diffequations.cpp

Go to the documentation of this file.

/*************************************************************************
Copyright (c) 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 >>>
*************************************************************************/
#include "stdafx.h"
#include "diffequations.h"

// disable some irrelevant warnings
#if (AE_COMPILER==AE_MSVC)
#pragma warning(disable:4100)
#pragma warning(disable:4127)
#pragma warning(disable:4702)
#pragma warning(disable:4996)
#endif
using namespace std;

//
// THIS SECTION CONTAINS IMPLEMENTATION OF C++ INTERFACE
//
namespace alglib
{


/*************************************************************************

*************************************************************************/
_odesolverstate_owner::_odesolverstate_owner()
{
    p_struct = (alglib_impl::odesolverstate*)alglib_impl::ae_malloc(sizeof(alglib_impl::odesolverstate), NULL);
    if( p_struct==NULL )
        throw ap_error("ALGLIB: malloc error");
    if( !alglib_impl::_odesolverstate_init(p_struct, NULL, ae_false) )
        throw ap_error("ALGLIB: malloc error");
}

_odesolverstate_owner::_odesolverstate_owner(const _odesolverstate_owner &rhs)
{
    p_struct = (alglib_impl::odesolverstate*)alglib_impl::ae_malloc(sizeof(alglib_impl::odesolverstate), NULL);
    if( p_struct==NULL )
        throw ap_error("ALGLIB: malloc error");
    if( !alglib_impl::_odesolverstate_init_copy(p_struct, const_cast<alglib_impl::odesolverstate*>(rhs.p_struct), NULL, ae_false) )
        throw ap_error("ALGLIB: malloc error");
}

_odesolverstate_owner& _odesolverstate_owner::operator=(const _odesolverstate_owner &rhs)
{
    if( this==&rhs )
        return *this;
    alglib_impl::_odesolverstate_clear(p_struct);
    if( !alglib_impl::_odesolverstate_init_copy(p_struct, const_cast<alglib_impl::odesolverstate*>(rhs.p_struct), NULL, ae_false) )
        throw ap_error("ALGLIB: malloc error");
    return *this;
}

_odesolverstate_owner::~_odesolverstate_owner()
{
    alglib_impl::_odesolverstate_clear(p_struct);
    ae_free(p_struct);
}

alglib_impl::odesolverstate* _odesolverstate_owner::c_ptr()
{
    return p_struct;
}

alglib_impl::odesolverstate* _odesolverstate_owner::c_ptr() const
{
    return const_cast<alglib_impl::odesolverstate*>(p_struct);
}
odesolverstate::odesolverstate() : _odesolverstate_owner() ,needdy(p_struct->needdy),y(&p_struct->y),dy(&p_struct->dy),x(p_struct->x)
{
}

odesolverstate::odesolverstate(const odesolverstate &rhs):_odesolverstate_owner(rhs) ,needdy(p_struct->needdy),y(&p_struct->y),dy(&p_struct->dy),x(p_struct->x)
{
}

odesolverstate& odesolverstate::operator=(const odesolverstate &rhs)
{
    if( this==&rhs )
        return *this;
    _odesolverstate_owner::operator=(rhs);
    return *this;
}

odesolverstate::~odesolverstate()
{
}


/*************************************************************************

*************************************************************************/
_odesolverreport_owner::_odesolverreport_owner()
{
    p_struct = (alglib_impl::odesolverreport*)alglib_impl::ae_malloc(sizeof(alglib_impl::odesolverreport), NULL);
    if( p_struct==NULL )
        throw ap_error("ALGLIB: malloc error");
    if( !alglib_impl::_odesolverreport_init(p_struct, NULL, ae_false) )
        throw ap_error("ALGLIB: malloc error");
}

_odesolverreport_owner::_odesolverreport_owner(const _odesolverreport_owner &rhs)
{
    p_struct = (alglib_impl::odesolverreport*)alglib_impl::ae_malloc(sizeof(alglib_impl::odesolverreport), NULL);
    if( p_struct==NULL )
        throw ap_error("ALGLIB: malloc error");
    if( !alglib_impl::_odesolverreport_init_copy(p_struct, const_cast<alglib_impl::odesolverreport*>(rhs.p_struct), NULL, ae_false) )
        throw ap_error("ALGLIB: malloc error");
}

_odesolverreport_owner& _odesolverreport_owner::operator=(const _odesolverreport_owner &rhs)
{
    if( this==&rhs )
        return *this;
    alglib_impl::_odesolverreport_clear(p_struct);
    if( !alglib_impl::_odesolverreport_init_copy(p_struct, const_cast<alglib_impl::odesolverreport*>(rhs.p_struct), NULL, ae_false) )
        throw ap_error("ALGLIB: malloc error");
    return *this;
}

_odesolverreport_owner::~_odesolverreport_owner()
{
    alglib_impl::_odesolverreport_clear(p_struct);
    ae_free(p_struct);
}

alglib_impl::odesolverreport* _odesolverreport_owner::c_ptr()
{
    return p_struct;
}

alglib_impl::odesolverreport* _odesolverreport_owner::c_ptr() const
{
    return const_cast<alglib_impl::odesolverreport*>(p_struct);
}
odesolverreport::odesolverreport() : _odesolverreport_owner() ,nfev(p_struct->nfev),terminationtype(p_struct->terminationtype)
{
}

odesolverreport::odesolverreport(const odesolverreport &rhs):_odesolverreport_owner(rhs) ,nfev(p_struct->nfev),terminationtype(p_struct->terminationtype)
{
}

odesolverreport& odesolverreport::operator=(const odesolverreport &rhs)
{
    if( this==&rhs )
        return *this;
    _odesolverreport_owner::operator=(rhs);
    return *this;
}

odesolverreport::~odesolverreport()
{
}

/*************************************************************************
Cash-Karp adaptive ODE solver.

