Template Class LeastSqFitter2d

Class Documentation

template<class FittingFunc>
class LeastSqFitter2d

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 \(ax^2+bx+c\)

See

LeastSqFitter1d

Template Parameters
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

Public Functions

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

Eigen::MatrixXd 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

Eigen::MatrixXd getErrors()

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

double valueAt(double x, double y)

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

std::vector<double> 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.

double getChiSq()

Return a measure of the goodness of fit.

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

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.