lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc > Class Template Reference

Fit an lsst::afw::math::Function1 object to a set of data points in two dimensions. More...

#include <LeastSqFitter2d.h>

Public Member Functions
	LeastSqFitter2d (const std::vector< double > &x, const std::vector< double > &y, const std::vector< double > &z, const std::vector< double > &s, int order)
Eigen::MatrixXd	getParams ()
Eigen::MatrixXd	getErrors ()
	Companion function to getParams(). Returns uncertainties in the parameters as a matrix. More...
double	valueAt (double x, double y)
	Return the value of the best fit function at a given position (x,y) More...
std::vector< double >	residuals ()
double	getChiSq ()
	Return a measure of the goodness of fit. \[ \chi^2 = \sum \left( \frac{z_i - f(x_i, y_i)}{s_i} \right)^2 \] . More...
double	getReducedChiSq ()
	Return a measure of the goodness of fit. \[ \chi_r^2 = \sum \left( \frac{z_i - f(x_i, y_i)}{s} \right)^2 \div (N-p) \] Where \( N \) is the number of data points, and \( p \) is the number of parameters in the fit. More...

Private Member Functions
void	initFunctions ()
Eigen::MatrixXd	expandParams (Eigen::VectorXd const &input) const
	Turn a flattened parameter-like vector into a triangular matrix. More...
double	func2d (double x, double y, int term)
double	func1d (double value, int exponent)

Private Attributes
std::vector< double >	_x
std::vector< double >	_y
std::vector< double >	_z
std::vector< double >	_s
int	_order
int	_nPar
int	_nData
Eigen::JacobiSVD< Eigen::MatrixXd >	_svd
Eigen::VectorXd	_par
std::vector< boost::shared_ptr < FittingFunc > >	_funcArray

Detailed Description

template<class FittingFunc>
class lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc >

Fit an lsst::afw::math::Function1 object to a set of data points in two dimensions.

The class is templated over the kind of object to fit. Note that we fit the 1d object in each dimension, not the 2d one.

Input is a list of x and y ordinates for a set of points, the z coordinate, and the uncertainties, s. order is order of the polynomial to fit (e.g if the templated function is lsst::afw::math::PolynomialFunction1, then order=3 => fit a function of the form \(ax^2+bx+c\)

Template Parameters

FittingFunc

The 1d function to fit in both dimensions. Must inherit from lsst::afw::math::Function1

Parameters

x	Ordinate of points to fit
y	Ordinate of points to fit
z	Co-ordinate of pionts to fit
s	1 \(\sigma\) uncertainties in z
order	Polynomial order to fit

See Also

LeastSqFitter1d

Definition at line 71 of file LeastSqFitter2d.h.

Constructor & Destructor Documentation

template<class FittingFunc >

lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc >::LeastSqFitter2d	(	const std::vector< double > &	x,
		const std::vector< double > &	y,
		const std::vector< double > &	z,
		const std::vector< double > &	s,
		int	order
	)

Fit a 2d polynomial to a set of data points z(x, y)

Template Parameters

FittingFunc

The type of function to fit in each dimension. This function should extend the base class of lsst::afw::math::Function1. Note that this is a 1d function

Parameters

x	vector of x positions of data
y	vector of y positions of data
z	Value of data for a given x,y. \(z = z_i = z_i(x_i, y_i)\)
s	Vector of measured uncertainties in the values of z
order	Order of 2d function to fit

Definition at line 121 of file LeastSqFitter2d.h.

