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, int order)
	Fit a 1d polynomial to a set of data points z(x, y)
Eigen::VectorXd	getParams ()
	Return the best fit parameters as an Eigen::Matrix.
Eigen::VectorXd	getErrors ()
	Return the 1 sigma uncertainties in the best fit parameters as an Eigen::Matrix.
FittingFunc	getBestFitFunction ()
	Return the best fit polynomial as a lsst::afw::math::Function1 object.
double	valueAt (double x)
	Calculate the value of the function at a given point.
std::vector< double >	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.
double	getChiSq ()
	Return a measure of the goodness of fit.
double	getReducedChiSq ()
	Return a measure of the goodness of fit.

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 64 of file LeastSqFitter1d.h.

Constructor & Destructor Documentation

LeastSqFitter1d()

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,
		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 104 of file LeastSqFitter1d.h.

        : _x(x), _y(y), _s(s), _order(order) {
    if (order == 0) {
        throw LSST_EXCEPT(pex::exceptions::RuntimeError, "Fit order must be >= 1");
    }
 
    _nData = _x.size();
    if (_nData != static_cast<int>(_y.size())) {
        throw LSST_EXCEPT(pex::exceptions::RuntimeError, "x and y vectors of different lengths");
    }
    if (_nData != static_cast<int>(_s.size())) {
        throw LSST_EXCEPT(pex::exceptions::RuntimeError, "x and s vectors of different lengths");
    }
 
    if (_nData < _order) {
        throw LSST_EXCEPT(pex::exceptions::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

getBestFitFunction()

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 160 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;
}

getChiSq()

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 199 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;
}

getErrors()

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 149 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();
}

getParams()

template<class FittingFunc >

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

(

)

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

Definition at line 139 of file LeastSqFitter1d.h.

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

getReducedChiSq()

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 218 of file LeastSqFitter1d.h.

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

residuals()

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 182 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;
}

valueAt()

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 173 of file LeastSqFitter1d.h.

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

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

• /j/snowflake/release/lsstsw/stack/lsst-scipipe-8.0.0/Linux64/meas_astrom/gf1cff7945b+21ad69e7e1/include/lsst/meas/astrom/sip/LeastSqFitter1d.h