LSSTApplications
19.0.0-14-gb0260a2+72efe9b372,20.0.0+7927753e06,20.0.0+8829bf0056,20.0.0+995114c5d2,20.0.0+b6f4b2abd1,20.0.0+bddc4f4cbe,20.0.0-1-g253301a+8829bf0056,20.0.0-1-g2b7511a+0d71a2d77f,20.0.0-1-g5b95a8c+7461dd0434,20.0.0-12-g321c96ea+23efe4bbff,20.0.0-16-gfab17e72e+fdf35455f6,20.0.0-2-g0070d88+ba3ffc8f0b,20.0.0-2-g4dae9ad+ee58a624b3,20.0.0-2-g61b8584+5d3db074ba,20.0.0-2-gb780d76+d529cf1a41,20.0.0-2-ged6426c+226a441f5f,20.0.0-2-gf072044+8829bf0056,20.0.0-2-gf1f7952+ee58a624b3,20.0.0-20-geae50cf+e37fec0aee,20.0.0-25-g3dcad98+544a109665,20.0.0-25-g5eafb0f+ee58a624b3,20.0.0-27-g64178ef+f1f297b00a,20.0.0-3-g4cc78c6+e0676b0dc8,20.0.0-3-g8f21e14+4fd2c12c9a,20.0.0-3-gbd60e8c+187b78b4b8,20.0.0-3-gbecbe05+48431fa087,20.0.0-38-ge4adf513+a12e1f8e37,20.0.0-4-g97dc21a+544a109665,20.0.0-4-gb4befbc+087873070b,20.0.0-4-gf910f65+5d3db074ba,20.0.0-5-gdfe0fee+199202a608,20.0.0-5-gfbfe500+d529cf1a41,20.0.0-6-g64f541c+d529cf1a41,20.0.0-6-g9a5b7a1+a1cd37312e,20.0.0-68-ga3f3dda+5fca18c6a4,20.0.0-9-g4aef684+e18322736b,w.2020.45
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.
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.
Definition at line 63 of file HermiteTransformMatrix.h.
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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.