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#include <thrust/device_vector.h>
#include <thrust/host_vector.h>
#include <thrust/transform_reduce.h>
#include <thrust/functional.h>
#include <thrust/extrema.h>
#include <cmath>
#include <limits>
// This example computes several statistical properties of a data
// series in a single reduction. The algorithm is described in detail here:
// http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Parallel_algorithm
//
// Thanks to Joseph Rhoads for contributing this example
// structure used to accumulate the moments and other
// statistical properties encountered so far.
template <typename T>
struct summary_stats_data
{
T n;
T min;
T max;
T mean;
T M2;
T M3;
T M4;
// initialize to the identity element
void initialize()
{
n = mean = M2 = M3 = M4 = 0;
min = std::numeric_limits<T>::max();
max = std::numeric_limits<T>::min();
}
T variance() { return M2 / (n - 1); }
T variance_n() { return M2 / n; }
T skewness() { return std::sqrt(n) * M3 / std::pow(M2, (T) 1.5); }
T kurtosis() { return n * M4 / (M2 * M2); }
};
// stats_unary_op is a functor that takes in a value x and
// returns a variace_data whose mean value is initialized to x.
template <typename T>
struct summary_stats_unary_op
{
__host__ __device__
summary_stats_data<T> operator()(const T& x) const
{
summary_stats_data<T> result;
result.n = 1;
result.min = x;
result.max = x;
result.mean = x;
result.M2 = 0;
result.M3 = 0;
result.M4 = 0;
return result;
}
};
// summary_stats_binary_op is a functor that accepts two summary_stats_data
// structs and returns a new summary_stats_data which are an
// approximation to the summary_stats for
// all values that have been agregated so far
template <typename T>
struct summary_stats_binary_op
: public thrust::binary_function<const summary_stats_data<T>&,
const summary_stats_data<T>&,
summary_stats_data<T> >
{
__host__ __device__
summary_stats_data<T> operator()(const summary_stats_data<T>& x, const summary_stats_data <T>& y) const
{
summary_stats_data<T> result;
// precompute some common subexpressions
T n = x.n + y.n;
T n2 = n * n;
T n3 = n2 * n;
T delta = y.mean - x.mean;
T delta2 = delta * delta;
T delta3 = delta2 * delta;
T delta4 = delta3 * delta;
//Basic number of samples (n), min, and max
result.n = n;
result.min = thrust::min(x.min, y.min);
result.max = thrust::max(x.max, y.max);
result.mean = x.mean + delta * y.n / n;
result.M2 = x.M2 + y.M2;
result.M2 += delta2 * x.n * y.n / n;
result.M3 = x.M3 + y.M3;
result.M3 += delta3 * x.n * y.n * (x.n - y.n) / n2;
result.M3 += (T) 3.0 * delta * (x.n * y.M2 - y.n * x.M2) / n;
result.M4 = x.M4 + y.M4;
result.M4 += delta4 * x.n * y.n * (x.n * x.n - x.n * y.n + y.n * y.n) / n3;
result.M4 += (T) 6.0 * delta2 * (x.n * x.n * y.M2 + y.n * y.n * x.M2) / n2;
result.M4 += (T) 4.0 * delta * (x.n * y.M3 - y.n * x.M3) / n;
return result;
}
};
template <typename Iterator>
void print_range(const std::string& name, Iterator first, Iterator last)
{
typedef typename std::iterator_traits<Iterator>::value_type T;
std::cout << name << ": ";
thrust::copy(first, last, std::ostream_iterator<T>(std::cout, " "));
std::cout << "\n";
}
int main(void)
{
typedef float T;
// initialize host array
T h_x[] = {4, 7, 13, 16};
// transfer to device
thrust::device_vector<T> d_x(h_x, h_x + sizeof(h_x) / sizeof(T));
// setup arguments
summary_stats_unary_op<T> unary_op;
summary_stats_binary_op<T> binary_op;
summary_stats_data<T> init;
init.initialize();
// compute summary statistics
summary_stats_data<T> result = thrust::transform_reduce(d_x.begin(), d_x.end(), unary_op, init, binary_op);
std::cout <<"******Summary Statistics Example*****"<<std::endl;
print_range("The data", d_x.begin(), d_x.end());
std::cout <<"Count : "<< result.n << std::endl;
std::cout <<"Minimum : "<< result.min <<std::endl;
std::cout <<"Maximum : "<< result.max <<std::endl;
std::cout <<"Mean : "<< result.mean << std::endl;
std::cout <<"Variance : "<< result.variance() << std::endl;
std::cout <<"Standard Deviation : "<< std::sqrt(result.variance_n()) << std::endl;
std::cout <<"Skewness : "<< result.skewness() << std::endl;
std::cout <<"Kurtosis : "<< result.kurtosis() << std::endl;
return 0;
}
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