source: trunk/sources/HeuristicLab.ExtLibs/HeuristicLab.ALGLIB/2.1.2.2591/ALGLIB-2.1.2.2591/minlm.cs @ 3031

/*************************************************************************
Copyright (c) 2009, Sergey Bochkanov (ALGLIB project).

>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the 
License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses

>>> END OF LICENSE >>>
*************************************************************************/

using System;

namespace alglib
{
    public class minlm
    {
        public struct lmstate
        {
            public bool wrongparams;
            public int n;
            public int m;
            public double epsf;
            public double epsx;
            public int maxits;
            public int flags;
            public int usermode;
            public double[] x;
            public double f;
            public double[] fi;
            public double[,] j;
            public double[,] h;
            public double[] g;
            public bool needf;
            public bool needfg;
            public bool needfgh;
            public bool needfij;
            public bool xupdated;
            public lbfgs.lbfgsstate internalstate;
            public lbfgs.lbfgsreport internalrep;
            public double[] xprec;
            public double[] xbase;
            public double[] xdir;
            public double[] gbase;
            public double[,] rawmodel;
            public double[,] model;
            public double[] work;
            public AP.rcommstate rstate;
            public int repiterationscount;
            public int repterminationtype;
            public int repnfunc;
            public int repnjac;
            public int repngrad;
            public int repnhess;
            public int repncholesky;
        };


        public struct lmreport
        {
            public int iterationscount;
            public int terminationtype;
            public int nfunc;
            public int njac;
            public int ngrad;
            public int nhess;
            public int ncholesky;
        };




        public const int lmmodefj = 0;
        public const int lmmodefgj = 1;
        public const int lmmodefgh = 2;
        public const int lmflagnoprelbfgs = 1;
        public const int lmflagnointlbfgs = 2;
        public const int lmprelbfgsm = 5;
        public const int lmintlbfgsits = 5;
        public const int lbfgsnorealloc = 1;


        /*************************************************************************
            LEVENBERG-MARQUARDT-LIKE METHOD FOR NON-LINEAR OPTIMIZATION

        Optimization using function gradient and Hessian.  Algorithm -  Levenberg-
        Marquardt   modification   with   L-BFGS   pre-optimization  and  internal
        pre-conditioned L-BFGS optimization after each Levenberg-Marquardt step.

        Function F has general form (not "sum-of-squares"):

            F = F(x[0], ..., x[n-1])

        EXAMPLE

        See HTML-documentation.

        INPUT PARAMETERS:
            N       -   dimension, N>1
            X       -   initial solution, array[0..N-1]
            EpsF    -   stopping criterion. Algorithm stops if
                        |F(k+1)-F(k)| <= EpsF*max{|F(k)|, |F(k+1)|, 1}
            EpsX    -   stopping criterion. Algorithm stops if
                        |X(k+1)-X(k)| <= EpsX*(1+|X(k)|)
            MaxIts  -   stopping criterion. Algorithm stops after MaxIts iterations.
                        MaxIts=0 means no stopping criterion.

        OUTPUT PARAMETERS:
            State   -   structure which stores algorithm state between subsequent
                        calls of MinLMIteration. Used for reverse communication.
                        This structure should be passed to MinLMIteration subroutine.

        See also MinLMIteration, MinLMResults.

        NOTE

        Passing EpsF=0, EpsX=0 and MaxIts=0 (simultaneously) will lead to automatic
        stopping criterion selection (small EpsX).

          -- ALGLIB --
             Copyright 30.03.2009 by Bochkanov Sergey
        *************************************************************************/
        public static void minlmfgh(int n,
            ref double[] x,
            double epsf,
            double epsx,
            int maxits,
            ref lmstate state)
        {
            int i_ = 0;

            
            //
            // Prepare RComm
            //
            state.rstate.ia = new int[3+1];
            state.rstate.ba = new bool[0+1];
            state.rstate.ra = new double[8+1];
            state.rstate.stage = -1;
            
            //
            // prepare internal structures
            //
            lmprepare(n, 0, true, ref state);
            
