[math] Struggling with least squares Classic List Threaded 4 messages Open this post in threaded view
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[math] Struggling with least squares

 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? 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;         observedPoints = new Vector2D(388, 250); // maps power in watts to time in seconds         observedPoints = new Vector2D(368, 450);         observedPoints = 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);     } } -- Sent from: http://apache-commons.680414.n4.nabble.com/Commons-User-f735979.html--------------------------------------------------------------------- To unsubscribe, e-mail: [hidden email] For additional commands, e-mail: [hidden email]
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Re: [math] Struggling with least squares

 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; >         observedPoints = new Vector2D(388, 250); // maps power in > watts > to time in seconds >         observedPoints = new Vector2D(368, 450); >         observedPoints = 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); >     } > } > --------------------------------------------------------------------- To unsubscribe, e-mail: [hidden email] For additional commands, e-mail: [hidden email]