QPair<int,double> ConnectivityMeasures::calcCrossCorrelation(const RowVectorXd& vecFirst, const RowVectorXd& vecSecond)
{
Eigen::FFT<double> fft;
int N = std::max(vecFirst.cols(), vecSecond.cols());
//Compute the FFT size as the "next power of 2" of the input vector's length (max)
int b = ceil(log2(2.0 * N - 1));
int fftsize = pow(2,b);
// int end = fftsize - 1;
// int maxlag = N - 1;
//Zero Padd
RowVectorXd xCorrInputVecFirst = RowVectorXd::Zero(fftsize);
xCorrInputVecFirst.head(vecFirst.cols()) = vecFirst;
RowVectorXd xCorrInputVecSecond = RowVectorXd::Zero(fftsize);
xCorrInputVecSecond.head(vecSecond.cols()) = vecSecond;
//FFT for freq domain to both vectors
RowVectorXcd freqvec;
RowVectorXcd freqvec2;
fft.fwd(freqvec, xCorrInputVecFirst);
fft.fwd(freqvec2, xCorrInputVecSecond);
//Create conjugate complex
freqvec2.conjugate();
//Main step of cross corr
for (int i = 0; i < fftsize; i++) {
freqvec[i] = freqvec[i] * freqvec2[i];
}
RowVectorXd result;
fft.inv(result, freqvec);
//Will get rid of extra zero padding
RowVectorXd result2 = result;//.segment(maxlag, N);
QPair<int,int> minMaxRange;
int idx = 0;
result2.minCoeff(&idx);
minMaxRange.first = idx;
result2.maxCoeff(&idx);
minMaxRange.second = idx;
// std::cout<<"result2(minMaxRange.first)"<<result2(minMaxRange.first)<<std::endl;
// std::cout<<"result2(minMaxRange.second)"<<result2(minMaxRange.second)<<std::endl;
// std::cout<<"b"<<b<<std::endl;
// std::cout<<"fftsize"<<fftsize<<std::endl;
// std::cout<<"end"<<end<<std::endl;
// std::cout<<"maxlag"<<maxlag<<std::endl;
//Return val
int resultIndex = minMaxRange.second;
double maxValue = result2(resultIndex);
return QPair<int,double>(resultIndex, maxValue);
}
MatrixXd Spectrogram::make_spectrogram(VectorXd signal, qint32 window_size = 0)
{
if(window_size == 0)
window_size = signal.rows()/4;
Eigen::FFT<double> fft;
MatrixXd tf_matrix = MatrixXd::Zero(signal.rows()/2, signal.rows());
for(qint32 translate = 0; translate < signal.rows(); translate++)
{
VectorXd envelope = gauss_window(signal.rows(), window_size, translate);
VectorXd windowed_sig = VectorXd::Zero(signal.rows());
VectorXcd fft_win_sig = VectorXcd::Zero(signal.rows());
VectorXd real_coeffs = VectorXd::Zero(signal.rows()/2);
for(qint32 sample = 0; sample < signal.rows(); sample++)
windowed_sig[sample] = signal[sample] * envelope[sample];
fft.fwd(fft_win_sig, windowed_sig);
for(qint32 i= 0; i<signal.rows()/2; i++)
{
qreal value = pow(abs(fft_win_sig[i]), 2.0);
real_coeffs[i] = value;
}
tf_matrix.col(translate) = real_coeffs;
}
return tf_matrix;
}
RowVectorXd FilterData::applyFFTFilter(const RowVectorXd& data, bool keepOverhead, CompensateEdgeEffects compensateEdgeEffects) const
{
#ifdef EIGEN_FFTW_DEFAULT
fftw_make_planner_thread_safe();
#endif
if(data.cols()<m_dCoeffA.cols() && compensateEdgeEffects==MirrorData) {
qDebug()<<QString("Error in FilterData: Number of filter taps(%1) bigger then data size(%2). Not enough data to perform mirroring!").arg(m_dCoeffA.cols()).arg(data.cols());
return data;
}
// std::cout<<"m_iFFTlength: "<<m_iFFTlength<<std::endl;
// std::cout<<"2*m_dCoeffA.cols() + data.cols(): "<<2*m_dCoeffA.cols() + data.cols()<<std::endl;
