brent_iterate(ref brent_state_t state, Func<double, double> f, out double root, ref double x_lower, ref double x_upper)
{
double tol, m;
bool ac_equal = false;
double a = state.a, b = state.b, c = state.c;
double fa = state.fa, fb = state.fb, fc = state.fc;
double d = state.d, e = state.e;
if ((fb < 0 && fc < 0) || (fb > 0 && fc > 0))
{
ac_equal = true;
c = a;
fc = fa;
d = b - a;
e = b - a;
}
if (Math.Abs(fc) < Math.Abs(fb))
{
ac_equal = true;
a = b;
b = c;
c = a;
fa = fb;
fb = fc;
fc = fa;
}
tol = 0.5 * DoubleConstants.DBL_EPSILON * Math.Abs(b);
m = 0.5 * (c - b);
if (fb == 0)
{
root = b;
x_lower = b;
x_upper = b;
return null;
}
if (Math.Abs(m) <= tol)
{
root = b;
if (b < c)
{
x_lower = b;
x_upper = c;
}
else
{
x_lower = c;
x_upper = b;
}
return null;
}
if (Math.Abs(e) < tol || Math.Abs(fa) <= Math.Abs(fb))
{
d = m; /* use bisection */
e = m;
}
else
{
double p, q, r; /* use inverse cubic interpolation */
double s = fb / fa;
if (ac_equal)
{
p = 2 * m * s;
q = 1 - s;
}
else
{
q = fa / fc;
r = fb / fc;
p = s * (2 * m * q * (q - r) - (b - a) * (r - 1));
q = (q - 1) * (r - 1) * (s - 1);
}
if (p > 0)
{
q = -q;
}
else
{
p = -p;
}
if (2 * p < Math.Min(3 * m * q - Math.Abs(tol * q), Math.Abs(e * q)))
{
e = d;
d = p / q;
}
else
{
/* interpolation failed, fall back to bisection */
d = m;
e = m;
}
}
a = b;
fa = fb;
if (Math.Abs(d) > tol)
{
b += d;
}
else
{
b += (m > 0 ? +tol : -tol);
}
fb = f(b);
state.a = a;
state.b = b;
state.c = c;
state.d = d;
state.e = e;
state.fa = fa;
state.fb = fb;
state.fc = fc;
/* Update the best estimate of the root and bounds on each
iteration */
root = b;
if ((fb < 0 && fc < 0) || (fb > 0 && fc > 0))
{
c = a;
}
if (b < c)
{
x_lower = b;
x_upper = c;
}
else
{
x_lower = c;
x_upper = b;
}
return null;
}
brent_iterate(ref brent_state_t state, Func <double, double> f, out double root, ref double x_lower, ref double x_upper)
{
double tol, m;
bool ac_equal = false;
double a = state.a, b = state.b, c = state.c;
double fa = state.fa, fb = state.fb, fc = state.fc;
double d = state.d, e = state.e;
if ((fb < 0 && fc < 0) || (fb > 0 && fc > 0))
{
ac_equal = true;
c = a;
fc = fa;
d = b - a;
e = b - a;
}
if (Math.Abs(fc) < Math.Abs(fb))
{
ac_equal = true;
a = b;
b = c;
c = a;
fa = fb;
fb = fc;
fc = fa;
}
tol = 0.5 * DoubleConstants.DBL_EPSILON * Math.Abs(b);
m = 0.5 * (c - b);
if (fb == 0)
{
root = b;
x_lower = b;
x_upper = b;
return(null);
}
if (Math.Abs(m) <= tol)
{
root = b;
if (b < c)
{
x_lower = b;
x_upper = c;
}
else
{
x_lower = c;
x_upper = b;
}
return(null);
}
if (Math.Abs(e) < tol || Math.Abs(fa) <= Math.Abs(fb))
{
d = m; /* use bisection */
e = m;
}
else
{
double p, q, r; /* use inverse cubic interpolation */
double s = fb / fa;
if (ac_equal)
{
p = 2 * m * s;
q = 1 - s;
}
else
{
q = fa / fc;
r = fb / fc;
p = s * (2 * m * q * (q - r) - (b - a) * (r - 1));
q = (q - 1) * (r - 1) * (s - 1);
}
if (p > 0)
{
q = -q;
}
else
{
p = -p;
}
if (2 * p < Math.Min(3 * m * q - Math.Abs(tol * q), Math.Abs(e * q)))
{
e = d;
d = p / q;
}
else
{
/* interpolation failed, fall back to bisection */
d = m;
e = m;
}
}
a = b;
fa = fb;
if (Math.Abs(d) > tol)
{
b += d;
}
else
{
b += (m > 0 ? +tol : -tol);
}
fb = f(b);
state.a = a;
state.b = b;
state.c = c;
state.d = d;
state.e = e;
state.fa = fa;
state.fb = fb;
state.fc = fc;
/* Update the best estimate of the root and bounds on each
* iteration */
root = b;
if ((fb < 0 && fc < 0) || (fb > 0 && fc > 0))
{
c = a;
}
if (b < c)
{
x_lower = b;
x_upper = c;
}
else
{
x_lower = c;
x_upper = b;
}
return(null);
}
brent_init(Func<double, double> f, double x_lower, double x_upper, out double root, out brent_state_t state)
{
double f_lower, f_upper;
root = 0.5 * (x_lower + x_upper);
f_lower = f(x_lower);
f_upper = f(x_upper);
state.a = x_lower;
state.fa = f_lower;
state.b = x_upper;
state.fb = f_upper;
state.c = x_upper;
state.fc = f_upper;
state.d = x_upper - x_lower;
state.e = x_upper - x_lower;
if ((f_lower < 0.0 && f_upper < 0.0) || (f_lower > 0.0 && f_upper > 0.0))
{
return new GSL_ERROR("endpoints do not straddle y=0", GSL_ERR.GSL_EINVAL, false);
}
return null;
}
brent_init(Func <double, double> f, double x_lower, double x_upper, out double root, out brent_state_t state)
{
double f_lower, f_upper;
root = 0.5 * (x_lower + x_upper);
f_lower = f(x_lower);
f_upper = f(x_upper);
state.a = x_lower;
state.fa = f_lower;
state.b = x_upper;
state.fb = f_upper;
state.c = x_upper;
state.fc = f_upper;
state.d = x_upper - x_lower;
state.e = x_upper - x_lower;
if ((f_lower < 0.0 && f_upper < 0.0) || (f_lower > 0.0 && f_upper > 0.0))
{
return(new GSL_ERROR("endpoints do not straddle y=0", GSL_ERR.GSL_EINVAL, false));
}
return(null);
}
