RealType
nextGamma ( RealType const alpha )
{
assert( alpha > 0 );
if( alpha < 1.0 ) {
// See the note on Page 9 of the above reference. The method only
// works for alpha > 1.0, but you can do this trick to work around the
// problem.
RealType tmp_gamma = ( RealType )nextGamma( alpha + 1.0 );
RealType U = ( RealType )nextUniform();
return ( tmp_gamma * ( pow( U, ( 1.0 / alpha ) ) ) );
}
RealType d = alpha - ( 1.0 / 3.0 );
RealType c = ( 1.0 / sqrt( 9.0 * d ) );
RealType x,v,U;
RealType x_squared;
while( true ) { // Keep trying until we draw a variate. (Acceptance rate
// is high, above .9 for at least alpha < 100)
// get x and v
do {
x = ( RealType )nextNormal();
v = 1.0 + ( c * x );
} while( v <= 0.0 );
v = ( v * v * v );
// Use them for acceptance-rejection
x_squared = ( x * x );
U = ( RealType )nextUniform();
// Cheaper 'squeeze method'
if( U < ( 1.0 - ( .0331 * ( x_squared * x_squared ) ) ) ) {
return ( d * v );
}
// If that doesn't work, try version with logs.
if( log( U ) <
( ( 0.5 * x_squared ) + ( d * ( 1.0 - v + log( v ) ) ) ) ) {
return ( d * v );
}
} // Until we get a variate...
} // nextGamma( RealType )
double nextGaussian(double mean, double stdev)
{
return mean + stdev * nextNormal();
}