                                                                                                   :
    _x(x), _y(y), _z(z), _s(s), _order(order), _nPar(0), _par(1) {
    
    //_nPar, the number of terms to fix (x^2, xy, y^2 etc.) is \Sigma^(order+1) 1
    _nPar = 0;
    for (int i = 0; i < order; ++i) {
        _nPar += i + 1;
    }
    
    //Check input vectors are the same size
    _nData = _x.size();
    if (_nData != static_cast<int>(_y.size())) {
        throw LSST_EXCEPT(except::RuntimeError, "x and y vectors of different lengths");        
    }
    if (_nData != static_cast<int>(_s.size())) {
        throw LSST_EXCEPT(except::RuntimeError, "x and s vectors of different lengths");        
    }
    if (_nData != static_cast<int>(_z.size())) {
        throw LSST_EXCEPT(except::RuntimeError, "x and z vectors of different lengths");        
    }

    for (int i = 0; i < _nData; ++i) {
        if ( _s[i] == 0.0 ) {
            std::string msg = "Illegal zero value for fit weight encountered.";
            throw LSST_EXCEPT(except::RuntimeError, msg);        
        }
    }

    if (_nData < _order) {
        throw LSST_EXCEPT(except::RuntimeError, "Fewer data points than parameters");        
    }
    
    initFunctions();

    Eigen::MatrixXd design(_nData, _nPar);
    Eigen::VectorXd rhs(_nData);
    for (int i = 0; i < _nData; ++i) {
        rhs[i] = z[i] / s[i];
        for (int j = 0; j < _nPar; ++j) {
            design(i, j) = func2d(_x[i], _y[i], j) / _s[i];
        }
    }
    _svd.compute(design, Eigen::ComputeThinU | Eigen::ComputeThinV);
    _par = _svd.solve(rhs);
}

Member Function Documentation

template<class FittingFunc >

Eigen::MatrixXd lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc >::expandParams ( Eigen::VectorXd const &  input ) const

private

Turn a flattened parameter-like vector into a triangular matrix.

Definition at line 184 of file LeastSqFitter2d.h.

                                                                                          {
    Eigen::MatrixXd out = Eigen::MatrixXd::Zero(_order, _order);
    int count = 0;
    for (int i = 0; i < _order; ++i) {
        for (int j = 0; j < _order - i; ++j) {
            out(i, j) = input[count++];
        }
    }
    return out;
}

template<class FittingFunc >

double lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc >::func1d ( double  value, int  exponent  )

private

Definition at line 302 of file LeastSqFitter2d.h.

                                                                                                  {
    return (*_funcArray[exponent])(value);
}

template<class FittingFunc >

double lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc >::func2d ( double  x, double  y, int  term  )

private

Definition at line 280 of file LeastSqFitter2d.h.

                                                                                                    {

    int yexp = 0;  //y exponent
    int xexp = 0;  //x exponent

    for (int i = 0; i<term; ++i) {
        yexp = (yexp + 1) % (_order - xexp);
        if ( yexp == 0){
            xexp++;
        }
    }

    double xcomp = func1d(x, xexp);  //x component of polynomial
    double ycomp = func1d(y, yexp);  //y component

    #if 0   //A useful debugging printf statement
        printf("The %i(th) function: x^%i * y^%i = %.1f * %.1f\n", term, xexp, yexp, xcomp, ycomp);
    #endif
    
    return xcomp*ycomp;
}

template<class FittingFunc >

double lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc >::getChiSq

(

)

Return a measure of the goodness of fit.

\[ \chi^2 = \sum \left( \frac{z_i - f(x_i, y_i)}{s_i} \right)^2 \]

.

Definition at line 197 of file LeastSqFitter2d.h.

                                                                          {
    
    double chisq = 0;
    for (int i = 0; i < _nData; ++i) {
        double val = _z[i] - valueAt(_x[i], _y[i]);
        val /= _s[i];
        chisq += pow(val, 2);
    }
    
    return chisq;
}

template<class FittingFunc >

Eigen::MatrixXd lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc >::getErrors

(

)

Companion function to getParams(). Returns uncertainties in the parameters as a matrix.

Definition at line 249 of file LeastSqFitter2d.h.

                                                      {
    Eigen::ArrayXd variance(_nPar);
    for (int i = 0; i < _nPar; ++i) {
        variance[i] = _svd.matrixV().row(i).dot(
            (_svd.singularValues().array().inverse().square() * _svd.matrixV().col(i).array()).matrix()
        );
    }
    return expandParams(variance.sqrt().matrix());
}

template<class FittingFunc >

Eigen::MatrixXd lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc >::getParams

(

)

Build up a triangular matrix of the parameters. The shape of the matrix is such that the values correspond to the coefficients of the following polynomials
1 y y^2 y^3
x xy xy^2 0
x^2 x^2y 0 0
x^3 0 0 0
(order==4)
where row x column < order

Definition at line 178 of file LeastSqFitter2d.h.

