lsst::jointcal::AstrometryTransformPolynomial Class Reference

Polynomial transformation class. More...

#include <AstrometryTransform.h>

Inheritance diagram for lsst::jointcal::AstrometryTransformPolynomial:

Public Member Functions
	AstrometryTransformPolynomial (std::size_t order=1)
	Default transform : identity for all orders (>=1 ). More...
	AstrometryTransformPolynomial (const AstrometryTransform *transform, const Frame &frame, std::size_t order, std::size_t nPoint=1000)
	Constructs a "polynomial image" from an existing transform, over a specified domain. More...
	AstrometryTransformPolynomial (std::shared_ptr< afw::geom::TransformPoint2ToPoint2 > transform, jointcal::Frame const &domain, std::size_t order, std::size_t nSteps=50)
	Constructs a polynomial approximation to an afw::geom::TransformPoint2ToPoint2. More...
void	setOrder (std::size_t order)
	Sets the polynomial order (the highest sum of exponents of the largest monomial). More...
std::size_t	getOrder () const
	Returns the polynomial order. More...
void	apply (const double xIn, const double yIn, double &xOut, double &yOut) const override
void	computeDerivative (Point const &where, AstrometryTransformLinear &derivative, const double step=0.01) const override
	specialised analytic routine More...
virtual void	transformPosAndErrors (const FatPoint &in, FatPoint &out) const override
	a mix of apply and Derivative More...
std::size_t	getNpar () const override
	total number of parameters More...
void	dump (std::ostream &stream=std::cout) const override
	print out of coefficients in a readable form. More...
double	fit (StarMatchList const &starMatchList) override
	guess what More...
AstrometryTransformPolynomial	operator* (AstrometryTransformPolynomial const &right) const
	Composition (internal stuff in quadruple precision) More...
AstrometryTransformPolynomial	operator+ (AstrometryTransformPolynomial const &right) const
	Addition. More...
AstrometryTransformPolynomial	operator- (AstrometryTransformPolynomial const &right) const
	Subtraction. More...
std::unique_ptr< AstrometryTransform >	composeAndReduce (AstrometryTransformPolynomial const &right) const
	Return a reduced composition of newTransform = this(right()), or nullptr if it cannot be reduced. More...
std::unique_ptr< AstrometryTransform >	clone () const override
	returns a copy (allocated by new) of the transformation. More...
double	coeff (std::size_t powX, std::size_t powY, std::size_t whichCoord) const
	access to coefficients (read only) More...
double &	coeff (std::size_t powX, std::size_t powY, std::size_t whichCoord)
	write access More...
double	coeffOrZero (std::size_t powX, std::size_t powY, std::size_t whichCoord) const
	read access, zero if beyond order More...
double	determinant () const
double	paramRef (Eigen::Index const i) const override
double &	paramRef (Eigen::Index const i) override
void	paramDerivatives (Point const &where, double *dx, double *dy) const override
	Derivative w.r.t parameters. More...
std::shared_ptr< ast::Mapping >	toAstMap (jointcal::Frame const &domain) const override
	Create an equivalent AST mapping for this transformation, including an analytic inverse if possible. More...
void	write (std::ostream &s) const override
void	read (std::istream &s)
void	apply (Point const &in, Point &out) const
	applies the tranfo to in and writes into out. Is indeed virtual. More...
Point	apply (Point const &in) const
	All these apply(..) shadow the virtual one in derived classes, unless one writes "using AstrometryTransform::apply". More...
Frame	apply (Frame const &inputframe, bool inscribed) const
	Transform a bounding box, taking either the inscribed or circumscribed box. More...
std::string	__str__ ()
void	transformStar (FatPoint &in) const
virtual double	getJacobian (Point const &point) const
	returns the local jacobian. More...
virtual double	getJacobian (const double x, const double y) const
	returns the local jacobian. More...
virtual std::unique_ptr< AstrometryTransform >	composeAndReduce (AstrometryTransform const &right) const
	Return a reduced composition of newTransform = this(right()), or nullptr if it cannot be reduced. More...
virtual AstrometryTransformLinear	linearApproximation (Point const &where, const double step=0.01) const
	linear (local) approximation. More...
virtual void	transformErrors (Point const &where, const double *vIn, double *vOut) const
	transform errors (represented as double[3] in order V(xx),V(yy),Cov(xy)) More...
virtual std::unique_ptr< AstrometryTransform >	inverseTransform (const double precision, const Frame &region) const
	returns an inverse transform. Numerical if not overloaded. More...
void	getParams (double *params) const
	params should be at least Npar() long More...
void	offsetParams (Eigen::VectorXd const &delta)
virtual std::unique_ptr< AstrometryTransform >	roughInverse (const Frame &region) const
	Rough inverse. More...
void	write (const std::string &fileName) const

Detailed Description

Polynomial transformation class.

Definition at line 281 of file AstrometryTransform.h.

