source: trunk/sources/ALGLIB/autogk.cs @ 2563

/*************************************************************************
Copyright (c) 2005-2009, 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 autogk
    {
        /*************************************************************************
        Integration report:
        * TerminationType = completetion code:
            * -5    non-convergence of Gauss-Kronrod nodes
                    calculation subroutine.
            * -1    incorrect parameters were specified
            *  1    OK
        * Rep.NFEV countains number of function calculations
        * Rep.NIntervals contains number of intervals [a,b]
          was partitioned into.
        *************************************************************************/
        public struct autogkreport
        {
            public int terminationtype;
            public int nfev;
            public int nintervals;
        };


        public struct autogkinternalstate
        {
            public double a;
            public double b;
            public double eps;
            public double xwidth;
            public double x;
            public double f;
            public int info;
            public double r;
            public double[,] heap;
            public int heapsize;
            public int heapwidth;
            public int heapused;
            public double sumerr;
            public double sumabs;
            public double[] qn;
            public double[] wg;
            public double[] wk;
            public double[] wr;
            public int n;
            public AP.rcommstate rstate;
        };


        /*************************************************************************
        This structure stores internal state of the integration algorithm  between
        subsequent calls of the AutoGKIteration() subroutine.
        *************************************************************************/
        public struct autogkstate
        {
            public double a;
            public double b;
            public double alpha;
            public double beta;
            public double xwidth;
            public double x;
            public double xminusa;
            public double bminusx;
            public double f;
            public int wrappermode;
            public autogkinternalstate internalstate;
            public AP.rcommstate rstate;
            public double v;
            public int terminationtype;
            public int nfev;
            public int nintervals;
        };




        /*************************************************************************
        Integration of a smooth function F(x) on a finite interval [a,b].

        Fast-convergent algorithm based on a Gauss-Kronrod formula is used. Result
        is calculated with accuracy close to the machine precision.

        Algorithm works well only with smooth integrands.  It  may  be  used  with
        continuous non-smooth integrands, but with  less  performance.

        It should never be used with integrands which have integrable singularities
        at lower or upper limits - algorithm may crash. Use AutoGKSingular in such
        cases.

        INPUT PARAMETERS:
            A, B    -   interval boundaries (A<B, A=B or A>B)
            
        OUTPUT PARAMETERS
            State   -   structure which stores algorithm state between  subsequent
                        calls of AutoGKIteration.  Used for reverse communication.
                        This structure should be  passed  to  the  AutoGKIteration
                        subroutine.

        SEE ALSO
            AutoGKSmoothW, AutoGKSingular, AutoGKIteration, AutoGKResults.
            

          -- ALGLIB --
             Copyright 06.05.2009 by Bochkanov Sergey
        *************************************************************************/
        public static void autogksmooth(double a,
            double b,
            ref autogkstate state)
        {
            autogksmoothw(a, b, 0.0, ref state);
        }


        /*************************************************************************
        Integration of a smooth function F(x) on a finite interval [a,b].

        This subroutine is same as AutoGKSmooth(), but it guarantees that interval
        [a,b] is partitioned into subintervals which have width at most XWidth.

        Subroutine  can  be  used  when  integrating nearly-constant function with
        narrow "bumps" (about XWidth wide). If "bumps" are too narrow, AutoGKSmooth
        subroutine can overlook them.

        INPUT PARAMETERS:
            A, B    -   interval boundaries (A<B, A=B or A>B)

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

        SEE ALSO
            AutoGKSmooth, AutoGKSingular, AutoGKIteration, AutoGKResults.


          -- ALGLIB --
             Copyright 06.05.2009 by Bochkanov Sergey
        *************************************************************************/
        public static void autogksmoothw(double a,
            double b,
            double xwidth,
            ref autogkstate state)
        {
            state.wrappermode = 0;
            state.a = a;
            state.b = b;
            state.xwidth = xwidth;
            state.rstate.ra = new double[10+1];
            state.rstate.stage = -1;
        }


        /*************************************************************************
        Integration on a finite interval [A,B].
        Integrand have integrable singularities at A/B.

        F(X) must diverge as "(x-A)^alpha" at A, as "(B-x)^beta" at B,  with known
        alpha/beta (alpha>-1, beta>-1).  If alpha/beta  are  not known,  estimates
        from below can be used (but these estimates should be greater than -1 too).

