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script/test30.py

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+################################################################################################### 
+# Example of least squares optimization
+# http://commons.apache.org/proper/commons-math/userguide/leastsquares.html
+################################################################################################### 
+
+
+from mathutils import *
+from plotutils import *
+
+[p1,p2] = plot([None, None], [None, None])
+
+################################################################################################### 
+#Fitting the quadratic function f(x) = a x2 + b x + c  
+################################################################################################### 
+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)
+weigths = [ 1.0] * num_samples
+
+p1.getSeries(0).setData(x, y)
+p1.getSeries(0)
+
+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)                                    
+            jacobian.setEntry(i, 0,  x[i]*x[i])  # derivative with respect to p0 = a            
+            jacobian.setEntry(i, 1,  x[i])       # derivative with respect to p1 = b            
+            jacobian.setEntry(i, 2,  1.0)        # derivative with respect to p2 = c        
+        return Pair(value, jacobian)
+
+model = Model()
+initial = [1.0, 1.0, 1.0]    #parameters = a, b, c
+target = [v for v in y]      #the target is to have all points at the positios
+
+(parameters, residuals, rms, evals, iters) = optimize_least_squares(model, target, initial, weigths)
+
+(a,b,c) = parameters
+
+print "A: ",  a , "  B: ",  b, "  C: ",  c
+print "RMS: " , rms,  "  evals: "  , evals,  "  iters: "   , iters
+for i in range (num_samples):
+    print x[i], y[i], poly(x[i], [c,b,a])
+
+plot_function(p1, PolynomialFunction((c,b,a)), "Fit", x)
+print "----------------------------------------------------------------------------\n"
+
+
+################################################################################################### 
+#Fiting center of circle of known radius to observerd points
+################################################################################################### 
+
+
+#Fiting center of circle of radius 70  to observerd points
+radius = 70.0
+x = [30.0,  50.0, 110.0, 35.0, 45.0]
+y = [68.0,  -6.0, -20.0, 15.0, 97.0]
+num_samples = len(x)
+weigths = [ 1.0] * num_samples
+weigths = [0.1,  0.1, 1.0, 0.1, 1.0]
+
+p2.getSeries(0).setData(x, y)
+p2.getSeries(0).setLinesVisible(False)
+p2.getSeries(0).setPointSize(4)
+
+# the model function components are the distances to current estimated center,
+# they should be as close as possible to the specified radius
+class Model(MultivariateJacobianFunction):
+    def value(self, variables):
+        (cx,cy) = (variables.getEntry(0), variables.getEntry(1))  
+        value = ArrayRealVector(num_samples)
+        jacobian = Array2DRowRealMatrix(num_samples, 2)
+        for i in range(num_samples):
+            model = math.hypot(cx-x[i], cy-y[i]) 
+            value.setEntry(i, model)            
+            jacobian.setEntry(i, 0, (cx - x[i]) / model)  # derivative with respect to p0 = x center                
+            jacobian.setEntry(i, 1, (cy - y[i]) / model)  # derivative with respect to p1 = y center
+        return Pair(value, jacobian)
+
+model = Model()                    #modeled radius should be close to target radius
+initial = [mean(x), mean(y)]       #parameters = cx, cy
+target = [radius,] * num_samples   #the target is to have all points at the specified radius from the center
+
+(parameters, residuals, rms, evals, iters) = optimize_least_squares(model, target, initial, weigths)
+
+(cx, cy) = parameters
+
+print "CX: ",  cx , "  CY: ",  cy
+print "RMS: " , rms,  "  evals: "  , evals,  "  iters: "   , iters
+
+
+from plotutils import *        
+plot_point(p2, cx, cy, name="Fit Cente")
+plot_circle(p2, cx, cy, radius, name="Fit")