c++实现
#include <iostream>
#include <vector>
#include <algorithm>
#include <unordered_map>
#include <cmath>
#include <iterator>
#include <numeric>
using namespace std;
typedef long double ld;
typedef unsigned int uint;
typedef std::vector<ld>::iterator vec_iter_ld;
/**
* Overriding the ostream operator for pretty printing vectors.
*/
template<typename T>
std::ostream &operator<<(std::ostream &os, std::vector<T> vec) {
os << "[";
if (vec.size() != 0) {
std::copy(vec.begin(), vec.end() - 1, std::ostream_iterator<T>(os, " "));
os << vec.back();
}
os << "]";
return os;
}
/**
* This class calculates mean and standard deviation of a subvector.
* This is basically stats computation of a subvector of a window size qual to "lag".
*/
class VectorStats {
public:
/**
* Constructor for VectorStats class.
*
* @param start - This is the iterator position of the start of the window,
* @param end - This is the iterator position of the end of the window,
*/
VectorStats(vec_iter_ld start, vec_iter_ld end) {
this->start = start;
this->end = end;
this->compute();
}
/**
* This method calculates the mean and standard deviation using STL function.
* This is the Two-Pass implementation of the Mean & Variance calculation.
*/
void compute() {
ld sum = std::accumulate(start, end, 0.0);
uint slice_size = std::distance(start, end);
ld mean = sum / slice_size;
std::vector<ld> diff(slice_size);
std::transform(start, end, diff.begin(), [mean](ld x) { return x - mean; });
ld sq_sum = std::inner_product(diff.begin(), diff.end(), diff.begin(), 0.0);
ld std_dev = std::sqrt(sq_sum / slice_size);
this->m1 = mean;
this->m2 = std_dev;
}
ld mean() {
return m1;
}
ld standard_deviation() {
return m2;
}
private:
vec_iter_ld start;
vec_iter_ld end;
ld m1;
ld m2;
};
/**
* This is the implementation of the Smoothed Z-Score Algorithm.
* This is direction translation of https://stackoverflow.com/a/22640362/1461896.
*
* @param input - input signal
* @param lag - the lag of the moving window
* @param threshold - the z-score at which the algorithm signals
* @param influence - the influence (between 0 and 1) of new signals on the mean and standard deviation
* @return a hashmap containing the filtered signal and corresponding mean and standard deviation.
*/
unordered_map<string, vector<ld>> z_score_thresholding(vector<ld> input, int lag, ld threshold, ld influence) {
unordered_map<string, vector<ld>> output;
uint n = (uint) input.size();
vector<ld> signals(input.size());
vector<ld> filtered_input(input.begin(), input.end());
vector<ld> filtered_mean(input.size());
vector<ld> filtered_stddev(input.size());
VectorStats lag_subvector_stats(input.begin(), input.begin() + lag);
filtered_mean[lag - 1] = lag_subvector_stats.mean();
filtered_stddev[lag - 1] = lag_subvector_stats.standard_deviation();
for (int i = lag; i < n; i++) {
if (abs(input[i] - filtered_mean[i - 1]) > threshold * filtered_stddev[i - 1]) {
signals[i] = (input[i] > filtered_mean[i - 1]) ? 1.0 : -1.0;
filtered_input[i] = influence * input[i] + (1 - influence) * filtered_input[i - 1];
} else {
signals[i] = 0.0;
filtered_input[i] = input[i];
}
VectorStats lag_subvector_stats(filtered_input.begin() + (i - lag), filtered_input.begin() + i);
filtered_mean[i] = lag_subvector_stats.mean();
filtered_stddev[i] = lag_subvector_stats.standard_deviation();
}
output["signals"] = signals;
output["filtered_mean"] = filtered_mean;
output["filtered_stddev"] = filtered_stddev;
return output;
};
int main() {
vector<ld> input = {1.0, 1.0, 1.1, 1.0, 0.9, 1.0, 1.0, 1.1, 1.0, 0.9, 1.0, 1.1, 1.0, 1.0, 0.9, 1.0, 1.0, 1.1, 1.0,
1.0, 1.0, 1.0, 1.1, 0.9, 1.0, 1.1, 1.0, 1.0, 0.9, 1.0, 1.1, 1.0, 1.0, 1.1, 1.0, 0.8, 0.9, 1.0,
1.2, 0.9, 1.0, 1.0, 1.1, 1.2, 1.0, 1.5, 1.0, 3.0, 2.0, 5.0, 3.0, 2.0, 1.0, 1.0, 1.0, 0.9, 1.0,
1.0, 3.0, 2.6, 4.0, 3.0, 3.2, 2.0, 1.0, 1.0, 0.8, 4.0, 4.0, 2.0, 2.5, 1.0, 1.0, 1.0};
int lag = 30;
ld threshold = 5.0;
ld influence = 0.0;
unordered_map<string, vector<ld>> output = z_score_thresholding(input, lag, threshold, influence);
cout << output["signals"] << endl;
}
