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
GridTransform.cc
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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  *
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29 
30 namespace lsst {
31 namespace afw {
32 namespace geom {
33 namespace ellipses {
34 
36  : _input(input), _eig(Quadrupole(input).getMatrix()) {}
37 
39  return _eig.operatorInverseSqrt();
40 }
41 
42 BaseCore::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);
88  mid(lsst::geom::LinearTransform::XY, C::RADIUS) = mid(lsst::geom::LinearTransform::YX, C::RADIUS) =
89  dtInv_dr(0, 1);
90  mid(lsst::geom::LinearTransform::YY, C::RADIUS) = dtInv_dr(1, 1);
91  return mid * rhs;
92 }
93 
94 double BaseCore::GridTransform::getDeterminant() const { return sqrt(1.0 / _eig.eigenvalues().prod()); }
95 
97  return lsst::geom::LinearTransform(_eig.operatorSqrt());
98 }
99 
100 Ellipse::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 
135 double Ellipse::GridTransform::getDeterminant() const { return _coreGt.getDeterminant(); }
136 
137 Ellipse::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 
143  return lsst::geom::AffineTransform(_coreGt.inverted(), lsst::geom::Extent2D(_input.getCenter()));
144 }
145 } // namespace ellipses
146 } // namespace geom
147 } // namespace afw
148 } // namespace lsst
y
int y
Definition: SpanSet.cc:49
lsst::geom::LinearTransform::XX
@ XX
Definition: LinearTransform.h:71
lsst::afw::geom::ellipses::Separable::getE1
double const getE1() const
Definition: Separable.h:57
lsst::afw::geom::ellipses::Ellipse::Y
@ Y
Definition: Ellipse.h:59
ellipses
lsst::afw::geom::ellipses::Ellipse::GridTransform::inverted
lsst::geom::AffineTransform inverted() const
Return the inverse of the AffineTransform.
Definition: GridTransform.cc:142
lsst::geom::LinearTransform
A 2D linear coordinate transformation.
Definition: LinearTransform.h:69
lsst::afw::geom::ellipses::Ellipse::GridTransform::getMatrix
lsst::geom::AffineTransform::Matrix getMatrix() const
Return the transform matrix as an Eigen object.
Definition: GridTransform.cc:102
lsst::geom::AffineTransform::XY
@ XY
Definition: AffineTransform.h:77
lsst::afw
Definition: imageAlgorithm.dox:1
Separable.h
Quadrupole.h
lsst::afw::geom::ellipses::BaseCore::GridTransform::GridTransform
GridTransform(BaseCore const &input)
Standard constructor.
Definition: GridTransform.cc:35
GridTransform.h
radii.h
lsst::afw::geom::ellipses::Ellipse::GridTransform::GridTransform
GridTransform(Ellipse const &input)
Standard constructor.
Definition: GridTransform.cc:100
lsst::geom::LinearTransform::XY
@ XY
Definition: LinearTransform.h:71
lsst::afw::geom::ellipses::Ellipse::GridTransform::d
DerivativeMatrix d() const
Return the derivative of transform with respect to input ellipse.
Definition: GridTransform.cc:110
std::sqrt
T sqrt(T... args)
lsst::geom::AffineTransform::YX
@ YX
Definition: AffineTransform.h:77
lsst::geom::AffineTransform
An affine coordinate transformation consisting of a linear transformation and an offset.
Definition: AffineTransform.h:75
lsst::afw::geom::ellipses::Ellipse::GridTransform::DerivativeMatrix
Eigen::Matrix< double, 6, 5 > DerivativeMatrix
Matrix type for derivative with respect to input ellipse parameters.
Definition: GridTransform.h:85
lsst::geom::AffineTransform::YY
@ YY
Definition: AffineTransform.h:77
lsst::geom::LinearTransform::YX
@ YX
Definition: LinearTransform.h:71
lsst::geom::AffineTransform::Matrix
Eigen::Matrix3d Matrix
Definition: AffineTransform.h:79
lsst::afw::geom::ellipses::BaseCore::GridTransform::getDeterminant
double getDeterminant() const
Return the determinant of the lsst::geom::LinearTransform.
Definition: GridTransform.cc:94
lsst::afw::geom::ellipses::BaseCore
A base class for parametrizations of the "core" of an ellipse - the ellipticity and size.
Definition: BaseCore.h:55
lsst::afw::geom::ellipses::Ellipse::GridTransform::getDeterminant
double getDeterminant() const
Return the determinant of the lsst::geom::AffineTransform.
Definition: GridTransform.cc:135
lsst::afw::geom::ellipses::Separable
An ellipse core with a complex ellipticity and radius parameterization.
Definition: radii.h:44
x
double x
Definition: ChebyshevBoundedField.cc:277
lsst::geom::LinearTransform::YY
@ YY
Definition: LinearTransform.h:71
lsst::geom::AffineTransform::XX
@ XX
Definition: AffineTransform.h:77
lsst
A base class for image defects.
Definition: imageAlgorithm.dox:1
lsst::afw::geom::ellipses::Ellipse
An ellipse defined by an arbitrary BaseCore and a center point.
Definition: Ellipse.h:51
lsst::afw::geom::ellipses::Ellipse::X
@ X
Definition: Ellipse.h:59
lsst::afw::geom::ellipses::Quadrupole
An ellipse core with quadrupole moments as parameters.
Definition: Quadrupole.h:47
lsst::geom
Definition: AffineTransform.h:36
lsst::afw::geom::ellipses::BaseCore::Jacobian
Eigen::Matrix3d Jacobian
Parameter Jacobian matrix type.
Definition: BaseCore.h:64
lsst::afw::geom::ellipses::BaseCore::GridTransform::getMatrix
lsst::geom::LinearTransform::Matrix getMatrix() const
Return the transform matrix as an Eigen object.
Definition: GridTransform.cc:38
lsst::geom::AffineTransform::Y
@ Y
Definition: AffineTransform.h:77
lsst::afw::geom::ellipses::BaseCore::GridTransform::d
DerivativeMatrix d() const
Return the derivative of the transform with respect to input core.
Definition: GridTransform.cc:46
lsst::geom::Point< double, 2 >
lsst::afw::geom::ellipses::BaseCore::GridTransform::DerivativeMatrix
Eigen::Matrix< double, 4, 3 > DerivativeMatrix
Matrix type for derivative with respect to ellipse parameters.
Definition: GridTransform.h:51
ReducedShear.h
lsst::afw::geom::ellipses::BaseCore::GridTransform::inverted
lsst::geom::LinearTransform inverted() const
Return the inverse of the lsst::geom::LinearTransform;.
Definition: GridTransform.cc:96
lsst::geom::AffineTransform::X
@ X
Definition: AffineTransform.h:77
lsst::geom::LinearTransform::Matrix
Eigen::Matrix< double, 2, 2, Eigen::DontAlign > Matrix
Definition: LinearTransform.h:77
lsst::geom::Extent< double, 2 >