I figured it out. The issue was with my derivative calculation. I was using
(a - b) / DELTA * 2. Changing this to (b - a) / DELTA * 2 fixes this
problem.
a = morton3pTime(cp - DELTA, wPrime, pmax, p);
b = morton3pTime(cp + DELTA, wPrime, pmax, p);
jacobian.setEntry(i, 0, (b - a) / (DELTA * 2));
Thanks
On Fri, Dec 28, 2018 at 8:33 PM Gilles <gil...@harfang.homelinux.org> wrote:
> Hello.
>
> On Thu, 27 Dec 2018 07:32:30 -0600 (CST), David Tinker wrote:
> > Hi Guys. I am struggling to use the least squares optimizer to fit a
> > 2
> > variable non-linear function to a curve of observed data points. I am
> > pretty
> > sure I am doing something stupid because I don't know the maths. My
> > MultivariateJacobianFunction moves away from my starting values on
> > the first
> > iteration but then converges back to the starting values. My
> > variables are
> > CP and W' and this is what happens:
> >
> > cp 250.0 W' 24000.0 (starting values)
> > cp 197.17292724155843 W' 5627.212534968825
> > cp 233.7927945744999 W' 18662.916420529345
> > cp 245.72618039512386 W' 22592.92114117481
> > cp 248.91747806252718 W' 23643.613738664597
> > cp 249.99999974080222 W' 23999.9999146684
> > ...
> > cp 249.99999993520052 W' 23999.99997866709
> > optimum {250; 24,000}
> >
> > Any ideas?
>
> What happens when different starting points?
>
> Gilles
>
> > Here is the code:
> >
> > public class LeastSquaresExample {
> >
> > private static final double DELTA = 0.000001; // for calculating
> > derivatives
> >
> > public static void main(String[] args) {
> > Vector2D[] observedPoints = new Vector2D[3];
> > observedPoints[0] = new Vector2D(388, 250); // maps power in
> > watts
> > to time in seconds
> > observedPoints[1] = new Vector2D(368, 450);
> > observedPoints[2] = new Vector2D(321, 780);
> >
> > int pmax = 961;
> >
> > MultivariateJacobianFunction fn = point -> {
> > double cp = point.getEntry(0);
> > double wPrime = point.getEntry(1);
> > System.out.println("cp " + cp + " W' " + wPrime);
> >
> > RealVector value = new
> > ArrayRealVector(observedPoints.length);
> > RealMatrix jacobian = new
> > Array2DRowRealMatrix(observedPoints.length, 2);
> > for (int i = 0; i < observedPoints.length; i++) {
> > double p = observedPoints[i].getX();
> > value.setEntry(i, morton3pTime(cp, wPrime, pmax, p));
> >
> > // each row in the jacobian is a measurement and cols
> > are
> > partial derivatives wrt cp(0) and wPrime(1)
> > double a, b;
> > a = morton3pTime(cp - DELTA, wPrime, pmax, p);
> > b = morton3pTime(cp + DELTA, wPrime, pmax, p);
> > jacobian.setEntry(i, 0, (a - b) / (DELTA * 2));
> >
> > a = morton3pTime(cp, wPrime - DELTA, pmax, p);
> > b = morton3pTime(cp, wPrime + DELTA, pmax, p);
> > jacobian.setEntry(i, 1, (a - b) / (DELTA * 2));
> > }
> > return new Pair<>(value, jacobian);
> > };
> >
> > double[] target = new double[observedPoints.length];
> > for (int i = 0; i < observedPoints.length; i++) target[i] =
> > observedPoints[i].getY();
> >
> > LeastSquaresProblem problem = new LeastSquaresBuilder()
> > .start(new double[]{250.0, 24000.0})
> > .model(fn)
> > .target(target)
> > .maxEvaluations(1000)
> > .maxIterations(1000)
> > .build();
> > LeastSquaresOptimizer.Optimum optimum = new
> > LevenbergMarquardtOptimizer().optimize(problem);
> > RealVector pt = optimum.getPoint();
> > System.out.println("optimum " + pt);
> > }
> >
> > private static double morton3pTime(double cp, double wPrime,
> > double
> > pmax, double p) {
> > return wPrime / (p - cp) + wPrime / (cp - pmax);
> > }
> > }
> >
>
>
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