/// <summary>
/// Find value x that minimizes the scalar function f(x), constrained within bounds, using the Golden Section algorithm.
/// For more options and diagnostics consider to use <see cref="GoldenSectionMinimizer"/> directly.
/// </summary>
public static double OfScalarFunctionConstrained(Func <double, double> function, double lowerBound, double upperBound, double tolerance = 1e-5, int maxIterations = 1000)
{
var objective = ObjectiveFunction.ScalarValue(function);
var result = GoldenSectionMinimizer.Minimum(objective, lowerBound, upperBound, tolerance, maxIterations);
return(result.MinimizingPoint);
}
public void Test_ExpansionWorks()
{
var algorithm = new GoldenSectionMinimizer(1e-5, 1000);
var f1 = new Func <double, double>(x => (x - 3) * (x - 3));
var obj = ObjectiveFunction.ScalarValue(f1);
var r1 = algorithm.FindMinimum(obj, -5, 5);
Assert.That(Math.Abs(r1.MinimizingPoint - 3.0), Is.LessThan(1e-4));
}
// try this for multiparameter optimization: https://numerics.mathdotnet.com/api/MathNet.Numerics.Optimization.TrustRegion/index.htm
// Golden Section Minimizer
public static Value Argmin(Value function, Value lowerBound, Value upperBound, Value tolerance, Netlist netlist, Style style, int s)
{
if (!(lowerBound is NumberValue) || !(upperBound is NumberValue))
{
throw new Error("argmin: expecting numbers for lower and upper bounds");
}
double lower = (lowerBound as NumberValue).value;
double upper = (upperBound as NumberValue).value;
if (lower > upper)
{
throw new Error("argmin: lower bound greater than upper bound");
}
if (!(function is FunctionValue))
{
throw new Error("argmin: expecting a function as first argument");
}
FunctionValue closure = function as FunctionValue;
if (closure.parameters.parameters.Count != 1)
{
throw new Error("argmin: initial values and function parameters have different lengths");
}
IScalarObjectiveFunction objectiveFunction = ObjectiveFunction.ScalarValue(
(double parameter) => {
List <Value> arguments = new List <Value>(); arguments.Add(new NumberValue(parameter));
bool autoContinue = netlist.autoContinue; netlist.autoContinue = true;
Value result = closure.ApplyReject(arguments, netlist, style, s);
if (result == null)
{
throw new Error("Objective function returned null");
}
netlist.autoContinue = autoContinue;
if (!(result is NumberValue))
{
throw new Error("Objective function must return a number, not: " + result.Format(style));
}
KGui.gui.GuiOutputAppendText("argmin: parameter=" + Style.FormatSequence(arguments, ", ", x => x.Format(style)) + " => cost=" + result.Format(style) + Environment.NewLine);
return((result as NumberValue).value);
});
try {
ScalarMinimizationResult result = GoldenSectionMinimizer.Minimum(objectiveFunction, lower, upper);
if (result.ReasonForExit == ExitCondition.Converged || result.ReasonForExit == ExitCondition.BoundTolerance)
{
KGui.gui.GuiOutputAppendText("argmin: converged with parameter=" + result.MinimizingPoint + " and reason '" + result.ReasonForExit + "'" + Environment.NewLine);
return(new NumberValue(result.MinimizingPoint));
}
else
{
throw new Error("reason '" + result.ReasonForExit.ToString() + "'");
}
} catch (Exception e) { throw new Error("argmin ended: " + ((e.InnerException == null) ? e.Message : e.InnerException.Message)); } // somehow we need to recatch the inner exception coming from CostAndGradient
}
public SubtaskResult Compute(SubtaskInput subtask)
{
var goldenSectionMinimizer = new GoldenSectionMinimizer();
var polynomial = new Polynomial(subtask.Coefficients);
var function = new Func <double, double>(polynomial.Evaluate);
var objectiveFunction = ObjectiveFunction.ScalarValue(function);
var result = goldenSectionMinimizer.FindMinimum(objectiveFunction, subtask.LowerBound, subtask.UpperBound);
return(new SubtaskResult {
Point = result.MinimizingPoint, Value = result.FunctionInfoAtMinimum.Value
});
}
/// <summary>
/// 只有一个参数时的拟合方法
/// </summary>
public double[] ScalarHuberLossSolver()
{
var f1 = new Func <double, double>(ScalarHuberLoss);
var obj = ObjectiveFunction.ScalarValue(f1);
var r1 = GoldenSectionMinimizer.Minimum(obj, -10, 10);
var theta1 = r1.MinimizingPoint;
Console.WriteLine("theta1 = " + theta1);//最小时的 x 值 -> theta1
Console.WriteLine("Minimum Loss = " + ScalarHuberLoss(theta1));
scalarPred = new double[_xArr.Length];
for (var i = 0; i < _xArr.Length; i++)
{
//输出预测的y值
scalarPred[i] = theta1 * _xArr[i];
}
return(scalarPred);
}