lsst::meas.astrom.sip::LeastSqFitter1d< FittingFunc > Class Template Reference

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

#include <LeastSqFitter1d.h>

Public Member Functions
	LeastSqFitter1d (const std::vector< double > &x, const std::vector< double > &y, const std::vector< double > &s, unsigned int order)
Eigen::VectorXd	getParams ()
	Return the best fit parameters as an Eigen::Matrix. More...
Eigen::VectorXd	getErrors ()
	Return the 1 sigma uncertainties in the best fit parameters as an Eigen::Matrix. More...
FittingFunc	getBestFitFunction ()
	Return the best fit polynomial as a lsst::afw::math::Function1 object. More...
double	valueAt (double x)
	Calculate the value of the function at a given point. More...
std::vector< double >	residuals ()
double	getChiSq ()
	Return a measure of the goodness of fit. \[ \chi_r^2 = \sum \left( \frac{y_i - f(x_i)}{s} \right)^2 \] . More...
double	getReducedChiSq ()
	Return a measure of the goodness of fit. \[ \chi_r^2 = \sum \left( \frac{y_i - f(x_i)}{s} \right)^2 \div (N-p) \] Where \( N \) is the number of data points, and \( p \) is the number of parameters in the fit. More...

Private Member Functions
void	initFunctions ()
double	func1d (double value, int exponent)

Private Attributes
std::vector< double >	_x
std::vector< double >	_y
std::vector< double >	_s
int	_order
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::LeastSqFitter1d< FittingFunc >

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

The class is templated over the kind of object to fit.

Input is a list of x ordinates for a set of points, the y 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	Co-ordinate of pionts to fit
s	1 \(\sigma\) uncertainties in z
order	Polynomial order to fit

See Also

LeastSqFitter1d

Definition at line 69 of file LeastSqFitter1d.h.

Constructor & Destructor Documentation

template<class FittingFunc >

lsst::meas.astrom.sip::LeastSqFitter1d< FittingFunc >::LeastSqFitter1d	(	const std::vector< double > &	x,
		const std::vector< double > &	y,
		const std::vector< double > &	s,
		unsigned int	order
	)

Fit a 1d polynomial to a set of data points z(x, y)

Template Parameters

FittingFunc

The type of function to fit. This function extends the base class of lsst::afw::math::Function1

Parameters

x	vector of x positions of data
y	vector of y positions of data
s	Vector of measured uncertainties in the values of z
order	Order of 2d function to fit

Definition at line 110 of file LeastSqFitter1d.h.

                                                                                :
    _x(x), _y(y), _s(s), _order(order) {
    
    if (order == 0) {
        throw LSST_EXCEPT(except::RuntimeError, "Fit order must be >= 1");        
    }
    
    _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 < _order) {
        throw LSST_EXCEPT(except::RuntimeError, "Fewer data points than parameters");        
    }

    initFunctions();

    Eigen::MatrixXd design(_nData, _order);
    Eigen::VectorXd rhs(_nData);
    for (int i = 0; i < _nData; ++i) {
        rhs[i] = y[i] / _s[i];
        for (int j = 0; j < _order; ++j) {
            design(i, j) = func1d(_x[i], j) / _s[i];
        }
    }
    _svd.compute(design, Eigen::ComputeThinU | Eigen::ComputeThinV);
    _par = _svd.solve(rhs);
}

Member Function Documentation

template<class FittingFunc >

double lsst::meas.astrom.sip::LeastSqFitter1d< FittingFunc >::func1d ( double  value, int  exponent  )

private

Definition at line 254 of file LeastSqFitter1d.h.

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

template<class FittingFunc >

FittingFunc lsst::meas.astrom.sip::LeastSqFitter1d< FittingFunc >::getBestFitFunction

(

)

Return the best fit polynomial as a lsst::afw::math::Function1 object.

Definition at line 170 of file LeastSqFitter1d.h.

                                                                                         {

    //FittingFunc and LeastSqFitter disagree on the definition of order of a function.
    //LSF says that a linear function is order 2 (two coefficients), FF says only 1
    FittingFunc func(_order - 1);

    for (int i = 0; i < _order; ++i) {
        func.setParameter(i, _par(i));
    }
    return func;
}

template<class FittingFunc >

double lsst::meas.astrom.sip::LeastSqFitter1d< FittingFunc >::getChiSq

(

)

Return a measure of the goodness of fit.