            //
            // initialize, check parameters
            //
            state.xupdated = false;
            state.n = n;
            state.m = 0;
            state.epsf = epsf;
            state.epsx = epsx;
            state.maxits = maxits;
            state.flags = 0;
            if( (double)(state.epsf)==(double)(0) & (double)(state.epsx)==(double)(0) & state.maxits==0 )
            {
                state.epsx = 1.0E-6;
            }
            state.usermode = lmmodefgh;
            state.wrongparams = false;
            if( n<1 | (double)(epsf)<(double)(0) | (double)(epsx)<(double)(0) | maxits<0 )
            {
                state.wrongparams = true;
                return;
            }
            for(i_=0; i_<=n-1;i_++)
            {
                state.x[i_] = x[i_];
            }
        }


        /*************************************************************************
            LEVENBERG-MARQUARDT-LIKE METHOD FOR NON-LINEAR OPTIMIZATION

        Optimization using function gradient and Jacobian.  Algorithm -  Levenberg-
        Marquardt   modification   with   L-BFGS   pre-optimization  and  internal
        pre-conditioned L-BFGS optimization after each Levenberg-Marquardt step.

        Function F is represented as sum of squares:

            F = f[0]^2(x[0],...,x[n-1]) + ... + f[m-1]^2(x[0],...,x[n-1])

        EXAMPLE

        See HTML-documentation.

        INPUT PARAMETERS:
            N       -   dimension, N>1
            M       -   number of functions f[i]
            X       -   initial solution, array[0..N-1]
            EpsF    -   stopping criterion. Algorithm stops if
                        |F(k+1)-F(k)| <= EpsF*max{|F(k)|, |F(k+1)|, 1}
            EpsX    -   stopping criterion. Algorithm stops if
                        |X(k+1)-X(k)| <= EpsX*(1+|X(k)|)
            MaxIts  -   stopping criterion. Algorithm stops after MaxIts iterations.
                        MaxIts=0 means no stopping criterion.

        OUTPUT PARAMETERS:
            State   -   structure which stores algorithm state between subsequent
                        calls of MinLMIteration. Used for reverse communication.
                        This structure should be passed to MinLMIteration subroutine.

        See also MinLMIteration, MinLMResults.

        NOTE

        Passing EpsF=0, EpsX=0 and MaxIts=0 (simultaneously) will lead to automatic
        stopping criterion selection (small EpsX).

          -- ALGLIB --
             Copyright 30.03.2009 by Bochkanov Sergey
        *************************************************************************/
        public static void minlmfgj(int n,
            int m,
            ref double[] x,
            double epsf,
            double epsx,
            int maxits,
            ref lmstate state)
        {
            int i_ = 0;

            
            //
            // Prepare RComm
            //
            state.rstate.ia = new int[3+1];
            state.rstate.ba = new bool[0+1];
            state.rstate.ra = new double[8+1];
            state.rstate.stage = -1;
            
            //
            // prepare internal structures
            //
            lmprepare(n, m, true, ref state);
            
            //
            // initialize, check parameters
            //
            state.xupdated = false;
            state.n = n;
            state.m = m;
            state.epsf = epsf;
            state.epsx = epsx;
            state.maxits = maxits;
            state.flags = 0;
            if( (double)(state.epsf)==(double)(0) & (double)(state.epsx)==(double)(0) & state.maxits==0 )
            {
                state.epsx = 1.0E-6;
            }
            state.usermode = lmmodefgj;
            state.wrongparams = false;
            if( n<1 | m<1 | (double)(epsf)<(double)(0) | (double)(epsx)<(double)(0) | maxits<0 )
            {
                state.wrongparams = true;
                return;
            }
            for(i_=0; i_<=n-1;i_++)
            {
                state.x[i_] = x[i_];
            }
        }


        /*************************************************************************
            CLASSIC LEVENBERG-MARQUARDT METHOD FOR NON-LINEAR OPTIMIZATION

        Optimization using Jacobi matrix. Algorithm  -  classic Levenberg-Marquardt
        method.

        Function F is represented as sum of squares:

            F = f[0]^2(x[0],...,x[n-1]) + ... + f[m-1]^2(x[0],...,x[n-1])

        EXAMPLE

        See HTML-documentation.

        INPUT PARAMETERS:
            N       -   dimension, N>1
            M       -   number of functions f[i]
            X       -   initial solution, array[0..N-1]
            EpsF    -   stopping criterion. Algorithm stops if
                        |F(k+1)-F(k)| <= EpsF*max{|F(k)|, |F(k+1)|, 1}
            EpsX    -   stopping criterion. Algorithm stops if
                        |X(k+1)-X(k)| <= EpsX*(1+|X(k)|)
            MaxIts  -   stopping criterion. Algorithm stops after MaxIts iterations.
                        MaxIts=0 means no stopping criterion.

