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diffequations.cpp
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diffequations.cpp
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/*************************************************************************
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 (usualy 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 (usualy 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 completetion 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 (usualy 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 completetion 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;