if(2*m_dCoeffA.cols() + data.cols()>m_iFFTlength) {
qDebug()<<"Error in FilterData: Number of mirroring/zeropadding size plus data size is bigger then fft length!";
return data;
}
//Do zero padding or mirroring depending on user input
RowVectorXd t_dataZeroPad = RowVectorXd::Zero(m_iFFTlength);
switch(compensateEdgeEffects) {
case MirrorData:
t_dataZeroPad.head(m_dCoeffA.cols()) = data.head(m_dCoeffA.cols()).reverse(); //front
t_dataZeroPad.segment(m_dCoeffA.cols(), data.cols()) = data; //middle
t_dataZeroPad.tail(m_dCoeffA.cols()) = data.tail(m_dCoeffA.cols()).reverse(); //back
break;
case ZeroPad:
t_dataZeroPad.head(data.cols()) = data;
break;
default:
t_dataZeroPad.head(data.cols()) = data;
break;
}
//generate fft object
Eigen::FFT<double> fft;
fft.SetFlag(fft.HalfSpectrum);
//fft-transform data sequence
RowVectorXcd t_freqData;
fft.fwd(t_freqData,t_dataZeroPad);
//perform frequency-domain filtering
RowVectorXcd t_filteredFreq = m_dFFTCoeffA.array()*t_freqData.array();
//inverse-FFT
RowVectorXd t_filteredTime;
fft.inv(t_filteredTime,t_filteredFreq);
//Return filtered data
if(!keepOverhead)
return t_filteredTime.segment(m_dCoeffA.cols()/2, data.cols());
return t_filteredTime.head(data.cols()+m_dCoeffA.cols());
}
Vector<Pointf> DataSource::FFT(Getdatafun getdata, double tSample, bool frequency, int type, bool window) {
int numData = int(GetCount());
VectorXd timebuf(numData);
int num = 0;
for (int i = 0; i < numData; ++i) {
double data = Membercall(getdata)(i);
if (!IsNull(data)) {
timebuf[i] = Membercall(getdata)(i);
num++;
}
}
Vector<Pointf> res;
if (num < 3)
return res;
timebuf.resize(num);
double windowSum = 0;
if (window) {
for (int i = 0; i < numData; ++i) {
double windowDat = 0.54 - 0.46*cos(2*M_PI*i/numData);
windowSum += windowDat;
timebuf[i] *= windowDat; // Hamming window
}
} else
windowSum = numData;
VectorXcd freqbuf;
try {
Eigen::FFT<double> fft;
fft.SetFlag(fft.HalfSpectrum);
fft.fwd(freqbuf, timebuf);
} catch(...) {
return res;
}
if (frequency) {
for (int i = 0; i < int(freqbuf.size()); ++i) {
double xdata = i/(tSample*numData);
switch (type) {
case T_PHASE: res << Pointf(xdata, std::arg(freqbuf[i])); break;
case T_FFT: res << Pointf(xdata, 2*std::abs(freqbuf[i])/windowSum); break;
case T_PSD: res << Pointf(xdata, 2*sqr(std::abs(freqbuf[i]))/(windowSum/tSample));
}
}
} else {
for (int i = int(freqbuf.size()) - 1; i > 0; --i) {
double xdata = (tSample*numData)/i;
switch (type) {
case T_PHASE: res << Pointf(xdata, std::arg(freqbuf[i])); break;
case T_FFT: res << Pointf(xdata, 2*std::abs(freqbuf[i])/windowSum); break;
case T_PSD: res << Pointf(xdata, 2*sqr(std::abs(freqbuf[i]))/(windowSum/tSample));
}
}
}
return res;
}
void FilterData::fftTransformCoeffs()
{
#ifdef EIGEN_FFTW_DEFAULT
fftw_make_planner_thread_safe();
#endif
//zero-pad m_dCoeffA to m_iFFTlength
RowVectorXd t_coeffAzeroPad = RowVectorXd::Zero(m_iFFTlength);
t_coeffAzeroPad.head(m_dCoeffA.cols()) = m_dCoeffA;
//generate fft object
Eigen::FFT<double> fft;
fft.SetFlag(fft.HalfSpectrum);
//fft-transform filter coeffs
m_dFFTCoeffA = RowVectorXcd::Zero(m_iFFTlength);
fft.fwd(m_dFFTCoeffA,t_coeffAzeroPad);
}