        OUTPUT PARAMETERS:
            State   -   structure which stores algorithm state between subsequent
                        calls of MinLMIteration. Used for reverse communication.
                        This structure should be passed to MinLMIteration subroutine.

        See also MinLMIteration, MinLMResults.

        NOTE

        Passing EpsF=0, EpsX=0 and MaxIts=0 (simultaneously) will lead to automatic
        stopping criterion selection (small EpsX).

          -- ALGLIB --
             Copyright 30.03.2009 by Bochkanov Sergey
        *************************************************************************/
        public static void minlmfj(int n,
            int m,
            ref double[] x,
            double epsf,
            double epsx,
            int maxits,
            ref lmstate state)
        {
            int i_ = 0;

            
            //
            // Prepare RComm
            //
            state.rstate.ia = new int[3+1];
            state.rstate.ba = new bool[0+1];
            state.rstate.ra = new double[8+1];
            state.rstate.stage = -1;
            
            //
            // prepare internal structures
            //
            lmprepare(n, m, true, ref state);
            
            //
            // initialize, check parameters
            //
            state.xupdated = false;
            state.n = n;
            state.m = m;
            state.epsf = epsf;
            state.epsx = epsx;
            state.maxits = maxits;
            state.flags = 0;
            if( (double)(state.epsf)==(double)(0) & (double)(state.epsx)==(double)(0) & state.maxits==0 )
            {
                state.epsx = 1.0E-6;
            }
            state.usermode = lmmodefj;
            state.wrongparams = false;
            if( n<1 | m<1 | (double)(epsf)<(double)(0) | (double)(epsx)<(double)(0) | maxits<0 )
            {
                state.wrongparams = true;
                return;
            }
            for(i_=0; i_<=n-1;i_++)
            {
                state.x[i_] = x[i_];
            }
        }


        /*************************************************************************
        One Levenberg-Marquardt iteration.

        Called after inialization of State structure with MinLMXXX subroutine.
        See HTML docs for examples.

        Input parameters:
            State   -   structure which stores algorithm state between subsequent
                        calls and which is used for reverse communication. Must be
                        initialized with MinLMXXX call first.

        If subroutine returned False, iterative algorithm has converged.

        If subroutine returned True, then:
        * if State.NeedF=True,      -   function value F at State.X[0..N-1]
                                        is required
        * if State.NeedFG=True      -   function value F and gradient G
                                        are required
        * if State.NeedFiJ=True     -   function vector f[i] and Jacobi matrix J
                                        are required
        * if State.NeedFGH=True     -   function value F, gradient G and Hesian H
                                        are required

        One and only one of this fields can be set at time.

        Results are stored:
        * function value            -   in LMState.F
        * gradient                  -   in LMState.G[0..N-1]
        * Jacobi matrix             -   in LMState.J[0..M-1,0..N-1]
        * Hessian                   -   in LMState.H[0..N-1,0..N-1]

          -- ALGLIB --
             Copyright 10.03.2009 by Bochkanov Sergey
        *************************************************************************/
        public static bool minlmiteration(ref lmstate state)
        {
            bool result = new bool();
            int n = 0;
            int m = 0;
            int i = 0;
            double xnorm = 0;
            double stepnorm = 0;
            bool spd = new bool();
            double fbase = 0;
            double fnew = 0;
            double lambda = 0;
            double nu = 0;
            double lambdaup = 0;
            double lambdadown = 0;
            int lbfgsflags = 0;
            double v = 0;
            int i_ = 0;

