Real invertCDF(const Real input) const {
Real x = a_;
Real fx = evaluateCDF(x)-input;
Real s = 0.0;
Real xs = 0.0;
Real a = 1.0;
Real tmp = 0.0;
for (int i = 0; i < 100; i++) {
if ( std::abs(fx) < ROL_EPSILON ) { break; }
s = -fx/evaluatePDF(x);
a = 1.0;
xs = x + a*s;
tmp = fx;
fx = evaluateCDF(xs)-input;
while ( std::abs(fx) > (1.0 - 1.e-4*a)*std::abs(tmp) ) {
a *= 0.5;
xs = x + a*s;
fx = evaluateCDF(xs)-input;
}
x = xs;
}
return x;
}
Real invertCDF(const Real input) const {
if ( input <= 0. ) {
return 0.;
}
Real x = input*gamma_shape_;
Real fx = evaluateCDF(x)-input;
Real s = 0., xs = 0., a = 1., tmp = 0.;
for (size_t i = 0; i < 100; i++) {
if ( std::abs(fx) < ROL_EPSILON ) { break; }
s = -fx/evaluatePDF(x);
a = 1.0;
xs = x + a*s;
tmp = fx;
fx = evaluateCDF(xs)-input;
while ( std::abs(fx) > (1.0 - 1.e-4*a)*std::abs(tmp) ) {
a *= 0.5;
xs = x + a*s;
fx = evaluateCDF(xs)-input;
}
x = xs;
}
return x;
}
void test_centered(const Real x, std::ostream &outStream = std::cout) const {
Real X = x, vx = 0., vy = 0., dv = 0., t = 1., diff = 0., err = 0.;
try {
vx = 0.0;
vy = 0.0;
dv = evaluatePDF(X);
t = 1.0;
diff = 0.0;
err = 0.0;
outStream << std::scientific << std::setprecision(11);
outStream << std::right << std::setw(20) << "CHECK DENSITY: f(x) = cdf(x) with x = "
<< X << " is correct?" << std::endl;
outStream << std::right << std::setw(20) << "t"
<< std::setw(20) << "f'(x)"
<< std::setw(20) << "(f(x+t)-f(x-t))/2t"
<< std::setw(20) << "Error"
<< std::endl;
for (int i = 0; i < 13; i++) {
vx = evaluateCDF(X+t);
vy = evaluateCDF(X-t);
diff = 0.5*(vx-vy)/t;
err = std::abs(diff-dv);
outStream << std::scientific << std::setprecision(11) << std::right
<< std::setw(20) << t
<< std::setw(20) << dv
<< std::setw(20) << diff
<< std::setw(20) << err
<< std::endl;
t *= 0.1;
}
outStream << "\n";
}
catch(std::exception &e) {
outStream << "Either evaluateCDF or evaluatePDF is not implemented!"
<< std::endl << std::endl;
}
// CHECK INTCDF
try {
vx = 0.0;
vy = 0.0;
dv = evaluateCDF(X);
t = 1.0;
diff = 0.0;
err = 0.0;
outStream << std::scientific << std::setprecision(11);
outStream << std::right << std::setw(20) << "CHECK DENSITY: f(x) = intcdf(x) with x = "
<< X << " is correct?" << std::endl;
outStream << std::right << std::setw(20) << "t"
<< std::setw(20) << "f'(x)"
<< std::setw(20) << "(f(x+t)-f(x-t))/2t"
<< std::setw(20) << "Error"
<< std::endl;
for (int i = 0; i < 13; i++) {
vx = integrateCDF(X+t);
vy = integrateCDF(X-t);
diff = 0.5*(vx-vy)/t;
err = std::abs(diff-dv);
outStream << std::scientific << std::setprecision(11) << std::right
<< std::setw(20) << t
<< std::setw(20) << dv
<< std::setw(20) << diff
<< std::setw(20) << err
<< std::endl;
t *= 0.1;
}
outStream << std::endl;
}
catch(std::exception &e) {
outStream << "Either evaluateCDF or integrateCDF is not implemented!"
<< std::endl << std::endl;
}
// CHECK INVCDF
try {
vx = evaluateCDF(X);
vy = invertCDF(vx);
err = std::abs(X-vy);
outStream << std::scientific << std::setprecision(11);
outStream << std::right << std::setw(20) << "CHECK DENSITY: f(x) = invcdf(x) with x = "
<< X << " is correct?" << std::endl;
outStream << std::right << std::setw(20) << "cdf(x)"
<< std::setw(20) << "invcdf(cdf(x))"
<< std::setw(20) << "Error"
<< std::endl;
outStream << std::scientific << std::setprecision(11) << std::right
<< std::setw(20) << vx
<< std::setw(20) << vy
<< std::setw(20) << err
<< std::endl << std::endl;
}
catch(std::exception &e) {
outStream << "Either evaluateCDF or invertCDF is not implemented!"
<< std::endl << std::endl;
}
}