This subroutine solves ODE  Y'=f(Y,x)  with  initial  conditions  Y(xs)=Ys
(here Y may be single variable or vector of N variables).

INPUT PARAMETERS:
    Y       -   initial conditions, array[0..N-1].
                contains values of Y[] at X[0]
    N       -   system size
    X       -   points at which Y should be tabulated, array[0..M-1]
                integrations starts at X[0], ends at X[M-1],  intermediate
                values at X[i] are returned too.
                SHOULD BE ORDERED BY ASCENDING OR BY DESCENDING!!!!
    M       -   number of intermediate points + first point + last point:
                * M>2 means that you need both Y(X[M-1]) and M-2 values at
                  intermediate points
                * M=2 means that you want just to integrate from  X[0]  to
                  X[1] and don't interested in intermediate values.
                * M=1 means that you don't want to integrate :)
                  it is degenerate case, but it will be handled correctly.
                * M<1 means error
    Eps     -   tolerance (absolute/relative error on each  step  will  be
                less than Eps). When passing:
                * Eps>0, it means desired ABSOLUTE error
                * Eps<0, it means desired RELATIVE error.  Relative errors
                  are calculated with respect to maximum values of  Y seen
                  so far. Be careful to use this criterion  when  starting
                  from Y[] that are close to zero.
    H       -   initial  step  lenth,  it  will  be adjusted automatically
                after the first  step.  If  H=0,  step  will  be  selected
                automatically  (usually  it  will  be  equal  to  0.001  of
                min(x[i]-x[j])).

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

SEE ALSO
    AutoGKSmoothW, AutoGKSingular, AutoGKIteration, AutoGKResults.


  -- ALGLIB --
     Copyright 01.09.2009 by Bochkanov Sergey
*************************************************************************/
void odesolverrkck(const real_1d_array &y, const ae_int_t n, const real_1d_array &x, const ae_int_t m, const double eps, const double h, odesolverstate &state)
{
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    try
    {
        alglib_impl::odesolverrkck(const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, const_cast<alglib_impl::ae_vector*>(x.c_ptr()), m, eps, h, const_cast<alglib_impl::odesolverstate*>(state.c_ptr()), &_alglib_env_state);
        alglib_impl::ae_state_clear(&_alglib_env_state);
        return;
    }
    catch(alglib_impl::ae_error_type)
    {
        throw ap_error(_alglib_env_state.error_msg);
    }
}

/*************************************************************************
Cash-Karp adaptive ODE solver.

This subroutine solves ODE  Y'=f(Y,x)  with  initial  conditions  Y(xs)=Ys
(here Y may be single variable or vector of N variables).

INPUT PARAMETERS:
    Y       -   initial conditions, array[0..N-1].
                contains values of Y[] at X[0]
    N       -   system size
    X       -   points at which Y should be tabulated, array[0..M-1]
                integrations starts at X[0], ends at X[M-1],  intermediate
                values at X[i] are returned too.
                SHOULD BE ORDERED BY ASCENDING OR BY DESCENDING!!!!
    M       -   number of intermediate points + first point + last point:
                * M>2 means that you need both Y(X[M-1]) and M-2 values at
                  intermediate points
                * M=2 means that you want just to integrate from  X[0]  to
                  X[1] and don't interested in intermediate values.
                * M=1 means that you don't want to integrate :)
                  it is degenerate case, but it will be handled correctly.
                * M<1 means error
    Eps     -   tolerance (absolute/relative error on each  step  will  be
                less than Eps). When passing:
                * Eps>0, it means desired ABSOLUTE error
                * Eps<0, it means desired RELATIVE error.  Relative errors
                  are calculated with respect to maximum values of  Y seen
                  so far. Be careful to use this criterion  when  starting
                  from Y[] that are close to zero.
    H       -   initial  step  lenth,  it  will  be adjusted automatically
                after the first  step.  If  H=0,  step  will  be  selected
                automatically  (usually  it  will  be  equal  to  0.001  of
                min(x[i]-x[j])).

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

SEE ALSO
    AutoGKSmoothW, AutoGKSingular, AutoGKIteration, AutoGKResults.


