# Interface UnconstrainedLeastSquares<S extends DMatrix>

All Superinterfaces:
`IterativeOptimization`, `Serializable`
All Known Implementing Classes:
`UnconLeastSqLevenbergMarquardt_F64`, `UnconLeastSqTrustRegion_F64`

public interface UnconstrainedLeastSquares<S extends DMatrix> extends IterativeOptimization

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 `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'.

• ## Method Summary

Modifier and Type
Method
Description
`double`
`getFunctionValue()`
Returns the value of the objective function being evaluated at the current parameters value.
`double[]`
`getParameters()`
After each iteration this function can be called to get the current best set of parameters.
`void`
```initialize(double[] initial, double ftol, double gtol)```
Specify the initial set of parameters from which to start from.
`void`
```setFunction(FunctionNtoM function, @Nullable FunctionNtoMxN<S> jacobian)```
Specifies a set of functions and their Jacobian.

### Methods inherited from interface org.ddogleg.optimization.IterativeOptimization

`isConverged, isUpdated, iterate, setVerbose`
• ## Method Details

• ### setFunction

void setFunction(FunctionNtoM function, @Nullable @Nullable FunctionNtoMxN<S> jacobian)
Specifies a set of functions and their Jacobian. See class description for documentation on output data format.
Parameters:
`function` - Computes the output of M functions fi(x) which take in N fit parameters as input.
`jacobian` - Computes the Jacobian of the M functions. If null a numerical Jacobian will be used.
• ### initialize

void initialize(double[] initial, double ftol, double gtol)
Specify the initial set of parameters from which to start from. Call after `setFunction(org.ddogleg.optimization.functions.FunctionNtoM, org.ddogleg.optimization.functions.FunctionNtoMxN<S>)` has been called.
Parameters:
`initial` - Initial parameters or guess with N elements..
`ftol` - Relative threshold for change in function value between iterations. 0 ≤ ftol ≤ 1. Try 1e-12
`gtol` - Absolute threshold for convergence based on the gradient's norm. 0 disables test. 0 ≤ gtol. Try 1e-12
• ### getParameters

double[] getParameters()
After each iteration this function can be called to get the current best set of parameters.
• ### getFunctionValue

double getFunctionValue()
Returns the value of the objective function being evaluated at the current parameters value. If not supported then an exception is thrown.
Returns:
Objective function's value.