public static Vector <double> GetShift(Vector <double> angles, Vector <double> expectedPosition)
{
if (angles.Count < 2)
{
throw new ArgumentException("Angles vector length must be at least 2");
}
if (expectedPosition.Count != 3)
{
throw new ArgumentException("Expected position must be 3 dimensional");
}
var derr = MatrixOperations.GetDerrivativeApproximation(angles);
var res = (MatrixOperations.GetPosition(angles) - expectedPosition) * -1;
if (derr.ColumnCount > derr.RowCount)
{
var qr = derr.Transpose().QR(QRMethod.Full);
var R1 = qr.R.SubMatrix(0, 3, 0, 3);
var tmp = Vector <double> .Build.DenseOfArray(new double[angles.Count]);
tmp.SetSubVector(0, 3, R1.Transpose().Inverse() * res);
return(qr.Q * tmp);
}
else
{
return(derr.QR().Solve(res));
}
}
public static double[] GetSolution(double[] startAnglesApproximation, double[] expectedPosition, double accuracy = 0.01, int iterationLimit = 2000)
{
if (startAnglesApproximation.Length < 1)
{
throw new ArgumentException("Angles array must be at least 1 long");
}
if (expectedPosition.Length != 3)
{
throw new ArgumentException("Expeced position array must be 3 long");
}
var angles = Vector <double> .Build.DenseOfArray(startAnglesApproximation);
var position = Vector <double> .Build.DenseOfArray(expectedPosition);
double dist = 1;
Vector <double> newPosition = null;
for (int i = 0; i < iterationLimit && dist > accuracy; i++)
{
var result = GetShift(angles, position);
angles += result;
newPosition = MatrixOperations.GetPosition(angles);
dist = (newPosition - position).L2Norm();
}
int digits = Math.Max(-(int)Math.Log10(accuracy), 0);
return(dist > accuracy ? null : angles.ToArray().Select(el =>
{
var rem = (el - 180) % 360;
if (rem < 0)
{
rem += 360;
}
return Math.Round(rem - 180, digits);
}).ToArray());
}