  -- ALGLIB --
     Copyright 01.09.2009 by Bochkanov Sergey
*************************************************************************/
void odesolverrkck(const real_1d_array &y, const real_1d_array &x, const double eps, const double h, odesolverstate &state)
{
    alglib_impl::ae_state _alglib_env_state;    
    ae_int_t n;
    ae_int_t m;

    n = y.length();
    m = x.length();
    alglib_impl::ae_state_init(&_alglib_env_state);
    try
    {
        alglib_impl::odesolverrkck(const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, const_cast<alglib_impl::ae_vector*>(x.c_ptr()), m, eps, h, const_cast<alglib_impl::odesolverstate*>(state.c_ptr()), &_alglib_env_state);

        alglib_impl::ae_state_clear(&_alglib_env_state);
        return;
    }
    catch(alglib_impl::ae_error_type)
    {
        throw ap_error(_alglib_env_state.error_msg);
    }
}

/*************************************************************************
This function provides reverse communication interface
Reverse communication interface is not documented or recommended to use.
See below for functions which provide better documented API
*************************************************************************/
bool odesolveriteration(const odesolverstate &state)
{
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    try
    {
        ae_bool result = alglib_impl::odesolveriteration(const_cast<alglib_impl::odesolverstate*>(state.c_ptr()), &_alglib_env_state);
        alglib_impl::ae_state_clear(&_alglib_env_state);
        return *(reinterpret_cast<bool*>(&result));
    }
    catch(alglib_impl::ae_error_type)
    {
        throw ap_error(_alglib_env_state.error_msg);
    }
}


void odesolversolve(odesolverstate &state,
    void (*diff)(const real_1d_array &y, double x, real_1d_array &dy, void *ptr),
    void *ptr){
    alglib_impl::ae_state _alglib_env_state;
    if( diff==NULL )
        throw ap_error("ALGLIB: error in 'odesolversolve()' (diff is NULL)");
    alglib_impl::ae_state_init(&_alglib_env_state);
    try
    {
        while( alglib_impl::odesolveriteration(state.c_ptr(), &_alglib_env_state) )
        {
            if( state.needdy )
            {
                diff(state.y, state.x, state.dy, ptr);
                continue;
            }
            throw ap_error("ALGLIB: unexpected error in 'odesolversolve'");
        }
        alglib_impl::ae_state_clear(&_alglib_env_state);
    }
    catch(alglib_impl::ae_error_type)
    {
        throw ap_error(_alglib_env_state.error_msg);
    }
}



/*************************************************************************
ODE solver results

Called after OdeSolverIteration returned False.

INPUT PARAMETERS:
    State   -   algorithm state (used by OdeSolverIteration).

OUTPUT PARAMETERS:
    M       -   number of tabulated values, M>=1
    XTbl    -   array[0..M-1], values of X
    YTbl    -   array[0..M-1,0..N-1], values of Y in X[i]
    Rep     -   solver report:
                * Rep.TerminationType completion code:
                    * -2    X is not ordered  by  ascending/descending  or
                            there are non-distinct X[],  i.e.  X[i]=X[i+1]
                    * -1    incorrect parameters were specified
                    *  1    task has been solved
                * Rep.NFEV contains number of function calculations

  -- ALGLIB --
     Copyright 01.09.2009 by Bochkanov Sergey
*************************************************************************/
void odesolverresults(const odesolverstate &state, ae_int_t &m, real_1d_array &xtbl, real_2d_array &ytbl, odesolverreport &rep)
{
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    try
    {
        alglib_impl::odesolverresults(const_cast<alglib_impl::odesolverstate*>(state.c_ptr()), &m, const_cast<alglib_impl::ae_vector*>(xtbl.c_ptr()), const_cast<alglib_impl::ae_matrix*>(ytbl.c_ptr()), const_cast<alglib_impl::odesolverreport*>(rep.c_ptr()), &_alglib_env_state);
        alglib_impl::ae_state_clear(&_alglib_env_state);
        return;
    }
    catch(alglib_impl::ae_error_type)
    {
        throw ap_error(_alglib_env_state.error_msg);
    }
}
}

//
// THIS SECTION CONTAINS IMPLEMENTATION OF COMPUTATIONAL CORE
//
namespace alglib_impl
{
static double odesolver_odesolvermaxgrow = 3.0;
static double odesolver_odesolvermaxshrink = 10.0;
static void odesolver_odesolverinit(ae_int_t solvertype,
     /* Real    */ ae_vector* y,
     ae_int_t n,
     /* Real    */ ae_vector* x,
     ae_int_t m,
     double eps,
     double h,
     odesolverstate* state,
     ae_state *_state);





/*************************************************************************
Cash-Karp adaptive ODE solver.

This subroutine solves ODE  Y'=f(Y,x)  with  initial  conditions  Y(xs)=Ys
(here Y may be single variable or vector of N variables).

INPUT PARAMETERS:
    Y       -   initial conditions, array[0..N-1].
                contains values of Y[] at X[0]
    N       -   system size
    X       -   points at which Y should be tabulated, array[0..M-1]
                integrations starts at X[0], ends at X[M-1],  intermediate
                values at X[i] are returned too.
                SHOULD BE ORDERED BY ASCENDING OR BY DESCENDING!!!!
    M       -   number of intermediate points + first point + last point:
                * M>2 means that you need both Y(X[M-1]) and M-2 values at
                  intermediate points
                * M=2 means that you want just to integrate from  X[0]  to
                  X[1] and don't interested in intermediate values.
                * M=1 means that you don't want to integrate :)
                  it is degenerate case, but it will be handled correctly.
                * M<1 means error
    Eps     -   tolerance (absolute/relative error on each  step  will  be
                less than Eps). When passing:
                * Eps>0, it means desired ABSOLUTE error
                * Eps<0, it means desired RELATIVE error.  Relative errors
                  are calculated with respect to maximum values of  Y seen
                  so far. Be careful to use this criterion  when  starting
                  from Y[] that are close to zero.
    H       -   initial  step  lenth,  it  will  be adjusted automatically
                after the first  step.  If  H=0,  step  will  be  selected
                automatically  (usually  it  will  be  equal  to  0.001  of
                min(x[i]-x[j])).

