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From Evan Ward <evan.w...@nrl.navy.mil>
Subject Re: [math] Side effect of LevenbergMarquardtOptimizer
Date Mon, 08 Sep 2014 12:56:36 GMT
Gilles,

I like this approach. My only thought is that a separate interface for
the validate method would be nicer for our Java  8 users. Then the
implementation could be a lambda: (p) -> p.unitVector()

Best Regards,
Evan

On 09/07/2014 08:11 PM, Gilles wrote:
> On Thu, 4 Sep 2014 12:52:24 -0400, Evan Ward wrote:
>> Hi Olexiy,
>>
>> In my field we often encounter a similar problem when estimating
>> attitude since a quaternion is only a valid rotation when it is
>> normalized. We often escape this issue by estimating a "small"
>> adjustment to an apriori guess. (For the details see [1].)  For this
>> technique to work the cost function must be smooth and the apriori guess
>> must be "close enough" to the true value. Both of these assumptions are
>> also required to apply a non-linear least squares optimizer. Perhaps you
>> can apply a similar technique to your problem. (It seems that your 'A'
>> parameter is orientation in 3D space.)
>>
>> If there is a need for an extra steps, I would prefer to make those
>> explicit rather than depending on side effects of cost function
>> evaluation.
>
> IIUC, the feature could be made explicit by adding a method to the
> "MultivariateJacobianFunction" interface to allow the user to change
> the point about to be evaluated:
>
> interface MultivariateJacobianFunction {
>   Pair<RealVector, RealMatrix> value(RealVector point);
>
>   /** @param point Point provided by the optimizer. */
>   /** @return the point that will actually be evaluated. */
>   RealVector validate(RealVector point);
> }
>
> Thus, in "LeastSquaresFactory":
>
> private static class LocalLeastSquaresProblem
>    extends AbstractOptimizationProblem<Evaluation>
>    implements LeastSquaresProblem {
>
>    // ...
>
>    private final MultivariateJacobianFunction model;
>
>    // ...
>
>    public Evaluation evaluate(final RealVector point) {
>      final RealVector p = model.validate(point).copy(); // <--- Change
> here (at line 403).
>
>      if (lazyEvaluation) {
>        return new LazyUnweightedEvaluation(model,
>                                            target,
>                                            p);
>      } else {
>        final Pair<RealVector, RealMatrix> value = model.value(p);
>        return new UnweightedEvaluation(value.getFirst(),
>                                        value.getSecond(),
>                                        target,
>                                        p);
>      }
>   }
>
>   // ...
> }
>
> What do you think?
>
> Best,
> Gilles
>
>>
>> Best Regards,
>> Evan
>>
>> [1] Crassidis, John L., and John L. Junkins. /Optimal Estimation of
>> Dynamic Systems/. Boca Raton, FL: CRC, 2012.
>>
>> On 09/04/2014 05:37 AM, Olexiy Movchan wrote:
>>> Hello,
>>>
>>> I created the math issue
>>> https://issues.apache.org/jira/browse/MATH-1144.
>>>
>>> In version 2.0, LevenbergMarquardtOptimizer passed point to
>>> evaluator by reference. So our software could modify it on every
>>> step of algorithm.
>>> In version 3.3, point is copied and then passed to evaluator, so it
>>> can't be updated by evaluator.
>>>
>>> We use LevenbergMarquardtOptimizer for 3d surface fitting
>>> (cylinders, cones, tori) by sampled points. And surface parameters
>>> should be renormalized on every step of algorithm. Please see this
>>> article:
>>>                 http://nvlpubs.nist.gov/nistpubs/jres/103/6/j36sha.pdf
>>>
>>> Also please read the description of MATH-1144 jira issue.
>>>
>>> Can you modify optimizer or evaluator interface to allow in/out
>>> parameters there?
>>>
>>> Thanks,
>>> Olexiy Movchan
>>>
>>>
>
>
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