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LSSTDataManagementBasePackage
GridTransform.cc
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1 // -*- lsst-c++ -*-
2 
3 /*
4  * LSST Data Management System
5  * Copyright 2008, 2009, 2010 LSST Corporation.
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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 
144 }
145 } // namespace ellipses
146 } // namespace geom
147 } // namespace afw
148 } // namespace lsst
An ellipse core with quadrupole moments as parameters.
Definition: Quadrupole.h:47
Jacobian dAssign(BaseCore const &other)
Assign other to this and return the derivative of the conversion, d(this)/d(other).
Definition: BaseCore.cc:169
lsst::geom::Point2D const & getCenter() const
Return the center point.
Definition: Ellipse.h:62
An affine coordinate transformation consisting of a linear transformation and an offset.
lsst::geom::AffineTransform::Matrix getMatrix() const
Return the transform matrix as an Eigen object.
int y
Definition: SpanSet.cc:49
Eigen::Matrix< double, 2, 2, Eigen::DontAlign > Matrix
DerivativeMatrix d() const
Return the derivative of the transform with respect to input core.
double getDeterminant() const
Return the determinant of the lsst::geom::LinearTransform.
Eigen::Matrix< double, 4, 3 > DerivativeMatrix
Matrix type for derivative with respect to ellipse parameters.
Definition: GridTransform.h:51
A base class for image defects.
An ellipse defined by an arbitrary BaseCore and a center point.
Definition: Ellipse.h:51
double getDeterminant() const
Return the determinant of the lsst::geom::AffineTransform.
lsst::geom::AffineTransform inverted() const
Return the inverse of the AffineTransform.
GridTransform(BaseCore const &input)
Standard constructor.
double x
GridTransform(Ellipse const &input)
Standard constructor.
An ellipse core with a complex ellipticity and radius parameterization.
Definition: radii.h:44
Eigen::Matrix3d Jacobian
Parameter Jacobian matrix type.
Definition: BaseCore.h:64
A base class for parametrizations of the "core" of an ellipse - the ellipticity and size...
Definition: BaseCore.h:55
lsst::geom::LinearTransform inverted() const
Return the inverse of the lsst::geom::LinearTransform;.
EigenVector const & asEigen() const noexcept(IS_ELEMENT_NOTHROW_COPYABLE)
Return a fixed-size Eigen representation of the coordinate object.
T sqrt(T... args)
Extent< double, 2 > Extent2D
Definition: Extent.h:400
Eigen::Matrix< double, 6, 5 > DerivativeMatrix
Matrix type for derivative with respect to input ellipse parameters.
Definition: GridTransform.h:90
lsst::geom::LinearTransform::Matrix getMatrix() const
Return the transform matrix as an Eigen object.
A 2D linear coordinate transformation.
DerivativeMatrix d() const
Return the derivative of transform with respect to input ellipse.