/// <summary>
/// Get Jacobian matrix of the objective function.
/// </summary>
/// <param name = "model">Model function.</param>
/// <param name = "pointCount">Number of data points.</param>
/// <param name = "dataX">X-coordinates of the data points.</param>
/// <param name = "dataY">Y-coordinates of the data points.</param>
/// <param name = "parameters">Model function parameters.</param>
/// <param name = "jacobian">Jacobian matrix of the objective function.</param>
private void GetObjectiveJacobian(PowerModel model, int pointCount, Vector <double> parameters, ref Matrix <double> jacobian)
{
int parameterCount = parameters.Count;
// fill rows of the Jacobian matrix
// j-th row of a Jacobian is the gradient of model function in j-th measurement
for (int j = 0; j < pointCount; j++)
{
Vector <double> gradient = new DenseVector(parameterCount);
model.GetGradient(
dataX[j],
parameters,
ref gradient);
jacobian.SetRow(j, gradient);
}
}
/// <summary>
/// Get value of the objective function.
/// </summary>
/// <param name = "model">Model function.</param>
/// <param name = "pointCount">Number of data points.</param>
/// <param name = "dataX">X-coordinates of the data points.</param>
/// <param name = "dataY">Y-coordinates of the data points.</param>
/// <param name = "parameters">Model function parameters.</param>
/// <param name = "value">Objective function value.</param>
private void GetObjectiveValue(PowerModel model, int pointCount, Vector <double> parameters, out double value)
{
value = 0.0;
double y = 0.0;
for (int j = 0; j < pointCount; j++)
{
model.GetValue(
dataX[j],
parameters,
out y);
value += Math.Pow(
y - dataY[j],
2.0);
}
value *= 0.5;
}
/// <summary>
/// Estimates the specified model.
/// </summary>
/// <param name = "model">Model function.</param>
/// <param name = "solverOptions">Least squares solver options.</param>
/// <param name = "pointCount">Number of data points.</param>
/// <param name = "dataX">X-coordinates of the data points.</param>
/// <param name = "dataY">Y-coordinates of the data points.</param>
/// <param name = "iterations">Estimated model function parameters.</param>
public void Estimate(PowerModel model, int pointCount, Vector <double> dataX, Vector <double> dataY, ref List <Vector <double> > iterations)
{
this.dataX = dataX;
this.dataY = dataY;
int n = guess.Count;
Vector <double> parametersCurrent = guess;
Vector <double> parametersNew = new DenseVector(n);
double valueCurrent;
double valueNew;
GetObjectiveValue(model, pointCount, parametersCurrent, out valueCurrent);
while (true)
{
Matrix <double> jacobian = new DenseMatrix(pointCount, n);
Vector <double> residual = new DenseVector(pointCount);
GetObjectiveJacobian(model, pointCount, parametersCurrent, ref jacobian);
model.GetResidualVector(pointCount, dataX, dataY, parametersCurrent, ref residual);
Vector <double> step = jacobian.Transpose().Multiply(jacobian).Cholesky().Solve(jacobian.Transpose().Multiply(residual));
parametersCurrent.Subtract(step, parametersNew);
GetObjectiveValue(model, pointCount, parametersNew, out valueNew);
iterations.Add(parametersNew);
if (ShouldTerminate(valueCurrent, valueNew, iterations.Count, parametersCurrent, parametersNew))
{
break;
}
parametersNew.CopyTo(parametersCurrent);
valueCurrent = valueNew;
}
}