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CEEMDAN_Utils.cpp
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250 lines (211 loc) · 6.09 KB
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#include "CEEMDAN.h"
#include "Spline.h"
using namespace std;
vector<vector<double>> CEEMDAN(vector<double> data, double I, double sd, int max_extr) {
double epsilon = 0.08;
int L = int(data.size());
vector<vector<double>> imfs;
vector<vector<double>> imfs1;
vector<double> reside = data;
const int Imfs_max = 50;
for (int i = 0; i < I; i++) {
vector<double> imf1 = imf_n(randomList(reside, epsilon), 1);
imfs1.emplace_back(imf1);
}
imfs.emplace_back(vec2DMeanCol(imfs1));
cout << "imf 0 is ready" << endl;
int num = 1;
bool last_imf = false;
for (int k = 0; k < Imfs_max; k++) {
vector<double> imf_prev = imfs[num - 1];
reside = vecDoubleMinus(reside, imf_prev);
vector<vector<double>> imfs_num;
vector<double> imf_num;
for (int i = 0; i < I; i++) {
vector<double> imf_num = imf_n(randomList(reside, epsilon), num);
if (imf_num.empty()) {
last_imf = true;
break;
}
imfs_num.emplace_back(imf_num);
}
if (!last_imf) {
imf_num = vec2DMeanCol(imfs_num);
}
vector<double> maxima_idx, minima_idx;
vector<double> maxSeq, minSeq;
vector<double> maxInterSeq(L, 0), minInterSeq(L, 0);
argrelMaxminList(imf_num, maxima_idx, minima_idx, maxSeq, minSeq);
if (int(maxima_idx.size()) + int(minima_idx.size()) <= (max_extr)) {
last_imf = true;
}
/* finish criterion by difference in amps */
if (sdCal(imf_num, imf_prev) < sd)
last_imf = true;
if (last_imf) {
imfs.emplace_back(reside);
cout << "last imf is ready" << endl;
break;
}
imfs.emplace_back(imf_num);
cout << "imf" << dec << num << "is ready" << endl;
num += 1;
}
return imfs;
}
vector<double> imf_n(vector<double> data, int num) {
vector<vector<double>> imfs = EMD(data);
int len = int(data.size());
if (int(imfs.size()) > num)
return imfs[num];
vector<double> emptylist(0);
return emptylist;
}
vector<vector<double>> EMD(vector<double> data, double sd) {
int L = int(data.size());
vector<double> timeSeq(L, 0);
for (int i = 1; i < L; i++)
timeSeq[i] = double(i);
vector<vector<double>>imfs;
bool last_imf = false;
vector<double> residue = data;
double leftBound = 0, RightBound = 0;
for (int i = 0; i < 20; ++i) {
vector<double> h_prev = residue;
vector<double> iterSignal;
for (int j = 0; j < 100; ++j) {
vector<double> maxima_idx, minima_idx;
vector<double> maxSeq, minSeq;
vector<double> maxInterSeq(L, 0), minInterSeq(L, 0);
argrelMaxminList(h_prev, maxima_idx, minima_idx, maxSeq, minSeq);
if (int(maxima_idx.size()) + int(minima_idx.size()) <= 6) {
last_imf = true;
break;
}
SplineSpace::Spline spmin(
minima_idx, minSeq,
int(minima_idx.size()), SplineSpace::GivenSecondOrder,
leftBound, RightBound);
spmin.MultiPointInterp(timeSeq, L, minInterSeq);
SplineSpace::Spline spmax(
maxima_idx, maxSeq,
int(maxima_idx.size()), SplineSpace::GivenSecondOrder,
leftBound, RightBound);
spmax.MultiPointInterp(timeSeq, L, maxInterSeq);
iterSignal = meanNewSeq(h_prev, maxInterSeq, minInterSeq);
if (sdCal(iterSignal, h_prev) < sd)
break;
h_prev = iterSignal;
}
if (last_imf)
break;
imfs.emplace_back(iterSignal);
residue = vecDoubleMinus(residue, iterSignal);
}
imfs.emplace_back(vecDoubleMinus(data, vec2DMeanCol(imfs)));
return imfs;
}
vector<double> vec2DMeanCol(const vector<vector<double>> data) {
int W = int(data.size());
int M = int(data[0].size());
vector<double> resCol(M, 0);
for (int i = 0; i < W; i++) {
for (int j = 0; j < M; j++) {
resCol[j] += data[i][j];
}
}
for (int j = 0; j < M; j++) {
resCol[j] /= double(W);
}
return resCol;
}
vector<double> randomList(vector<double> data, double epsilon) {
std::default_random_engine gen;
std::normal_distribution<double> dis(0, 1);
vector<double> newData = data;
int L = int(newData.size());
for (int i = 0; i < L; i++) {
newData[i] += epsilon * dis(gen);
}
return newData;
}
double vec2DMean(vector<vector<double>> data) {
int M = int(data.size());
int N = int(data[0].size());
double sum = 0.0;
for (int i = 0; i < M; i++) {
for (int j = 0; j < N; j++) {
sum += data[i][j];
}
}
return (sum / (M * N));
}
double sdCal(vector<double> signal, vector<double> signal_prev) {
double sd = 0, sqsum = 0, diffsqsum = 0;
int L = int(signal_prev.size());
if (signal.empty())
signal.resize(L, 0);
for (int i = 0; i < L; i++) {
sqsum += signal_prev[i] * signal_prev[i];
diffsqsum += (signal[i] - signal_prev[i]) * (signal[i] - signal_prev[i]);
}
// # sifting criterion
sd = diffsqsum / sqsum;
return sd;
}
vector<double> vecDoubleMinus(vector<double> subtractee, vector<double> subtracter) {
int L = int(subtractee.size());
vector<double> diff(L, 0);
for (int i = 0; i < L; i++) {
diff[i] = subtractee[i] - subtracter[i];
}
return diff;
}
vector<double> vecDoubleMinus(vector<double> subtractee, double subtracter) {
int L = int(subtractee.size());
vector<double> diff(L, 0);
for (int i = 0; i < L; i++) {
diff[i] = subtractee[i] - subtracter;
}
return diff;
}
vector<double> meanNewSeq(vector<double> signal_prev, vector<double>& maxima_vals, vector<double>& minima_vals) {
/*
mean = 0.5*(maxima_vals + minima_vals)
h = h_prev - mean
*/
int L = int(signal_prev.size());
vector<double> h(L);
for (int i = 0; i < L; i++) {
h[i] = signal_prev[i] - 0.5 * (maxima_vals[i] + minima_vals[i]);
}
return h;
}
static void argrelMaxminList(
vector<double> signal,
vector<double>& maxlist, vector<double>& minlist,
vector<double>& maxSiglist, vector<double>& minSiglist
) {
maxlist.resize(1.0, 0);
minlist.resize(1.0, 0);
int L = int(signal.size());
if (L <= 2)
return;
maxSiglist.resize(1, signal[0]);
minSiglist.resize(1, signal[0]);
for (int i = 1; i <= L - 2; i++) {
if (signal[i] > signal[i - 1] && signal[i] > signal[i + 1]) {
maxlist.push_back(double(i));
maxSiglist.push_back(signal[i]);
}
else if (signal[i] < signal[i - 1] && signal[i] < signal[i + 1]) {
minlist.push_back(double(i));
minSiglist.push_back(signal[i]);
}
}
maxlist.push_back(double(L - 1));
minlist.push_back(double(L - 1));
maxSiglist.push_back(signal[L - 1]);
minSiglist.push_back(signal[L - 1]);
return;
}