void operator()(tbb::blocked_range2d<int> i_range) const {
ewav::Rand48_Engine r48;
std::normal_distribution<float> gdist{0.0f, 1.0f};
const float maxKmag = float(N / 2) * M_TAU / Domain;
const float dk = float(1) * M_TAU / Domain;
for (int j = i_range.rows().begin(); j != i_range.rows().end(); ++j) {
// kj is the wave number in the j direction.
int realJ = j <= (N / 2) ? j : j - N;
float kj = float(realJ) * M_TAU / Domain;
for (int i = i_range.cols().begin(); i != i_range.cols().end(); ++i) {
// ki is the wave number in the i direction
float ki = float(i) * M_TAU / Domain;
// Magnitude of the wave vector.
float kMag = std::hypot(ki, kj);
// Index into the array.
std::size_t index = (std::size_t(j) * StrideJ) + i;
// If the wavenumber is zero, or we're in the outer ring,
// set it to zero.
if ((i == 0 && realJ == 0) || (kMag > maxKmag)) {
Spectral[index] = Cf(0.0, 0.0);
} else {
r48.seed(ewav::SeedFromWavenumber(Imath::V2f(ki, kj), Seed));
Spectral[index] = dk * dk * Cf(gdist(r48), gdist(r48));
}
}
}
}
int geodesicCenter( const Edges &edges, const VectorXf &edge_weights ) {
// Find the geodesic center of a graph
GeodesicDistance gdist( edges, edge_weights );
// First find a few corners of the graph (a point with the maximal distance to any other point)
ArrayXf max_geodesic = ArrayXf::Zero( gdist.N() );
// 3 iterations should be enough, but you can never be paranoid enough
int seed = 0;
for( int it=0; it<3; it++ ) {
// Update the geodesic from the new seed
ArrayXf d = gdist.compute( seed );
max_geodesic = d.max( max_geodesic );
d.maxCoeff( &seed );
}
// The center is the point with the minimal max_geodesic (distance to the side of the graph)
int center;
max_geodesic.minCoeff(¢er);
return center;
}
int main(int, char**) {
// Create r with a random seed
RandomLib::Random r; r.Reseed();
std::cout << "Using " << r.Name() << "\n"
<< "with seed " << r.SeedString() << "\n\n";
{
std::cout
<< "Sampling exactly from the normal distribution. First number is\n"
<< "in binary with ... indicating an infinite sequence of random\n"
<< "bits. Second number gives the corresponding interval. Third\n"
<< "number is the result of filling in the missing bits and rounding\n"
<< "exactly to the nearest representable double.\n";
const int bits = 1;
RandomLib::ExactNormal<bits> ndist;
long long num = 20000000ll;
long long bitcount = 0;
int numprint = 16;
for (long long i = 0; i < num; ++i) {
long long k = r.Count();
RandomLib::RandomNumber<bits> x = ndist(r); // Sample
bitcount += r.Count() - k;
if (i < numprint) {
std::pair<double, double> z = x.Range();
std::cout << x << " = " // Print in binary with ellipsis
<< "(" << z.first << "," << z.second << ")"; // Print range
double v = x.Value<double>(r); // Round exactly to nearest double
std::cout << " = " << v << "\n";
} else if (i == numprint)
std::cout << std::flush;
}
std::cout
<< "Number of bits needed to obtain the binary representation averaged\n"
<< "over " << num << " samples = " << bitcount/double(num) << "\n\n";
}
{
std::cout
<< "Sampling exactly from exp(-x). First number is in binary with\n"
<< "... indicating an infinite sequence of random bits. Second\n"
<< "number gives the corresponding interval. Third number is the\n"
<< "result of filling in the missing bits and rounding exactly to\n"
<< "the nearest representable double.\n";
const int bits = 1;
RandomLib::ExactExponential<bits> edist;
long long num = 50000000ll;
long long bitcount = 0;
int numprint = 16;
for (long long i = 0; i < num; ++i) {
long long k = r.Count();
RandomLib::RandomNumber<bits> x = edist(r); // Sample
bitcount += r.Count() - k;
if (i < numprint) {
std::pair<double, double> z = x.Range();
std::cout << x << " = " // Print in binary with ellipsis
<< "(" << z.first << "," << z.second << ")"; // Print range
double v = x.Value<double>(r); // Round exactly to nearest double
std::cout << " = " << v << "\n";
} else if (i == numprint)
std::cout << std::flush;
}
std::cout
<< "Number of bits needed to obtain the binary representation averaged\n"
<< "over " << num << " samples = " << bitcount/double(num) << "\n\n";
}
{
std::cout
<< "Sampling exactly from the discrete normal distribution with\n"
<< "sigma = 7 and mu = 1/2.\n";
RandomLib::DiscreteNormal<int> gdist(7,1,1,2);
long long num = 50000000ll;
long long count = r.Count();
int numprint = 16;
for (long long i = 0; i < num; ++i) {
int k = gdist(r); // Sample
if (i < numprint)
std::cout << k << " ";
else if (i == numprint)
std::cout << std::endl;
}
count = r.Count() - count;
std::cout
<< "Number of random variates needed averaged\n"
<< "over " << num << " samples = " << count/double(num) << "\n\n";
}
{
std::cout
<< "Sampling exactly from the discrete normal distribution with\n"
<< "sigma = 1024 and mu = 1/7. First result printed is a uniform\n"
<< "range (with covers a power of two). The second number is the\n"
<< "result of sampling additional bits within that range to obtain\n"
<< "a definite result.\n";
RandomLib::DiscreteNormalAlt<int,1> gdist(1024,1,1,7);
long long num = 20000000ll;
long long count = r.Count();
long long entropy = 0;
int numprint = 16;
for (long long i = 0; i < num; ++i) {
RandomLib::UniformInteger<int,1> u = gdist(r);
entropy += u.Entropy();
if (i < numprint)
std::cout << u << " = ";
int k = u(r);
if (i < numprint)
std::cout << k << "\n";
else if (i == numprint)
std::cout << std::flush;
}
count = r.Count() - count;
std::cout
<< "Number of random bits needed for full result (for range) averaged\n"
<< "over " << num << " samples = " << count/double(num) << " ("
<< (count - entropy)/double(num) << ")\n\n";
}
{
std::cout
<< "Random bits with 1 occurring with probability 1/pi exactly:\n";
long long num = 100000000ll;
int numprint = 72;
RandomLib::InversePiProb pp;
long long nbits = 0;
long long k = r.Count();
for (long long i = 0; i < num; ++i) {
bool b = pp(r);
nbits += int(b);
if (i < numprint) std::cout << int(b);
else if (i == numprint) std::cout << "..." << std::flush;
}
std::cout << "\n";
std::cout << "Frequency of 1 averaged over " << num << " samples = 1/"
<< double(num)/nbits << "\n"
<< "bits/sample = " << (r.Count() - k)/double(num) << "\n\n";
}
{
std::cout
<< "Random bits with 1 occurring with probability 1/e exactly:\n";
long long num = 200000000ll;
int numprint = 72;
RandomLib::InverseEProb ep;
long long nbits = 0;
long long k = r.Count();
for (long long i = 0; i < num; ++i) {
bool b = ep(r);
nbits += int(b);
if (i < numprint) std::cout << int(b);
else if (i == numprint) std::cout << "..." << std::flush;
}
std::cout << "\n";
std::cout << "Frequency of 1 averaged over " << num << " samples = 1/"
<< double(num)/nbits << "\n"
<< "bits/sample = " << (r.Count() - k)/double(num) << "\n";
}
return 0;
}