NonLinearLeastSquare Class Reference

Non-linear least-square method. More...

#include <ql/math/optimization/leastsquare.hpp>

Public Member Functions
	NonLinearLeastSquare (Constraint &c, Real accuracy=1e-4, Size maxiter=100)
	Default constructor.
	NonLinearLeastSquare (Constraint &c, Real accuracy, Size maxiter, ext::shared_ptr< OptimizationMethod > om)
	Default constructor.
	~NonLinearLeastSquare ()=default
	Destructor.
Array &	perform (LeastSquareProblem &lsProblem)
	Solve least square problem using numerix solver.
void	setInitialValue (const Array &initialValue)
Array &	results ()
	return the results
Real	residualNorm () const
	return the least square residual norm
Real	lastValue () const
	return last function value
Integer	exitFlag () const
	return exit flag
Integer	iterationsNumber () const
	return the performed number of iterations

Detailed Description

Non-linear least-square method.

Using a given optimization algorithm (default is conjugate gradient),

\[ min \{ r(x) : x in R^n \} \]

where \( r(x) = |f(x)|^2 \) is the Euclidean norm of \(f(x) \) for some vector-valued function \( f \) from \( R^n \) to \( R^m \),

\[ f = (f_1, ..., f_m) \]

with \( f_i(x) = b_i - \phi(x,t_i) \) where \( b \) is the vector of target data and \( phi \) is a scalar function.

Assuming the differentiability of \( f \), the gradient of \( r \) is defined by

\[ grad r(x) = f'(x)^t.f(x) \]