CoordinateTransform

java.lang.Object
- wsh.opt.CoordinateTransform

```
public class CoordinateTransform
extends java.lang.Object
```
Find a best linear combination of input coordinates to fit output coordinates. Finds a_io (a with subscripts i and o) to best approximate the linear transform.
```
 out_o = sum_i ( a_io * in_i )
 
```
where in_i are input coordinates,
out_o are output coordinates,
i is the index of each input dimension,
and o is the index of each output dimension.

The optimum coefficients minimize this least squares error:
```
 sum_oj [ sum_i ( a_io * in_ij ) - out_oj ]^2
 
```
where in_ij is an input array of different coordinates,
out_oj is an output array of corresponding coordinates,
and j is the index of pairs of coordinates to be fit in a least-squares sense.
Normal equations (indexed by k) are solved independently for each o:
```
 sum_ij ( in_kj * in_ij * a_io ) = sum_j ( in_kj * out_oj )
 
```
The Hessian is H = sum_j ( in_kj * in_ij ) and the gradient b = - sum_j ( in_kj * out_oj )
The solution is undamped and may not behave as you want for degenerate solutions.
If the linear transform needs a translation shift, then include a constant as one of the input coordinates.

Constructor Summary

Constructors
Constructor Description

CoordinateTransform(int dimensionOut, int dimensionIn)
Constructor sets number of input and output coordinates.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`void`	`add(double[] out, double[] in)`	Add an observation of a set of input and output coordinates You should add enough of these to determine (or overdetermine) a unique linear mapping.
`double[]`	`get(double[] in)`	For a given set of input coordinates, return the linearly predicted output coordinates.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - CoordinateTransform
```
public CoordinateTransform(int dimensionOut,
                           int dimensionIn)
```
    Constructor sets number of input and output coordinates.
    
    Parameters:
    
    dimensionOut - Number of output coordinates.
    
    dimensionIn - Number of input coordinates.
- Method Detail
  - add
```
public void add(double[] out,
                double[] in)
```
    Add an observation of a set of input and output coordinates You should add enough of these to determine (or overdetermine) a unique linear mapping. To allow translation, include a constant 1 as an input coordinate.
    
    Parameters:
    
    out - A set of observed output coordinates with an unknown linear relationship to input coordinates.
    
    in - A set of observed input coordinates that should be linearly combined to calculate each of the output coordinates. To allow translation, include a constant 1.
  - get
```
public double[] get(double[] in)
```
    For a given set of input coordinates, return the linearly predicted output coordinates.
    
    Parameters:
    
    in - A set of input coordinates
    
    Returns:
    
    A computed set of output coordinates.