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LSST Data Management Base Package
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GridTransform.cc
Go to the documentation of this file.
1// -*- lsst-c++ -*-
2
3/*
4 * LSST Data Management System
5 * Copyright 2008, 2009, 2010 LSST Corporation.
6 *
7 * This product includes software developed by the
8 * LSST Project (http://www.lsst.org/).
9 *
10 * This program is free software: you can redistribute it and/or modify
11 * it under the terms of the GNU General Public License as published by
12 * the Free Software Foundation, either version 3 of the License, or
13 * (at your option) any later version.
14 *
15 * This program is distributed in the hope that it will be useful,
16 * but WITHOUT ANY WARRANTY; without even the implied warranty of
17 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
18 * GNU General Public License for more details.
19 *
20 * You should have received a copy of the LSST License Statement and
21 * the GNU General Public License along with this program. If not,
22 * see <http://www.lsstcorp.org/LegalNotices/>.
23 */
29
30namespace lsst {
31namespace afw {
32namespace geom {
33namespace ellipses {
34
36 : _input(input), _eig(Quadrupole(input).getMatrix()) {}
37
39 return _eig.operatorInverseSqrt();
40}
41
42BaseCore::GridTransform::operator lsst::geom::LinearTransform() const {
43 return lsst::geom::LinearTransform(_eig.operatorInverseSqrt());
44}
45
47 /*
48 Grid transform is easiest to differentiate in the ReducedShear/DeterminantRadius parametrization.
49 But we actually differentiate the inverse of the transform, and then use
50 $dM^{-1}/dt = -M^{-1} dM/dt M^{-1} to compute the derivative of the inverse.
51
52 The inverse of the grid transform in ReducedShear/DeterminantRadius is:
53 $\frac{r}{\sqrt{1-g^2}}(\sigma_x + g_1 \sigma_z + g2 \sigma_y)$, where $\sigma_i$ are the
54 Pauli spin matrices.
55 */
57 C core;
58 Jacobian rhs = core.dAssign(_input);
59 double g1 = core.getE1();
60 double g2 = core.getE2();
61 double g = core.getEllipticity().getE();
62 double r = core.getRadius();
63 double beta = 1.0 - g * g;
64 double alpha = r / std::sqrt(beta);
65
66 Eigen::Matrix2d sigma_z, sigma_y;
67 sigma_z << 1.0, 0.0, 0.0, -1.0;
68 sigma_y << 0.0, 1.0, 1.0, 0.0;
69 Eigen::Matrix2d t = _eig.operatorSqrt();
70 Eigen::Matrix2d tInv = _eig.operatorInverseSqrt();
71 Eigen::Matrix2d dt_dg1 = t * g1 / beta + alpha * sigma_z;
72 Eigen::Matrix2d dt_dg2 = t * g2 / beta + alpha * sigma_y;
73 Eigen::Matrix2d dt_dr = t * (1.0 / r);
74 Eigen::Matrix2d dtInv_dg1 = -tInv * dt_dg1 * tInv;
75 Eigen::Matrix2d dtInv_dg2 = -tInv * dt_dg2 * tInv;
76 Eigen::Matrix2d dtInv_dr = -tInv * dt_dr * tInv;
77
79 mid(lsst::geom::LinearTransform::XX, C::E1) = dtInv_dg1(0, 0);
81 dtInv_dg1(0, 1);
82 mid(lsst::geom::LinearTransform::YY, C::E1) = dtInv_dg1(1, 1);
83 mid(lsst::geom::LinearTransform::XX, C::E2) = dtInv_dg2(0, 0);
85 dtInv_dg2(0, 1);
86 mid(lsst::geom::LinearTransform::YY, C::E2) = dtInv_dg2(1, 1);
87 mid(lsst::geom::LinearTransform::XX, C::RADIUS) = dtInv_dr(0, 0);
89 dtInv_dr(0, 1);
90 mid(lsst::geom::LinearTransform::YY, C::RADIUS) = dtInv_dr(1, 1);
91 return mid * rhs;
92}
93
94double BaseCore::GridTransform::getDeterminant() const { return sqrt(1.0 / _eig.eigenvalues().prod()); }
95
99
100Ellipse::GridTransform::GridTransform(Ellipse const& input) : _input(input), _coreGt(input.getCore()) {}
101
103 lsst::geom::AffineTransform::Matrix r = lsst::geom::AffineTransform::Matrix::Zero();
104 r.block<2, 2>(0, 0) = _coreGt.getMatrix();
105 r.block<2, 1>(0, 2) = -r.block<2, 2>(0, 0) * _input.getCenter().asEigen();
106 r(2, 2) = 1.0;
107 return r;
108}
109
111 DerivativeMatrix r = DerivativeMatrix::Zero();
112 lsst::geom::LinearTransform linear = _coreGt;
113 r.block<4, 3>(0, 0) = _coreGt.d();
114 double x = -_input.getCenter().getX();
115 double y = -_input.getCenter().getY();
132 return r;
133}
134
135double Ellipse::GridTransform::getDeterminant() const { return _coreGt.getDeterminant(); }
136
137Ellipse::GridTransform::operator lsst::geom::AffineTransform() const {
138 lsst::geom::LinearTransform linear = _coreGt;
139 return lsst::geom::AffineTransform(linear, linear(lsst::geom::Point2D() - _input.getCenter()));
140}
141
145} // namespace ellipses
146} // namespace geom
147} // namespace afw
148} // namespace lsst
double getDeterminant() const
Return the determinant of the lsst::geom::LinearTransform.
lsst::geom::LinearTransform inverted() const
Return the inverse of the lsst::geom::LinearTransform;.
DerivativeMatrix d() const
Return the derivative of the transform with respect to input core.
GridTransform(BaseCore const &input)
Standard constructor.
Eigen::Matrix< double, 4, 3 > DerivativeMatrix
Matrix type for derivative with respect to ellipse parameters.
lsst::geom::LinearTransform::Matrix getMatrix() const
Return the transform matrix as an Eigen object.
BaseCore()=default
Return the size of the bounding box for the ellipse core.
Eigen::Matrix3d Jacobian
Parameter Jacobian matrix type.
Definition BaseCore.h:64
double getDeterminant() const
Return the determinant of the lsst::geom::AffineTransform.
DerivativeMatrix d() const
Return the derivative of transform with respect to input ellipse.
lsst::geom::AffineTransform::Matrix getMatrix() const
Return the transform matrix as an Eigen object.
Eigen::Matrix< double, 6, 5 > DerivativeMatrix
Matrix type for derivative with respect to input ellipse parameters.
lsst::geom::AffineTransform inverted() const
Return the inverse of the AffineTransform.
GridTransform(Ellipse const &input)
Standard constructor.
BaseCore const & getCore() const
Return the ellipse core.
Definition Ellipse.h:71
Ellipse(BaseCore const &core, lsst::geom::Point2D const &center=lsst::geom::Point2D())
Return the transform that maps the ellipse to the unit circle.
Definition Ellipse.h:164
An ellipse core with quadrupole moments as parameters.
Definition Quadrupole.h:47
An ellipse core with a complex ellipticity and radius parameterization.
Definition Separable.h:50
An affine coordinate transformation consisting of a linear transformation and an offset.
A 2D linear coordinate transformation.
Eigen::Matrix< double, 2, 2, Eigen::DontAlign > Matrix
Extent< double, 2 > Extent2D
Definition Extent.h:400
Point< double, 2 > Point2D
Definition Point.h:324
T sqrt(T... args)