        One  of  alpha/beta variables (or even both alpha/beta) may be equal to 0,
        which means than function F(x) is non-singular at A/B. Anyway (singular at
        bounds or not), function F(x) is supposed to be continuous on (A,B).

        Fast-convergent algorithm based on a Gauss-Kronrod formula is used. Result
        is calculated with accuracy close to the machine precision.

        INPUT PARAMETERS:
            A, B    -   interval boundaries (A<B, A=B or A>B)
            Alpha   -   power-law coefficient of the F(x) at A,
                        Alpha>-1
            Beta    -   power-law coefficient of the F(x) at B,
                        Beta>-1

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

        SEE ALSO
            AutoGKSmooth, AutoGKSmoothW, AutoGKIteration, AutoGKResults.


          -- ALGLIB --
             Copyright 06.05.2009 by Bochkanov Sergey
        *************************************************************************/
        public static void autogksingular(double a,
            double b,
            double alpha,
            double beta,
            ref autogkstate state)
        {
            state.wrappermode = 1;
            state.a = a;
            state.b = b;
            state.alpha = alpha;
            state.beta = beta;
            state.xwidth = 0.0;
            state.rstate.ra = new double[10+1];
            state.rstate.stage = -1;
        }


        /*************************************************************************
        One step of adaptive integration process.

        Called after initialization with one of AutoGKXXX subroutines.
        See HTML documentation for examples.

        Input parameters:
            State   -   structure which stores algorithm state between  calls  and
                        which  is  used  for   reverse   communication.   Must  be
                        initialized with one of AutoGKXXX subroutines.

        If suborutine returned False, iterative proces has converged. If subroutine
        returned True, caller should calculate function value State.F  at  State.X
        and call AutoGKIteration again.

        NOTE:

        When integrating "difficult" functions with integrable singularities like

            F(x) = (x-A)^alpha * (B-x)^beta

        subroutine may require the value of F at points which are too close to A/B.
        Sometimes to calculate integral with high enough precision we  may need to
        calculate F(A+delta) when delta is less than machine  epsilon.  In  finite
        precision arithmetics A+delta will be effectively equal to A,  so  we  may
        find us in situation when  we  are  trying  to  calculate  something  like
        1/sqrt(1-1).

        To avoid  such  situations,  AutoGKIteration  subroutine  fills  not  only
        State.X  field,  but  also   State.XMinusA   (which  equals  to  X-A)  and
        State.BMinusX  (which  equals to B-X) fields.  If X is too close to A or B
        (X-A<0.001*A, or B-X<0.001*B, for example) use  these  fields  instead  of
        State.X


          -- ALGLIB --
             Copyright 07.05.2009 by Bochkanov Sergey
        *************************************************************************/
        public static bool autogkiteration(ref autogkstate state)
        {
            bool result = new bool();
            double s = 0;
            double tmp = 0;
            double eps = 0;
            double a = 0;
            double b = 0;
            double x = 0;
            double t = 0;
            double alpha = 0;
            double beta = 0;
            double v1 = 0;
            double v2 = 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 )
            {
                s = state.rstate.ra[0];
                tmp = state.rstate.ra[1];
                eps = state.rstate.ra[2];
                a = state.rstate.ra[3];
                b = state.rstate.ra[4];
                x = state.rstate.ra[5];
                t = state.rstate.ra[6];
                alpha = state.rstate.ra[7];
                beta = state.rstate.ra[8];
                v1 = state.rstate.ra[9];
                v2 = state.rstate.ra[10];
            }
            else
            {
                s = -983;
                tmp = -989;
                eps = -834;
                a = 900;
                b = -287;
                x = 364;
                t = 214;
                alpha = -338;
                beta = -686;
                v1 = 912;
                v2 = 585;
            }
            if( state.rstate.stage==0 )
            {
                goto lbl_0;
            }
            if( state.rstate.stage==1 )
            {
                goto lbl_1;
            }
            if( state.rstate.stage==2 )
            {
                goto lbl_2;
            }
            