Constructor & Destructor Documentation

AstrometryTransformPolynomial() [1/3]

lsst::jointcal::AstrometryTransformPolynomial::AstrometryTransformPolynomial

(

std::size_t

order = 1

)

Default transform : identity for all orders (>=1 ).

Default transform : identity for all orders (>=1 )

Parameters

order

The highest total power (x+y) of monomials of this polynomial.

Definition at line 468 of file AstrometryTransform.cc.

                                                                            : _order(order) {
    _nterms = (order + 1) * (order + 2) / 2;

    // allocate and fill coefficients
    _coeffs.resize(2 * _nterms, 0.);
    // the default is supposed to be the identity, (for order>=1).
    if (_order >= 1) {
        coeff(1, 0, 0) = 1;
        coeff(0, 1, 1) = 1;
    }
}

AstrometryTransformPolynomial() [2/3]

lsst::jointcal::AstrometryTransformPolynomial::AstrometryTransformPolynomial	(	const AstrometryTransform *	transform,
		const Frame &	frame,
		std::size_t	order,
		std::size_t	nPoint = 1000
	)

Constructs a "polynomial image" from an existing transform, over a specified domain.

Definition at line 481 of file AstrometryTransform.cc.

                                                                               {
    StarMatchList sm;

    double step = std::sqrt(fabs(frame.getArea()) / double(nPoint));
    for (double x = frame.xMin + step / 2; x <= frame.xMax; x += step)
        for (double y = frame.yMin + step / 2; y <= frame.yMax; y += step) {
            auto pix = std::make_shared<BaseStar>(x, y, 0, 0);
            double xtr, ytr;
            transform->apply(x, y, xtr, ytr);
            auto tp = std::make_shared<BaseStar>(xtr, ytr, 0, 0);
            /* These are fake stars so no need to transform fake errors.
               all errors (and weights) will be equal : */
            sm.push_back(StarMatch(*pix, *tp, pix, tp));
        }
    AstrometryTransformPolynomial ret(order);
    ret.fit(sm);
    *this = ret;
}

AstrometryTransformPolynomial() [3/3]

lsst::jointcal::AstrometryTransformPolynomial::AstrometryTransformPolynomial	(	std::shared_ptr< afw::geom::TransformPoint2ToPoint2 >	transform,
		jointcal::Frame const &	domain,
		std::size_t	order,
		std::size_t	nSteps = 50
	)

Constructs a polynomial approximation to an afw::geom::TransformPoint2ToPoint2.

Parameters

[in]	transform	The transform to be approximated.
[in]	domain	The valid domain of the transform.
[in]	order	The polynomial order to use when approximating.
[in]	nSteps	The number of sample points per axis (nSteps^2 total points).

Definition at line 503 of file AstrometryTransform.cc.

                                           {
    jointcal::StarMatchList starMatchList;
    double xStart = domain.xMin;
    double yStart = domain.yMin;
    double xStep = domain.getWidth() / (nSteps + 1);
    double yStep = domain.getHeight() / (nSteps + 1);
    for (std::size_t i = 0; i < nSteps; ++i) {
        for (std::size_t j = 0; j < nSteps; ++j) {
            // TODO: once DM-4044 is done, we can remove the redundancy in `Point`/`Point2D` here
            jointcal::Point in(xStart + i * xStep, yStart + j * yStep);
            geom::Point2D inAfw(in.x, in.y);
            geom::Point2D outAfw = transform->applyForward(inAfw);
            jointcal::Point out(outAfw.getX(), outAfw.getY());
            starMatchList.emplace_back(in, out, nullptr, nullptr);
        }
    }
    AstrometryTransformPolynomial poly(order);
    poly.fit(starMatchList);
    *this = poly;
}

Member Function Documentation

__str__()

std::string lsst::jointcal::AstrometryTransform::__str__ ( )

inlineinherited

Definition at line 94 of file AstrometryTransform.h.

                        {
        std::stringstream s;
        dump(s);
        return s.str();
    }

apply() [1/4]

void lsst::jointcal::AstrometryTransform::apply ( Point const &  in, Point &  out  ) const

inlineinherited

applies the tranfo to in and writes into out. Is indeed virtual.

Definition at line 71 of file AstrometryTransform.h.

{ apply(in.x, in.y, out.x, out.y); }

apply() [2/4]

Point lsst::jointcal::AstrometryTransform::apply ( Point const &  in ) const

inlineinherited

All these apply(..) shadow the virtual one in derived classes, unless one writes "using AstrometryTransform::apply".

Definition at line 75 of file AstrometryTransform.h.

                                       {
        double xout, yout;
        apply(in.x, in.y, xout, yout);
        return Point(xout, yout);
    }

apply() [3/4]

Frame lsst::jointcal::AstrometryTransform::apply ( Frame const &  inputframe, bool  inscribed  ) const

inherited

Transform a bounding box, taking either the inscribed or circumscribed box.

