lsst.afw  20.0.0-14-g1a12fe12b+614f89f815
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lsst::afw::geom::SipApproximation Class Referencefinal

A fitter and results class for approximating a general Transform in a form compatible with FITS WCS persistence. More...

#include <SipApproximation.h>

Classes

struct  Grid
 
struct  Solution
 

Public Member Functions

 SipApproximation (std::shared_ptr< TransformPoint2ToPoint2 > pixelToIwc, lsst::geom::Point2D const &crpix, Eigen::Matrix2d const &cd, lsst::geom::Box2D const &bbox, lsst::geom::Extent2I const &gridShape, int order, bool useInverse=true, double svdThreshold=-1)
 Construct a new approximation by fitting on a grid of points. More...
 
 SipApproximation (std::shared_ptr< TransformPoint2ToPoint2 > pixelToIwc, lsst::geom::Point2D const &crpix, Eigen::Matrix2d const &cd, lsst::geom::Box2D const &bbox, lsst::geom::Extent2I const &gridShape, ndarray::Array< double const, 2 > const &a, ndarray::Array< double const, 2 > const &b, ndarray::Array< double const, 2 > const &ap, ndarray::Array< double const, 2 > const &bp, bool useInverse=true)
 Construct from existing SIP coefficients. More...
 
 SipApproximation (SipApproximation const &)=delete
 
SipApproximationoperator= (SipApproximation const &)=delete
 
 SipApproximation (SipApproximation &&) noexcept=default
 
SipApproximationoperator= (SipApproximation &&) noexcept=default
 
 ~SipApproximation () noexcept
 
int getOrder () const noexcept
 Return the polynomial order of the current solution (same for forward and reverse). More...
 
double getA (int p, int q) const
 Return a coefficient of the forward transform polynomial. More...
 
double getB (int p, int q) const
 Return a coefficient of the forward transform polynomial. More...
 
double getAP (int p, int q) const
 Return a coefficient of the reverse transform polynomial. More...
 
double getBP (int p, int q) const
 Return a coefficient of the reverse transform polynomial. More...
 
Eigen::MatrixXd getA () const noexcept
 Return the coefficients of the forward transform polynomial. More...
 
Eigen::MatrixXd getB () const noexcept
 Return the coefficients of the forward transform polynomial. More...
 
Eigen::MatrixXd getAP () const noexcept
 Return the coefficients of the reverse transform polynomial. More...
 
Eigen::MatrixXd getBP () const noexcept
 Return the coefficients of the reverse transform polynomial. More...
 
lsst::geom::Point2D applyForward (lsst::geom::Point2D const &pix) const
 Convert a point from pixels to intermediate world coordinates. More...
 
std::vector< lsst::geom::Point2DapplyForward (std::vector< lsst::geom::Point2D > const &pix) const
 Convert an array of points from pixels to intermediate world coordinates. More...
 
lsst::geom::Point2D applyInverse (lsst::geom::Point2D const &iwcs) const
 Convert a point from intermediate world coordinates to pixels. More...
 
std::vector< lsst::geom::Point2DapplyInverse (std::vector< lsst::geom::Point2D > const &iwcs) const
 Convert an array of points from intermediate world coordinates to pixels. More...
 
lsst::geom::Extent2D getGridStep () const noexcept
 Return the distance between grid points in pixels. More...
 
lsst::geom::Extent2I getGridShape () const noexcept
 Return the number of grid points in x and y. More...
 
lsst::geom::Box2D getBBox () const noexcept
 Return the pixel-coordinate bounding box over which the approximation should be valid. More...
 
lsst::geom::Point2D getPixelOrigin () const noexcept
 Return the pixel origin of the WCS being approximated. More...
 
Eigen::Matrix2d getCdMatrix () const noexcept
 Return the CD matrix of the WCS being approximated. More...
 
void updateGrid (lsst::geom::Extent2I const &shape)
 Update the grid to the given number of points in x and y. More...
 
void refineGrid (int factor=2)
 Update the grid by making it finer by a given integer factor. More...
 
void fit (int order, double svdThreshold=-1)
 Obtain a new solution at the given order with the current grid. More...
 
std::pair< double, double > computeMaxDeviation () const noexcept
 Return the maximum deviation of the solution from the exact transform on the current grid. More...
 

Detailed Description

A fitter and results class for approximating a general Transform in a form compatible with FITS WCS persistence.

