Enum BasisTypeEnum

Enum Documentation

enum lsst::shapelet::BasisTypeEnum

An enum that sets whether to use real-valued polar shapelets or Cartesian shapelets.

The conversion between the two bases is theoretically exact, but of course subject to round-off error here.

Values:

HERMITE

Cartesian shapelets or Gauss-Hermite functions, as defined in Refregier, 2003. That is, \( \psi(x, y)_{n_x, n_y} = \frac{H_{n_x}(x) H_{n_y}(y) e^{-\frac{x^2 + y^2}{2}}} {\sigma 2^{n_x + n_y} \sqrt{\pi n_x! n_y!}} \) where \(H_n(x)\) is a Hermite polynomial.

The ordering of coefficients [n_x, n_y] is (row-major packed): [0,0], [0,1], [1,0], [0,2], [1,1], [2,0], [0,3], [1,2], [2,1], [3,0], [0,4], [1,3], [2,2], [3,1], [4,0] etc.

LAGUERRE

Polar shapelets or Gauss-Laguerre functions, as defined in Bernstein and Jarvis, 2002. That is, \( \psi(x, y, \sigma)_{p, q} = (-1)^q \sqrt{\frac{q!}{p!}} (x + i y)^{p-q} e^{-\frac{x^2 + y^2}{2}} L^{(p-q)}_q(x^2 + y^2) \) where \(L^{(m)}_n(r)\) is an associated Laguerre polynomial.

The ordering of coefficients [p, q] is (row-major packed): [0,0], Re([1,0]), Im([1,0]), Re([2,0]), Im([2,0]), [1,1], Re([3,0]), Im([3,0], Re([2,1]), Im([2,1]), Re([4,0]), Im([4,0], Re([3,1]), Im([3,1]), [2,2] etc.

Elements with p < q are redundant in representing real-valued functions, while those with p == q are inherently real.