float liquid_gammaf(float _z)
{
if (_z < 0) {
// use identities
// (1) gamma(z)*gamma(-z) = -pi / (z*sin(pi*z))
// (2) z*gamma(z) = gamma(1+z)
//
// therefore:
// gamma(z) = pi / ( gamma(1-z) * sin(pi*z) )
float t0 = liquid_gammaf(1.0 - _z);
float t1 = sinf(M_PI*_z);
if (t0==0 || t1==0)
fprintf(stderr,"warning: liquid_gammaf(), divide by zero\n");
return M_PI / (t0 * t1);
} else {
return expf( liquid_lngammaf(_z) );
}
}
// Gamma distribution cumulative distribution function
// F(x) = gamma(a,x/b) / Gamma(a)
// where
// a = alpha, alpha > 0
// b = beta, beta > 0
// gamma(a,z) = lower incomplete gamma function
// Gamma(z) = regular gamma function
//
float randgammaf_cdf(float _x,
float _alpha,
float _beta)
{
// validate input
if (_alpha <= 0.0f) {
fprintf(stderr,"error: randgammaf_cdf(), alpha must be greater than zero\n");
exit(1);
} else if (_beta <= 0.0f) {
fprintf(stderr,"error: randgammaf_cdf(), beta must be greater than zero\n");
exit(1);
}
if (_x <= 0.0f)
return 0.0f;
return liquid_lowergammaf(_alpha, _x/_beta) / liquid_gammaf(_alpha);
}
//
// AUTOTEST: Gamma
//
void autotest_gamma()
{
// error tolerance
float tol = 1e-5f;
// test vectors
float v[12][2] = {
{0.0001f, 9999.42288323161f },
{0.001f, 999.423772484595f },
{0.01f, 99.4325851191505f },
{0.1f, 9.51350769866873f },
{0.2f, 4.59084371199880f },
{0.5f, 1.77245385090552f },
{1.5f, 0.886226925452758f },
{2.5f, 1.329340388179140f },
{3.2f, 2.42396547993537f },
{4.1f, 6.81262286301667f },
{5.3f, 38.0779764499523f },
{12.0f, 39916800.0000000f }};
unsigned int i;
for (i=0; i<12; i++) {
// extract test vector
float z = v[i][0];
float g = v[i][1];
// compute gamma
float gamma = liquid_gammaf(z);
// compute relative error
float error = fabsf(gamma-g) / fabsf(g);
// print results
if (liquid_autotest_verbose)
printf(" gamma(%12.4e) = %12.4e (expected %12.4e) %12.4e\n", z, gamma, g, error);
// run test
CONTEND_LESS_THAN(error, tol);
}
}
// Gamma distribution cumulative distribution function
// x^(a-1) exp{-x/b)
// f(x) = -------------------
// Gamma(a) b^a
// where
// a = alpha, a > 0
// b = beta, b > 0
// Gamma(z) = regular gamma function
// x >= 0
float randgammaf_pdf(float _x,
float _alpha,
float _beta)
{
// validate input
if (_alpha <= 0.0f) {
fprintf(stderr,"error: randgammaf_pdf(), alpha must be greater than zero\n");
exit(1);
} else if (_beta <= 0.0f) {
fprintf(stderr,"error: randgammaf_pdf(), beta must be greater than zero\n");
exit(1);
}
if (_x <= 0.0f)
return 0.0f;
float t0 = powf(_x, _alpha-1.0f);
float t1 = expf(-_x / _beta);
float t2 = liquid_gammaf(_alpha);
float t3 = powf(_beta, _alpha);
return (t0*t1)/(t2*t3);
}
// compute _n!
float liquid_factorialf(unsigned int _n) {
return fabsf(liquid_gammaf((float)(_n+1)));
}
// ln( Gamma(z,alpha) ) : upper incomplete gamma function
float liquid_lnuppergammaf(float _z, float _alpha)
{
return logf( liquid_gammaf(_z) - liquid_lowergammaf(_z,_alpha) );
}
