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#include "sys-defines.h"
#include "ode.h"
#include "extern.h"
#include "num.h"
#define PASTVAL (3) /* past values, val[0] is current value */
#define T_LT_TSTOP (tstep>0 ? t<tstop:t>tstop)
#define NEARSTOP (tstep > 0 ? \
t+0.9375*tstep > tstop && t+0.0625*tstep < tstop : \
t+0.9375*tstep < tstop && t+0.0625*tstep > tstop)
/*
* Adams-Moulton with adaptive step size
* Copyright Nicholas B. Tufillaro, 1982-1994. All rights reserved.
* GNU enhancements copyright (C) 1996-1997 Free Software Foundation, Inc.
*/
void
#ifdef _HAVE_PROTOS
ama (void)
#else
ama ()
#endif
{
bool gdval = true; /* good value to print ? */
int overtime = 1;
long startit = 0;
double prevstep = 0.0;
double t = tstart;
top:
/* fifth-order Runge-Kutta startup */
it = startit;
while (it <= startit + PASTVAL&&(T_LT_TSTOP || overtime--))
{
symtab->sy_value = t;
field();
if (gdval)
{
for (fsp = symtab; fsp != NULL; fsp = fsp->sy_link)
{
int j;
for (j = it - startit; j > 0; j--)
{
fsp->sy_val[j] = fsp->sy_val[j-1];
fsp->sy_pri[j] = fsp->sy_pri[j-1];
}
fsp->sy_val[0] = fsp->sy_value;
fsp->sy_pri[0] = fsp->sy_prime;
}
printq(); /* output */
if (it == startit + PASTVAL)
break; /* startup complete */
}
if (tstep * (t+tstep-tstop) > 0)
tstep = tstop - t;
for (fsp = dqueue; fsp != NULL; fsp = fsp->sy_link)
{
fsp->sy_k[0] = tstep * fsp->sy_prime;
fsp->sy_value = fsp->sy_val[0] + C20 * fsp->sy_k[0];
}
symtab->sy_value = t + C2t * tstep;
field();
for (fsp = dqueue; fsp != NULL; fsp = fsp->sy_link)
{
fsp->sy_k[1] = tstep * fsp->sy_prime;
fsp->sy_value = fsp->sy_val[0] + C30 * fsp->sy_k[0]
+ C31 * fsp->sy_k[1];
}
symtab->sy_value = t + C3t * tstep;
field();
for (fsp = dqueue; fsp != NULL; fsp = fsp->sy_link)
{
fsp->sy_k[2] = tstep * fsp->sy_prime;
fsp->sy_value = fsp->sy_val[0]
+ (C40 * fsp->sy_k[0]
+ C41 * fsp->sy_k[1]
+ C42 * fsp->sy_k[2]);
}
symtab->sy_value = t + C4t * tstep;
field();
for (fsp = dqueue; fsp != NULL; fsp = fsp->sy_link)
{
fsp->sy_k[3] = tstep * fsp->sy_prime;
fsp->sy_value = fsp->sy_val[0]
+ (C50 * fsp->sy_k[0]
+ C51 * fsp->sy_k[1]
+ C52 * fsp->sy_k[2]
+ C53 * fsp->sy_k[3]);
}
symtab->sy_value = t + tstep;
field();
for (fsp = dqueue; fsp != NULL; fsp = fsp->sy_link)
{
fsp->sy_k[4] = tstep * fsp->sy_prime;
fsp->sy_value = fsp->sy_val[0]
+ (C60 * fsp->sy_k[0]
+ C61 * fsp->sy_k[1]
+ C62 * fsp->sy_k[2]
+ C63 * fsp->sy_k[3]
+ C64 * fsp->sy_k[4]);
}
symtab->sy_value = t + C6t * tstep;
field();
for (fsp = dqueue; fsp != NULL; fsp = fsp->sy_link)
fsp->sy_k[5] = tstep * fsp->sy_prime;
