LSST Applications g04a91732dc+cc8870d3f5,g07dc498a13+5aa0b8792f,g0fba68d861+80045be308,g1409bbee79+5aa0b8792f,g1a7e361dbc+5aa0b8792f,g1fd858c14a+f64bc332a9,g208c678f98+1ae86710ed,g35bb328faa+fcb1d3bbc8,g4d2262a081+47ad8a29a8,g4d39ba7253+9633a327c1,g4e0f332c67+5d362be553,g53246c7159+fcb1d3bbc8,g60b5630c4e+9633a327c1,g668ecb457e+25d63fd678,g78460c75b0+2f9a1b4bcd,g786e29fd12+cf7ec2a62a,g7b71ed6315+fcb1d3bbc8,g8852436030+8b64ca622a,g89139ef638+5aa0b8792f,g89e1512fd8+04325574d3,g8d6b6b353c+9633a327c1,g9125e01d80+fcb1d3bbc8,g989de1cb63+5aa0b8792f,g9f33ca652e+b196626af7,ga9baa6287d+9633a327c1,gaaedd4e678+5aa0b8792f,gabe3b4be73+1e0a283bba,gb1101e3267+71e32094df,gb58c049af0+f03b321e39,gb90eeb9370+2807b1ad02,gcf25f946ba+8b64ca622a,gd315a588df+a39986a76f,gd6cbbdb0b4+c8606af20c,gd9a9a58781+fcb1d3bbc8,gde0f65d7ad+4e42d81ab7,ge278dab8ac+932305ba37,ge82c20c137+76d20ab76d,gfe73954cf8+a1301e4c20,w.2025.11
LSST Data Management Base Package
|
A class that computes a matrix that applies a linear transform to a 2-d Hermite polynomial expansion. More...
#include <HermiteTransformMatrix.h>
Public Member Functions | |
Eigen::MatrixXd | compute (Eigen::Matrix2d const &transform) const |
Compute the matrix for a new linear transform. | |
Eigen::MatrixXd | compute (geom::LinearTransform const &transform) const |
Compute the matrix for a new linear transform. | |
Eigen::MatrixXd | compute (Eigen::Matrix2d const &transform, int order) const |
Compute the matrix for a new linear transform at the given order (must be <= getOrder()). | |
Eigen::MatrixXd | compute (geom::LinearTransform const &transform, int order) const |
Compute the matrix for a new linear transform at the given order (must be <= getOrder()). | |
Eigen::MatrixXd | getCoefficientMatrix () const |
Return the matrix that maps (1-d) regular polynomials to the alternate Hermite polynomials. | |
Eigen::MatrixXd | getInverseCoefficientMatrix () const |
Return the matrix that maps (1-d) alternate Hermite polynomials to regular polynomials. | |
int | getOrder () const |
Return the maximum order at which the matrix can be computed. | |
HermiteTransformMatrix (int order) | |
Construct an instance able to compute the transform matrix at up to the given order. | |
A class that computes a matrix that applies a linear transform to a 2-d Hermite polynomial expansion.
Let
\[ Z_{\boldsymbol{n}}\!(\boldsymbol{x}) \equiv \mathcal{H}_{n_0}\!(x_0)\;\mathcal{H}_{n_1}\!(x_1) \]
where
\[ \mathcal{H}_n(x)=(2^n \pi^{1/2} n!)^{-1/2}H_n(x) \]
is the \(i\)th "alternate" Hermite polynomial. This function computes the matrix \(\boldsymbol{Q}(\boldsymbol{U})\) given a linear transform \(\boldsymbol{U}\) such that
\[ Z_{\boldsymbol{m}}\!(\boldsymbol{U}\boldsymbol{x}) = \sum_{\boldsymbol{n}} Q_{\boldsymbol{m},\boldsymbol{n}}\!(\boldsymbol{U})\,Z_{\boldsymbol{n}}\!(\boldsymbol{x}) \]
Definition at line 54 of file HermiteTransformMatrix.h.
|
explicit |
Construct an instance able to compute the transform matrix at up to the given order.
|
inline |
Compute the matrix for a new linear transform.
Definition at line 58 of file HermiteTransformMatrix.h.
Eigen::MatrixXd lsst::shapelet::HermiteTransformMatrix::compute | ( | Eigen::Matrix2d const & | transform, |
int | order ) const |
Compute the matrix for a new linear transform at the given order (must be <= getOrder()).
|
inline |
Compute the matrix for a new linear transform.
Definition at line 63 of file HermiteTransformMatrix.h.
|
inline |
Compute the matrix for a new linear transform at the given order (must be <= getOrder()).
Definition at line 71 of file HermiteTransformMatrix.h.
|
inline |
Return the matrix that maps (1-d) regular polynomials to the alternate Hermite polynomials.
The matrix is always lower triangular, and has size equal to getOrder()+1.
Definition at line 80 of file HermiteTransformMatrix.h.
|
inline |
Return the matrix that maps (1-d) alternate Hermite polynomials to regular polynomials.
The matrix is always lower triangular, and has size equal to getOrder()+1.
Definition at line 87 of file HermiteTransformMatrix.h.
|
inline |
Return the maximum order at which the matrix can be computed.
Definition at line 90 of file HermiteTransformMatrix.h.