public VectorMinimizationResult FindRoot(IObjectiveVectorFunction objective, Vector <double> initialGuess)
{
var jacobian = Matrix <double> .Build.Dense(initialGuess.Count, initialGuess.Count);
var guess = initialGuess.Clone();
int iterCount;
for (iterCount = 0; iterCount < _maximumIterations; iterCount++)
{
objective.EvaluateAt(guess);
var baseValues = objective.Value.Clone();
if (baseValues.AbsoluteMaximum() < _convergenceTolerance)
{
break;
}
UpdateJacobian(jacobian, objective);
var inverse = jacobian.Inverse();
guess = guess - inverse * baseValues;
}
var result = new VectorMinimizationResult
{
FunctionInfoAtMinimum = objective,
Iterations = iterCount,
MinimizingPoint = guess,
ReasonForExit = ExitCondition.Converged
};
return(result);
}
/// <summary>
/// Element (i, j) is the df_i/dx_j. i.e it is the partial derivative of the ith element of f with respect to the jth input.
/// </summary>
/// <param name="jacobian"></param>
/// <param name="objective"></param>
private void UpdateJacobian(Matrix <double> jacobian, IObjectiveVectorFunction objective)
{
var baseValues = objective.Value.Clone();
var point = objective.Point;
for (var col = 0; col < jacobian.ColumnCount; col++)
{
point[col] += shift;
objective.EvaluateAt(point);
var allZero = true;
for (var row = 0; row < jacobian.RowCount; row++)
{
jacobian[row, col] = (objective.Value[row] - baseValues[row]) / shift;
if (allZero && Math.Abs(jacobian[row, col]) > 1e-12)
{
allZero = false;
}
}
if (allZero)
{
throw new ArgumentException($"instrument at position {col} has no sensitivity to any inputs.");
}
point[col] -= shift;
}
}
internal double[] Eval(double[] point)
{
_objective.EvaluateAt(new DenseVector(point));
return(_objective.Value.AsArray());
}