The Simple Imaging Polynomial (SIP) convention (Shupe et al 2005) adds forward and reverse polynomial mappings to a standard projection FITS WCS projection (e.g. "TAN" for gnomonic) that relate Intermediate World Coordinates (see Calabretta & Greisen 2002) to image pixel coordinates. The SIP "forward" transform is defined by polynomial coeffients \(A\) and \(B\) that map pixel coordinates \((u, v)\) to Intermediate World Coordinates \((x, y)\) via

\[ \boldsymbol{S}\left[\begin{array}{c} x \\ y \end{array}\right] \equiv \left[\begin{array}{c} x_s \\ y_s \end{array}\right] = \left[\begin{array}{c} (u - u_0) + \displaystyle\sum_{p,q}^{0 \le p + q \le N} \mathrm{A}_{p,q} (u - u_0)^p (v - v_0)^q \\ (v - v_0) + \displaystyle\sum_{p,q}^{0 \le p + q \le N} \mathrm{B}_{p,q} (u - u_0)^p (v - v_0)^q \end{array}\right] \]

The reverse transform has essentially the same form:

\[ \left[\begin{array}{c} u - u_0 \\ v - v_0 \end{array}\right] = \left[\begin{array}{c} x_s + \displaystyle\sum_{p,q}^{0 \le p + q \le N} \mathrm{AP}_{p,q} x_s^p y_s^q \\ y_s + \displaystyle\sum_{p,q}^{0 \le p + q \le N} \mathrm{BP}_{p,q} x_s^p y_s^q \end{array}\right] \]

In both cases, \((u_0, v_0)\) is the pixel origin (CRPIX in FITS WCS) and \(\boldsymbol{S}\) is the inverse of the Jacobian "CD" matrix. Both CRPIX and CD are considered fixed inputs, and we do not attempt to null the zeroth- and first-order terms of \(A\) and \(B\) (as some SIP fitters do); together, these conventions make solving for the coefficients a much simpler linear problem.

Note
In the implementation, we typically refer to \((u-u_0, v-v_0)\) as dpix (for "pixel delta"), and \((x_s, y_s)\) as siwc (for "scaled intermediate world coordinates").

While LSST WCSs are in general too complex to be described exactly in FITS WCS, they can generally be closely approximated by standard FITS WCS projection with additional SIP distortions. This class fits such an approximation, given a TransformPoint2ToPoint2 object that represents the exact mapping from pixels to Intermediate World Coordinates with a SIP distortion.

Definition at line 94 of file SipApproximation.h.

Constructor & Destructor Documentation

◆ SipApproximation() [1/4]

lsst::afw::geom::SipApproximation::SipApproximation ( std::shared_ptr< TransformPoint2ToPoint2 pixelToIwc,
lsst::geom::Point2D const &  crpix,
Eigen::Matrix2d const &  cd,
lsst::geom::Box2D const &  bbox,
lsst::geom::Extent2I const &  gridShape,
int  order,
bool  useInverse = true,
double  svdThreshold = -1 
)

Construct a new approximation by fitting on a grid of points.

Parameters
[in]pixelToIwcThe true Transform to approximate. Should go from pixels to Intermediate World Coordinates when applyForward is called.
[in]crpixPixel origin, using the LSST 0-indexed convention rather than the FITS 1-indexed convention; equal to (CRPIX1 - 1, CRPIX2 - 1).
[in]cdNominal Jacobian ("CD" in FITS WCS).
[in]bboxPixel-coordinate bounding box over which the approximation should be valid. Used to construct the grid of points to fit.
[in]gridShapeNumber of points in x and y for the grid of points.
[in]orderOrder of the polynomial (same for forward and reverse transforms).
[in]useInverseIf true, the inverse SIP transform will be fit and compared to data points generated by calls to pixelToIwc.applyInverse instead of pixelToIwc.applyForward.
[in]svdThresholdFraction of the largest singular value at which to declare smaller singular values zero in the least squares solution. Negative values use Eigen's internal default.
Exceptions
lsst::pex::exceptions::InvalidParameterErrorThrown if order is negative or gridShape is non-positive.
Exception Safety\n strong

Definition at line 210 of file SipApproximation.cc.

◆ SipApproximation() [2/4]

lsst::afw::geom::SipApproximation::SipApproximation ( std::shared_ptr< TransformPoint2ToPoint2 pixelToIwc,
lsst::geom::Point2D const &  crpix,
Eigen::Matrix2d const &  cd,
lsst::geom::Box2D const &  bbox,
lsst::geom::Extent2I const &  gridShape,
ndarray::Array< double const, 2 > const &  a,
ndarray::Array< double const, 2 > const &  b,
ndarray::Array< double const, 2 > const &  ap,
ndarray::Array< double const, 2 > const &  bp,
bool  useInverse = true 
)

Construct from existing SIP coefficients.

This constructor is primarily intended for testing purposes.