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

.

Definition at line 211 of file LeastSqFitter1d.h.

                                                                          {
    FittingFunc f = getBestFitFunction();

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

    return chisq;
}

template<class FittingFunc >

Eigen::VectorXd lsst::meas.astrom.sip::LeastSqFitter1d< FittingFunc >::getErrors

(

)

Return the 1 sigma uncertainties in the best fit parameters as an Eigen::Matrix.

Definition at line 158 of file LeastSqFitter1d.h.

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

template<class FittingFunc >

Eigen::VectorXd lsst::meas.astrom.sip::LeastSqFitter1d< FittingFunc >::getParams

(

)

Return the best fit parameters as an Eigen::Matrix.

Definition at line 147 of file LeastSqFitter1d.h.

                                                                                  {

    Eigen::VectorXd vec = Eigen::VectorXd::Zero(_order);
    for (int i = 0; i < _order; ++i) {
        vec(i) = _par(i);
    }
    return vec;
}

template<class FittingFunc >

double lsst::meas.astrom.sip::LeastSqFitter1d< FittingFunc >::getReducedChiSq

(

)

Return a measure of the goodness of fit.

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

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

Definition at line 230 of file LeastSqFitter1d.h.

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

template<class FittingFunc >

void lsst::meas.astrom.sip::LeastSqFitter1d< FittingFunc >::initFunctions ( )

private

Initialise the array of functions. _funcArray[i] is a object of type math::Function1 of order _norder

Definition at line 238 of file LeastSqFitter1d.h.

                                                                             {

    _funcArray.reserve(_order);
    
    std::vector<double> coeff;
    coeff.reserve( _order);
    
    coeff.push_back(1.0);
    for (int i = 0; i < _order; ++i) {
        boost::shared_ptr<FittingFunc> p(new FittingFunc(coeff));
        _funcArray.push_back(p);
        coeff[i] = 0.0;
        coeff.push_back(1.0);  //coeff now looks like [0,0,...,0,1]
    }
}

template<class FittingFunc >

std::vector< double > lsst::meas.astrom.sip::LeastSqFitter1d< FittingFunc >::residuals

(

)

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

Definition at line 194 of file LeastSqFitter1d.h.

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

template<class FittingFunc >

double lsst::meas.astrom.sip::LeastSqFitter1d< FittingFunc >::valueAt

(

double

x

)

Calculate the value of the function at a given point.

Definition at line 184 of file LeastSqFitter1d.h.

                                                                                 {
        FittingFunc f = getBestFitFunction();
        
        return f(x);
}

Member Data Documentation

template<class FittingFunc >

std::vector<boost::shared_ptr<FittingFunc> > lsst::meas.astrom.sip::LeastSqFitter1d< FittingFunc >::_funcArray

private

Definition at line 97 of file LeastSqFitter1d.h.

template<class FittingFunc >

int lsst::meas.astrom.sip::LeastSqFitter1d< FittingFunc >::_nData

private

Definition at line 92 of file LeastSqFitter1d.h.

template<class FittingFunc >

int lsst::meas.astrom.sip::LeastSqFitter1d< FittingFunc >::_order

private

Definition at line 91 of file LeastSqFitter1d.h.

template<class FittingFunc >

Eigen::VectorXd lsst::meas.astrom.sip::LeastSqFitter1d< FittingFunc >::_par

private

Definition at line 95 of file LeastSqFitter1d.h.

template<class FittingFunc >

std::vector<double> lsst::meas.astrom.sip::LeastSqFitter1d< FittingFunc >::_s

private

Definition at line 90 of file LeastSqFitter1d.h.

template<class FittingFunc >

Eigen::JacobiSVD<Eigen::MatrixXd> lsst::meas.astrom.sip::LeastSqFitter1d< FittingFunc >::_svd

private

Definition at line 94 of file LeastSqFitter1d.h.

template<class FittingFunc >

std::vector<double> lsst::meas.astrom.sip::LeastSqFitter1d< FittingFunc >::_x

private

Definition at line 90 of file LeastSqFitter1d.h.

template<class FittingFunc >

std::vector<double> lsst::meas.astrom.sip::LeastSqFitter1d< FittingFunc >::_y

private

Definition at line 90 of file LeastSqFitter1d.h.

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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/LeastSqFitter1d.h