Parameters

[in]	inputframe	The frame to be transformed.
[in]	inscribed	Return the inscribed (true) or circumscribed (false) box.

Returns

The transformed frame.

Definition at line 75 of file AstrometryTransform.cc.

                                                                              {
    // 2 opposite corners
    double xtmin1, xtmax1, ytmin1, ytmax1;
    apply(inputframe.xMin, inputframe.yMin, xtmin1, ytmin1);
    apply(inputframe.xMax, inputframe.yMax, xtmax1, ytmax1);
    Frame fr1(std::min(xtmin1, xtmax1), std::min(ytmin1, ytmax1), std::max(xtmin1, xtmax1),
              std::max(ytmin1, ytmax1));
    // 2 other corners
    double xtmin2, xtmax2, ytmin2, ytmax2;
    apply(inputframe.xMin, inputframe.yMax, xtmin2, ytmax2);
    apply(inputframe.xMax, inputframe.yMin, xtmax2, ytmin2);
    Frame fr2(std::min(xtmin2, xtmax2), std::min(ytmin2, ytmax2), std::max(xtmin2, xtmax2),
              std::max(ytmin2, ytmax2));

    if (inscribed) return fr1 * fr2;
    return fr1 + fr2;
}

apply() [4/4]

void lsst::jointcal::AstrometryTransformPolynomial::apply ( const double  xIn, const double  yIn, double &  xOut, double &  yOut  ) const

overridevirtual

Implements lsst::jointcal::AstrometryTransform.

Definition at line 570 of file AstrometryTransform.cc.

                                                              {
    /*
      This routine computes the monomials only once for both
      polynomials.  This is why AstrometryTransformPolynomial does not use an auxilary
      class (such as PolyXY) to handle each polynomial.

      The code works even if &xIn == &xOut (or &yIn == &yOut)
      It uses Variable Length Allocation (VLA) rather than a vector<double>
      because allocating the later costs about 50 ns. All VLA uses are tagged.
    */
    double monomials[_nterms];  // this is VLA, which is (perhaps) not casher C++
    computeMonomials(xIn, yIn, monomials);

    xOut = 0;
    yOut = 0;
    const double *c = &_coeffs[0];
    const double *pm = &monomials[0];
    // the ordering of the coefficients and the monomials are identical.
    for (int k = _nterms; k--;) xOut += (*(pm++)) * (*(c++));
    pm = &monomials[0];
    for (int k = _nterms; k--;) yOut += (*(pm++)) * (*(c++));
}

clone()

std::unique_ptr<AstrometryTransform> lsst::jointcal::AstrometryTransformPolynomial::clone ( ) const

inlineoverridevirtual

returns a copy (allocated by new) of the transformation.

Implements lsst::jointcal::AstrometryTransform.

Reimplemented in lsst::jointcal::AstrometryTransformLinear.

Definition at line 346 of file AstrometryTransform.h.

                                                              {
        return std::unique_ptr<AstrometryTransform>(new AstrometryTransformPolynomial(*this));
    }

coeff() [1/2]

double lsst::jointcal::AstrometryTransformPolynomial::coeff	(	std::size_t	powX,
		std::size_t	powY,
		std::size_t	whichCoord
	)		const

access to coefficients (read only)

Definition at line 738 of file AstrometryTransform.cc.

                                                                        {
    assert((degX + degY <= _order) && whichCoord < 2);
    /* this assertion above is enough to ensure that the index used just
       below is within bounds since the reserved length is
       2*_nterms=(order+1)*(order+2) */
    return _coeffs[(degX + degY) * (degX + degY + 1) / 2 + degY + whichCoord * _nterms];
}

coeff() [2/2]

double & lsst::jointcal::AstrometryTransformPolynomial::coeff	(	std::size_t	powX,
		std::size_t	powY,
		std::size_t	whichCoord
	)

write access

Definition at line 747 of file AstrometryTransform.cc.

                                                                   {
    assert((degX + degY <= _order) && whichCoord < 2);
    return _coeffs[(degX + degY) * (degX + degY + 1) / 2 + degY + whichCoord * _nterms];
}

coeffOrZero()

double lsst::jointcal::AstrometryTransformPolynomial::coeffOrZero	(	std::size_t	powX,
		std::size_t	powY,
		std::size_t	whichCoord
	)		const

read access, zero if beyond order

Definition at line 753 of file AstrometryTransform.cc.

                                                                              {
    //  assert((degX+degY<=order) && whichCoord<2);
    assert(whichCoord < 2);
    if (degX + degY <= _order)
        return _coeffs[(degX + degY) * (degX + degY + 1) / 2 + degY + whichCoord * _nterms];
    return 0;
}

composeAndReduce() [1/2]

std::unique_ptr< AstrometryTransform > lsst::jointcal::AstrometryTransform::composeAndReduce ( AstrometryTransform const &  right ) const

virtualinherited

Return a reduced composition of newTransform = this(right()), or nullptr if it cannot be reduced.

