/// <summary>
/// Uses Infer3DExactLMS to infer a random world point from a number of different projections of the point.
/// It writes out the squared errors corresponding to different number of projections into a file.
/// </summary>
/// <param name="numProjections">the max number of projections to use.</param>
/// <param name="gaussianNoiseSigma">the standard deviation of the gaussian noise to be added to the projected points.</param>
public static void ShowErrorInfer3DExactLMS(int numProjections, double gaussianNoiseSigma, string fileName)
{
ContinuousUniform dist = new ContinuousUniform(0, 1);
Normal gaussianNoise = new Normal(0, gaussianNoiseSigma);
DenseMatrix worldPoint = new DenseMatrix(4,1);
worldPoint = (DenseMatrix) worldPoint.Random(4,1, dist);
ProjectedPoint[] projections = new ProjectedPoint[numProjections];
for (int i = 0; i < projections.Length; i++)
{
projections[i] = new ProjectedPoint();
projections[i].worldToImage = new DenseMatrix(3, 4);
projections[i].worldToImage = (DenseMatrix)projections[i].worldToImage.Random(3, 4, dist);
projections[i].projectedPoint = (projections[i].worldToImage * worldPoint);
projections[i].projectedPoint += (DenseMatrix)projections[i].projectedPoint.Random(3, 1, gaussianNoise);
}
File.WriteAllLines(fileName,
Enumerable.Range(2, numProjections)
.Select(i => String.Format("{0}\t{1}", i, (worldPoint - Infer3DExactLMS(projections.Take(i))).L2Norm())));
}