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

SEE ALSO
    AutoGKSmoothW, AutoGKSingular, AutoGKIteration, AutoGKResults.


  -- ALGLIB --
     Copyright 01.09.2009 by Bochkanov Sergey
*************************************************************************/
void odesolverrkck(/* Real    */ ae_vector* y,
     ae_int_t n,
     /* Real    */ ae_vector* x,
     ae_int_t m,
     double eps,
     double h,
     odesolverstate* state,
     ae_state *_state)
{

    _odesolverstate_clear(state);

    ae_assert(n>=1, "ODESolverRKCK: N<1!", _state);
    ae_assert(m>=1, "ODESolverRKCK: M<1!", _state);
    ae_assert(y->cnt>=n, "ODESolverRKCK: Length(Y)<N!", _state);
    ae_assert(x->cnt>=m, "ODESolverRKCK: Length(X)<M!", _state);
    ae_assert(isfinitevector(y, n, _state), "ODESolverRKCK: Y contains infinite or NaN values!", _state);
    ae_assert(isfinitevector(x, m, _state), "ODESolverRKCK: Y contains infinite or NaN values!", _state);
    ae_assert(ae_isfinite(eps, _state), "ODESolverRKCK: Eps is not finite!", _state);
    ae_assert(ae_fp_neq(eps,0), "ODESolverRKCK: Eps is zero!", _state);
    ae_assert(ae_isfinite(h, _state), "ODESolverRKCK: H is not finite!", _state);
    odesolver_odesolverinit(0, y, n, x, m, eps, h, state, _state);
}


/*************************************************************************

  -- ALGLIB --
     Copyright 01.09.2009 by Bochkanov Sergey
*************************************************************************/
ae_bool odesolveriteration(odesolverstate* state, ae_state *_state)
{
    ae_int_t n;
    ae_int_t m;
    ae_int_t i;
    ae_int_t j;
    ae_int_t k;
    double xc;
    double v;
    double h;
    double h2;
    ae_bool gridpoint;
    double err;
    double maxgrowpow;
    ae_int_t klimit;
    ae_bool result;


    
    /*
     * 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.ptr.p_int[0];
        m = state->rstate.ia.ptr.p_int[1];
        i = state->rstate.ia.ptr.p_int[2];
        j = state->rstate.ia.ptr.p_int[3];
        k = state->rstate.ia.ptr.p_int[4];
        klimit = state->rstate.ia.ptr.p_int[5];
        gridpoint = state->rstate.ba.ptr.p_bool[0];
        xc = state->rstate.ra.ptr.p_double[0];
        v = state->rstate.ra.ptr.p_double[1];
        h = state->rstate.ra.ptr.p_double[2];
        h2 = state->rstate.ra.ptr.p_double[3];
        err = state->rstate.ra.ptr.p_double[4];
        maxgrowpow = state->rstate.ra.ptr.p_double[5];
    }
    else
    {
        n = -983;
        m = -989;
        i = -834;
        j = 900;
        k = -287;
        klimit = 364;
        gridpoint = ae_false;
        xc = -338;
        v = -686;
        h = 912;
        h2 = 585;
        err = 497;
        maxgrowpow = -271;
    }
    if( state->rstate.stage==0 )
    {
        goto lbl_0;
    }
    
    /*
     * Routine body
     */
    
    /*
     * prepare
     */
    if( state->repterminationtype!=0 )
    {
        result = ae_false;
        return result;
    }
    n = state->n;
    m = state->m;
    h = state->h;
    maxgrowpow = ae_pow(odesolver_odesolvermaxgrow, 5, _state);
    state->repnfev = 0;
    
    /*
     * some preliminary checks for internal errors
     * after this we assume that H>0 and M>1
     */
    ae_assert(ae_fp_greater(state->h,0), "ODESolver: internal error", _state);
    ae_assert(m>1, "ODESolverIteration: internal error", _state);
    
    /*
     * choose solver
     */
    if( state->solvertype!=0 )
    {
        goto lbl_1;
    }
    
