/// <summary>
/// Nonlinear Least Squares Solver. Fx = F(x). minimizes Norm_2(F(x))
/// </summary>
/// <param name="F">objective function</param>
/// <param name="x">input values, initial guess to start, solution on exit</param>
/// <param name="Fx">function values, just zero to start, solution on exit</param>
/// <param name="eps">precisions for stop-criteria, defaults to all 1e-9</param>
/// <param name="iter1">maximum number of iterations, defaults of 1000</param>
/// <param name="iter2">maximum number of iterations of calculation of trial-step, default of 100</param>
/// <param name="rs">initial step bound (0.1 - 100.0 recommended), default of 0.0 which MKL defaults as 100.0</param>
/// <param name="jeps">precision of the Jacobian matrix calculation</param>
/// <returns>stop criterion</returns>
public static SolveResult NonLinearLeastSquares(Action <double[], double[]> F,
double[] x, double[] Fx, double[] eps,
int iter1 = 100, int iter2 = 10,
double rs = 0.0, double jeps = 1e-7)
{
int n = x.Length;
int m = Fx.Length;
var jac = new double[n * m];
var f1 = new double[m];
var f2 = new double[m];
fixed(double *xp = &x[0], epsp = &eps[0], Fxp = &Fx[0], jacp = &jac[0], f1p = &f1[0], f2p = &f2[0])
{
IntPtr handle;
int request;
int status = dtrnlsp_init(&handle, &n, &m, xp, epsp, &iter1, &iter2, &rs);
while (status == SUCCESS && (status = dtrnlsp_solve(&handle, Fxp, jacp, &request)) == SUCCESS)
{
if (request == CALCULATE_FUNCTION)
{
if (MKL.IsNaN(x))
{
return(SolveResult.NAN_PARAMETER);
}
F(x, Fx);
}
else if (request == CALCULATE_JACOBIAN)
{
IntPtr jacHandle;
int jacRequest;
status = djacobi_init(&jacHandle, &n, &m, xp, jacp, &jeps);
if (status == SUCCESS)
{
while ((status = djacobi_solve(&jacHandle, f1p, f2p, &jacRequest)) == SUCCESS && jacRequest != 0)
{
if (MKL.IsNaN(x))
{
return(SolveResult.NAN_PARAMETER);
}
F(x, jacRequest == 1 ? f1 : f2);
}
}
djacobi_delete(&jacHandle);
}
else if (request != ONE_ITERATION)
{
status = request;
break;
}
}
dtrnlsp_delete(&handle);
return((SolveResult)status);
}
}
/// <summary>
/// Nonlinear Least Squares Solver. Fx = F(x). minimizes Norm_2(F(x))
/// </summary>
/// <param name="F">objective function</param>
/// <param name="J">Jacobian function, J_ij = df_i / dx_j as a column major array</param>
/// <param name="x">input values, initial guess to start, solution on exit</param>
/// <param name="Fx">function values, just zero to start, solution on exit</param>
/// <param name="eps">precisions for stop-criteria, defaults to all 1e-9</param>
/// <param name="iter1">maximum number of iterations, defaults of 1000</param>
/// <param name="iter2">maximum number of iterations of calculation of trial-step, default of 100</param>
/// <param name="rs">initial step bound (0.1 - 100.0 recommended), default of 0.0 which MKL defaults as 100.0</param>
/// <returns>stop criterion</returns>
public static SolveResult NonLinearLeastSquares(SolveFn F, Action <double[], double[]> J,
double[] x, double[] Fx, double[] eps,
int iter1 = 100, int iter2 = 10, double rs = 0.0)
{
int n = x.Length;
int m = Fx.Length;
var jac = new double[n * m];
fixed(double *xp = &x[0], epsp = &eps[0], Fxp = &Fx[0], jacp = &jac[0])