QList<QList<GaborAtom> > AdaptiveMp::matching_pursuit(MatrixXd signal, qint32 max_iterations, qreal epsilon, bool fix_phase = false, qint32 boost = 0,
qint32 simplex_it = 1E3, qreal simplex_reflection = 1.0, qreal simplex_expansion = 0.2 ,
qreal simplex_contraction = 0.5, qreal simplex_full_contraction = 0.5, bool trial_separation = false)
{
//stop_running = false;
std::cout << "\nAdaptive Matching Pursuit Algorithm started...\n";
max_it = max_iterations;
Eigen::FFT<double> fft;
MatrixXd residuum = signal; //residuum initialised with signal
qint32 sample_count = signal.rows();
qint32 channel_count = signal.cols();
signal_energy = 0;
qreal residuum_energy = 0;
qreal energy_threshold = 0;
//calculate signal_energy
for(qint32 channel = 0; channel < channel_count; channel++)
{
for(qint32 sample = 0; sample < sample_count; sample++)
signal_energy += (signal(sample, channel) * signal(sample, channel));
energy_threshold = 0.01 * epsilon * signal_energy;
residuum_energy = signal_energy;
}
std::cout << "absolute energy of signal: " << residuum_energy << "\n";
while(it < max_iterations && (energy_threshold < residuum_energy) && sample_count > 1)
{
channel_count = channel_count * (boost / 100.0); //reducing the number of observed channels in the algorithm to increase speed performance
if(boost == 0 || channel_count == 0)
channel_count = 1;
//variables for dyadic sampling
qreal s = 1; //scale
qint32 j = 1;
VectorXd max_scalar_product = VectorXd::Zero(channel_count); //inner product for choosing the best matching atom
qreal k = 0; //for modulation 2*pi*k/N
qint32 p = floor(sample_count / 2); //translation
GaborAtom *gabor_Atom = new GaborAtom();
gabor_Atom->sample_count = sample_count;
gabor_Atom->energy = 0;
qreal phase = 0;
while(s < sample_count)
{
k = 0; //for modulation 2*pi*k/N
p = floor(sample_count / 2); //translation
VectorXd envelope = GaborAtom::gauss_function(sample_count, s, p);
VectorXcd fft_envelope = RowVectorXcd::Zero(sample_count);
fft.fwd(fft_envelope, envelope);
while(k < sample_count/2)
{
p = floor(sample_count/2);
VectorXcd modulation = modulation_function(sample_count, k);
VectorXcd modulated_resid = VectorXcd::Zero(sample_count);
VectorXcd fft_modulated_resid = VectorXcd::Zero(sample_count);
VectorXcd fft_m_e_resid = VectorXcd::Zero(sample_count);
VectorXd corr_coeffs = VectorXd::Zero(sample_count);
//iteration for multichannel, depending on boost setting
for(qint32 chn = 0; chn < channel_count; chn++)
{
qint32 max_index = 0;
qreal maximum = 0;
phase = 0;
p = floor(sample_count/2);//here is difference to dr. gratkowski´s code (he didn´t reset parameter p)
//complex correlation of signal and sinus-modulated gaussfunction
for(qint32 l = 0; l< sample_count; l++)
modulated_resid[l] = residuum(l, chn) * modulation[l];
fft.fwd(fft_modulated_resid, modulated_resid);
for( qint32 m = 0; m < sample_count; m++)
fft_m_e_resid[m] = fft_modulated_resid[m] * conj(fft_envelope[m]);
fft.inv(corr_coeffs, fft_m_e_resid);
maximum = corr_coeffs[0];
//find index of maximum correlation-coefficient to use in translation
for(qint32 i = 1; i < corr_coeffs.rows(); i++)
if(maximum < corr_coeffs[i])
{
maximum = corr_coeffs[i];
max_index = i;
}
