LSST Applications 27.0.0,g0265f82a02+469cd937ee,g02d81e74bb+21ad69e7e1,g1470d8bcf6+cbe83ee85a,g2079a07aa2+e67c6346a6,g212a7c68fe+04a9158687,g2305ad1205+94392ce272,g295015adf3+81dd352a9d,g2bbee38e9b+469cd937ee,g337abbeb29+469cd937ee,g3939d97d7f+72a9f7b576,g487adcacf7+71499e7cba,g50ff169b8f+5929b3527e,g52b1c1532d+a6fc98d2e7,g591dd9f2cf+df404f777f,g5a732f18d5+be83d3ecdb,g64a986408d+21ad69e7e1,g858d7b2824+21ad69e7e1,g8a8a8dda67+a6fc98d2e7,g99cad8db69+f62e5b0af5,g9ddcbc5298+d4bad12328,ga1e77700b3+9c366c4306,ga8c6da7877+71e4819109,gb0e22166c9+25ba2f69a1,gb6a65358fc+469cd937ee,gbb8dafda3b+69d3c0e320,gc07e1c2157+a98bf949bb,gc120e1dc64+615ec43309,gc28159a63d+469cd937ee,gcf0d15dbbd+72a9f7b576,gdaeeff99f8+a38ce5ea23,ge6526c86ff+3a7c1ac5f1,ge79ae78c31+469cd937ee,gee10cc3b42+a6fc98d2e7,gf1cff7945b+21ad69e7e1,gfbcc870c63+9a11dc8c8f
LSST Data Management Base Package
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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. | |
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.
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explicit |
Construct an instance able to compute the transform matrix at up to the given order.
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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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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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Return the maximum order at which the matrix can be computed.
Definition at line 90 of file HermiteTransformMatrix.h.