{
IntPtr handle;
int request;
var status = dtrnlsp_init(&handle, &n, &m, xp, epsp, &iter1, &iter2, &rs);
if (status == SUCCESS)
{
while ((status = dtrnlsp_solve(&handle, Fxp, jacp, &request)) == SUCCESS)
{
if (request == CALCULATE_FUNCTION)
{
if (MKL.IsNaN(x))
{
return(SolveResult.NAN_PARAMETER);
}
F(&m, &n, xp, Fxp);
}
else if (request == CALCULATE_JACOBIAN)
{
if (MKL.IsNaN(x))
{
return(SolveResult.NAN_PARAMETER);
}
J(x, jac);
}
else if (request != ONE_ITERATION)
{
status = request;
break;
}
}
}
dtrnlsp_delete(&handle);
return((SolveResult)status);
}
}
/// <summary>
/// Nonlinear Least Squares Solver. Fx = F(x). minimizes Norm_2(F(x))
/// </summary>
/// <param name="F">objective function, not called in parallel</param>
/// <param name="x">input values, initial guess to start, solution on exit</param>
/// <param name="lower">x lower bound</param>
/// <param name="upper">x upper bound</param>
/// <param name="Fx">function values, just zero to start, solution on exit</param>
/// <param name="eps">precisions for stop-criteria, defaults to all 1e-9</param>
/// <param name="iter1">maximum number of iterations, defaults of 1000</param>
/// <param name="iter2">maximum number of iterations of calculation of trial-step, default of 100</param>
/// <param name="rs">initial step bound (0.1 - 100.0 recommended), default of 0.0 which MKL defaults as 100.0</param>
/// <param name="jeps">precision of the Jacobian matrix calculation</param>
/// <returns>stop criterion</returns>
public static SolveResult NonLinearLeastSquaresBounded(Action <double[], double[]> F,
double[] x, double[] lower, double[] upper, double[] Fx, double[] eps,
int iter1 = 100, int iter2 = 10, double rs = 0.1, double jeps = 1e-7)
{
//1. dtrnlsp_init(ref handle, ref n, ref m, x, eps, ref iter1, ref iter2, ref rs)
//2.dtrnlsp_check(ref handle, ref n, ref m, fjac, fvec, eps, info)
//3.LOOP dtrnlsp_solve(ref handle, fvec, fjac, ref RCI_Request)
//4.dtrnlsp_get(ref handle, ref iter, ref st_cr, ref r1, ref r2)
//5.dtrnlsp_delete(ref handle)
int n = x.Length;
int m = Fx.Length;
var jac = new double[n * m];
var f1 = new double[m];
var f2 = new double[m];
fixed(double *xp = &x[0], lowerp = &lower[0], upperp = &upper[0], epsp = &eps[0], Fxp = &Fx[0],
jacp = &jac[0], f1p = &f1[0], f2p = &f2[0])
{
IntPtr handle;
int RCI_request;
int status = dtrnlspbc_init(&handle, &n, &m, xp, lowerp, upperp, epsp, &iter1, &iter2, &rs);
while (status == SUCCESS && (status = dtrnlspbc_solve(&handle, Fxp, jacp, &RCI_request)) == SUCCESS)
{
if (RCI_request == CALCULATE_FUNCTION)
{
if (MKL.IsNaN(x))
{
return(SolveResult.NAN_PARAMETER);
}
F(x, Fx);
}
else if (RCI_request == CALCULATE_JACOBIAN)
{
IntPtr jacHandle;
int jacRequest;
status = djacobi_init(&jacHandle, &n, &m, xp, jacp, &jeps);
if (status == SUCCESS)
{
while ((status = djacobi_solve(&jacHandle, f1p, f2p, &jacRequest)) == SUCCESS && jacRequest != 0)
{
if (MKL.IsNaN(x))
{
return(SolveResult.NAN_PARAMETER);
}
F(x, jacRequest == 1 ? f1 : f2);
}
}
djacobi_delete(&jacHandle);
}
else if (RCI_request != ONE_ITERATION)
{
status = RCI_request;
break;
}
}
dtrnlspbc_delete(&handle);
return((SolveResult)status);
}
}