"Reduced" in this context means that they are capable of being merged into a single transform, for example, for two polynomials:

\[ f(x) = 1 + x^2, g(x) = -1 + 3x \]

we would have h = f.composeAndReduce(g) == 2 - 6x + 9x^2.

To be overloaded by derived classes if they can properly reduce the composition.

Parameters

right

The transform to apply first.

Returns

The new reduced and composed AstrometryTransform, or nullptr if no such reduction is possible.

Reimplemented in lsst::jointcal::AstrometryTransformIdentity.

Definition at line 93 of file AstrometryTransform.cc.

                                           {  // by default no way to compose
    return std::unique_ptr<AstrometryTransform>(nullptr);
}

composeAndReduce() [2/2]

std::unique_ptr< AstrometryTransform > lsst::jointcal::AstrometryTransformPolynomial::composeAndReduce

(

AstrometryTransformPolynomial const &

right

)

const

Return a reduced composition of newTransform = this(right()), or nullptr if it cannot be reduced.

"Reduced" in this context means that they are capable of being merged into a single transform, for example, for two polynomials:

\[ f(x) = 1 + x^2, g(x) = -1 + 3x \]

we would have h = f.composeAndReduce(g) == 2 - 6x + 9x^2.

To be overloaded by derived classes if they can properly reduce the composition.

Parameters

right

The transform to apply first.

Returns

The new reduced and composed AstrometryTransform, or nullptr if no such reduction is possible.

Definition at line 930 of file AstrometryTransform.cc.

                                                          {
    if (getOrder() == 1 && right.getOrder() == 1)
        return std::make_unique<AstrometryTransformLinear>((*this) * (right));  // does the composition
    else
        return std::make_unique<AstrometryTransformPolynomial>((*this) * (right));  // does the composition
}

computeDerivative()

void lsst::jointcal::AstrometryTransformPolynomial::computeDerivative ( Point const &  where, AstrometryTransformLinear &  derivative, const double  step = 0.01  ) const

overridevirtual

specialised analytic routine

Reimplemented from lsst::jointcal::AstrometryTransform.

Reimplemented in lsst::jointcal::AstrometryTransformLinear.

Definition at line 594 of file AstrometryTransform.cc.

              { /* routine checked against numerical derivatives from AstrometryTransform::Derivative */
    if (_order == 1) {
        derivative = AstrometryTransformLinear(*this);
        derivative.dx() = derivative.dy() = 0;
        return;
    }

    double dermx[2 * _nterms];  // VLA
    double *dermy = dermx + _nterms;
    double xin = where.x;
    double yin = where.y;

    double xx = 1;
    double xxm1 = 1;  // xx^(ix-1)
    for (std::size_t ix = 0; ix <= _order; ++ix) {
        std::size_t k = (ix) * (ix + 1) / 2;
        // iy = 0
        dermx[k] = ix * xxm1;
        dermy[k] = 0;
        k += ix + 2;
        double yym1 = 1;  // yy^(iy-1)
        for (std::size_t iy = 1; iy <= _order - ix; ++iy) {
            dermx[k] = ix * xxm1 * yym1 * yin;
            dermy[k] = iy * xx * yym1;
            yym1 *= yin;
            k += ix + iy + 2;
        }
        xx *= xin;
        if (ix >= 1) xxm1 *= xin;
    }

    derivative.dx() = 0;
    derivative.dy() = 0;

    const double *mx = &dermx[0];
    const double *my = &dermy[0];
    const double *c = &_coeffs[0];
    // dx'
    double a11 = 0, a12 = 0;
    for (int k = _nterms; k--;) {
        a11 += (*(mx++)) * (*c);
        a12 += (*(my++)) * (*(c++));
    }
    derivative.a11() = a11;
    derivative.a12() = a12;
    // dy'
    double a21 = 0, a22 = 0;
    mx = &dermx[0];
    my = &dermy[0];
    for (int k = _nterms; k--;) {
        a21 += (*(mx++)) * (*c);
        a22 += (*(my++)) * (*(c++));
    }
    derivative.a21() = a21;
    derivative.a22() = a22;
}

determinant()

double lsst::jointcal::AstrometryTransformPolynomial::determinant

(

)

const

Definition at line 812 of file AstrometryTransform.cc.

                                                        {
    if (_order >= 1) return coeff(1, 0, 0) * coeff(0, 1, 1) - coeff(0, 1, 0) * coeff(1, 0, 1);
    return 0;
}

dump()

void lsst::jointcal::AstrometryTransformPolynomial::dump ( std::ostream &  stream = std::cout ) const

overridevirtual

print out of coefficients in a readable form.

Implements lsst::jointcal::AstrometryTransform.

Definition at line 793 of file AstrometryTransform.cc.