Parameters
[in]pixelToIwcThe true Transform to approximate. Should go from pixels to Intermediate World Coordinates when applyForward is called.
[in]crpixPixel origin, using the LSST 0-indexed convention rather than the FITS 1-indexed convention; equal to (CRPIX1 - 1, CRPIX - 1).
[in]cdNominal Jacobian ("CD" in FITS WCS).
[in]bboxPixel-coordinate bounding box over which the approximation should be valid. Used to construct the grid of points to fit.
[in]gridShapeNumber of points in x and y for the grid of points.
[in]aMatrix of A coefficients, with the first dimension corresponding to powers of \((u - u_0)\) and the second corresponding to powers of \((v - v_0)\).
[in]bMatrix of B coefficients, with the first dimension corresponding to powers of \((u - u_0)\) and the second corresponding to powers of \((v - v_0)\).
[in]apMatrix of AP coefficients, with the first dimension corresponding to powers of \(x_s\) and the second corresponding to powers of \(y_s\).
[in]bpMatrix of BP coefficients, with the first dimension corresponding to powers of \(x_s\) and the second corresponding to powers of \(y_s\).
[in]useInverseIf true, the inverse SIP transform will be compared to data points generated by calls to pixelToIwc.applyInverse instead of pixelToIwc.applyForward.
Exceptions
lsst::pex::exceptions::InvalidParameterErrorThrown if gridShape is non-positive, or any matrix argument is non-square.
Exception Safety\n strong

Definition at line 229 of file SipApproximation.cc.

◆ SipApproximation() [3/4]

lsst::afw::geom::SipApproximation::SipApproximation ( SipApproximation const &  )
delete

◆ SipApproximation() [4/4]

lsst::afw::geom::SipApproximation::SipApproximation ( SipApproximation &&  )
defaultnoexcept

◆ ~SipApproximation()

lsst::afw::geom::SipApproximation::~SipApproximation ( )
noexcept

Definition at line 257 of file SipApproximation.cc.

Member Function Documentation

◆ applyForward() [1/2]

lsst::geom::Point2D lsst::afw::geom::SipApproximation::applyForward ( lsst::geom::Point2D const &  pix) const

Convert a point from pixels to intermediate world coordinates.

This method is inefficient and should only be used for diagnostic purposes.

Exception Safety\n strong

Definition at line 322 of file SipApproximation.cc.

◆ applyForward() [2/2]

std::vector< lsst::geom::Point2D > lsst::afw::geom::SipApproximation::applyForward ( std::vector< lsst::geom::Point2D > const &  pix) const

Convert an array of points from pixels to intermediate world coordinates.

Exception Safety\n strong

Definition at line 328 of file SipApproximation.cc.

◆ applyInverse() [1/2]

lsst::geom::Point2D lsst::afw::geom::SipApproximation::applyInverse ( lsst::geom::Point2D const &  iwcs) const

Convert a point from intermediate world coordinates to pixels.

This method is inefficient and should only be used for diagnostic purposes.

Exception Safety\n strong

Definition at line 340 of file SipApproximation.cc.

◆ applyInverse() [2/2]

std::vector< lsst::geom::Point2D > lsst::afw::geom::SipApproximation::applyInverse ( std::vector< lsst::geom::Point2D > const &  iwcs) const

Convert an array of points from intermediate world coordinates to pixels.

Exception Safety\n strong

Definition at line 345 of file SipApproximation.cc.

◆ computeMaxDeviation()

std::pair< double, double > lsst::afw::geom::SipApproximation::computeMaxDeviation ( ) const
noexcept

Return the maximum deviation of the solution from the exact transform on the current grid.

The deviations are in scaled intermediate world coordinates \(\sqrt{\delta x_s^2 \delta y_s^2}\) for the forward transform and in pixels \((\delta u^2, \delta v^2)\) for the reverse transform (respectively). Note that in the common case where the CD matrix includes the scaling from angle units to pixel units, the scaled intermediate world coordinate values are also in (nominal) pixel units.

Definition at line 381 of file SipApproximation.cc.

◆ fit()

void lsst::afw::geom::SipApproximation::fit ( int  order,
double  svdThreshold = -1 
)

Obtain a new solution at the given order with the current grid.

Parameters
[in]orderPolynomial order to fit.
[in]svdThresholdFraction of the largest singular value at which to declare smaller singular values zero in the least squares solution. Negative values use Eigen's internal default.
Exceptions
pex::exceptions::LogicErrorThrown if the number of free parameters implied by order is larger than the number of data points defined by the grid.
Exception Safety\n strong

Definition at line 377 of file SipApproximation.cc.