//adapting translation p to create atomtranslation correctly
if(max_index >= p) p = max_index - p + 1;
else p = max_index + p;
VectorXd atom_parameters = calculate_atom(sample_count, s, p, k, chn, residuum, RETURNPARAMETERS, fix_phase);
qreal temp_scalar_product = 0;
if(trial_separation) temp_scalar_product = max_scalar_product[chn];
else temp_scalar_product = max_scalar_product[0];
if(abs(atom_parameters[4]) >= abs(temp_scalar_product))
{
//set highest scalarproduct, in comparison to best matching atom
gabor_Atom->scale = atom_parameters[0];
gabor_Atom->translation = atom_parameters[1];
gabor_Atom->modulation = atom_parameters[2];
gabor_Atom->phase = atom_parameters[3];
gabor_Atom->max_scalar_product = atom_parameters[4];
gabor_Atom->bm_channel = chn;
if(trial_separation)
{
max_scalar_product[chn] = atom_parameters[4];
if(atoms_in_chns.length() < channel_count)
atoms_in_chns.append(*gabor_Atom);
else
atoms_in_chns.replace(chn, *gabor_Atom);
}
else
max_scalar_product[0] = atom_parameters[4];
}
}
k += pow(2.0,(-j))*sample_count/2;
}
j++;
s = pow(2.0,j);
}
std::cout << "\n" << "===============" << " found parameters " << it + 1 << "===============" << ":\n\n"<<
"scale: " << gabor_Atom->scale << " trans: " << gabor_Atom->translation <<
" modu: " << gabor_Atom->modulation << " phase: " << gabor_Atom->phase << " sclr_prdct: " << gabor_Atom->max_scalar_product << "\n";
//replace atoms with s==N and p = floor(N/2) by such atoms that do not have an envelope
k = 0;
s = sample_count;
p = floor(sample_count / 2);
j = floor(log10(sample_count)/log10(2));//log(sample_count) / log(2));
phase = 0;
//iteration for multichannel, depending on boost setting
for(qint32 chn = 0; chn < channel_count; chn++)
{
k = 0;
while(k < sample_count / 2)
{
VectorXd parameters_no_envelope = calculate_atom(sample_count, s, p, k, chn, residuum, RETURNPARAMETERS, fix_phase);
qreal temp_scalar_product = 0;
if(trial_separation) temp_scalar_product = max_scalar_product[chn];
else temp_scalar_product = max_scalar_product[0];
if(abs(parameters_no_envelope[4]) > abs(temp_scalar_product))
{
//set highest scalarproduct, in comparison to best matching atom
gabor_Atom->scale = parameters_no_envelope[0];
gabor_Atom->translation = parameters_no_envelope[1];
gabor_Atom->modulation = parameters_no_envelope[2];
gabor_Atom->phase = parameters_no_envelope[3];
gabor_Atom->max_scalar_product = parameters_no_envelope[4];
gabor_Atom->bm_channel = chn;
if(trial_separation)
{
max_scalar_product[chn] = parameters_no_envelope[4];
atoms_in_chns.replace(chn, *gabor_Atom);
}
else
max_scalar_product[0] = parameters_no_envelope[4];
}
k += pow(2.0,(-j))*sample_count/2;
}
}
std::cout << " after comparison to NoEnvelope " << ":\n"<< "scale: " << gabor_Atom->scale << " trans: " << gabor_Atom->translation <<
" modu: " << gabor_Atom->modulation << " phase: " << gabor_Atom->phase << " sclr_prdct: " << gabor_Atom->max_scalar_product << "\n\n";
//simplexfunction to find minimum of target among parameters s, p, k
if(trial_separation && simplex_it != 0)
{
for(qint32 chn = 0; chn < atoms_in_chns.length(); chn++)
{
*gabor_Atom = atoms_in_chns.at(chn);