                                                              {
    auto oldPrecision = stream.precision();
    stream.precision(12);
    for (std::size_t ic = 0; ic < 2; ++ic) {
        if (ic == 0)
            stream << "newx = ";
        else
            stream << "newy = ";
        for (std::size_t p = 0; p <= _order; ++p)
            for (std::size_t py = 0; py <= p; ++py) {
                if (p + py != 0) stream << " + ";
                stream << coeff(p - py, py, ic) << monomialString(p - py, py);
            }
        stream << endl;
    }
    if (_order > 0) stream << " Linear determinant = " << determinant() << endl;
    stream.precision(oldPrecision);
}

fit()

double lsst::jointcal::AstrometryTransformPolynomial::fit ( StarMatchList const &  starMatchList )

overridevirtual

guess what

Implements lsst::jointcal::AstrometryTransform.

Reimplemented in lsst::jointcal::AstrometryTransformLinearRot, and lsst::jointcal::AstrometryTransformLinearShift.

Definition at line 912 of file AstrometryTransform.cc.

                                                                            {
    if (starMatchList.size() < _nterms) {
        LOGLS_FATAL(_log, "AstrometryTransformPolynomial::fit trying to fit a polynomial transform of order "
                                  << _order << " with only " << starMatchList.size() << " matches.");
        return -1;
    }

    AstrometryTransformPolynomial conditionner = shiftAndNormalize(starMatchList);

    computeFit(starMatchList, conditionner, false);               // get a rough solution
    computeFit(starMatchList, conditionner, true);                // weight with it
    double chi2 = computeFit(starMatchList, conditionner, true);  // once more

    (*this) = (*this) * conditionner;
    if (starMatchList.size() == _nterms) return 0;
    return chi2;
}

getJacobian() [1/2]

virtual double lsst::jointcal::AstrometryTransform::getJacobian ( Point const &  point ) const

inlinevirtualinherited

returns the local jacobian.

Definition at line 110 of file AstrometryTransform.h.

{ return getJacobian(point.x, point.y); }

getJacobian() [2/2]

double lsst::jointcal::AstrometryTransform::getJacobian ( const double  x, const double  y  ) const

virtualinherited

returns the local jacobian.

Definition at line 98 of file AstrometryTransform.cc.

                                                                            {
    double x2, y2;
    double eps = x * 0.01;
    if (eps == 0) eps = 0.01;
    apply(x, y, x2, y2);
    double dxdx, dydx;
    apply(x + eps, y, dxdx, dydx);
    dxdx -= x2;
    dydx -= y2;
    double dxdy, dydy;
    apply(x, y + eps, dxdy, dydy);
    dxdy -= x2;
    dydy -= y2;
    return ((dxdx * dydy - dxdy * dydx) / (eps * eps));
}

getNpar()

std::size_t lsst::jointcal::AstrometryTransformPolynomial::getNpar ( ) const

inlineoverridevirtual

total number of parameters

Reimplemented from lsst::jointcal::AstrometryTransform.

Reimplemented in lsst::jointcal::AstrometryTransformLinearScale, lsst::jointcal::AstrometryTransformLinearRot, and lsst::jointcal::AstrometryTransformLinearShift.

Definition at line 323 of file AstrometryTransform.h.

{ return 2 * _nterms; }

getOrder()

std::size_t lsst::jointcal::AstrometryTransformPolynomial::getOrder ( ) const

inline

Returns the polynomial order.

Definition at line 309 of file AstrometryTransform.h.

{ return _order; }

getParams()

void lsst::jointcal::AstrometryTransform::getParams ( double *  params ) const

inherited

params should be at least Npar() long

Definition at line 215 of file AstrometryTransform.cc.

                                                        {
    std::size_t npar = getNpar();
    for (std::size_t i = 0; i < npar; ++i) params[i] = paramRef(i);
}

inverseTransform()

std::unique_ptr< AstrometryTransform > lsst::jointcal::AstrometryTransform::inverseTransform ( const double  precision, const Frame &  region  ) const

virtualinherited

returns an inverse transform. Numerical if not overloaded.

precision and region refer to the "input" side of this, and hence to the output side of the returned AstrometryTransform.

Reimplemented in lsst::jointcal::TanRaDecToPixel, lsst::jointcal::TanSipPixelToRaDec, lsst::jointcal::TanPixelToRaDec, lsst::jointcal::AstrometryTransformLinear, and lsst::jointcal::AstrometryTransformInverse.

Definition at line 302 of file AstrometryTransform.cc.

                                                                                                      {
    return std::unique_ptr<AstrometryTransform>(new AstrometryTransformInverse(this, precision, region));
}

linearApproximation()

AstrometryTransformLinear lsst::jointcal::AstrometryTransform::linearApproximation ( Point const &  where, const double  step = 0.01  ) const

virtualinherited

linear (local) approximation.

Reimplemented in lsst::jointcal::AstrometryTransformLinear, and lsst::jointcal::AstrometryTransformIdentity.

