NonLinearLeastSquare Class Reference

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

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

Collaboration diagram for NonLinearLeastSquare:

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

Private Attributes
Array	results_
	solution vector More...
Array	initialValue_
Real	resnorm_
	least square residual norm More...
Integer	exitFlag_
	Exit flag of the optimization process. More...
Real	accuracy_
	required accuracy of the solver More...
Real	bestAccuracy_
Size	maxIterations_
	maximum and real number of iterations More...
Size	nbIterations_
ext::shared_ptr< OptimizationMethod >	om_
	Optimization method. More...
Constraint &	c_

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

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

Definition at line 97 of file leastsquare.hpp.

Constructor & Destructor Documentation

NonLinearLeastSquare() [1/2]

NonLinearLeastSquare	(	Constraint &	c,
		Real	accuracy = 1e-4,
		Size	maxiter = 100
	)

Default constructor.

Definition at line 79 of file leastsquare.cpp.

NonLinearLeastSquare() [2/2]

NonLinearLeastSquare	(	Constraint &	c,
		Real	accuracy,
		Size	maxiter,
		ext::shared_ptr< OptimizationMethod >	om
	)

Default constructor.

Definition at line 87 of file leastsquare.cpp.

~NonLinearLeastSquare()

~NonLinearLeastSquare ( )

default

Destructor.

Member Function Documentation

perform()

Array & perform

(

LeastSquareProblem &

lsProblem

)

Solve least square problem using numerix solver.

Definition at line 93 of file leastsquare.cpp.

Here is the call graph for this function:

setInitialValue()

void setInitialValue

(

const Array &

initialValue

)

Definition at line 114 of file leastsquare.hpp.

results()

Array & results

(

)

return the results

Definition at line 119 of file leastsquare.hpp.

residualNorm()

Real residualNorm

(

)

const

return the least square residual norm

Definition at line 122 of file leastsquare.hpp.

lastValue()

Real lastValue

(

)

const

return last function value

Definition at line 125 of file leastsquare.hpp.

exitFlag()

Integer exitFlag

(

)

const

return exit flag

Definition at line 128 of file leastsquare.hpp.

iterationsNumber()

Integer iterationsNumber

(

)

const

return the performed number of iterations

Definition at line 131 of file leastsquare.hpp.

Member Data Documentation

results_

Array results_

private

solution vector

Definition at line 135 of file leastsquare.hpp.

initialValue_

Array initialValue_

private

Definition at line 135 of file leastsquare.hpp.

resnorm_

Real resnorm_

private

least square residual norm

Definition at line 137 of file leastsquare.hpp.

exitFlag_

Integer exitFlag_

private

Exit flag of the optimization process.

Definition at line 139 of file leastsquare.hpp.

accuracy_

Real accuracy_

private

required accuracy of the solver

Definition at line 141 of file leastsquare.hpp.

bestAccuracy_

Real bestAccuracy_

private

Definition at line 141 of file leastsquare.hpp.

maxIterations_

Size maxIterations_

private

maximum and real number of iterations

Definition at line 143 of file leastsquare.hpp.

nbIterations_

Size nbIterations_

private

Definition at line 143 of file leastsquare.hpp.

om_

ext::shared_ptr<OptimizationMethod> om_

private

Optimization method.

Definition at line 145 of file leastsquare.hpp.

c_

Constraint& c_

private

Definition at line 147 of file leastsquare.hpp.