lsst::afw::geom::ellipses::BaseCore::GridTransform Class Reference

A temporary-only expression object representing an lsst::geom::LinearTransform that maps the ellipse core to a unit circle. More...

#include <GridTransform.h>

Public Types
typedef Eigen::Matrix< double, 4, 3 >	DerivativeMatrix
	Matrix type for derivative with respect to ellipse parameters. More...

Public Member Functions
	GridTransform (BaseCore const &input)
	Standard constructor. More...
	operator lsst::geom::LinearTransform () const
	Convert the proxy to an lsst::geom::LinearTransform. More...
lsst::geom::LinearTransform::Matrix	getMatrix () const
	Return the transform matrix as an Eigen object. More...
DerivativeMatrix	d () const
	Return the derivative of the transform with respect to input core. More...
double	getDeterminant () const
	Return the determinant of the lsst::geom::LinearTransform. More...
lsst::geom::LinearTransform	inverted () const
	Return the inverse of the lsst::geom::LinearTransform;. More...

Detailed Description

A temporary-only expression object representing an lsst::geom::LinearTransform that maps the ellipse core to a unit circle.

Definition at line 48 of file GridTransform.h.

Member Typedef Documentation

DerivativeMatrix

typedef Eigen::Matrix<double, 4, 3> lsst::afw::geom::ellipses::BaseCore::GridTransform::DerivativeMatrix

Matrix type for derivative with respect to ellipse parameters.

Definition at line 51 of file GridTransform.h.

Constructor & Destructor Documentation

GridTransform()

lsst::afw::geom::ellipses::BaseCore::GridTransform::GridTransform ( BaseCore const &  input )

explicit

Standard constructor.

Definition at line 35 of file GridTransform.cc.

        : _input(input), _eig(Quadrupole(input).getMatrix()) {}

Member Function Documentation

d()

BaseCore::GridTransform::DerivativeMatrix lsst::afw::geom::ellipses::BaseCore::GridTransform::d

(

)

const

Return the derivative of the transform with respect to input core.

Definition at line 46 of file GridTransform.cc.

                                                                     {
    /*
       Grid transform is easiest to differentiate in the ReducedShear/DeterminantRadius parametrization.
       But we actually differentiate the inverse of the transform, and then use
       $dM^{-1}/dt = -M^{-1} dM/dt M^{-1} to compute the derivative of the inverse.
 
       The inverse of the grid transform in ReducedShear/DeterminantRadius is:
       $\frac{r}{\sqrt{1-g^2}}(\sigma_x + g_1 \sigma_z + g2 \sigma_y)$, where $\sigma_i$ are the
       Pauli spin matrices.
    */
    typedef Separable<ReducedShear, DeterminantRadius> C;
    C core;
    Jacobian rhs = core.dAssign(_input);
    double g1 = core.getE1();
    double g2 = core.getE2();
    double g = core.getEllipticity().getE();
    double r = core.getRadius();
    double beta = 1.0 - g * g;
    double alpha = r / std::sqrt(beta);
 
    Eigen::Matrix2d sigma_z, sigma_y;
    sigma_z << 1.0, 0.0, 0.0, -1.0;
    sigma_y << 0.0, 1.0, 1.0, 0.0;
    Eigen::Matrix2d t = _eig.operatorSqrt();
    Eigen::Matrix2d tInv = _eig.operatorInverseSqrt();
    Eigen::Matrix2d dt_dg1 = t * g1 / beta + alpha * sigma_z;
    Eigen::Matrix2d dt_dg2 = t * g2 / beta + alpha * sigma_y;
    Eigen::Matrix2d dt_dr = t * (1.0 / r);
    Eigen::Matrix2d dtInv_dg1 = -tInv * dt_dg1 * tInv;
    Eigen::Matrix2d dtInv_dg2 = -tInv * dt_dg2 * tInv;
    Eigen::Matrix2d dtInv_dr = -tInv * dt_dr * tInv;
 
    GridTransform::DerivativeMatrix mid;
    mid(lsst::geom::LinearTransform::XX, C::E1) = dtInv_dg1(0, 0);
    mid(lsst::geom::LinearTransform::XY, C::E1) = mid(lsst::geom::LinearTransform::YX, C::E1) =
            dtInv_dg1(0, 1);
    mid(lsst::geom::LinearTransform::YY, C::E1) = dtInv_dg1(1, 1);
    mid(lsst::geom::LinearTransform::XX, C::E2) = dtInv_dg2(0, 0);
    mid(lsst::geom::LinearTransform::XY, C::E2) = mid(lsst::geom::LinearTransform::YX, C::E2) =
            dtInv_dg2(0, 1);
    mid(lsst::geom::LinearTransform::YY, C::E2) = dtInv_dg2(1, 1);
    mid(lsst::geom::LinearTransform::XX, C::RADIUS) = dtInv_dr(0, 0);
    mid(lsst::geom::LinearTransform::XY, C::RADIUS) = mid(lsst::geom::LinearTransform::YX, C::RADIUS) =
            dtInv_dr(0, 1);
    mid(lsst::geom::LinearTransform::YY, C::RADIUS) = dtInv_dr(1, 1);
    return mid * rhs;
}

getDeterminant()

double lsst::afw::geom::ellipses::BaseCore::GridTransform::getDeterminant

(

)

const

Return the determinant of the lsst::geom::LinearTransform.

Definition at line 94 of file GridTransform.cc.

{ return sqrt(1.0 / _eig.eigenvalues().prod()); }

getMatrix()

lsst::geom::LinearTransform::Matrix lsst::afw::geom::ellipses::BaseCore::GridTransform::getMatrix

(

)

const

Return the transform matrix as an Eigen object.

Definition at line 38 of file GridTransform.cc.

                                                                     {
    return _eig.operatorInverseSqrt();
}

inverted()

lsst::geom::LinearTransform lsst::afw::geom::ellipses::BaseCore::GridTransform::inverted

(

)

const

Return the inverse of the lsst::geom::LinearTransform;.

Definition at line 96 of file GridTransform.cc.

                                                              {
    return lsst::geom::LinearTransform(_eig.operatorSqrt());
}

operator lsst::geom::LinearTransform()

lsst::afw::geom::ellipses::BaseCore::GridTransform::operator lsst::geom::LinearTransform

(

)

const

Convert the proxy to an lsst::geom::LinearTransform.

Definition at line 42 of file GridTransform.cc.

                                                              {
    return lsst::geom::LinearTransform(_eig.operatorInverseSqrt());
}

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The documentation for this class was generated from the following files:

• /j/snowflake/release/lsstsw/stack/0.4.3/Linux64/afw/21.0.0-25-g1d57be3cd+e73869a214/include/lsst/afw/geom/ellipses/GridTransform.h
• /j/snowflake/release/lsstsw/stack/0.4.3/Linux64/afw/21.0.0-25-g1d57be3cd+e73869a214/src/geom/ellipses/GridTransform.cc