/// <summary>
/// Owen's T function for a restricted range of parameters.
/// </summary>
///
/// <param name="h">Owen's T function argument H (where 0 <= H).</param>
/// <param name="a">Owen's T function argument A (where 0 <= A <= 1).</param>
/// <param name="ah">The value of A*H.</param>
///
/// <returns>The value of Owen's T function.</returns>
///
public static double Function(double h, double a, double ah)
{
double ai;
double aj;
double AS;
double dhs;
double dj;
double gj;
double hs;
int i;
int iaint;
int icode;
int ihint;
int ii;
int j;
int jj;
int m;
int maxii;
double normh;
double r;
const double rrtpi = 0.39894228040143267794;
const double rtwopi = 0.15915494309189533577;
double y;
double yi;
double z;
double zi;
double value = 0;
double vi;
double[] arange =
{
0.025, 0.09, 0.15, 0.36, 0.5,
0.9, 0.99999
};
double[] c2 =
{
0.99999999999999987510,
-0.99999999999988796462, 0.99999999998290743652,
-0.99999999896282500134, 0.99999996660459362918,
-0.99999933986272476760, 0.99999125611136965852,
-0.99991777624463387686, 0.99942835555870132569,
-0.99697311720723000295, 0.98751448037275303682,
-0.95915857980572882813, 0.89246305511006708555,
-0.76893425990463999675, 0.58893528468484693250,
-0.38380345160440256652, 0.20317601701045299653,
-0.82813631607004984866E-01, 0.24167984735759576523E-01,
-0.44676566663971825242E-02, 0.39141169402373836468E-03
};
double[] hrange =
{
0.02, 0.06, 0.09, 0.125, 0.26,
0.4, 0.6, 1.6, 1.7, 2.33,
2.4, 3.36, 3.4, 4.8
};
int[] meth =
{
1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 5, 6
};
int[] ord =
{
2, 3, 4, 5, 7, 10, 12, 18, 10, 20, 30, 20, 4, 7, 8, 20, 13, 0
};
double[] pts =
{
0.35082039676451715489E-02,
0.31279042338030753740E-01, 0.85266826283219451090E-01,
0.16245071730812277011, 0.25851196049125434828,
0.36807553840697533536, 0.48501092905604697475,
0.60277514152618576821, 0.71477884217753226516,
0.81475510988760098605, 0.89711029755948965867,
0.95723808085944261843, 0.99178832974629703586
};
int[] select =
{
1, 1, 2, 13, 13, 13, 13, 13, 13, 13, 13, 16, 16, 16, 9,
1, 2, 2, 3, 3, 5, 5, 14, 14, 15, 15, 16, 16, 16, 9,
2, 2, 3, 3, 3, 5, 5, 15, 15, 15, 15, 16, 16, 16, 10,
2, 2, 3, 5, 5, 5, 5, 7, 7, 16, 16, 16, 16, 16, 10,
2, 3, 3, 5, 5, 6, 6, 8, 8, 17, 17, 17, 12, 12, 11,
2, 3, 5, 5, 5, 6, 6, 8, 8, 17, 17, 17, 12, 12, 12,
2, 3, 4, 4, 6, 6, 8, 8, 17, 17, 17, 17, 17, 12, 12,
2, 3, 4, 4, 6, 6, 18, 18, 18, 18, 17, 17, 17, 12, 12
};
double[] wts =
{
0.18831438115323502887E-01,
0.18567086243977649478E-01, 0.18042093461223385584E-01,
0.17263829606398753364E-01, 0.16243219975989856730E-01,
0.14994592034116704829E-01, 0.13535474469662088392E-01,
0.11886351605820165233E-01, 0.10070377242777431897E-01,
0.81130545742299586629E-02, 0.60419009528470238773E-02,
