UnbiasedImages	double*	Array of pixel values of biased images.
GalSet/UnbiasedCentX	double*	If TrueCentroid is set, an array of the "true" x-coordinate of the galaxy centroid for each image.
GalSet/UnbiasedCentY	double*	If TrueCentroid is set, an array of the "true" y-coordinate of the galaxy centroid for each image.

Outputs

Name	Type	Description
KSBMoments/BiasedQuadXX	double*	Array of the measured X-X quadrapole moments for each biased galaxy.
KSBMoments/BiasedQuadXY	double*	Array of the measured X-Y quadrapole moments for each biased galaxy.
KSBMoments/BiasedQuadXX	double*	Array of the measured Y-Y quadrapole moments for each biased galaxy.
KSBMoments/BiasedEllip1	double*	Array of the measured elliptical moments (ellipticy aligned with X,Y axis) for each biased galaxy.
KSBMoments/BiasedEllip2	double*	Array of the measured elliptical moments (ellipticy 45 degrees to X,Y axis) for each biased galaxy
KSBMoments/BiasedMeanGamma1	double	Estimate for shear bias (aligned with X,Y axis) of biased galaxies.
KSBMoments/BiasedMeanGamma2	double	Estimate for shear bias (45 degrees to X,Y axis) of biased galaxies.
KSBMoments/BiasedMeanEllip	double	Average ellipticity of all biased galaxies.
KSBMoments/BiasedMeanAngle	double	Average orientation of all biased galaxies in radians.
KSBMoments/UnbiasedQuadXX	double*	Array of the measured X-X quadrapole moments for each unbiased galaxy.
KSBMoments/UnbiasedQuadXY	double*	Array of the measured X-Y quadrapole moments for each unbiased galaxy.
KSBMoments/UnbiasedQuadXX	double*	Array of the measured Y-Y quadrapole moments for each unbiased galaxy.
KSBMoments/UnbiasedEllip1	double*	Array of the measured elliptical moments (ellipticy aligned with X,Y axis) for each unbiased galaxy.
KSBMoments/UnbiasedEllip2	double*	Array of the measured elliptical moments (ellipticy 45 degrees to X,Y axis) for each unbiased galaxy
KSBMoments/UnbiasedMeanGamma1	double	Estimate for shear unbias (aligned with X,Y axis) of unbiased galaxies.
KSBMoments/UnbiasedMeanGamma2	double	Estimate for shear unbias (45 degrees to X,Y axis) of unbiased galaxies.
KSBMoments/UnbiasedMeanEllip	double	Average ellipticity of all unbiased galaxies.
KSBMoments/UnbiasedMeanAngle	double	Average orientation of all unbiased galaxies in radians.