            
            //
            // Reverse communication preparations
            // I know it looks ugly, but it works the same way
            // anywhere from C++ to Python.
            //
            // This code initializes locals by:
            // * random values determined during code
            //   generation - on first subroutine call
            // * values from previous call - on subsequent calls
            //
            if( state.rstate.stage>=0 )
            {
                n = state.rstate.ia[0];
                m = state.rstate.ia[1];
                i = state.rstate.ia[2];
                lbfgsflags = state.rstate.ia[3];
                spd = state.rstate.ba[0];
                xnorm = state.rstate.ra[0];
                stepnorm = state.rstate.ra[1];
                fbase = state.rstate.ra[2];
                fnew = state.rstate.ra[3];
                lambda = state.rstate.ra[4];
                nu = state.rstate.ra[5];
                lambdaup = state.rstate.ra[6];
                lambdadown = state.rstate.ra[7];
                v = state.rstate.ra[8];
            }
            else
            {
                n = -983;
                m = -989;
                i = -834;
                lbfgsflags = 900;
                spd = true;
                xnorm = 364;
                stepnorm = 214;
                fbase = -338;
                fnew = -686;
                lambda = 912;
                nu = 585;
                lambdaup = 497;
                lambdadown = -271;
                v = -581;
            }
            if( state.rstate.stage==0 )
            {
                goto lbl_0;
            }
            if( state.rstate.stage==1 )
            {
                goto lbl_1;
            }
            if( state.rstate.stage==2 )
            {
                goto lbl_2;
            }
            if( state.rstate.stage==3 )
            {
                goto lbl_3;
            }
            if( state.rstate.stage==4 )
            {
                goto lbl_4;
            }
            if( state.rstate.stage==5 )
            {
                goto lbl_5;
            }
            if( state.rstate.stage==6 )
            {
                goto lbl_6;
            }
            
            //
            // Routine body
            //
            System.Diagnostics.Debug.Assert(state.usermode==lmmodefj | state.usermode==lmmodefgj | state.usermode==lmmodefgh, "LM: internal error");
            if( state.wrongparams )
            {
                state.repterminationtype = -1;
                result = false;
                return result;
            }
            
            //
            // prepare params
            //
            n = state.n;
            m = state.m;
            lambdaup = 10;
            lambdadown = 0.3;
            nu = 2;
            lbfgsflags = 0;
            
            //
            // if we have F and G
            //
            if( ! ((state.usermode==lmmodefgj | state.usermode==lmmodefgh) & state.flags/lmflagnoprelbfgs%2==0) )
            {
                goto lbl_7;
            }
            
            //
            // First stage of the hybrid algorithm: LBFGS
            //
            lbfgs.minlbfgs(n, Math.Min(n, lmprelbfgsm), ref state.x, 0.0, 0.0, 0.0, Math.Max(25, n), 0, ref state.internalstate);
        lbl_9:
            if( ! lbfgs.minlbfgsiteration(ref state.internalstate) )
            {
                goto lbl_10;
            }
            
            //
            // RComm
            //
            for(i_=0; i_<=n-1;i_++)
            {
                state.x[i_] = state.internalstate.x[i_];
            }
            lmclearrequestfields(ref state);
            state.needfg = true;
            state.rstate.stage = 0;
            goto lbl_rcomm;
        lbl_0:
            state.repnfunc = state.repnfunc+1;
            state.repngrad = state.repngrad+1;
            
            //
            // Call LBFGS
            //
            state.internalstate.f = state.f;
            for(i_=0; i_<=n-1;i_++)
            {
                state.internalstate.g[i_] = state.g[i_];
            }
            goto lbl_9;
        lbl_10:
            lbfgs.minlbfgsresults(ref state.internalstate, ref state.x, ref state.internalrep);
        lbl_7:
            
            //
            // Second stage of the hybrid algorithm: LM
            // Initialize quadratic model.
            //
            if( state.usermode!=lmmodefgh )
            {
                goto lbl_11;
            }
            
            //
            // RComm
            //
            lmclearrequestfields(ref state);
            state.needfgh = true;
            state.rstate.stage = 1;
            goto lbl_rcomm;
        lbl_1:
            state.repnfunc = state.repnfunc+1;
            state.repngrad = state.repngrad+1;
            state.repnhess = state.repnhess+1;
            
            //
            // generate raw quadratic model
            //
            for(i=0; i<=n-1; i++)
            {
                for(i_=0; i_<=n-1;i_++)
                {
                    state.rawmodel[i,i_] = state.h[i,i_];
                }
            }
            for(i_=0; i_<=n-1;i_++)
            {
                state.gbase[i_] = state.g[i_];
            }
            fbase = state.f;
        lbl_11:
            if( ! (state.usermode==lmmodefgj | state.usermode==lmmodefj) )
            {
                goto lbl_13;
            }
            
            //
            // RComm
            //
            lmclearrequestfields(ref state);
            state.needfij = true;
            state.rstate.stage = 2;
            goto lbl_rcomm;
        lbl_2:
            state.repnfunc = state.repnfunc+1;
            state.repnjac = state.repnjac+1;
            
