public void Rosenbrock()
{
// starting point for search is somewhere
var initialTheta = Vector <double> .Build.DenseOfArray(new[] { -1D, 1D });
// define the hypothesis with default parameter
var rosenbrockParameter = Vector <double> .Build.DenseOfArray(new[] { 1D, 100D });
var hypothesis = new RosenbrockHypothesis();
// cost function is sum of squared errors
var costFunction = new FunctionValueOptimization <double>(hypothesis, rosenbrockParameter);
// define the optimization problem
var problem = new OptimizationProblem <double, IDifferentiableCostFunction <double> >(costFunction, initialTheta);
// optimize!
var gd = new HagerZhangCG()
{
MaxIterations = 10000,
ErrorTolerance = 1E-8D
};
var result = gd.Minimize(problem);
// assert!
var coefficients = result.Coefficients;
coefficients[0].Should().BeApproximately(rosenbrockParameter[0], 1E-5D, "because the Rosenbrock function has a minimum at x={0}, y={1}", rosenbrockParameter[0], Math.Sqrt(rosenbrockParameter[0]));
coefficients[1].Should().BeApproximately(Math.Sqrt(rosenbrockParameter[0]), 1E-5D, "because the Rosenbrock function has a minimum at x={0}, y={1}", rosenbrockParameter[0], Math.Sqrt(rosenbrockParameter[0]));
}
public void UnivariateExponentialRegressionWithResidualSumOfSquares()
{
var theta = Vector <double> .Build.DenseOfArray(new[] { 0D, 13500D, -1.7D });
var initialTheta = Vector <double> .Build.DenseOfArray(new[] { 0D, 10000D, -1D });
// define the hypothesis
var hypothesis = new UnivariateExponentialHypothesis();
// define a probability distribution
var distribution = new ContinuousUniform(0D, 1000D);
// obtain the test data
const int dataPoints = 100;
var trainingSet = new List <DataPoint <double> >(dataPoints);
for (int i = 0; i < dataPoints; ++i)
{
var inputs = Vector <double> .Build.Random(1, distribution);
var output = hypothesis.Evaluate(theta, inputs);
trainingSet.Add(new DataPoint <double>(inputs, output));
}
;
// cost function is sum of squared errors
var costFunction = new ResidualSumOfSquaresCostFunction(hypothesis, trainingSet);
// define the optimization problem
var problem = new OptimizationProblem <double, IDifferentiableCostFunction <double> >(costFunction, initialTheta);
// optimize!
var gd = new HagerZhangCG();
var result = gd.Minimize(problem);
// assert!
var coefficients = result.Coefficients;
coefficients[1].Should().BeApproximately(theta[1], 1000D, "because that's the underlying system's [a] parameter");
coefficients[2].Should().BeApproximately(theta[2], 1E-2D, "because that's the underlying system's [b] parameter");
coefficients[0].Should().BeApproximately(theta[0], 1E-5D, "because that's the underlying system's offset");
}