    /*
     * Cask-Karp solver
     * Prepare coefficients table.
     * Check it for errors
     */
    ae_vector_set_length(&state->rka, 6, _state);
    state->rka.ptr.p_double[0] = 0;
    state->rka.ptr.p_double[1] = (double)1/(double)5;
    state->rka.ptr.p_double[2] = (double)3/(double)10;
    state->rka.ptr.p_double[3] = (double)3/(double)5;
    state->rka.ptr.p_double[4] = 1;
    state->rka.ptr.p_double[5] = (double)7/(double)8;
    ae_matrix_set_length(&state->rkb, 6, 5, _state);
    state->rkb.ptr.pp_double[1][0] = (double)1/(double)5;
    state->rkb.ptr.pp_double[2][0] = (double)3/(double)40;
    state->rkb.ptr.pp_double[2][1] = (double)9/(double)40;
    state->rkb.ptr.pp_double[3][0] = (double)3/(double)10;
    state->rkb.ptr.pp_double[3][1] = -(double)9/(double)10;
    state->rkb.ptr.pp_double[3][2] = (double)6/(double)5;
    state->rkb.ptr.pp_double[4][0] = -(double)11/(double)54;
    state->rkb.ptr.pp_double[4][1] = (double)5/(double)2;
    state->rkb.ptr.pp_double[4][2] = -(double)70/(double)27;
    state->rkb.ptr.pp_double[4][3] = (double)35/(double)27;
    state->rkb.ptr.pp_double[5][0] = (double)1631/(double)55296;
    state->rkb.ptr.pp_double[5][1] = (double)175/(double)512;
    state->rkb.ptr.pp_double[5][2] = (double)575/(double)13824;
    state->rkb.ptr.pp_double[5][3] = (double)44275/(double)110592;
    state->rkb.ptr.pp_double[5][4] = (double)253/(double)4096;
    ae_vector_set_length(&state->rkc, 6, _state);
    state->rkc.ptr.p_double[0] = (double)37/(double)378;
    state->rkc.ptr.p_double[1] = 0;
    state->rkc.ptr.p_double[2] = (double)250/(double)621;
    state->rkc.ptr.p_double[3] = (double)125/(double)594;
    state->rkc.ptr.p_double[4] = 0;
    state->rkc.ptr.p_double[5] = (double)512/(double)1771;
    ae_vector_set_length(&state->rkcs, 6, _state);
    state->rkcs.ptr.p_double[0] = (double)2825/(double)27648;
    state->rkcs.ptr.p_double[1] = 0;
    state->rkcs.ptr.p_double[2] = (double)18575/(double)48384;
    state->rkcs.ptr.p_double[3] = (double)13525/(double)55296;
    state->rkcs.ptr.p_double[4] = (double)277/(double)14336;
    state->rkcs.ptr.p_double[5] = (double)1/(double)4;
    ae_matrix_set_length(&state->rkk, 6, n, _state);
    
    /*
     * Main cycle consists of two iterations:
     * * outer where we travel from X[i-1] to X[i]
     * * inner where we travel inside [X[i-1],X[i]]
     */
    ae_matrix_set_length(&state->ytbl, m, n, _state);
    ae_vector_set_length(&state->escale, n, _state);
    ae_vector_set_length(&state->yn, n, _state);
    ae_vector_set_length(&state->yns, n, _state);
    xc = state->xg.ptr.p_double[0];
    ae_v_move(&state->ytbl.ptr.pp_double[0][0], 1, &state->yc.ptr.p_double[0], 1, ae_v_len(0,n-1));
    for(j=0; j<=n-1; j++)
    {
        state->escale.ptr.p_double[j] = 0;
    }
    i = 1;
lbl_3:
    if( i>m-1 )
    {
        goto lbl_5;
    }
    
    /*
     * begin inner iteration
     */
lbl_6:
    if( ae_false )
    {
        goto lbl_7;
    }
    
    /*
     * truncate step if needed (beyond right boundary).
     * determine should we store X or not
     */
    if( ae_fp_greater_eq(xc+h,state->xg.ptr.p_double[i]) )
    {
        h = state->xg.ptr.p_double[i]-xc;
        gridpoint = ae_true;
    }
    else
    {
        gridpoint = ae_false;
    }
    
    /*
     * Update error scale maximums
     *
     * These maximums are initialized by zeros,
     * then updated every iterations.
     */
    for(j=0; j<=n-1; j++)
    {
        state->escale.ptr.p_double[j] = ae_maxreal(state->escale.ptr.p_double[j], ae_fabs(state->yc.ptr.p_double[j], _state), _state);
    }
    
    /*
     * make one step:
     * 1. calculate all info needed to do step
     * 2. update errors scale maximums using values/derivatives
     *    obtained during (1)
     *
     * Take into account that we use scaling of X to reduce task
     * to the form where x[0] < x[1] < ... < x[n-1]. So X is
     * replaced by x=xscale*t, and dy/dx=f(y,x) is replaced
     * by dy/dt=xscale*f(y,xscale*t).
     */
    ae_v_move(&state->yn.ptr.p_double[0], 1, &state->yc.ptr.p_double[0], 1, ae_v_len(0,n-1));
    ae_v_move(&state->yns.ptr.p_double[0], 1, &state->yc.ptr.p_double[0], 1, ae_v_len(0,n-1));
    k = 0;
lbl_8:
    if( k>5 )
    {
        goto lbl_10;
    }
    
    /*
     * prepare data for the next update of YN/YNS
     */
    state->x = state->xscale*(xc+state->rka.ptr.p_double[k]*h);
    ae_v_move(&state->y.ptr.p_double[0], 1, &state->yc.ptr.p_double[0], 1, ae_v_len(0,n-1));
    for(j=0; j<=k-1; j++)
    {
        v = state->rkb.ptr.pp_double[k][j];
        ae_v_addd(&state->y.ptr.p_double[0], 1, &state->rkk.ptr.pp_double[j][0], 1, ae_v_len(0,n-1), v);
    }
    state->needdy = ae_true;
    state->rstate.stage = 0;
    goto lbl_rcomm;
lbl_0:
    state->needdy = ae_false;
    state->repnfev = state->repnfev+1;
    v = h*state->xscale;
    ae_v_moved(&state->rkk.ptr.pp_double[k][0], 1, &state->dy.ptr.p_double[0], 1, ae_v_len(0,n-1), v);
    