Definition at line 135 of file AstrometryTransform.cc.

                                                                                            {
    Point outwhere = apply(where);
    AstrometryTransformLinear der;
    computeDerivative(where, der, step);
    return AstrometryTransformLinearShift(outwhere.x, outwhere.y) * der *
           AstrometryTransformLinearShift(-where.x, -where.y);
}

offsetParams()

void lsst::jointcal::AstrometryTransform::offsetParams ( Eigen::VectorXd const &  delta )

inherited

Definition at line 220 of file AstrometryTransform.cc.

                                                                 {
    std::size_t npar = getNpar();
    for (std::size_t i = 0; i < npar; ++i) paramRef(i) += delta[i];
}

operator*()

AstrometryTransformPolynomial lsst::jointcal::AstrometryTransformPolynomial::operator*

(

AstrometryTransformPolynomial const &

right

)

const

Composition (internal stuff in quadruple precision)

Definition at line 1035 of file AstrometryTransform.cc.

                                                          {
    // split each transform into 2d polynomials
    PolyXY plx(*this, 0);
    PolyXY ply(*this, 1);
    PolyXY prx(right, 0);
    PolyXY pry(right, 1);

    // compute the compositions
    PolyXY rx(composition(plx, prx, pry));
    PolyXY ry(composition(ply, prx, pry));

    // copy the results the hard way.
    AstrometryTransformPolynomial result(_order * right._order);
    for (std::size_t px = 0; px <= result._order; ++px)
        for (std::size_t py = 0; py <= result._order - px; ++py) {
            result.coeff(px, py, 0) = rx.coeff(px, py);
            result.coeff(px, py, 1) = ry.coeff(px, py);
        }
    return result;
}

operator+()

AstrometryTransformPolynomial lsst::jointcal::AstrometryTransformPolynomial::operator+

(

AstrometryTransformPolynomial const &

right

)

const

Addition.

Definition at line 1057 of file AstrometryTransform.cc.

                                                          {
    if (_order >= right._order) {
        AstrometryTransformPolynomial res(*this);
        for (std::size_t i = 0; i <= right._order; ++i)
            for (std::size_t j = 0; j <= right._order - i; ++j) {
                res.coeff(i, j, 0) += right.coeff(i, j, 0);
                res.coeff(i, j, 1) += right.coeff(i, j, 1);
            }
        return res;
    } else
        return (right + (*this));
}

operator-()

AstrometryTransformPolynomial lsst::jointcal::AstrometryTransformPolynomial::operator-

(

AstrometryTransformPolynomial const &

right

)

const

Subtraction.

Definition at line 1071 of file AstrometryTransform.cc.

                                                          {
    AstrometryTransformPolynomial res(std::max(_order, right._order));
    for (std::size_t i = 0; i <= res._order; ++i)
        for (std::size_t j = 0; j <= res._order - i; ++j) {
            res.coeff(i, j, 0) = coeffOrZero(i, j, 0) - right.coeffOrZero(i, j, 0);
            res.coeff(i, j, 1) = coeffOrZero(i, j, 1) - right.coeffOrZero(i, j, 1);
        }
    return res;
}

paramDerivatives()

void lsst::jointcal::AstrometryTransformPolynomial::paramDerivatives ( Point const &  where, double *  dx, double *  dy  ) const

overridevirtual

Derivative w.r.t parameters.

Derivatives should be al least 2*NPar long. first Npar, for x, last Npar for y.

Reimplemented from lsst::jointcal::AstrometryTransform.

Definition at line 773 of file AstrometryTransform.cc.

              { /* first half : dxout/dpar, second half : dyout/dpar */
    computeMonomials(where.x, where.y, dx);
    for (std::size_t k = 0; k < _nterms; ++k) {
        dy[_nterms + k] = dx[k];
        dx[_nterms + k] = dy[k] = 0;
    }
}

paramRef() [1/2]

double lsst::jointcal::AstrometryTransformPolynomial::paramRef ( Eigen::Index const  i ) const

overridevirtual

Reimplemented from lsst::jointcal::AstrometryTransform.

Definition at line 763 of file AstrometryTransform.cc.

                                                                       {
    assert(i < 2 * Eigen::Index(_nterms));
    return _coeffs[i];
}

paramRef() [2/2]

double & lsst::jointcal::AstrometryTransformPolynomial::paramRef ( Eigen::Index const  i )

overridevirtual

Reimplemented from lsst::jointcal::AstrometryTransform.

Definition at line 768 of file AstrometryTransform.cc.

                                                                  {
    assert(i < 2 * Eigen::Index(_nterms));
    return _coeffs[i];
}

read()

void lsst::jointcal::AstrometryTransformPolynomial::read

(

std::istream &

s

)

Definition at line 1097 of file AstrometryTransform.cc.