0.38862217010742057883E-02, 0.16793031084546090448E-02
};
/*
* Determine appropriate method from t1...t6
*/
ihint = 15;
for (i = 1; i <= 14; i++)
{
if (h <= hrange[i - 1])
{
ihint = i;
break;
}
}
iaint = 8;
for (i = 1; i <= 7; i++)
{
if (a <= arange[i - 1])
{
iaint = i;
break;
}
}
icode = select[ihint - 1 + (iaint - 1) * 15];
m = ord[icode - 1];
/*
* t1(h, a, m) ; m = 2, 3, 4, 5, 7, 10, 12 or 18
* jj = 2j - 1 ; gj = exp(-h*h/2) * (-h*h/2)**j / j
* aj = a**(2j-1) / (2*pi)
*/
if (meth[icode - 1] == 1)
{
hs = -0.5 * h * h;
dhs = Math.Exp(hs);
AS = a * a;
j = 1;
jj = 1;
aj = rtwopi * a;
value = rtwopi * Math.Atan(a);
dj = dhs - 1.0;
gj = hs * dhs;
for (; ;)
{
value = value + dj * aj / (double)(jj);
if (m <= j)
{
return(value);
}
j = j + 1;
jj = jj + 2;
aj = aj * AS;
dj = gj - dj;
gj = gj * hs / (double)(j);
}
}
/*
* t2(h, a, m) ; m = 10, 20 or 30
* z = (-1)^(i-1) * zi ; ii = 2i - 1
* vi = (-1)^(i-1) * a^(2i-1) * exp[-(a*h)^2/2] / sqrt(2*pi)
*/
else if (meth[icode - 1] == 2)
{
maxii = m + m + 1;
ii = 1;
value = 0.0;
hs = h * h;
AS = -a * a;
vi = rrtpi * a * Math.Exp(-0.5 * ah * ah);
z = 0.5 * (-0.5 + Normal.Function(ah)) / h;
y = 1.0 / hs;
for (; ;)
{
value = value + z;
if (maxii <= ii)
{
value = value * rrtpi * Math.Exp(-0.5 * hs);
return(value);
}
z = y * (vi - (double)(ii) * z);
vi = AS * vi;
ii = ii + 2;
}
}
/*
* t3(h, a, m) ; m = 20
* ii = 2i - 1
* vi = a**(2i-1) * exp[-(a*h)**2/2] / sqrt(2*pi)
*/
else if (meth[icode - 1] == 3)
{
i = 1;
ii = 1;
value = 0.0;
hs = h * h;
AS = a * a;
vi = rrtpi * a * Math.Exp(-0.5 * ah * ah);
zi = 0.5 * (-0.5 + Normal.Function(ah)) / h;
y = 1.0 / hs;
for (; ;)
{
value = value + zi * c2[i - 1];
if (m < i)
{
value = value * rrtpi * Math.Exp(-0.5 * hs);
return(value);
}
zi = y * ((double)(ii) * zi - vi);
vi = AS * vi;
i = i + 1;
ii = ii + 2;
}
}
/*
* t4(h, a, m) ; m = 4, 7, 8 or 20; ii = 2i + 1
* ai = a * exp[-h*h*(1+a*a)/2] * (-a*a)**i / (2*pi)
*/
else if (meth[icode - 1] == 4)
{
maxii = m + m + 1;
ii = 1;
hs = h * h;
AS = -a * a;
value = 0.0;
ai = rtwopi * a * Math.Exp(-0.5 * hs * (1.0 - AS));
yi = 1.0;
for (; ;)
{
value = value + ai * yi;
if (maxii <= ii)
{
return(value);
}
ii = ii + 2;
yi = (1.0 - hs * yi) / (double)(ii);
ai = ai * AS;
}
}
/*
* t5(h, a, m) ; m = 13
* 2m - point gaussian quadrature
*/
else if (meth[icode - 1] == 5)
{
value = 0.0;
AS = a * a;
hs = -0.5 * h * h;
for (i = 1; i <= m; i++)
{
r = 1.0 + AS * pts[i - 1];
value = value + wts[i - 1] * Math.Exp(hs * r) / r;
}
value = a * value;
}
/*
* t6(h, a); approximation for a near 1, (a<=1)
*/
else if (meth[icode - 1] == 6)
{
normh = Normal.Complemented(h);
value = 0.5 * normh * (1.0 - normh);
y = 1.0 - a;
r = Math.Atan(y / (1.0 + a));
if (r != 0.0)
{
value = value - rtwopi * r * Math.Exp(-0.5 * y * h * h / r);
}
}
return(value);
}