    /*
     * update YN/YNS
     */
    v = state->rkc.ptr.p_double[k];
    ae_v_addd(&state->yn.ptr.p_double[0], 1, &state->rkk.ptr.pp_double[k][0], 1, ae_v_len(0,n-1), v);
    v = state->rkcs.ptr.p_double[k];
    ae_v_addd(&state->yns.ptr.p_double[0], 1, &state->rkk.ptr.pp_double[k][0], 1, ae_v_len(0,n-1), v);
    k = k+1;
    goto lbl_8;
lbl_10:
    
    /*
     * estimate error
     */
    err = 0;
    for(j=0; j<=n-1; j++)
    {
        if( !state->fraceps )
        {
            
            /*
             * absolute error is estimated
             */
            err = ae_maxreal(err, ae_fabs(state->yn.ptr.p_double[j]-state->yns.ptr.p_double[j], _state), _state);
        }
        else
        {
            
            /*
             * Relative error is estimated
             */
            v = state->escale.ptr.p_double[j];
            if( ae_fp_eq(v,0) )
            {
                v = 1;
            }
            err = ae_maxreal(err, ae_fabs(state->yn.ptr.p_double[j]-state->yns.ptr.p_double[j], _state)/v, _state);
        }
    }
    
    /*
     * calculate new step, restart if necessary
     */
    if( ae_fp_less_eq(maxgrowpow*err,state->eps) )
    {
        h2 = odesolver_odesolvermaxgrow*h;
    }
    else
    {
        h2 = h*ae_pow(state->eps/err, 0.2, _state);
    }
    if( ae_fp_less(h2,h/odesolver_odesolvermaxshrink) )
    {
        h2 = h/odesolver_odesolvermaxshrink;
    }
    if( ae_fp_greater(err,state->eps) )
    {
        h = h2;
        goto lbl_6;
    }
    
    /*
     * advance position
     */
    xc = xc+h;
    ae_v_move(&state->yc.ptr.p_double[0], 1, &state->yn.ptr.p_double[0], 1, ae_v_len(0,n-1));
    
    /*
     * update H
     */
    h = h2;
    
    /*
     * break on grid point
     */
    if( gridpoint )
    {
        goto lbl_7;
    }
    goto lbl_6;
lbl_7:
    
    /*
     * save result
     */
    ae_v_move(&state->ytbl.ptr.pp_double[i][0], 1, &state->yc.ptr.p_double[0], 1, ae_v_len(0,n-1));
    i = i+1;
    goto lbl_3;
lbl_5:
    state->repterminationtype = 1;
    result = ae_false;
    return result;
lbl_1:
    result = ae_false;
    return result;
    
    /*
     * Saving state
     */
lbl_rcomm:
    result = ae_true;
    state->rstate.ia.ptr.p_int[0] = n;
    state->rstate.ia.ptr.p_int[1] = m;
    state->rstate.ia.ptr.p_int[2] = i;
    state->rstate.ia.ptr.p_int[3] = j;
    state->rstate.ia.ptr.p_int[4] = k;
    state->rstate.ia.ptr.p_int[5] = klimit;
    state->rstate.ba.ptr.p_bool[0] = gridpoint;
    state->rstate.ra.ptr.p_double[0] = xc;
    state->rstate.ra.ptr.p_double[1] = v;
    state->rstate.ra.ptr.p_double[2] = h;
    state->rstate.ra.ptr.p_double[3] = h2;
    state->rstate.ra.ptr.p_double[4] = err;
    state->rstate.ra.ptr.p_double[5] = maxgrowpow;
    return result;
}


/*************************************************************************
ODE solver results

Called after OdeSolverIteration returned False.

INPUT PARAMETERS:
    State   -   algorithm state (used by OdeSolverIteration).

OUTPUT PARAMETERS:
    M       -   number of tabulated values, M>=1
    XTbl    -   array[0..M-1], values of X
    YTbl    -   array[0..M-1,0..N-1], values of Y in X[i]
    Rep     -   solver report:
                * Rep.TerminationType completion code:
                    * -2    X is not ordered  by  ascending/descending  or
                            there are non-distinct X[],  i.e.  X[i]=X[i+1]
                    * -1    incorrect parameters were specified
                    *  1    task has been solved
                * Rep.NFEV contains number of function calculations

  -- ALGLIB --
     Copyright 01.09.2009 by Bochkanov Sergey
*************************************************************************/
void odesolverresults(odesolverstate* state,
     ae_int_t* m,
     /* Real    */ ae_vector* xtbl,
     /* Real    */ ae_matrix* ytbl,
     odesolverreport* rep,
     ae_state *_state)
{
    double v;
    ae_int_t i;

    *m = 0;
    ae_vector_clear(xtbl);
    ae_matrix_clear(ytbl);
    _odesolverreport_clear(rep);

    rep->terminationtype = state->repterminationtype;
    if( rep->terminationtype>0 )
    {
        *m = state->m;
        rep->nfev = state->repnfev;
        ae_vector_set_length(xtbl, state->m, _state);
        v = state->xscale;
        ae_v_moved(&xtbl->ptr.p_double[0], 1, &state->xg.ptr.p_double[0], 1, ae_v_len(0,state->m-1), v);
        ae_matrix_set_length(ytbl, state->m, state->n, _state);
        for(i=0; i<=state->m-1; i++)
        {
            ae_v_move(&ytbl->ptr.pp_double[i][0], 1, &state->ytbl.ptr.pp_double[i][0], 1, ae_v_len(0,state->n-1));
        }
    }
    else
    {
        rep->nfev = 0;
    }
}


