/* Max # of iterations */
/* R_zeroin2() is faster for "expensive" f(), in those typical cases where
* f(ax) and f(bx) are available anyway : */
double R_zeroin2( /* An estimate of the root */
double ax, /* Left border | of the range */
double bx, /* Right border| the root is seeked*/
double fa, double fb, /* f(a), f(b) */
R_zeroin_fn f, /* Function under investigation */
dynamic info, /* Add'l info passed on to f */
ref double Tol, /* Acceptable tolerance */
ref int Maxit)
{
double a, b, c, fc; /* Abscissae, descr. see above, f(c) */
double tol;
int maxit;
a = ax; b = bx;
c = a; fc = fa;
maxit = Maxit + 1; tol = Tol;
/* First test if we have found a root at an endpoint */
if (fa == 0.0)
{
Tol = 0.0;
Maxit = 0;
return a;
}
if (fb == 0.0)
{
Tol = 0.0;
Maxit = 0;
return b;
}
while (maxit-- != 0) /* Main iteration loop */
{
double prev_step = b - a; /* Distance from the last but one
to the last approximation */
double tol_act; /* Actual tolerance */
double p; /* Interpolation step is calcu- */
double q; /* lated in the form p/q; divi-
* sion operations is delayed
* until the last moment */
double new_step; /* Step at this iteration */
if (Math.Abs(fc) < Math.Abs(fb))
{ /* Swap data for b to be the */
a = b; b = c; c = a; /* best approximation */
fa = fb; fb = fc; fc = fa;
}
tol_act = 2 * Double.Epsilon * Math.Abs(b) + tol / 2;
new_step = (c - b) / 2;
if (Math.Abs(new_step) <= tol_act || fb == (double)0)
{
Maxit -= maxit;
Tol = Math.Abs(c - b);
return b; /* Acceptable approx. is found */
}
/* Decide if the interpolation can be tried */
if (Math.Abs(prev_step) >= tol_act /* If prev_step was large enough*/
&& Math.Abs(fa) > Math.Abs(fb))
{ /* and was in true direction,
* Interpolation may be tried */
double t1, cb, t2;
cb = c - b;
if (a == c)
{ /* If we have only two distinct */
/* points linear interpolation */
t1 = fb / fa; /* can only be applied */
p = cb * t1;
q = 1.0 - t1;
}
else
{ /* Quadric inverse interpolation*/
q = fa / fc; t1 = fb / fc; t2 = fb / fa;
p = t2 * (cb * q * (q - t1) - (b - a) * (t1 - 1.0));
q = (q - 1.0) * (t1 - 1.0) * (t2 - 1.0);
}
if (p > (double)0) /* p was calculated with the */
q = -q; /* opposite sign; make p positive */
else /* and assign possible minus to */
p = -p; /* q */
if (p < (0.75 * cb * q - Math.Abs(tol_act * q) / 2) /* If b+p/q falls in [b,c]*/
&& p < Math.Abs(prev_step * q / 2)) /* and isn't too large */
new_step = p / q; /* it is accepted
* If p/q is too large then the
* bisection procedure can
* reduce [b,c] range to more
* extent */
}
if (Math.Abs(new_step) < tol_act)
{ /* Adjust the step to be not less*/
if (new_step > (double)0) /* than tolerance */
new_step = tol_act;
else
new_step = -tol_act;
}
a = b; fa = fb; /* Save the previous approx. */
b += new_step; fb = f(b, info); /* Do step to a new approxim. */
if ((fb > 0 && fc > 0) || (fb < 0 && fc < 0))
{
/* Adjust c for it to have a sign opposite to that of b */
c = a; fc = fa;
}
}
/* failed! */
Tol = Math.Abs(c - b);
Maxit = -1;
return b;
}
/*
* root finder routines are copied from stats/src/zeroin.c
*/
double R_zeroin( /* An estimate of the root */
double ax, /* Left border | of the range */
double bx, /* Right border| the root is seeked*/
R_zeroin_fn f, /* Function under investigation */
dynamic info, /* Add'l info passed on to f */
ref double Tol, /* Acceptable tolerance */
ref int Maxit) /* Max # of iterations */
{
double fa = f(ax, info);
double fb = f(bx, info);
return(R_zeroin2(ax, bx, fa, fb, f, info, ref Tol, ref Maxit));
}
