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script/weighted_least_square_opt.py

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+from mathutils import *
+from plotutils import *
+
+#Fitting the quadratic function f(x) = a x2 + b x + c
+#Data created with [a = 8, b = 10, c = 16] and 0<noise<1
+
+x = [ 1.0,  2.0,   3.0,   4.0,   5.0,   6.0,   7.0,   8.0,   9.0,  10.0]
+y = [36.0, 66.0, 121.0, 183.0, 263.0, 365.0, 473.0, 603.0, 753.0, 917.0]
+num_samples = len(x)
+w = [ 1.0] * num_samples
+W = MatrixUtils.createRealDiagonalMatrix(w)
+
+p=plot(y, xdata=x)[0]
+
+
+initial = [1.0, 1.0, 1.0]    #a, b, c
+
+class Model(MultivariateJacobianFunction):
+    def value(self, variables):
+        value = ArrayRealVector(num_samples)
+        jacobian = Array2DRowRealMatrix(num_samples, 3)        
+        for i in range(num_samples):
+            (a,b,c) = (variables.getEntry(0), variables.getEntry(1), variables.getEntry(2))   
+            model = a*x[i]*x[i] + b*x[i] + c
+            value.setEntry(i, model)                        
+            # derivative with respect to a
+            jacobian.setEntry(i, 0,  x[i]*x[i])
+            # derivative with respect to b
+            jacobian.setEntry(i, 1,  x[i])
+            # derivative with respect to c
+            jacobian.setEntry(i, 2,  1.0)            
+        
+        return Pair(value, jacobian)
+
+
+model = Model()
+
+# the target is to have all points at the specified radius from the center
+target = [v for v in y]
+problem = LeastSquaresBuilder().start(initial).model(model).target(target).lazyEvaluation(False).maxEvaluations(1000).maxIterations(1000).weight(W).build()
+optimizer = LevenbergMarquardtOptimizer()
+optimum = optimizer.optimize(problem)
+optimalValues = optimum.getPoint()
+a,b,c = optimum.getPoint().getEntry(0), optimum.getPoint().getEntry(1), optimum.getPoint().getEntry(2)
+
+print "A: ",  a 
+print "B: ",  b
+print "C: ",  c
+print ""
+print "RMS: "          , optimum.getRMS()
+print "evaluations: "  , optimum.getEvaluations()
+print "iterations: "   , optimum.getIterations()
+print ""
+for i in range (num_samples):
+    print x[i], y[i], poly(x[i], [c,b,a])
+
+ 
+plot_function(p, PolynomialFunction((c,b,a)), "Fit", x)