double gamma_cdf (double beta, double gamm, double pzero, double x)
{
if (x <= 0.0)
return (pzero);
else
return (pzero + (1.0 - pzero) * gammap (gamm, x / beta));
}
/** [chi_pp p v]
* Finds the percentage point [p] of the chi squared distribution of [v] degrees
* of freedom. The gamma is related to this distribution by the define below.
*
* Algorithm AS91: The Percentage Points of the chi^2 Distribution
* (translated to C, and removed goto's ~nrl) */
double chi_pp( double p, double v ){
double ch,s1,s2,s3,s4,s5,s6;
double e,aa,xx,c,g,x,p1,a,q,p2,t,ig,b;
assert( v > 0.0 );
if (p < 0.000002 || p > 0.999998)
failwith("Chi^2 Percentage Points incorrect.1");
e = 0.5e-6; /** error term **/
aa= 0.6931471805;
xx = 0.5 * v;
c = xx - 1.0;
g = lngamma( xx );
if( v < -1.24 * log(p) ){
ch = pow(p * xx * exp ( g + xx * aa), 1.0/xx);
if( ch - e < 0 ) return ch;
} else if( v > 0.32) {
x = point_normal( p );
p1 = 0.222222 / v;
ch = v * pow( x * sqrt( p1 ) + 1 - p1, 3.0) ;
if (ch > 2.2 * v + 6)
ch = -2.0 * (log(1-p) - c*log(0.5*ch)+g);
} else {
ch = 0.4;
a = log (1 - p);
do{
q = ch;
p1 = 1 + ch * (4.67 + ch);
p2 = ch * (6.73 + ch * (6.66 + ch));
t = -0.5 + (4.67 + 2*ch)/p1 - (6.73 + ch*(13.32 + 3*ch))/p2;
ch = ch - (1- exp( a + g + 0.5*ch+c*aa) * p2/p1)/t;
} while( fabs( q/ch - 1) - 0.01 > 0.0 );
}
do{
q = ch;
p1 = .5*ch;
ig = gammap( p1, xx );
if (ig < 0){ failwith("Chi^2 Percentage Points incorrect.2"); }
p2 = p - ig;
t = p2 * exp( xx*aa + g + p1 - c*log(ch));
b = t / ch;
a = (0.5*t) - (b*c);
/* Seven terms of the Taylor series */
s1 = (210 + a*(140 + a*(105 + a*(84 + a*(70 + 60*a))))) / 420.0;
s2 = (420 + a*(735 + a*(966 + a*(1141 + 1278*a)))) / 2520.0;
s3 = (210 + a*(462 + a*(707 + 932*a))) / 2520.0;
s4 = (252 + a*(672 + 1182*a) + c*(294 + a*(889 + 1740*a))) / 5040.0;
s5 = ( 84 + 264*a + c*(175 + 606*a)) / 2520.0;
s6 = (120 + c*(346 + 127*c)) / 5040.0;
ch+= t*(1+0.5*t*s1-b*c*(s1-b*(s2-b*(s3-b*(s4-b*(s5-b*s6))))));
} while( fabs(q / ch - 1.0) > e);
return (ch);
}
/** [gamma_rates rates alpha beta cuts k]
* calculates the rates into [rates] with percentage points [cuts] of [k]
* categories and shape parameters [alpha] and [beta] */
void
gamma_rates(double* rates,const double a,const double b,const double* cuts,const int k)
{
double fac, *ingam;
int j;
fac = a*((double)k)/b;
ingam = (double*) malloc( k * sizeof(double));
CHECK_MEM(ingam);
//calculate: rj = (A*k/B)*(I(bB,A+1)-I(aB,A+1))
for(j=0;j<(k-1);j++){
ingam[j] = gammap( cuts[j]*b, a+1 );
//printf("LG: %f\tNL: %f\n", ingam[j], gamma_i( cuts[j]*b, a+1 ) );
}
rates[0] = ingam[0] * fac; //lower rate
rates[k-1] = (1 - ingam[k-2]) * fac; //upper rate
for(j=1;j<k-1;j++)
rates[j] = (ingam[j] - ingam[j-1]) * fac;
free( ingam );
}
void Foam::varyingGammaTotalTemperatureFvPatchScalarField::updateCoeffs()
{
if (updated())
{
return;
}
const fluidThermo& thermo =
this->patch().boundaryMesh().mesh().thisDb().lookupObject<fluidThermo>("thermophysicalProperties");
const fvPatchVectorField& Up =
patch().lookupPatchField<volVectorField, vector>(UName_);
const fvsPatchField<scalar>& phip =
patch().lookupPatchField<surfaceScalarField, scalar>(phiName_);
const fvPatchField<scalar>& psip =
thermo.psi().boundaryField()[patch().index()];
const fvPatchField<scalar>& pp =
thermo.p().boundaryField()[patch().index()];
const fvPatchField<scalar>& Tp =
thermo.T().boundaryField()[patch().index()];
scalarField gammap
(
thermo.gamma(pp, Tp, patch().index())
);
scalarField gM1ByG ((gammap - 1.0)/gammap);
operator==
(
T0_/(1.0 + 0.5*psip*gM1ByG*(1.0 - pos(phip))*magSqr(Up))
);
fixedValueFvPatchScalarField::updateCoeffs();
}
/* gammacdf: cumulative distribution function for the gamma distribution.
* @x: the x-value for evaluation.
* @a: the first parameter.
* @b: the second parameter.
*/
double gammacdf (double x, double a, double b) {
/* return the value. */
return gammap (a, x / b);
}
double cumchi(double df,double x)
{
return gammap(df/2,x/2);
}
