qc25c(Func <double, double> f, double a, double b, double c,
out double result, out double abserr, out bool err_reliable)
{
double cc = (2 * c - b - a) / (b - a);
if (Math.Abs(cc) > 1.1)
{
fn_cauchy_params fn_params;
fn_params.function = f;
fn_params.singularity = c;
Func <double, double> weighted_function = delegate(double t)
{ return(fn_cauchy(t, fn_params)); };
QK15.Integration(weighted_function, a, b, out result, out abserr,
out var resabs, out var resasc);
if (abserr == resasc)
{
err_reliable = false; // 0;
}
else
{
err_reliable = true; // 1;
}
return;
}
else
{
double[] cheb12 = new double[13];
double[] cheb24 = new double[25];
double[] moment = new double[25];
double res12 = 0, res24 = 0;
int i;
Qcheb.Approximation(f, a, b, cheb12, cheb24);
compute_moments(cc, moment);
for (i = 0; i < 13; i++)
{
res12 += cheb12[i] * moment[i];
}
for (i = 0; i < 25; i++)
{
res24 += cheb24[i] * moment[i];
}
result = res24;
abserr = Math.Abs(res24 - res12);
err_reliable = false; // 0;
return;
}
}
qc25s(Func <double, double> f, double a, double b, double a1, double b1,
gsl_integration_qaws_table t,
out double result, out double abserr, out bool err_reliable)
{
var fn_params = new fn_qaws_params
{
function = f,
a = a,
b = b,
table = t
};
Func <double, double> weighted_function;
if (a1 == a && (t.alpha != 0.0 || t.mu != 0))
{
double[] cheb12 = new double[13], cheb24 = new double[25];
double factor = Math.Pow(0.5 * (b1 - a1), t.alpha + 1.0);
weighted_function = delegate(double tt)
{ return(fn_qaws_R(tt, fn_params)); };
Qcheb.Approximation(weighted_function, a1, b1, cheb12, cheb24);
if (t.mu == 0)
{
double u = factor;
compute_result(t.ri, cheb12, cheb24, out var res12, out var res24);
result = u * res24;
abserr = Math.Abs(u * (res24 - res12));
}
else
{
double u = factor * Math.Log(b1 - a1);
double v = factor;
compute_result(t.ri, cheb12, cheb24, out var res12a, out var res24a);
compute_result(t.rg, cheb12, cheb24, out var res12b, out var res24b);
result = u * res24a + v * res24b;
abserr = Math.Abs(u * (res24a - res12a)) + Math.Abs(v * (res24b - res12b));
}
err_reliable = false;
return;
}
else if (b1 == b && (t.beta != 0.0 || t.nu != 0))
{
double[] cheb12 = new double[13], cheb24 = new double[25];
double factor = Math.Pow(0.5 * (b1 - a1), t.beta + 1.0);
weighted_function = delegate(double tt)
{ return(fn_qaws_L(tt, fn_params)); };
Qcheb.Approximation(weighted_function, a1, b1, cheb12, cheb24);
if (t.nu == 0)
{
double u = factor;
compute_result(t.rj, cheb12, cheb24, out var res12, out var res24);
result = u * res24;
abserr = Math.Abs(u * (res24 - res12));
}
else
{
double u = factor * Math.Log(b1 - a1);
double v = factor;
compute_result(t.rj, cheb12, cheb24, out var res12a, out var res24a);
compute_result(t.rh, cheb12, cheb24, out var res12b, out var res24b);
result = u * res24a + v * res24b;
abserr = Math.Abs(u * (res24a - res12a)) + Math.Abs(v * (res24b - res12b));
}
err_reliable = false;
return;
}
else
{
weighted_function = delegate(double tt)
{ return(fn_qaws(tt, fn_params)); };
QK15.Integration(weighted_function, a1, b1, out result, out abserr,
out var resabs, out var resasc);
if (abserr == resasc)
{
err_reliable = false;
}
else
{
err_reliable = true;
}
return;
}
}
qc25f(Func <double, double> f, double a, double b,
gsl_integration_qawo_table wf, int level,
out double result, out double abserr, out double resabs, out double resasc)
{
double center = 0.5 * (a + b);
double half_length = 0.5 * (b - a);
double omega = wf.omega;
double par = omega * half_length;
if (Math.Abs(par) < 2)
{
Func <double, double> weighted_function;
fn_fourier_params fn_params;
fn_params.function = f;
fn_params.omega = omega;
if (wf.sine == gsl_integration_qawo_enum.GSL_INTEG_SINE)
{
weighted_function = delegate(double t)
{ return(fn_sin(t, fn_params)); };
}
else
{
weighted_function = delegate(double t)
{ return(fn_cos(t, fn_params)); };
}
QK15.Integration(weighted_function, a, b, out result, out abserr,
out resabs, out resasc);
return;
}
else
{
int momentix;
double[] cheb12 = new double[13];
double[] cheb24 = new double[25];
double result_abs, res12_cos, res12_sin, res24_cos, res24_sin;
double est_cos, est_sin;
double c, s;
int i;
Qcheb.Approximation(f, a, b, cheb12, cheb24);
if (level >= wf.n)
{
/* table overflow should not happen, check before calling */
new GSL_ERROR("table overflow in internal function", GSL_ERR.GSL_ESANITY, true);
throw new ArithmeticException("table overflow in internal function"); //
}
/* obtain moments from the table */
momentix = 25 * level;
res12_cos = cheb12[12] * wf.chebmo[momentix + 12];
res12_sin = 0;
for (i = 0; i < 6; i++)
{
int k = 10 - 2 * i;
res12_cos += cheb12[k] * wf.chebmo[momentix + k];
res12_sin += cheb12[k + 1] * wf.chebmo[momentix + k + 1];
}
res24_cos = cheb24[24] * wf.chebmo[momentix + 24];
res24_sin = 0;
result_abs = Math.Abs(cheb24[24]);
for (i = 0; i < 12; i++)
{
int k = 22 - 2 * i;
res24_cos += cheb24[k] * wf.chebmo[momentix + k];
res24_sin += cheb24[k + 1] * wf.chebmo[momentix + k + 1];
result_abs += Math.Abs(cheb24[k]) + Math.Abs(cheb24[k + 1]);
}
est_cos = Math.Abs(res24_cos - res12_cos);
est_sin = Math.Abs(res24_sin - res12_sin);
c = half_length * Math.Cos(center * omega);
s = half_length * Math.Sin(center * omega);
if (wf.sine == gsl_integration_qawo_enum.GSL_INTEG_SINE)
{
result = c * res24_sin + s * res24_cos;
abserr = Math.Abs(c * est_sin) + Math.Abs(s * est_cos);
}
else
{
result = c * res24_cos - s * res24_sin;
abserr = Math.Abs(c * est_cos) + Math.Abs(s * est_sin);
}
resabs = result_abs * half_length;
resasc = GSL_CONST.GSL_DBL_MAX;
return;
}
}