/*************************************************************************
Internal initialization subroutine
*************************************************************************/
static void odesolver_odesolverinit(ae_int_t solvertype,
     /* Real    */ ae_vector* y,
     ae_int_t n,
     /* Real    */ ae_vector* x,
     ae_int_t m,
     double eps,
     double h,
     odesolverstate* state,
     ae_state *_state)
{
    ae_int_t i;
    double v;

    _odesolverstate_clear(state);

    
    /*
     * Prepare RComm
     */
    ae_vector_set_length(&state->rstate.ia, 5+1, _state);
    ae_vector_set_length(&state->rstate.ba, 0+1, _state);
    ae_vector_set_length(&state->rstate.ra, 5+1, _state);
    state->rstate.stage = -1;
    state->needdy = ae_false;
    
    /*
     * check parameters.
     */
    if( (n<=0||m<1)||ae_fp_eq(eps,0) )
    {
        state->repterminationtype = -1;
        return;
    }
    if( ae_fp_less(h,0) )
    {
        h = -h;
    }
    
    /*
     * quick exit if necessary.
     * after this block we assume that M>1
     */
    if( m==1 )
    {
        state->repnfev = 0;
        state->repterminationtype = 1;
        ae_matrix_set_length(&state->ytbl, 1, n, _state);
        ae_v_move(&state->ytbl.ptr.pp_double[0][0], 1, &y->ptr.p_double[0], 1, ae_v_len(0,n-1));
        ae_vector_set_length(&state->xg, m, _state);
        ae_v_move(&state->xg.ptr.p_double[0], 1, &x->ptr.p_double[0], 1, ae_v_len(0,m-1));
        return;
    }
    
    /*
     * check again: correct order of X[]
     */
    if( ae_fp_eq(x->ptr.p_double[1],x->ptr.p_double[0]) )
    {
        state->repterminationtype = -2;
        return;
    }
    for(i=1; i<=m-1; i++)
    {
        if( (ae_fp_greater(x->ptr.p_double[1],x->ptr.p_double[0])&&ae_fp_less_eq(x->ptr.p_double[i],x->ptr.p_double[i-1]))||(ae_fp_less(x->ptr.p_double[1],x->ptr.p_double[0])&&ae_fp_greater_eq(x->ptr.p_double[i],x->ptr.p_double[i-1])) )
        {
            state->repterminationtype = -2;
            return;
        }
    }
    
    /*
     * auto-select H if necessary
     */
    if( ae_fp_eq(h,0) )
    {
        v = ae_fabs(x->ptr.p_double[1]-x->ptr.p_double[0], _state);
        for(i=2; i<=m-1; i++)
        {
            v = ae_minreal(v, ae_fabs(x->ptr.p_double[i]-x->ptr.p_double[i-1], _state), _state);
        }
        h = 0.001*v;
    }
    
    /*
     * store parameters
     */
    state->n = n;
    state->m = m;
    state->h = h;
    state->eps = ae_fabs(eps, _state);
    state->fraceps = ae_fp_less(eps,0);
    ae_vector_set_length(&state->xg, m, _state);
    ae_v_move(&state->xg.ptr.p_double[0], 1, &x->ptr.p_double[0], 1, ae_v_len(0,m-1));
    if( ae_fp_greater(x->ptr.p_double[1],x->ptr.p_double[0]) )
    {
        state->xscale = 1;
    }
    else
    {
        state->xscale = -1;
        ae_v_muld(&state->xg.ptr.p_double[0], 1, ae_v_len(0,m-1), -1);
    }
    ae_vector_set_length(&state->yc, n, _state);
    ae_v_move(&state->yc.ptr.p_double[0], 1, &y->ptr.p_double[0], 1, ae_v_len(0,n-1));
    state->solvertype = solvertype;
    state->repterminationtype = 0;
    
    /*
     * Allocate arrays
     */
    ae_vector_set_length(&state->y, n, _state);
    ae_vector_set_length(&state->dy, n, _state);
}


ae_bool _odesolverstate_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
    odesolverstate *p = (odesolverstate*)_p;
    ae_touch_ptr((void*)p);
    if( !ae_vector_init(&p->yc, 0, DT_REAL, _state, make_automatic) )
        return ae_false;
    if( !ae_vector_init(&p->escale, 0, DT_REAL, _state, make_automatic) )
        return ae_false;
    if( !ae_vector_init(&p->xg, 0, DT_REAL, _state, make_automatic) )
        return ae_false;
    if( !ae_vector_init(&p->y, 0, DT_REAL, _state, make_automatic) )
        return ae_false;
    if( !ae_vector_init(&p->dy, 0, DT_REAL, _state, make_automatic) )
        return ae_false;
    if( !ae_matrix_init(&p->ytbl, 0, 0, DT_REAL, _state, make_automatic) )
        return ae_false;
    if( !ae_vector_init(&p->yn, 0, DT_REAL, _state, make_automatic) )
        return ae_false;
    if( !ae_vector_init(&p->yns, 0, DT_REAL, _state, make_automatic) )
        return ae_false;
    if( !ae_vector_init(&p->rka, 0, DT_REAL, _state, make_automatic) )
        return ae_false;
    if( !ae_vector_init(&p->rkc, 0, DT_REAL, _state, make_automatic) )
        return ae_false;
    if( !ae_vector_init(&p->rkcs, 0, DT_REAL, _state, make_automatic) )
        return ae_false;
    if( !ae_matrix_init(&p->rkb, 0, 0, DT_REAL, _state, make_automatic) )
        return ae_false;
    if( !ae_matrix_init(&p->rkk, 0, 0, DT_REAL, _state, make_automatic) )
        return ae_false;
    if( !_rcommstate_init(&p->rstate, _state, make_automatic) )
        return ae_false;
    return ae_true;
}