            //
            // Routine body
            //
            eps = 0;
            a = state.a;
            b = state.b;
            alpha = state.alpha;
            beta = state.beta;
            state.terminationtype = -1;
            state.nfev = 0;
            state.nintervals = 0;
            
            //
            // smooth function  at a finite interval
            //
            if( state.wrappermode!=0 )
            {
                goto lbl_3;
            }
            
            //
            // special case
            //
            if( (double)(a)==(double)(b) )
            {
                state.terminationtype = 1;
                state.v = 0;
                result = false;
                return result;
            }
            
            //
            // general case
            //
            autogkinternalprepare(a, b, eps, state.xwidth, ref state.internalstate);
        lbl_5:
            if( ! autogkinternaliteration(ref state.internalstate) )
            {
                goto lbl_6;
            }
            x = state.internalstate.x;
            state.x = x;
            state.xminusa = x-a;
            state.bminusx = b-x;
            state.rstate.stage = 0;
            goto lbl_rcomm;
        lbl_0:
            state.nfev = state.nfev+1;
            state.internalstate.f = state.f;
            goto lbl_5;
        lbl_6:
            state.v = state.internalstate.r;
            state.terminationtype = state.internalstate.info;
            state.nintervals = state.internalstate.heapused;
            result = false;
            return result;
        lbl_3:
            
            //
            // function with power-law singularities at the ends of a finite interval
            //
            if( state.wrappermode!=1 )
            {
                goto lbl_7;
            }
            
            //
            // test coefficients
            //
            if( (double)(alpha)<=(double)(-1) | (double)(beta)<=(double)(-1) )
            {
                state.terminationtype = -1;
                state.v = 0;
                result = false;
                return result;
            }
            
            //
            // special cases
            //
            if( (double)(a)==(double)(b) )
            {
                state.terminationtype = 1;
                state.v = 0;
                result = false;
                return result;
            }
            
            //
            // reduction to general form
            //
            if( (double)(a)<(double)(b) )
            {
                s = +1;
            }
            else
            {
                s = -1;
                tmp = a;
                a = b;
                b = tmp;
                tmp = alpha;
                alpha = beta;
                beta = tmp;
            }
            alpha = Math.Min(alpha, 0);
            beta = Math.Min(beta, 0);
            
            //
            // first, integrate left half of [a,b]:
            //     integral(f(x)dx, a, (b+a)/2) =
            //     = 1/(1+alpha) * integral(t^(-alpha/(1+alpha))*f(a+t^(1/(1+alpha)))dt, 0, (0.5*(b-a))^(1+alpha))
            //
            autogkinternalprepare(0, Math.Pow(0.5*(b-a), 1+alpha), eps, state.xwidth, ref state.internalstate);
        lbl_9:
            if( ! autogkinternaliteration(ref state.internalstate) )
            {
                goto lbl_10;
            }
            
            //
            // Fill State.X, State.XMinusA, State.BMinusX.
            // Latter two are filled correctly even if B<A.
            //
            x = state.internalstate.x;
            t = Math.Pow(x, 1/(1+alpha));
            state.x = a+t;
            if( (double)(s)>(double)(0) )
            {
                state.xminusa = t;
                state.bminusx = b-(a+t);
            }
            else
            {
                state.xminusa = a+t-b;
                state.bminusx = -t;
            }
            state.rstate.stage = 1;
            goto lbl_rcomm;
        lbl_1:
            if( (double)(alpha)!=(double)(0) )
            {
                state.internalstate.f = state.f*Math.Pow(x, -(alpha/(1+alpha)))/(1+alpha);
            }
            else
            {
                state.internalstate.f = state.f;
            }
            state.nfev = state.nfev+1;
            goto lbl_9;
        lbl_10:
            v1 = state.internalstate.r;
            state.nintervals = state.nintervals+state.internalstate.heapused;
            
            //
            // then, integrate right half of [a,b]:
            //     integral(f(x)dx, (b+a)/2, b) =
            //     = 1/(1+beta) * integral(t^(-beta/(1+beta))*f(b-t^(1/(1+beta)))dt, 0, (0.5*(b-a))^(1+beta))
            //
            autogkinternalprepare(0, Math.Pow(0.5*(b-a), 1+beta), eps, state.xwidth, ref state.internalstate);
        lbl_11:
            if( ! autogkinternaliteration(ref state.internalstate) )
            {
                goto lbl_12;
            }
            