                                                   {
    int format;
    s >> format;
    if (format != 1)
        throw LSST_EXCEPT(pex::exceptions::InvalidParameterError,
                          " AstrometryTransformPolynomial::read : format is not 1 ");

    string order;
    s >> order >> _order;
    if (order != "order")
        throw LSST_EXCEPT(pex::exceptions::InvalidParameterError,
                          " AstrometryTransformPolynomial::read : expecting \"order\" and found " + order);
    setOrder(_order);
    for (std::size_t k = 0; k < 2 * _nterms; ++k) s >> _coeffs[k];
}

roughInverse()

std::unique_ptr< AstrometryTransform > lsst::jointcal::AstrometryTransform::roughInverse ( const Frame &  region ) const

virtualinherited

Rough inverse.

Stored by the numerical inverter to guess starting point for the trials. Just here to enable overloading.

Reimplemented in lsst::jointcal::TanRaDecToPixel, lsst::jointcal::TanPixelToRaDec, and lsst::jointcal::AstrometryTransformInverse.

Definition at line 194 of file AstrometryTransform.cc.

                                                                                              {
    // "in" and "out" refer to the inverse direction.
    Point centerOut = region.getCenter();
    Point centerIn = apply(centerOut);
    AstrometryTransformLinear der;
    computeDerivative(centerOut, der, std::sqrt(region.getArea()) / 5.);
    der = der.inverted();
    der = AstrometryTransformLinearShift(centerOut.x, centerOut.y) * der *
          AstrometryTransformLinearShift(-centerIn.x, -centerIn.y);
    return std::unique_ptr<AstrometryTransform>(new AstrometryTransformLinear(der));
}

setOrder()

void lsst::jointcal::AstrometryTransformPolynomial::setOrder

(

std::size_t

order

)

Sets the polynomial order (the highest sum of exponents of the largest monomial).

Definition at line 549 of file AstrometryTransform.cc.

                                                            {
    _order = order;
    std::size_t old_nterms = _nterms;
    _nterms = (_order + 1) * (_order + 2) / 2;

    // temporarily save coefficients
    vector<double> old_coeffs = _coeffs;
    // reallocate enough size
    _coeffs.resize(2 * _nterms);
    // reassign to zero (this is necessary because ycoeffs
    // are after xcoeffs and so their meaning changes
    for (std::size_t k = 0; k < _nterms; ++k) _coeffs[k] = 0;
    // put back what we had before
    std::size_t kmax = min(old_nterms, _nterms);
    for (std::size_t k = 0; k < kmax; ++k) {
        _coeffs[k] = old_coeffs[k];                         // x terms
        _coeffs[k + _nterms] = old_coeffs[k + old_nterms];  // y terms
    }
}

toAstMap()

std::shared_ptr< ast::Mapping > lsst::jointcal::AstrometryTransformPolynomial::toAstMap ( jointcal::Frame const &  domain ) const

overridevirtual

Create an equivalent AST mapping for this transformation, including an analytic inverse if possible.

Parameters

domain

The domain of the transform, to help find an inverse.

Returns

An AST Mapping that represents this transformation.

Reimplemented from lsst::jointcal::AstrometryTransform.

Definition at line 1082 of file AstrometryTransform.cc.

                                                                                                   {
    auto inverse = inversePolyTransform(*this, domain, 1e-7, _order + 2, 100);
    return std::make_shared<ast::PolyMap>(toAstPolyMapCoefficients(), inverse->toAstPolyMapCoefficients());
}

transformErrors()

void lsst::jointcal::AstrometryTransform::transformErrors ( Point const &  where, const double *  vIn, double *  vOut  ) const

virtualinherited

transform errors (represented as double[3] in order V(xx),V(yy),Cov(xy))

Definition at line 161 of file AstrometryTransform.cc.

                                                                                                   {
    AstrometryTransformLinear der;
    computeDerivative(where, der, 0.01);
    double a11 = der.A11();
    double a22 = der.A22();
    double a21 = der.A21();
    double a12 = der.A12();

    /*      (a11 a12)          (vxx  vxy)
       M =  (       )  and V = (        )
            (a21 a22)          (xvy  vyy)

       Vxx = Vin[0], vyy = Vin[1], Vxy = Vin[2];
       we want to compute M*V*tp(M)
       A lin alg light package would be perfect...
    */
    int xx = 0;
    int yy = 1;
    int xy = 2;
    // M*V :

    double b11 = a11 * vIn[xx] + a12 * vIn[xy];
    double b22 = a21 * vIn[xy] + a22 * vIn[yy];
    double b12 = a11 * vIn[xy] + a12 * vIn[yy];
    double b21 = a21 * vIn[xx] + a22 * vIn[xy];

    // (M*V) * tp(M)

    vOut[xx] = b11 * a11 + b12 * a12;
    vOut[xy] = b11 * a21 + b12 * a22;
    vOut[yy] = b21 * a21 + b22 * a22;
}

transformPosAndErrors()

void lsst::jointcal::AstrometryTransformPolynomial::transformPosAndErrors ( const FatPoint &  in, FatPoint &  out  ) const

overridevirtual

a mix of apply and Derivative

Reimplemented from lsst::jointcal::AstrometryTransform.