for (fsp = dqueue; fsp != NULL; fsp = fsp->sy_link)
{
fsp->sy_predi = fsp->sy_val[0]
+ (A0 * fsp->sy_k[0]
+ A2 * fsp->sy_k[2]
+ A3 * fsp->sy_k[3]
+ A4 * fsp->sy_k[4]);
fsp->sy_value = fsp->sy_val[0]
+ (B0 * fsp->sy_k[0]
+ B2 * fsp->sy_k[2]
+ B3 * fsp->sy_k[3]
+ B4 * fsp->sy_k[4]
+ B5 * fsp->sy_k[5]);
if (fsp->sy_value != 0.0)
fsp->sy_sserr = fabs(1.0 - fsp->sy_predi /
fsp->sy_value);
fsp->sy_aberr = fabs(fsp->sy_value - fsp->sy_predi);
}
if (!conflag && T_LT_TSTOP)
{
maxerr();
if (hierror())
{
tstep *= HALF;
for (fsp = symtab; fsp != NULL; fsp = fsp->sy_link)
fsp->sy_value = fsp->sy_val[0];
gdval = false;
continue;
}
else if (lowerror() && prevstep != tstep)
{
prevstep = tstep; /* prevent infinite loops */
tstep *= 2.0;
for (fsp = dqueue; fsp != NULL; fsp = fsp->sy_link)
fsp->sy_value = fsp->sy_val[0];
gdval = false;
continue;
}
}
gdval = true;
++it;
t += tstep; /* the roundoff error is gross */
}
/* predictor - corrector */
while (T_LT_TSTOP )
{
/* Adams-Bashforth predictor */
if (tstep*(t+tstep-tstop) > 0)
{
startit = it;
goto top;
}
for (fsp = dqueue; fsp != NULL ; fsp = fsp->sy_link)
{
fsp->sy_predi = fsp->sy_value
= fsp->sy_val[0] + tstep/24.0 *
(55 * fsp->sy_pri[0]
-59 * fsp->sy_pri[1]
+37 * fsp->sy_pri[2]
-9 * fsp->sy_pri[3]);
}
++it;
symtab->sy_value = t += tstep;
/* the roundoff error is gross */
field();
/* Adams-Moulton corrector */
for (fsp = dqueue; fsp != NULL; fsp = fsp->sy_link)
{
fsp->sy_value = fsp->sy_val[0] + tstep/24.0 *
(9 * fsp->sy_prime
+19 * fsp->sy_pri[0]
-5 * fsp->sy_pri[1]
+ fsp->sy_pri[2]);
if (fsp->sy_value != 0.0)
fsp->sy_sserr = ECONST *
fabs(1.0 - fsp->sy_predi / fsp->sy_value);
fsp->sy_aberr = ECONST *
fabs (fsp->sy_value - fsp->sy_predi);
fsp->sy_value += ECONST * (fsp->sy_predi - fsp->sy_value);
}
if (!conflag)
{
maxerr();
if (hierror())
{
tstep *= HALF;
t = symtab->sy_val[0];
for (fsp = symtab; fsp != NULL; fsp = fsp->sy_link)
{
fsp->sy_value = fsp->sy_val[0];
fsp->sy_prime = fsp->sy_pri[0];
}
startit = --it;
gdval = false;
goto top;
}
else if (lowerror())
{
tstep *= TWO;
t = symtab->sy_val[0];
for (fsp = symtab; fsp != NULL; fsp = fsp->sy_link)
{
fsp->sy_value = fsp->sy_val[0];
fsp->sy_prime = fsp->sy_pri[0];
}
startit = --it;
gdval = false;
goto top;
}
}
field();
/* cycle indices */
for (fsp = symtab; fsp != NULL; fsp = fsp->sy_link)
{
int j;
for (j = PASTVAL; j > 0; j--)
{
fsp->sy_val[j] = fsp->sy_val[j-1];
fsp->sy_pri[j] = fsp->sy_pri[j-1];
}
fsp->sy_val[0] = fsp->sy_value;
fsp->sy_pri[0] = fsp->sy_prime;
}
/* output */
printq();
}
}
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