            //
            // Fill State.X, State.XMinusA, State.BMinusX.
            // Latter two are filled correctly (X-A, B-X) even if B<A.
            //
            x = state.internalstate.x;
            t = Math.Pow(x, 1/(1+beta));
            state.x = b-t;
            if( (double)(s)>(double)(0) )
            {
                state.xminusa = b-t-a;
                state.bminusx = t;
            }
            else
            {
                state.xminusa = -t;
                state.bminusx = a-(b-t);
            }
            state.rstate.stage = 2;
            goto lbl_rcomm;
        lbl_2:
            if( (double)(beta)!=(double)(0) )
            {
                state.internalstate.f = state.f*Math.Pow(x, -(beta/(1+beta)))/(1+beta);
            }
            else
            {
                state.internalstate.f = state.f;
            }
            state.nfev = state.nfev+1;
            goto lbl_11;
        lbl_12:
            v2 = state.internalstate.r;
            state.nintervals = state.nintervals+state.internalstate.heapused;
            
            //
            // final result
            //
            state.v = s*(v1+v2);
            state.terminationtype = 1;
            result = false;
            return result;
        lbl_7:
            result = false;
            return result;
            
            //
            // Saving state
            //
        lbl_rcomm:
            result = true;
            state.rstate.ra[0] = s;
            state.rstate.ra[1] = tmp;
            state.rstate.ra[2] = eps;
            state.rstate.ra[3] = a;
            state.rstate.ra[4] = b;
            state.rstate.ra[5] = x;
            state.rstate.ra[6] = t;
            state.rstate.ra[7] = alpha;
            state.rstate.ra[8] = beta;
            state.rstate.ra[9] = v1;
            state.rstate.ra[10] = v2;
            return result;
        }


        /*************************************************************************
        Adaptive integration results

        Called after AutoGKIteration returned False.

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

        Output parameters:
            V       -   integral(f(x)dx,a,b)
            Rep     -   optimization report (see AutoGKReport description)

          -- ALGLIB --
             Copyright 14.11.2007 by Bochkanov Sergey
        *************************************************************************/
        public static void autogkresults(ref autogkstate state,
            ref double v,
            ref autogkreport rep)
        {
            v = state.v;
            rep.terminationtype = state.terminationtype;
            rep.nfev = state.nfev;
            rep.nintervals = state.nintervals;
        }


        /*************************************************************************
        Internal AutoGK subroutine
        eps<0   - error
        eps=0   - automatic eps selection

        width<0 -   error
        width=0 -   no width requirements
        *************************************************************************/
        private static void autogkinternalprepare(double a,
            double b,
            double eps,
            double xwidth,
            ref autogkinternalstate state)
        {
            
            //
            // Save settings
            //
            state.a = a;
            state.b = b;
            state.eps = eps;
            state.xwidth = xwidth;
            
            //
            // Prepare RComm structure
            //
            state.rstate.ia = new int[3+1];
            state.rstate.ra = new double[8+1];
            state.rstate.stage = -1;
        }


        /*************************************************************************
        Internal AutoGK subroutine
        *************************************************************************/
        private static bool autogkinternaliteration(ref autogkinternalstate state)
        {
            bool result = new bool();
            double c1 = 0;
            double c2 = 0;
            int i = 0;
            int j = 0;
            double intg = 0;
            double intk = 0;
            double inta = 0;
            double v = 0;
            double ta = 0;
            double tb = 0;
            int ns = 0;
            double qeps = 0;
            int info = 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 )
            {
                i = state.rstate.ia[0];
                j = state.rstate.ia[1];
                ns = state.rstate.ia[2];
                info = state.rstate.ia[3];
                c1 = state.rstate.ra[0];
                c2 = state.rstate.ra[1];
                intg = state.rstate.ra[2];
                intk = state.rstate.ra[3];
                inta = state.rstate.ra[4];
                v = state.rstate.ra[5];
                ta = state.rstate.ra[6];
                tb = state.rstate.ra[7];
                qeps = state.rstate.ra[8];
            }
            else
            {
                i = 497;
                j = -271;
                ns = -581;
                info = 745;
                c1 = -533;
                c2 = -77;
                intg = 678;
                intk = -293;
                inta = 316;
                v = 647;
                ta = -756;
                tb = 830;
                qeps = -871;
            }
            if( state.rstate.stage==0 )
            {
                goto lbl_0;
            }
            if( state.rstate.stage==1 )
            {
                goto lbl_1;
            }
            if( state.rstate.stage==2 )
            {
                goto lbl_2;
            }
            