ae_bool _odesolverstate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
    odesolverstate *dst = (odesolverstate*)_dst;
    odesolverstate *src = (odesolverstate*)_src;
    dst->n = src->n;
    dst->m = src->m;
    dst->xscale = src->xscale;
    dst->h = src->h;
    dst->eps = src->eps;
    dst->fraceps = src->fraceps;
    if( !ae_vector_init_copy(&dst->yc, &src->yc, _state, make_automatic) )
        return ae_false;
    if( !ae_vector_init_copy(&dst->escale, &src->escale, _state, make_automatic) )
        return ae_false;
    if( !ae_vector_init_copy(&dst->xg, &src->xg, _state, make_automatic) )
        return ae_false;
    dst->solvertype = src->solvertype;
    dst->needdy = src->needdy;
    dst->x = src->x;
    if( !ae_vector_init_copy(&dst->y, &src->y, _state, make_automatic) )
        return ae_false;
    if( !ae_vector_init_copy(&dst->dy, &src->dy, _state, make_automatic) )
        return ae_false;
    if( !ae_matrix_init_copy(&dst->ytbl, &src->ytbl, _state, make_automatic) )
        return ae_false;
    dst->repterminationtype = src->repterminationtype;
    dst->repnfev = src->repnfev;
    if( !ae_vector_init_copy(&dst->yn, &src->yn, _state, make_automatic) )
        return ae_false;
    if( !ae_vector_init_copy(&dst->yns, &src->yns, _state, make_automatic) )
        return ae_false;
    if( !ae_vector_init_copy(&dst->rka, &src->rka, _state, make_automatic) )
        return ae_false;
    if( !ae_vector_init_copy(&dst->rkc, &src->rkc, _state, make_automatic) )
        return ae_false;
    if( !ae_vector_init_copy(&dst->rkcs, &src->rkcs, _state, make_automatic) )
        return ae_false;
    if( !ae_matrix_init_copy(&dst->rkb, &src->rkb, _state, make_automatic) )
        return ae_false;
    if( !ae_matrix_init_copy(&dst->rkk, &src->rkk, _state, make_automatic) )
        return ae_false;
    if( !_rcommstate_init_copy(&dst->rstate, &src->rstate, _state, make_automatic) )
        return ae_false;
    return ae_true;
}


void _odesolverstate_clear(void* _p)
{
    odesolverstate *p = (odesolverstate*)_p;
    ae_touch_ptr((void*)p);
    ae_vector_clear(&p->yc);
    ae_vector_clear(&p->escale);
    ae_vector_clear(&p->xg);
    ae_vector_clear(&p->y);
    ae_vector_clear(&p->dy);
    ae_matrix_clear(&p->ytbl);
    ae_vector_clear(&p->yn);
    ae_vector_clear(&p->yns);
    ae_vector_clear(&p->rka);
    ae_vector_clear(&p->rkc);
    ae_vector_clear(&p->rkcs);
    ae_matrix_clear(&p->rkb);
    ae_matrix_clear(&p->rkk);
    _rcommstate_clear(&p->rstate);
}


void _odesolverstate_destroy(void* _p)
{
    odesolverstate *p = (odesolverstate*)_p;
    ae_touch_ptr((void*)p);
    ae_vector_destroy(&p->yc);
    ae_vector_destroy(&p->escale);
    ae_vector_destroy(&p->xg);
    ae_vector_destroy(&p->y);
    ae_vector_destroy(&p->dy);
    ae_matrix_destroy(&p->ytbl);
    ae_vector_destroy(&p->yn);
    ae_vector_destroy(&p->yns);
    ae_vector_destroy(&p->rka);
    ae_vector_destroy(&p->rkc);
    ae_vector_destroy(&p->rkcs);
    ae_matrix_destroy(&p->rkb);
    ae_matrix_destroy(&p->rkk);
    _rcommstate_destroy(&p->rstate);
}


ae_bool _odesolverreport_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
    odesolverreport *p = (odesolverreport*)_p;
    ae_touch_ptr((void*)p);
    return ae_true;
}


ae_bool _odesolverreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
    odesolverreport *dst = (odesolverreport*)_dst;
    odesolverreport *src = (odesolverreport*)_src;
    dst->nfev = src->nfev;
    dst->terminationtype = src->terminationtype;
    return ae_true;
}


void _odesolverreport_clear(void* _p)
{
    odesolverreport *p = (odesolverreport*)_p;
    ae_touch_ptr((void*)p);
}


void _odesolverreport_destroy(void* _p)
{
    odesolverreport *p = (odesolverreport*)_p;
    ae_touch_ptr((void*)p);
}



}