public NewtonRaphson(Parameter[] parameters, Func <double>[] functions, int numberOfDerivativePoints = 3)
{
_parameters = parameters;
_functions = functions;
int numberOfFunctions = _functions.Length;
int numberOfParameters = _parameters.Length;
_derivatives = new Derivatives(numberOfDerivativePoints);
_jacobian = new Matrix(numberOfFunctions, numberOfParameters);
_functionMatrix = new Matrix(numberOfFunctions, 1);
_x0 = new Matrix(numberOfFunctions, 1);
}
public static Parameter[] Compute(Func <double>[] regressionFunctions, Parameter[] regressionParameters, Parameter[] observedParameters, double[,] data, int numberOfDerivativePoints)
{
double l0 = 100.0;
double v = 10.0;
Derivatives derivatives = new Derivatives(numberOfDerivativePoints);
Matrix jacobian = new Matrix(regressionFunctions.Length * data.GetLength(0), regressionParameters.Length);
Matrix residuals = new Matrix(regressionFunctions.Length * data.GetLength(0), 1);
Matrix regressionParameters0 = new Matrix(regressionParameters.Length, 1);
for (int f = 0; f < 10000; f++)
{
int numberOfPoints = data.GetLength(0);
int numberOfParameters = regressionParameters.Length;
int numberOfFunctions = regressionFunctions.Length;
double error = 0.0;
for (int i = 0; i < numberOfFunctions; i++)
{
for (int j = 0; j < numberOfPoints; j++)
{
for (int k = 0; k < observedParameters.Length; k++)
{
observedParameters[k].Value = data[j, k];
}
double functionValue = regressionFunctions[i]();
double residual = data[j, observedParameters.Length + i] - functionValue;
residuals[j + i * numberOfPoints, 0] = residual;
error += residual * residual;
for (int k = 0; k < numberOfParameters; k++)
{
jacobian[j + i * numberOfPoints, k] = derivatives.ComputePartialDerivative(regressionFunctions[i], regressionParameters[k], 1, functionValue);
}
}
}
for (int i = 0; i < numberOfParameters; i++)
{
regressionParameters0[i, 0] = regressionParameters[i];
}
Matrix jacobianTranspose = jacobian.Transpose();
Matrix jacobianTransposeResiduals = jacobianTranspose * residuals;
Matrix jacobianTransposeJacobian = jacobianTranspose * jacobian;
Matrix jacobianTransposeJacobianDiagnol = new Matrix(jacobianTransposeJacobian.RowCount, jacobianTransposeJacobian.RowCount);
for (int i = 0; i < jacobianTransposeJacobian.RowCount; i++)
{
jacobianTransposeJacobianDiagnol[i, i] = jacobianTransposeJacobian[i, i];
}
double newResidual = error + 1.0;
l0 /= v;
while (newResidual > error)
{
newResidual = 0.0; l0 *= v;
Matrix matLHS = jacobianTransposeJacobian + l0 * jacobianTransposeJacobianDiagnol;
var delta = matLHS.SolveFor(jacobianTransposeResiduals);
;
var newRegressionParameters = regressionParameters0 + delta;
for (int i = 0; i < numberOfParameters; i++)
{
regressionParameters[i].Value = newRegressionParameters[i, 0];
}
for (int i = 0; i < numberOfFunctions; i++)
{
for (int j = 0; j < numberOfPoints; j++)
{
for (int k = 0; k < observedParameters.Length; k++)
{
observedParameters[k].Value = data[j, k];
}
double functionValue = regressionFunctions[i]();
double residual = data[j, observedParameters.Length + i] - functionValue; newResidual += residual * residual;
}
}
}
l0 /= v;
}
return(regressionParameters);
}