            //
            // Routine body
            //
            
            //
            // initialize quadratures.
            // use 15-point Gauss-Kronrod formula.
            //
            state.n = 15;
            gkq.gkqgenerategausslegendre(state.n, ref info, ref state.qn, ref state.wk, ref state.wg);
            if( info<0 )
            {
                state.info = -5;
                state.r = 0;
                result = false;
                return result;
            }
            state.wr = new double[state.n];
            for(i=0; i<=state.n-1; i++)
            {
                if( i==0 )
                {
                    state.wr[i] = 0.5*Math.Abs(state.qn[1]-state.qn[0]);
                    continue;
                }
                if( i==state.n-1 )
                {
                    state.wr[state.n-1] = 0.5*Math.Abs(state.qn[state.n-1]-state.qn[state.n-2]);
                    continue;
                }
                state.wr[i] = 0.5*Math.Abs(state.qn[i-1]-state.qn[i+1]);
            }
            
            //
            // special case
            //
            if( (double)(state.a)==(double)(state.b) )
            {
                state.info = 1;
                state.r = 0;
                result = false;
                return result;
            }
            
            //
            // test parameters
            //
            if( (double)(state.eps)<(double)(0) | (double)(state.xwidth)<(double)(0) )
            {
                state.info = -1;
                state.r = 0;
                result = false;
                return result;
            }
            state.info = 1;
            if( (double)(state.eps)==(double)(0) )
            {
                state.eps = 1000*AP.Math.MachineEpsilon;
            }
            
            //
            // First, prepare heap
            // * column 0   -   absolute error
            // * column 1   -   integral of a F(x) (calculated using Kronrod extension nodes)
            // * column 2   -   integral of a |F(x)| (calculated using modified rect. method)
            // * column 3   -   left boundary of a subinterval
            // * column 4   -   right boundary of a subinterval
            //
            if( (double)(state.xwidth)!=(double)(0) )
            {
                goto lbl_3;
            }
            
            //
            // no maximum width requirements
            // start from one big subinterval
            //
            state.heapwidth = 5;
            state.heapsize = 1;
            state.heapused = 1;
            state.heap = new double[state.heapsize, state.heapwidth];
            c1 = 0.5*(state.b-state.a);
            c2 = 0.5*(state.b+state.a);
            intg = 0;
            intk = 0;
            inta = 0;
            i = 0;
        lbl_5:
            if( i>state.n-1 )
            {
                goto lbl_7;
            }
            
            //
            // obtain F
            //
            state.x = c1*state.qn[i]+c2;
            state.rstate.stage = 0;
            goto lbl_rcomm;
        lbl_0:
            v = state.f;
            
            //
            // Gauss-Kronrod formula
            //
            intk = intk+v*state.wk[i];
            if( i%2==1 )
            {
                intg = intg+v*state.wg[i];
            }
            
            //
            // Integral |F(x)|
            // Use rectangles method
            //
            inta = inta+Math.Abs(v)*state.wr[i];
            i = i+1;
            goto lbl_5;
        lbl_7:
            intk = intk*(state.b-state.a)*0.5;
            intg = intg*(state.b-state.a)*0.5;
            inta = inta*(state.b-state.a)*0.5;
            state.heap[0,0] = Math.Abs(intg-intk);
            state.heap[0,1] = intk;
            state.heap[0,2] = inta;
            state.heap[0,3] = state.a;
            state.heap[0,4] = state.b;
            state.sumerr = state.heap[0,0];
            state.sumabs = Math.Abs(inta);
            goto lbl_4;
        lbl_3:
            