            //
            // generate raw quadratic model
            //
            blas.matrixmatrixmultiply(ref state.j, 0, m-1, 0, n-1, true, ref state.j, 0, m-1, 0, n-1, false, 1.0, ref state.rawmodel, 0, n-1, 0, n-1, 0.0, ref state.work);
            blas.matrixvectormultiply(ref state.j, 0, m-1, 0, n-1, true, ref state.fi, 0, m-1, 1.0, ref state.gbase, 0, n-1, 0.0);
            fbase = 0.0;
            for(i_=0; i_<=m-1;i_++)
            {
                fbase += state.fi[i_]*state.fi[i_];
            }
        lbl_13:
            lambda = 0.001;
        lbl_15:
            if( false )
            {
                goto lbl_16;
            }
            
            //
            // 1. Model = RawModel+lambda*I
            // 2. Try to solve (RawModel+Lambda*I)*dx = -g.
            //    Increase lambda if left part is not positive definite.
            //
            for(i=0; i<=n-1; i++)
            {
                for(i_=0; i_<=n-1;i_++)
                {
                    state.model[i,i_] = state.rawmodel[i,i_];
                }
                state.model[i,i] = state.model[i,i]+lambda;
            }
            spd = cholesky.spdmatrixcholesky(ref state.model, n, true);
            state.repncholesky = state.repncholesky+1;
            if( !spd )
            {
                lambda = lambda*lambdaup*nu;
                nu = nu*2;
                goto lbl_15;
            }
            if( !spdsolve.spdmatrixcholeskysolve(ref state.model, state.gbase, n, true, ref state.xdir) )
            {
                lambda = lambda*lambdaup*nu;
                nu = nu*2;
                goto lbl_15;
            }
            for(i_=0; i_<=n-1;i_++)
            {
                state.xdir[i_] = -1*state.xdir[i_];
            }
            
            //
            // Candidate lambda found.
            // 1. Save old w in WBase
            // 1. Test some stopping criterions
            // 2. If error(w+wdir)>error(w), increase lambda
            //
            for(i_=0; i_<=n-1;i_++)
            {
                state.xbase[i_] = state.x[i_];
            }
            for(i_=0; i_<=n-1;i_++)
            {
                state.x[i_] = state.x[i_] + state.xdir[i_];
            }
            xnorm = 0.0;
            for(i_=0; i_<=n-1;i_++)
            {
                xnorm += state.xbase[i_]*state.xbase[i_];
            }
            stepnorm = 0.0;
            for(i_=0; i_<=n-1;i_++)
            {
                stepnorm += state.xdir[i_]*state.xdir[i_];
            }
            xnorm = Math.Sqrt(xnorm);
            stepnorm = Math.Sqrt(stepnorm);
            if( (double)(stepnorm)<=(double)(state.epsx*(1+xnorm)) )
            {
                
                //
                // step size if small enough
                //
                state.repterminationtype = 2;
                goto lbl_16;
            }
            lmclearrequestfields(ref state);
            state.needf = true;
            state.rstate.stage = 3;
            goto lbl_rcomm;
        lbl_3:
            state.repnfunc = state.repnfunc+1;
            fnew = state.f;
            if( (double)(Math.Abs(fnew-fbase))<=(double)(state.epsf*Math.Max(1, Math.Max(Math.Abs(fbase), Math.Abs(fnew)))) )
            {
                
                //
                // function change is small enough
                //
                state.repterminationtype = 1;
                goto lbl_16;
            }
            if( (double)(fnew)>(double)(fbase) )
            {
                
                //
                // restore state and continue out search for lambda
                //
                for(i_=0; i_<=n-1;i_++)
                {
                    state.x[i_] = state.xbase[i_];
                }
                lambda = lambda*lambdaup*nu;
                nu = nu*2;
                goto lbl_15;
            }
            if( ! ((state.usermode==lmmodefgj | state.usermode==lmmodefgh) & state.flags/lmflagnointlbfgs%2==0) )
            {
                goto lbl_17;
            }
            System.Diagnostics.Debug.Assert(state.usermode==lmmodefgh);
            
            //
            // Optimize using inv(cholesky(H)) as preconditioner
            //
            if( ! trinverse.rmatrixtrinverse(ref state.model, n, true, false) )
            {
                goto lbl_19;
            }
            