Definition at line 654 of file AstrometryTransform.cc.

                                                                                                 {
    /*
       The results from this routine were compared to what comes out
       from apply and transformErrors. The Derivative routine was
       checked against numerical derivatives from
       AstrometryTransform::Derivative. (P.A dec 2009).

       This routine could be made much simpler by calling apply and
       Derivative (i.e. you just suppress it, and the fallback is the
       generic version in AstrometryTransform).  BTW, I checked that both routines
       provide the same result. This version is however faster
       (monomials get recycled).
    */
    double monomials[_nterms];  // VLA

    FatPoint res;  // to store the result, because nothing forbids &in == &out.

    double dermx[2 * _nterms];        // monomials for derivative w.r.t. x (VLA)
    double *dermy = dermx + _nterms;  // same for y
    double xin = in.x;
    double yin = in.y;

    double xx = 1;
    double xxm1 = 1;  // xx^(ix-1)
    for (std::size_t ix = 0; ix <= _order; ++ix) {
        std::size_t k = (ix) * (ix + 1) / 2;
        // iy = 0
        dermx[k] = ix * xxm1;
        dermy[k] = 0;
        monomials[k] = xx;
        k += ix + 2;
        double yy = yin;
        double yym1 = 1;  // yy^(iy-1)
        for (std::size_t iy = 1; iy <= _order - ix; ++iy) {
            monomials[k] = xx * yy;
            dermx[k] = ix * xxm1 * yy;
            dermy[k] = iy * xx * yym1;
            yym1 *= yin;
            yy *= yin;
            k += ix + iy + 2;
        }
        xx *= xin;
        if (ix >= 1) xxm1 *= xin;
    }

    // output position
    double xout = 0, yout = 0;
    const double *c = &_coeffs[0];
    const double *pm = &monomials[0];
    for (int k = _nterms; k--;) xout += (*(pm++)) * (*(c++));
    pm = &monomials[0];
    for (int k = _nterms; k--;) yout += (*(pm++)) * (*(c++));
    res.x = xout;
    res.y = yout;

    // derivatives
    c = &_coeffs[0];
    const double *mx = &dermx[0];
    const double *my = &dermy[0];
    double a11 = 0, a12 = 0;
    for (int k = _nterms; k--;) {
        a11 += (*(mx++)) * (*c);
        a12 += (*(my++)) * (*(c++));
    }

    double a21 = 0, a22 = 0;
    mx = &dermx[0];
    my = &dermy[0];
    for (int k = _nterms; k--;) {
        a21 += (*(mx++)) * (*c);
        a22 += (*(my++)) * (*(c++));
    }

    // output co-variance
    res.vx = a11 * (a11 * in.vx + 2 * a12 * in.vxy) + a12 * a12 * in.vy;
    res.vy = a21 * a21 * in.vx + a22 * a22 * in.vy + 2. * a21 * a22 * in.vxy;
    res.vxy = a21 * a11 * in.vx + a22 * a12 * in.vy + (a21 * a12 + a11 * a22) * in.vxy;
    out = res;
}

transformStar()

void lsst::jointcal::AstrometryTransform::transformStar ( FatPoint &  in ) const

inlineinherited

Definition at line 107 of file AstrometryTransform.h.

{ transformPosAndErrors(in, in); }

write() [1/2]

void lsst::jointcal::AstrometryTransform::write ( const std::string &  fileName ) const

inherited

Definition at line 245 of file AstrometryTransform.cc.

                                                               {
    ofstream s(fileName.c_str());
    write(s);
    bool ok = !s.fail();
    s.close();
    if (!ok)
        throw LSST_EXCEPT(pex::exceptions::InvalidParameterError,
                          "AstrometryTransform::write, something went wrong for file " + fileName);
}

write() [2/2]

void lsst::jointcal::AstrometryTransformPolynomial::write ( std::ostream &  s ) const

overridevirtual

Reimplemented from lsst::jointcal::AstrometryTransform.

Definition at line 1087 of file AstrometryTransform.cc.

                                                          {
    s << " AstrometryTransformPolynomial 1" << endl;
    s << "order " << _order << endl;
    int oldprec = s.precision();
    s << setprecision(12);
    for (std::size_t k = 0; k < 2 * _nterms; ++k) s << _coeffs[k] << ' ';
    s << endl;
    s << setprecision(oldprec);
}

---

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

• /j/snowflake/release/lsstsw/stack/Linux64/jointcal/19.0.0-2-gb96a1c4+3/include/lsst/jointcal/AstrometryTransform.h
• /j/snowflake/release/lsstsw/stack/Linux64/jointcal/19.0.0-2-gb96a1c4+3/src/AstrometryTransform.cc