                                                                                  {
    return expandParams(_par);
}

template<class FittingFunc >

double lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc >::getReducedChiSq

(

)

Return a measure of the goodness of fit.

\[ \chi_r^2 = \sum \left( \frac{z_i - f(x_i, y_i)}{s} \right)^2 \div (N-p) \]

Where \( N \) is the number of data points, and \( p \) is the number of parameters in the fit.

Definition at line 215 of file LeastSqFitter2d.h.

                                                                                 {
    return getChiSq()/(double) (_nData - _nPar);
}

template<class FittingFunc >

void lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc >::initFunctions ( )

private

Definition at line 260 of file LeastSqFitter2d.h.

                                                                             {
    //Initialise the array of functions. _funcArray[i] is a object of type math::Function1 of order i
    _funcArray.reserve(_order);
    
    std::vector<double> coeff;
    coeff.reserve( _order);
    
    coeff.push_back(1);
    for (int i = 0; i < _order; ++i) {
        boost::shared_ptr<FittingFunc> p(new FittingFunc(coeff));
        _funcArray.push_back(p);
        
        coeff[i] = 0;
        coeff.push_back(1);  //coeff now looks like [0,0,...,0,1]
    }
}

template<class FittingFunc >

std::vector< double > lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc >::residuals

(

)

Return a vector of residuals of the fit (i.e the difference between the input z values, and the value of the fitting function at that point.

Definition at line 234 of file LeastSqFitter2d.h.

                                                                                      {

    std::vector<double> out;
    out.reserve(_nData);
    
    for (int i = 0; i < _nData; ++i) {
        out.push_back(_z[i] - valueAt(_x[i], _y[i]));
    }
    
    return out;
}

template<class FittingFunc >

double lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc >::valueAt	(	double	x,
		double	y
	)

Return the value of the best fit function at a given position (x,y)

Definition at line 222 of file LeastSqFitter2d.h.

                                                                                           {
    double val = 0;
    
    //Sum the values of the different orders to get the value of the fitted function
    for (int i = 0; i < _nPar; ++i) {
        val += _par[i] * func2d(x, y, i);
    }
    return val;
}

Member Data Documentation

template<class FittingFunc >

std::vector<boost::shared_ptr<FittingFunc> > lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc >::_funcArray

private

Definition at line 100 of file LeastSqFitter2d.h.

template<class FittingFunc >

int lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc >::_nData

private

Definition at line 95 of file LeastSqFitter2d.h.

template<class FittingFunc >

int lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc >::_nPar

private

Definition at line 94 of file LeastSqFitter2d.h.

template<class FittingFunc >

int lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc >::_order

private

Definition at line 93 of file LeastSqFitter2d.h.

template<class FittingFunc >

Eigen::VectorXd lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc >::_par

private

Definition at line 98 of file LeastSqFitter2d.h.

template<class FittingFunc >

std::vector<double> lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc >::_s

private

Definition at line 92 of file LeastSqFitter2d.h.

template<class FittingFunc >

Eigen::JacobiSVD<Eigen::MatrixXd> lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc >::_svd

private

Definition at line 97 of file LeastSqFitter2d.h.

template<class FittingFunc >

std::vector<double> lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc >::_x

private

Definition at line 92 of file LeastSqFitter2d.h.

template<class FittingFunc >

std::vector<double> lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc >::_y

private

Definition at line 92 of file LeastSqFitter2d.h.

template<class FittingFunc >

std::vector<double> lsst::meas.astrom.sip::LeastSqFitter2d< FittingFunc >::_z

private

Definition at line 92 of file LeastSqFitter2d.h.

---

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

• /home/lsstsw/stack/Linux64/meas_astrom/11.0-1-g60db491/include/lsst/meas/astrom/sip/LeastSqFitter2d.h