            //
            // maximum subinterval should be no more than XWidth.
            // so we create Ceil((B-A)/XWidth)+1 small subintervals
            //
            ns = (int)Math.Ceiling(Math.Abs(state.b-state.a)/state.xwidth)+1;
            state.heapsize = ns;
            state.heapused = ns;
            state.heapwidth = 5;
            state.heap = new double[state.heapsize, state.heapwidth];
            state.sumerr = 0;
            state.sumabs = 0;
            j = 0;
        lbl_8:
            if( j>ns-1 )
            {
                goto lbl_10;
            }
            ta = state.a+j*(state.b-state.a)/ns;
            tb = state.a+(j+1)*(state.b-state.a)/ns;
            c1 = 0.5*(tb-ta);
            c2 = 0.5*(tb+ta);
            intg = 0;
            intk = 0;
            inta = 0;
            i = 0;
        lbl_11:
            if( i>state.n-1 )
            {
                goto lbl_13;
            }
            
            //
            // obtain F
            //
            state.x = c1*state.qn[i]+c2;
            state.rstate.stage = 1;
            goto lbl_rcomm;
        lbl_1:
            v = state.f;
            
            //
            // Gauss-Kronrod formula
            //
            intk = intk+v*state.wk[i];
            if( i%2==1 )
            {
                intg = intg+v*state.wg[i];
            }
            
            //
            // Integral |F(x)|
            // Use rectangles method
            //
            inta = inta+Math.Abs(v)*state.wr[i];
            i = i+1;
            goto lbl_11;
        lbl_13:
            intk = intk*(tb-ta)*0.5;
            intg = intg*(tb-ta)*0.5;
            inta = inta*(tb-ta)*0.5;
            state.heap[j,0] = Math.Abs(intg-intk);
            state.heap[j,1] = intk;
            state.heap[j,2] = inta;
            state.heap[j,3] = ta;
            state.heap[j,4] = tb;
            state.sumerr = state.sumerr+state.heap[j,0];
            state.sumabs = state.sumabs+Math.Abs(inta);
            j = j+1;
            goto lbl_8;
        lbl_10:
        lbl_4:
            
            //
            // method iterations
            //
        lbl_14:
            if( false )
            {
                goto lbl_15;
            }
            
            //
            // additional memory if needed
            //
            if( state.heapused==state.heapsize )
            {
                mheapresize(ref state.heap, ref state.heapsize, 4*state.heapsize, state.heapwidth);
            }
            
            //
            // TODO: every 20 iterations recalculate errors/sums
            // TODO: one more criterion to prevent infinite loops with too strict Eps
            //
            if( (double)(state.sumerr)<=(double)(state.eps*state.sumabs) )
            {
                state.r = 0;
                for(j=0; j<=state.heapused-1; j++)
                {
                    state.r = state.r+state.heap[j,1];
                }
                result = false;
                return result;
            }
            
            //
            // Exclude interval with maximum absolute error
            //
            mheappop(ref state.heap, state.heapused, state.heapwidth);
            state.sumerr = state.sumerr-state.heap[state.heapused-1,0];
            state.sumabs = state.sumabs-state.heap[state.heapused-1,2];
            
            //
            // Divide interval, create subintervals
            //
            ta = state.heap[state.heapused-1,3];
            tb = state.heap[state.heapused-1,4];
            state.heap[state.heapused-1,3] = ta;
            state.heap[state.heapused-1,4] = 0.5*(ta+tb);
            state.heap[state.heapused,3] = 0.5*(ta+tb);
            state.heap[state.heapused,4] = tb;
            j = state.heapused-1;
        lbl_16:
            if( j>state.heapused )
            {
                goto lbl_18;
            }
            c1 = 0.5*(state.heap[j,4]-state.heap[j,3]);
            c2 = 0.5*(state.heap[j,4]+state.heap[j,3]);
            intg = 0;
            intk = 0;
            inta = 0;
            i = 0;
        lbl_19:
            if( i>state.n-1 )
            {
                goto lbl_21;
            }
            
            //
            // F(x)
            //
            state.x = c1*state.qn[i]+c2;
            state.rstate.stage = 2;
            goto lbl_rcomm;
        lbl_2:
            v = state.f;
            
            //
            // Gauss-Kronrod formula
            //
            intk = intk+v*state.wk[i];
            if( i%2==1 )
            {
                intg = intg+v*state.wg[i];
            }
            