◆ getA() [1/2]

Eigen::MatrixXd lsst::afw::geom::SipApproximation::getA ( ) const
noexcept

Return the coefficients of the forward transform polynomial.

Definition at line 294 of file SipApproximation.cc.

◆ getA() [2/2]

double lsst::afw::geom::SipApproximation::getA ( int  p,
int  q 
) const

Return a coefficient of the forward transform polynomial.

Out-of-bounds arguments yields undefined behavior.

Exception Safety\n strong

Definition at line 263 of file SipApproximation.cc.

◆ getAP() [1/2]

Eigen::MatrixXd lsst::afw::geom::SipApproximation::getAP ( ) const
noexcept

Return the coefficients of the reverse transform polynomial.

Definition at line 308 of file SipApproximation.cc.

◆ getAP() [2/2]

double lsst::afw::geom::SipApproximation::getAP ( int  p,
int  q 
) const

Return a coefficient of the reverse transform polynomial.

Out-of-bounds arguments yields undefined behavior.

Exception Safety\n strong

Definition at line 271 of file SipApproximation.cc.

◆ getB() [1/2]

Eigen::MatrixXd lsst::afw::geom::SipApproximation::getB ( ) const
noexcept

Return the coefficients of the forward transform polynomial.

Definition at line 301 of file SipApproximation.cc.

◆ getB() [2/2]

double lsst::afw::geom::SipApproximation::getB ( int  p,
int  q 
) const

Return a coefficient of the forward transform polynomial.

Out-of-bounds arguments yields undefined behavior.

Exception Safety\n strong

Definition at line 267 of file SipApproximation.cc.

◆ getBBox()

lsst::geom::Box2D lsst::afw::geom::SipApproximation::getBBox ( ) const
inlinenoexcept

Return the pixel-coordinate bounding box over which the approximation should be valid.

Definition at line 291 of file SipApproximation.h.

◆ getBP() [1/2]

Eigen::MatrixXd lsst::afw::geom::SipApproximation::getBP ( ) const
noexcept

Return the coefficients of the reverse transform polynomial.

Definition at line 315 of file SipApproximation.cc.

◆ getBP() [2/2]

double lsst::afw::geom::SipApproximation::getBP ( int  p,
int  q 
) const

Return a coefficient of the reverse transform polynomial.

Out-of-bounds arguments yields undefined behavior.

Exception Safety\n strong

Definition at line 275 of file SipApproximation.cc.

◆ getCdMatrix()

Eigen::Matrix2d lsst::afw::geom::SipApproximation::getCdMatrix ( ) const
inlinenoexcept

Return the CD matrix of the WCS being approximated.

Definition at line 297 of file SipApproximation.h.

◆ getGridShape()

lsst::geom::Extent2I lsst::afw::geom::SipApproximation::getGridShape ( ) const
noexcept

Return the number of grid points in x and y.

Definition at line 361 of file SipApproximation.cc.

◆ getGridStep()

lsst::geom::Extent2D lsst::afw::geom::SipApproximation::getGridStep ( ) const
noexcept

Return the distance between grid points in pixels.

Definition at line 356 of file SipApproximation.cc.

◆ getOrder()

int lsst::afw::geom::SipApproximation::getOrder ( ) const
noexcept

Return the polynomial order of the current solution (same for forward and reverse).

Definition at line 259 of file SipApproximation.cc.

◆ getPixelOrigin()

lsst::geom::Point2D lsst::afw::geom::SipApproximation::getPixelOrigin ( ) const
inlinenoexcept

Return the pixel origin of the WCS being approximated.

Definition at line 294 of file SipApproximation.h.

◆ operator=() [1/2]

SipApproximation& lsst::afw::geom::SipApproximation::operator= ( SipApproximation &&  )
defaultnoexcept

◆ operator=() [2/2]

SipApproximation& lsst::afw::geom::SipApproximation::operator= ( SipApproximation const &  )
delete

◆ refineGrid()

void lsst::afw::geom::SipApproximation::refineGrid ( int  factor = 2)

Update the grid by making it finer by a given integer factor.

Exceptions
lsst::pex::exceptions::InvalidParameterErrorThrown if factor is non-positive.
Exception Safety\n strong

Definition at line 369 of file SipApproximation.cc.

◆ updateGrid()

void lsst::afw::geom::SipApproximation::updateGrid ( lsst::geom::Extent2I const &  shape)

Update the grid to the given number of points in x and y.

This does not invalidate or modify the current solution; this allows the user to fit with a coarse grid and then check whether the solution still works well on a finer grid.

Exceptions
lsst::pex::exceptions::InvalidParameterErrorThrown if shape is non-positive.
Exception Safety\n strong

Definition at line 365 of file SipApproximation.cc.


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