/* Max # of iterations */
/*
* root finder routines are copied from stats/src/zeroin.c
*/
double R_zeroin( /* An estimate of the root */
double ax, /* Left border | of the range */
double bx, /* Right border| the root is seeked*/
R_zeroin_fn f, /* Function under investigation */
dynamic info, /* Add'l info passed on to f */
ref double Tol, /* Acceptable tolerance */
ref int Maxit)
{
double fa = f(ax, info);
double fb = f(bx, info);
return R_zeroin2(ax, bx, fa, fb, f, info, ref Tol, ref Maxit);
}
/* R_zeroin2() is faster for "expensive" f(), in those typical cases where
* f(ax) and f(bx) are available anyway : */
double R_zeroin2( /* An estimate of the root */
double ax, /* Left border | of the range */
double bx, /* Right border| the root is seeked*/
double fa, double fb, /* f(a), f(b) */
R_zeroin_fn f, /* Function under investigation */
dynamic info, /* Add'l info passed on to f */
ref double Tol, /* Acceptable tolerance */
ref int Maxit) /* Max # of iterations */
{
double a, b, c, fc; /* Abscissae, descr. see above, f(c) */
double tol;
int maxit;
a = ax; b = bx;
c = a; fc = fa;
maxit = Maxit + 1; tol = Tol;
/* First test if we have found a root at an endpoint */
if (fa == 0.0)
{
Tol = 0.0;
Maxit = 0;
return(a);
}
if (fb == 0.0)
{
Tol = 0.0;
Maxit = 0;
return(b);
}
while (maxit-- != 0) /* Main iteration loop */
{
double prev_step = b - a; /* Distance from the last but one
* to the last approximation */
double tol_act; /* Actual tolerance */
double p; /* Interpolation step is calcu- */
double q; /* lated in the form p/q; divi-
* sion operations is delayed
* until the last moment */
double new_step; /* Step at this iteration */
if (Math.Abs(fc) < Math.Abs(fb))
{ /* Swap data for b to be the */
a = b; b = c; c = a; /* best approximation */
fa = fb; fb = fc; fc = fa;
}
tol_act = 2 * Double.Epsilon * Math.Abs(b) + tol / 2;
new_step = (c - b) / 2;
if (Math.Abs(new_step) <= tol_act || fb == (double)0)
{
Maxit -= maxit;
Tol = Math.Abs(c - b);
return(b); /* Acceptable approx. is found */
}
/* Decide if the interpolation can be tried */
if (Math.Abs(prev_step) >= tol_act && /* If prev_step was large enough*/
Math.Abs(fa) > Math.Abs(fb))
{ /* and was in true direction,
* Interpolation may be tried */
double t1, cb, t2;
cb = c - b;
if (a == c)
{ /* If we have only two distinct */
/* points linear interpolation */
t1 = fb / fa; /* can only be applied */
p = cb * t1;
q = 1.0 - t1;
}
else
{ /* Quadric inverse interpolation*/
q = fa / fc; t1 = fb / fc; t2 = fb / fa;
p = t2 * (cb * q * (q - t1) - (b - a) * (t1 - 1.0));
q = (q - 1.0) * (t1 - 1.0) * (t2 - 1.0);
}
if (p > (double)0) /* p was calculated with the */
{
q = -q; /* opposite sign; make p positive */
}
else /* and assign possible minus to */
{
p = -p; /* q */
}
if (p < (0.75 * cb * q - Math.Abs(tol_act * q) / 2) && /* If b+p/q falls in [b,c]*/
p < Math.Abs(prev_step * q / 2)) /* and isn't too large */
{
new_step = p / q; /* it is accepted
* If p/q is too large then the
* bisection procedure can
* reduce [b,c] range to more
* extent */
}
}
if (Math.Abs(new_step) < tol_act)
{ /* Adjust the step to be not less*/
if (new_step > (double)0) /* than tolerance */
{
new_step = tol_act;
}
else
{
new_step = -tol_act;
}
}
a = b; fa = fb; /* Save the previous approx. */
b += new_step; fb = f(b, info); /* Do step to a new approxim. */
if ((fb > 0 && fc > 0) || (fb < 0 && fc < 0))
{
/* Adjust c for it to have a sign opposite to that of b */
c = a; fc = fa;
}
}
/* failed! */
Tol = Math.Abs(c - b);
Maxit = -1;
return(b);
}