            //
            // Integral |F(x)|
            // Use rectangles method
            //
            inta = inta+Math.Abs(v)*state.wr[i];
            i = i+1;
            goto lbl_19;
        lbl_21:
            intk = intk*(state.heap[j,4]-state.heap[j,3])*0.5;
            intg = intg*(state.heap[j,4]-state.heap[j,3])*0.5;
            inta = inta*(state.heap[j,4]-state.heap[j,3])*0.5;
            state.heap[j,0] = Math.Abs(intg-intk);
            state.heap[j,1] = intk;
            state.heap[j,2] = inta;
            state.sumerr = state.sumerr+state.heap[j,0];
            state.sumabs = state.sumabs+state.heap[j,2];
            j = j+1;
            goto lbl_16;
        lbl_18:
            mheappush(ref state.heap, state.heapused-1, state.heapwidth);
            mheappush(ref state.heap, state.heapused, state.heapwidth);
            state.heapused = state.heapused+1;
            goto lbl_14;
        lbl_15:
            result = false;
            return result;
            
            //
            // Saving state
            //
        lbl_rcomm:
            result = true;
            state.rstate.ia[0] = i;
            state.rstate.ia[1] = j;
            state.rstate.ia[2] = ns;
            state.rstate.ia[3] = info;
            state.rstate.ra[0] = c1;
            state.rstate.ra[1] = c2;
            state.rstate.ra[2] = intg;
            state.rstate.ra[3] = intk;
            state.rstate.ra[4] = inta;
            state.rstate.ra[5] = v;
            state.rstate.ra[6] = ta;
            state.rstate.ra[7] = tb;
            state.rstate.ra[8] = qeps;
            return result;
        }


        private static void mheappop(ref double[,] heap,
            int heapsize,
            int heapwidth)
        {
            int i = 0;
            int p = 0;
            double t = 0;
            int maxcp = 0;

            if( heapsize==1 )
            {
                return;
            }
            for(i=0; i<=heapwidth-1; i++)
            {
                t = heap[heapsize-1,i];
                heap[heapsize-1,i] = heap[0,i];
                heap[0,i] = t;
            }
            p = 0;
            while( 2*p+1<heapsize-1 )
            {
                maxcp = 2*p+1;
                if( 2*p+2<heapsize-1 )
                {
                    if( (double)(heap[2*p+2,0])>(double)(heap[2*p+1,0]) )
                    {
                        maxcp = 2*p+2;
                    }
                }
                if( (double)(heap[p,0])<(double)(heap[maxcp,0]) )
                {
                    for(i=0; i<=heapwidth-1; i++)
                    {
                        t = heap[p,i];
                        heap[p,i] = heap[maxcp,i];
                        heap[maxcp,i] = t;
                    }
                    p = maxcp;
                }
                else
                {
                    break;
                }
            }
        }


        private static void mheappush(ref double[,] heap,
            int heapsize,
            int heapwidth)
        {
            int i = 0;
            int p = 0;
            double t = 0;
            int parent = 0;

            if( heapsize==0 )
            {
                return;
            }
            p = heapsize;
            while( p!=0 )
            {
                parent = (p-1)/2;
                if( (double)(heap[p,0])>(double)(heap[parent,0]) )
                {
                    for(i=0; i<=heapwidth-1; i++)
                    {
                        t = heap[p,i];
                        heap[p,i] = heap[parent,i];
                        heap[parent,i] = t;
                    }
                    p = parent;
                }
                else
                {
                    break;
                }
            }
        }


        private static void mheapresize(ref double[,] heap,
            ref int heapsize,
            int newheapsize,
            int heapwidth)
        {
            double[,] tmp = new double[0,0];
            int i = 0;
            int i_ = 0;

            tmp = new double[heapsize, heapwidth];
            for(i=0; i<=heapsize-1; i++)
            {
                for(i_=0; i_<=heapwidth-1;i_++)
                {
                    tmp[i,i_] = heap[i,i_];
                }
            }
            heap = new double[newheapsize, heapwidth];
            for(i=0; i<=heapsize-1; i++)
            {
                for(i_=0; i_<=heapwidth-1;i_++)
                {
                    heap[i,i_] = tmp[i,i_];
                }
            }
            heapsize = newheapsize;
        }
    }
}