            //
            // if matrix can be inverted use it.
            // just silently move to next iteration otherwise.
            // (will be very, very rare, mostly for specially
            // designed near-degenerate tasks)
            //
            for(i_=0; i_<=n-1;i_++)
            {
                state.xbase[i_] = state.x[i_];
            }
            for(i=0; i<=n-1; i++)
            {
                state.xprec[i] = 0;
            }
            lbfgs.minlbfgs(n, Math.Min(n, lmintlbfgsits), ref state.xprec, 0.0, 0.0, 0.0, lmintlbfgsits, lbfgsflags, ref state.internalstate);
        lbl_21:
            if( ! lbfgs.minlbfgsiteration(ref state.internalstate) )
            {
                goto lbl_22;
            }
            
            //
            // convert XPrec to unpreconditioned form, then call RComm.
            //
            for(i=0; i<=n-1; i++)
            {
                v = 0.0;
                for(i_=i; i_<=n-1;i_++)
                {
                    v += state.internalstate.x[i_]*state.model[i,i_];
                }
                state.x[i] = state.xbase[i]+v;
            }
            lmclearrequestfields(ref state);
            state.needfg = true;
            state.rstate.stage = 4;
            goto lbl_rcomm;
        lbl_4:
            state.repnfunc = state.repnfunc+1;
            state.repngrad = state.repngrad+1;
            
            //
            // 1. pass State.F to State.InternalState.F
            // 2. convert gradient back to preconditioned form
            //
            state.internalstate.f = state.f;
            for(i=0; i<=n-1; i++)
            {
                state.internalstate.g[i] = 0;
            }
            for(i=0; i<=n-1; i++)
            {
                v = state.g[i];
                for(i_=i; i_<=n-1;i_++)
                {
                    state.internalstate.g[i_] = state.internalstate.g[i_] + v*state.model[i,i_];
                }
            }
            
            //
            // next iteration
            //
            goto lbl_21;
        lbl_22:
            
            //
            // change LBFGS flags to NoRealloc.
            // L-BFGS subroutine will use memory allocated from previous run.
            // it is possible since all subsequent calls will be with same N/M.
            //
            lbfgsflags = lbfgsnorealloc;
            
            //
            // back to unpreconditioned X
            //
            lbfgs.minlbfgsresults(ref state.internalstate, ref state.xprec, ref state.internalrep);
            for(i=0; i<=n-1; i++)
            {
                v = 0.0;
                for(i_=i; i_<=n-1;i_++)
                {
                    v += state.xprec[i_]*state.model[i,i_];
                }
                state.x[i] = state.xbase[i]+v;
            }
        lbl_19:
        lbl_17:
            
            //
            // Accept new position.
            // Calculate Hessian
            //
            if( state.usermode!=lmmodefgh )
            {
                goto lbl_23;
            }
            
            //
            // RComm
            //
            lmclearrequestfields(ref state);
            state.needfgh = true;
            state.rstate.stage = 5;
            goto lbl_rcomm;
        lbl_5:
            state.repnfunc = state.repnfunc+1;
            state.repngrad = state.repngrad+1;
            state.repnhess = state.repnhess+1;
            
            //
            // Update raw quadratic model
            //
            for(i=0; i<=n-1; i++)
            {
                for(i_=0; i_<=n-1;i_++)
                {
                    state.rawmodel[i,i_] = state.h[i,i_];
                }
            }
            for(i_=0; i_<=n-1;i_++)
            {
                state.gbase[i_] = state.g[i_];
            }
            fbase = state.f;
        lbl_23:
            if( ! (state.usermode==lmmodefgj | state.usermode==lmmodefj) )
            {
                goto lbl_25;
            }
            
            //
            // RComm
            //
            lmclearrequestfields(ref state);
            state.needfij = true;
            state.rstate.stage = 6;
            goto lbl_rcomm;
        lbl_6:
            state.repnfunc = state.repnfunc+1;
            state.repnjac = state.repnjac+1;
            
            //
            // generate raw quadratic model
            //
            blas.matrixmatrixmultiply(ref state.j, 0, m-1, 0, n-1, true, ref state.j, 0, m-1, 0, n-1, false, 1.0, ref state.rawmodel, 0, n-1, 0, n-1, 0.0, ref state.work);
            blas.matrixvectormultiply(ref state.j, 0, m-1, 0, n-1, true, ref state.fi, 0, m-1, 1.0, ref state.gbase, 0, n-1, 0.0);
            fbase = 0.0;
            for(i_=0; i_<=m-1;i_++)
            {
                fbase += state.fi[i_]*state.fi[i_];
            }
        lbl_25:
            state.repiterationscount = state.repiterationscount+1;
            if( state.repiterationscount>=state.maxits & state.maxits>0 )
            {
                state.repterminationtype = 5;
                goto lbl_16;
            }
            
