public CircleFitter2D(IEnumerable<Point3D> initialPoints)
{
this.points = initialPoints.ToList();
// Compute point centroid
Point3D center = Point3D.Centroid(this.points);
var distances = from x in this.points select x.DistanceTo(center);
double radius = distances.Average();
var solver = new LMSolver();
// Guess for x, y, and r
double[] guess = new[] {center.X, center.Y, radius};
var fit = solver.Minimize((p, r) =>
{
// unpack the minimization parameters, x, y, and r
double x = p[0];
double y = p[1];
double rad = p[2];
Point3D testCenter = new Point3D(x, y, this.points.First().Z);
// compute the residuals
for (int i = 0; i < this.points.Count; i++)
{
r[i] = this.points[i].DistanceTo(testCenter) - rad;
}
}, guess, this.points.Count);
this.CircleCenter = new Point3D(fit.OptimizedParameters[0], fit.OptimizedParameters[1], this.points.First().Z);
this.CircleRadius = fit.OptimizedParameters[2];
}
public double[] Solve(IReadOnlyList <EquationNode> nodes, IReadOnlyList <double[]> indices)
{
var indexList = nodes.FormatIndexList(indices);
var solver = new LMSolver();
var optimizationResult =
solver.Minimize(
(p, r) =>
{
indexList.AsParallel()
.Select((x, i) => new { Result = nodes.Calculate(x, p), Row = i })
.ForAll(x => r[x.Row] = x.Result);
},
new double[indexList.First().Length],
indexList.Count);
return(optimizationResult.OptimizedParameters);
}
/// <summary>
/// Demonstrantes the usage of the generic minimization API
/// LMSolver.Minimize
/// </summary>
static void GenericMinimizationExamples(LMBackend solverType)
{
var solver = new LMSolver(optimizerBackend: solverType);
// grid points
var xs = new[] { -1.0, -1.0, 1.0, 1.0 };
var zs = new[] { -1.0, 1.0, -1.0, 1.0 };
// data points/samples
var ys = new[] { 0.0, 1.0, 1.0, 2.0 };
// Aim: fit a regression model to the samples
// Model: y' = β0 + β1 * x + β2 * z
// Regressors: x and z (provided as grid points)
// Unknown paramters: β0, β1, β2
// Design matrix X = [1 xs zs] (4x3 matrix)
// Parameter vector ε = [β0 β1 β2]^T
// Residue: ε = y - y' = y - X β
// Find β' = argmin_β sum(ε²)
var fit = solver.Minimize((p, r) => {
// compute the residue vector ε = y - y' based on the
// current parameters p (== β0, β1, β2)
var β0 = p[0];
var β1 = p[1];
var β2 = p[2];
for (int i = 0; i < ys.Length; ++i)
{
r[i] = ys[i] - (β0 + β1 * xs[i] + β2 * zs[i]);
}
}, new[] { 0.0, 0.0, 0.0 }, // initial guess for β'
ys.Length); // number of samples
Console.WriteLine();
Console.WriteLine("Aim: fit a linear 2D regression model to four samples");
Console.WriteLine(" Model: y' = β0 + β1 * x + β2 * z");
Console.WriteLine(" Regressors: x and z (grid points)");
Console.WriteLine(" Unknown paramters: β0, β1, β2");
Console.WriteLine(" Design matrix X = [1 xs zs] (4x3 matrix)");
Console.WriteLine(" Parameter vector ε = [β0 β1 β2]^T");
Console.WriteLine(" Residue: ε = y - y' = y - X β");
Console.WriteLine(" Find β' = argmin_β sum(ε²)");
Console.WriteLine("Fit: y' = {0} + {1} x + {2} z", fit.OptimizedParameters[0], fit.OptimizedParameters[1], fit.OptimizedParameters[2]);
}
