LSSTApplications
18.0.0+106,18.0.0+50,19.0.0,19.0.0+1,19.0.0+10,19.0.0+11,19.0.0+13,19.0.0+17,19.0.0+2,19.0.0-1-g20d9b18+6,19.0.0-1-g425ff20,19.0.0-1-g5549ca4,19.0.0-1-g580fafe+6,19.0.0-1-g6fe20d0+1,19.0.0-1-g7011481+9,19.0.0-1-g8c57eb9+6,19.0.0-1-gb5175dc+11,19.0.0-1-gdc0e4a7+9,19.0.0-1-ge272bc4+6,19.0.0-1-ge3aa853,19.0.0-10-g448f008b,19.0.0-12-g6990b2c,19.0.0-2-g0d9f9cd+11,19.0.0-2-g3d9e4fb2+11,19.0.0-2-g5037de4,19.0.0-2-gb96a1c4+3,19.0.0-2-gd955cfd+15,19.0.0-3-g2d13df8,19.0.0-3-g6f3c7dc,19.0.0-4-g725f80e+11,19.0.0-4-ga671dab3b+1,19.0.0-4-gad373c5+3,19.0.0-5-ga2acb9c+2,19.0.0-5-gfe96e6c+2,w.2020.01
LSSTDataManagementBasePackage
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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. More... | |
Eigen::MatrixXd | compute (geom::LinearTransform const &transform) const |
Compute the matrix for a new linear transform. More... | |
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()). More... | |
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()). More... | |
Eigen::MatrixXd | getCoefficientMatrix () const |
Return the matrix that maps (1-d) regular polynomials to the alternate Hermite polynomials. More... | |
Eigen::MatrixXd | getInverseCoefficientMatrix () const |
Return the matrix that maps (1-d) alternate Hermite polynomials to regular polynomials. More... | |
int | getOrder () const |
Return the maximum order at which the matrix can be computed. More... | |
HermiteTransformMatrix (int order) | |
Construct an instance able to compute the transform matrix at up to the given order. More... | |
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.
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explicit |
Construct an instance able to compute the transform matrix at up to the given order.
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inline |
Compute the matrix for a new linear transform.
Definition at line 58 of file HermiteTransformMatrix.h.
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inline |
Compute the matrix for a new linear transform.
Definition at line 63 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()).
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inline |
Compute the matrix for a new linear transform at the given order (must be <= getOrder()).
Definition at line 71 of file HermiteTransformMatrix.h.
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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.
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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.
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inline |
Return the maximum order at which the matrix can be computed.
Definition at line 90 of file HermiteTransformMatrix.h.