Package org.ddogleg.optimization

Interface UnconstrainedLeastSquares<S extends DMatrix>

All Superinterfaces:
IterativeOptimization, Serializable, UnconstrainedLeastSquaresBase<S,FunctionNtoMxN<S>>, VerbosePrint
All Known Implementing Classes:
UnconLeastSqLevenbergMarquardt_F64, UnconLeastSqTrustRegion_F64
public interface UnconstrainedLeastSquares<S extends DMatrix> extends IterativeOptimization, UnconstrainedLeastSquaresBase<S,FunctionNtoMxN<S>>

Non-linear least squares problems have a special structure which can be taken advantage of for optimization. The least squares problem is defined below:
F(x) = 0.5*sum( i=1:M ; fi(x)2 )
where fi(x) is a function from ℜN to ℜ. M is number of functions, and N is number of fit parameters. M ≥ N
fi(x) = observed - predicted, which is known as the residual error.

F-Test: ftol ≤ 1 - f(x+p)/f(x)
G-Test: gtol ≤ ||g(x)||inf
An absolute f-test can be done by checking the value of UnconstrainedLeastSquaresBase.getFunctionValue() in each iteration.

NOTE: The function computes the M outputs of the fi(x), residual error functions, NOT [fi(x)]2

FORMATS:
Input functions are specified using FunctionNtoM for the set of M functions, and FunctionNtoMxN for the Jacobian. The function's output is a vector of length M, where element i correspond to function i's output. The Jacobian is an array containing the partial derivatives of each function. Element J(i,j) corresponds to the partial of function i and parameter j. The array is stored in a row major format. The partial for F(i,j) would be stored at index = i*N+j in the data array.

NOTE: If you need to modify the optimization parameters this can be done inside the 'function'.