            //
            // Update lambda
            //
            lambda = lambda*lambdadown;
            nu = 2;
            goto lbl_15;
        lbl_16:
            result = false;
            return result;
            
            //
            // Saving state
            //
        lbl_rcomm:
            result = true;
            state.rstate.ia[0] = n;
            state.rstate.ia[1] = m;
            state.rstate.ia[2] = i;
            state.rstate.ia[3] = lbfgsflags;
            state.rstate.ba[0] = spd;
            state.rstate.ra[0] = xnorm;
            state.rstate.ra[1] = stepnorm;
            state.rstate.ra[2] = fbase;
            state.rstate.ra[3] = fnew;
            state.rstate.ra[4] = lambda;
            state.rstate.ra[5] = nu;
            state.rstate.ra[6] = lambdaup;
            state.rstate.ra[7] = lambdadown;
            state.rstate.ra[8] = v;
            return result;
        }


        /*************************************************************************
        Levenberg-Marquardt algorithm results

        Called after MinLMIteration returned False.

        Input parameters:
            State   -   algorithm state (used by MinLMIteration).

        Output parameters:
            X       -   array[0..N-1], solution
            Rep     -   optimization report:
                        * Rep.TerminationType completetion code:
                            * -1    incorrect parameters were specified
                            *  1    relative function improvement is no more than
                                    EpsF.
                            *  2    relative step is no more than EpsX.
                            *  4    gradient norm is no more than EpsG
                            *  5    MaxIts steps was taken
                        * Rep.IterationsCount contains iterations count
                        * Rep.NFunc     - number of function calculations
                        * Rep.NJac      - number of Jacobi matrix calculations
                        * Rep.NGrad     - number of gradient calculations
                        * Rep.NHess     - number of Hessian calculations
                        * Rep.NCholesky - number of Cholesky decomposition calculations

          -- ALGLIB --
             Copyright 10.03.2009 by Bochkanov Sergey
        *************************************************************************/
        public static void minlmresults(ref lmstate state,
            ref double[] x,
            ref lmreport rep)
        {
            int i_ = 0;

            x = new double[state.n-1+1];
            for(i_=0; i_<=state.n-1;i_++)
            {
                x[i_] = state.x[i_];
            }
            rep.iterationscount = state.repiterationscount;
            rep.terminationtype = state.repterminationtype;
            rep.nfunc = state.repnfunc;
            rep.njac = state.repnjac;
            rep.ngrad = state.repngrad;
            rep.nhess = state.repnhess;
            rep.ncholesky = state.repncholesky;
        }


        /*************************************************************************
        Prepare internal structures (except for RComm).

        Note: M must be zero for FGH mode, non-zero for FJ/FGJ mode.
        *************************************************************************/
        private static void lmprepare(int n,
            int m,
            bool havegrad,
            ref lmstate state)
        {
            state.repiterationscount = 0;
            state.repterminationtype = 0;
            state.repnfunc = 0;
            state.repnjac = 0;
            state.repngrad = 0;
            state.repnhess = 0;
            state.repncholesky = 0;
            if( n<0 | m<0 )
            {
                return;
            }
            if( havegrad )
            {
                state.g = new double[n-1+1];
            }
            if( m!=0 )
            {
                state.j = new double[m-1+1, n-1+1];
                state.fi = new double[m-1+1];
                state.h = new double[0+1, 0+1];
            }
            else
            {
                state.j = new double[0+1, 0+1];
                state.fi = new double[0+1];
                state.h = new double[n-1+1, n-1+1];
            }
            state.x = new double[n-1+1];
            state.rawmodel = new double[n-1+1, n-1+1];
            state.model = new double[n-1+1, n-1+1];
            state.xbase = new double[n-1+1];
            state.xprec = new double[n-1+1];
            state.gbase = new double[n-1+1];
            state.xdir = new double[n-1+1];
            state.work = new double[Math.Max(n, m)+1];
        }


        /*************************************************************************
        Clears request fileds (to be sure that we don't forgot to clear something)
        *************************************************************************/
        private static void lmclearrequestfields(ref lmstate state)
        {
            state.needf = false;
            state.needfg = false;
            state.needfgh = false;
            state.needfij = false;
        }
    }
}