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QuickStart Samples

# Optimization In One Dimension QuickStart Sample (IronPython)

Illustrates the use of the Brent and Golden Section optimizer classes in the Extreme.Mathematics.Optimization namespace for one-dimensional optimization in IronPython.

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import numerics from math import exp, sqrt # The optimization classes resides in the # Extreme.Mathematics.EquationSolvers namespace. from Extreme.Mathematics.Optimization import * # Function delegates reside in the Extreme.Mathematics # namespace. from Extreme.Mathematics import * #/ Illustrates the use of the Brent and Golden Section optimizers #/ in the Extreme.Mathematics.Optimization namespace of the #/ Extreme Optimization Mathematics Library for .NET. # Several algorithms exist for optimizing functions # in one variable. The most common one is # Brent's algorithm. # The function we are trying to minimize is called the # objective function and must be provided as a Func<double, double>. # For more information about this delegate, see the # FunctionDelegates QuickStart sample. # # Brent's algorithm # # Now let's create the BrentOptimizer object. optimizer = BrentOptimizer() # Set the objective function: optimizer.ObjectiveFunction = lambda x: x ** 3 - 2 * x - 5 # Optimizers can find either a minimum or a maximum. # Which of the two is specified by the ExtremumType # property optimizer.ExtremumType = ExtremumType.Minimum # The first phase is to find an interval that contains # a local minimum. This is done by the FindBracket method. optimizer.FindBracket(0, 3) # You can verify that an interval was found from the # IsBracketValid property: if not optimizer.IsBracketValid: raise Exception("An interval containing a minimum was not found.") # Finally, we can run the optimizer by calling the FindExtremum method: optimizer.FindExtremum() print "Function 1: x^3 - 2x - 5" # The Status property indicates # the result of running the algorithm. print " Status:", optimizer.Status # The result is available through the # Result property. print " Minimum:", optimizer.Result exactResult = sqrt(2/3.0) result = optimizer.Extremum print " Exact minimum:", exactResult # You can find out the estimated error of the result # through the EstimatedError property: print " Estimated error:", optimizer.EstimatedError print " Actual error:", result - exactResult print " # iterations:", optimizer.IterationsNeeded print "Function 2: 1/Exp(x*x - 0.7*x +0.2)" f2 = lambda x: 1/exp(x**2 - 0.7*x +0.2) # You can also perform these calculations more directly # using the FindMinimum or FindMaximum methods. This implicitly # calls the FindBracket method. result = optimizer.FindMaximum(f2, 0) print " Maximum:", result print " Actual maximum:", 0.35 print " Estimated error:", optimizer.EstimatedError print " Actual error:", result - 0.35 print " # iterations:", optimizer.IterationsNeeded # # Golden section search # # A slower but simpler algorithm for finding an extremum # is the golden section search. It is implemented by the # GoldenSectionMinimizer class: optimizer2 = GoldenSectionOptimizer() # Maximum at x = 0.35 print "Using Golden Section optimizer:" result = optimizer2.FindMaximum(f2, 0) print " Maximum:", result print " Actual maximum:", 0.35 print " Estimated error:", optimizer2.EstimatedError print " Actual error:", result - 0.35 print " # iterations:", optimizer2.IterationsNeeded

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