/// <summary>
/// Compute the dot product of this vector and the given vector
/// </summary>
/// <param name="v"></param>
/// <returns></returns>
public double DotProduct(Vector v)
{
if (v.NDimensions != NDimensions)
throw new ArgumentException("Can only compute dot product for vectors of the same dimensionality");
double sum = 0;
for (int i = 0; i < v.NDimensions; i++)
{
sum += this[i]*v[i];
}
return sum;
}
/// <summary>
/// Add another vector to this one
/// </summary>
/// <param name="v"></param>
/// <returns></returns>
public Vector Add(Vector v)
{
if (v.NDimensions != NDimensions)
throw new ArgumentException("Can only add vectors of the same dimensionality");
var vector = new Vector(v.NDimensions);
for (int i = 0; i < v.NDimensions; i++)
{
vector[i] = this[i] + v[i];
}
return vector;
}
/// <summary>
/// Test a scaling operation of the high point, and replace it if it is an improvement
/// </summary>
/// <param name="scaleFactor"></param>
/// <param name="errorProfile"></param>
/// <param name="vertices"></param>
/// <param name="errorValues"></param>
/// <param name="objectiveFunction"></param>
/// <returns></returns>
private static double _tryToScaleSimplex(double scaleFactor, ref ErrorProfile errorProfile, Vector[] vertices,
double[] errorValues, ObjectiveFunctionDelegate objectiveFunction)
{
// find the centroid through which we will reflect
var centroid = _computeCentroid(vertices, errorProfile);
// define the vector from the centroid to the high point
var centroidToHighPoint = vertices[errorProfile.HighestIndex].Subtract(centroid);
// scale and position the vector to determine the new trial point
var newPoint = centroidToHighPoint.Multiply(scaleFactor).Add(centroid);
// evaluate the new point
var newErrorValue = objectiveFunction(newPoint.Components);
// if it's better, replace the old high point
if (newErrorValue < errorValues[errorProfile.HighestIndex])
{
vertices[errorProfile.HighestIndex] = newPoint;
errorValues[errorProfile.HighestIndex] = newErrorValue;
}
return newErrorValue;
}
/// <summary>
/// Contract the simplex uniformly around the lowest point
/// </summary>
/// <param name="errorProfile"></param>
/// <param name="vertices"></param>
/// <param name="errorValues"></param>
/// <param name="objectiveFunction"></param>
private static void _shrinkSimplex(ErrorProfile errorProfile, Vector[] vertices, double[] errorValues,
ObjectiveFunctionDelegate objectiveFunction)
{
var lowestVertex = vertices[errorProfile.LowestIndex];
for (int i = 0; i < vertices.Length; i++)
{
if (i != errorProfile.LowestIndex)
{
vertices[i] = (vertices[i].Add(lowestVertex)).Multiply(0.5);
errorValues[i] = objectiveFunction(vertices[i].Components);
}
}
}
/// <summary>
/// Construct an initial simplex, given starting guesses for the constants, and
/// initial step sizes for each dimension
/// </summary>
/// <param name="simplexConstants"></param>
/// <returns></returns>
private static Vector[] _initializeVertices(SimplexConstant[] simplexConstants)
{
int numDimensions = simplexConstants.Length;
var vertices = new Vector[numDimensions + 1];
// define one point of the simplex as the given initial guesses
var p0 = new Vector(numDimensions);
for (int i = 0; i < numDimensions; i++)
{
p0[i] = simplexConstants[i].Value;
}
// now fill in the vertices, creating the additional points as:
// P(i) = P(0) + Scale(i) * UnitVector(i)
vertices[0] = p0;
for (int i = 0; i < numDimensions; i++)
{
double scale = simplexConstants[i].InitialPerturbationScale;
var unitVector = new Vector(numDimensions);
unitVector[i] = 1;
vertices[i + 1] = p0.Add(unitVector.Multiply(scale));
}
return vertices;
}
/// <summary>
/// Evaluate the objective function at each vertex to create a corresponding
/// list of error values for each vertex
/// </summary>
/// <param name="vertices"></param>
/// <param name="objectiveFunction"></param>
/// <returns></returns>
private static double[] _initializeErrorValues(Vector[] vertices, ObjectiveFunctionDelegate objectiveFunction)
{
var errorValues = new double[vertices.Length];
for (int i = 0; i < vertices.Length; i++)
{
errorValues[i] = objectiveFunction(vertices[i].Components);
}
return errorValues;
}
/// <summary>
/// Compute the centroid of all points except the worst
/// </summary>
/// <param name="vertices"></param>
/// <param name="errorProfile"></param>
/// <returns></returns>
private static Vector _computeCentroid(Vector[] vertices, ErrorProfile errorProfile)
{
int numVertices = vertices.Length;
// find the centroid of all points except the worst one
var centroid = new Vector(numVertices - 1);
for (int i = 0; i < numVertices; i++)
{
if (i != errorProfile.HighestIndex)
{
centroid = centroid.Add(vertices[i]);
}
}
return centroid.Multiply(1.0d/(numVertices - 1));
}
/// <summary>
/// Multiply this vector by a scalar value
/// </summary>
/// <param name="scalar"></param>
/// <returns></returns>
public Vector Multiply(double scalar)
{
var scaledVector = new Vector(NDimensions);
for (int i = 0; i < NDimensions; i++)
{
scaledVector[i] = this[i]*scalar;
}
return scaledVector;
}