simplex_maximisation(simplex_it, simplex_reflection, simplex_expansion, simplex_contraction, simplex_full_contraction,
gabor_Atom, max_scalar_product, sample_count, fix_phase, residuum, trial_separation, chn);
}
}
else if(simplex_it != 0)
simplex_maximisation(simplex_it, simplex_reflection, simplex_expansion, simplex_contraction, simplex_full_contraction,
gabor_Atom, max_scalar_product, sample_count, fix_phase, residuum, trial_separation, gabor_Atom->bm_channel);
//calc multichannel parameters phase and max_scalar_product
channel_count = signal.cols();
VectorXd best_match = VectorXd::Zero(sample_count);
for(qint32 chn = 0; chn < channel_count; chn++)
{
if(trial_separation)
{
*gabor_Atom = atoms_in_chns.at(chn);
gabor_Atom->energy = 0;
best_match = gabor_Atom->create_real(gabor_Atom->sample_count, gabor_Atom->scale, gabor_Atom->translation,
gabor_Atom->modulation, gabor_Atom->phase);
}
else
{
VectorXd channel_params = calculate_atom(sample_count, gabor_Atom->scale, gabor_Atom->translation,
gabor_Atom->modulation, chn, residuum, RETURNPARAMETERS, fix_phase);
gabor_Atom->phase_list.append(channel_params[3]);
gabor_Atom->max_scalar_list.append(channel_params[4]);
best_match = gabor_Atom->create_real(gabor_Atom->sample_count, gabor_Atom->scale, gabor_Atom->translation,
gabor_Atom->modulation, gabor_Atom->phase_list.at(chn));
}
//substract best matching Atom from Residuum in each channel
for(qint32 j = 0; j < gabor_Atom->sample_count; j++)
{
if(!trial_separation)
{
residuum(j,chn) -= gabor_Atom->max_scalar_list.at(chn) * best_match[j];
gabor_Atom->energy += pow(gabor_Atom->max_scalar_list.at(chn) * best_match[j], 2);
}
else
{
residuum(j,chn) -= gabor_Atom->max_scalar_product * best_match[j];
gabor_Atom->energy += pow(gabor_Atom->max_scalar_product * best_match[j], 2);
}
}
if(trial_separation)
{
atoms_in_chns.replace(chn, *gabor_Atom); // change energy
residuum_energy -= atoms_in_chns.at(chn).energy;// / channel_count;;
current_energy += atoms_in_chns.at(chn).energy;// / channel_count;;
}
}
if(!trial_separation)
{
residuum_energy -= gabor_Atom->energy;
current_energy += gabor_Atom->energy;
}
else
/*for(qint32 i = 0; i < atoms_in_chns.length(); i++)
{
residuum_energy -= atoms_in_chns.at(i).energy / channel_count;
current_energy += atoms_in_chns.at(i).energy / channel_count;
}*/
std::cout << "absolute energy of residue: " << residuum_energy << "\n";
if(!trial_separation)
atoms_in_chns.append(*gabor_Atom);
atom_list.append(atoms_in_chns);
atoms_in_chns.clear();
delete gabor_Atom;
it++;
emit current_result(it, max_it, current_energy, signal_energy, residuum, atom_list, fix_dict_list);
if( QThread::currentThread()->isInterruptionRequested())
{
send_warning(10);
break;
}
}//end iterations
std::cout << "\nAdaptive Matching Pursuit Algorithm finished.\n";
emit finished_calc();
return atom_list;
}
// calc scalarproduct of Atom and Signal
FixDictAtom FixDictMp::correlation(Dictionary current_pdict, MatrixXd current_resid, qint32 boost)
{
qint32 channel_count = current_resid.cols() * (boost / 100.0); //reducing the number of observed channels in the algorithm to increase speed performance
if(boost == 0 || channel_count == 0)
channel_count = 1;
Eigen::FFT<double> fft;
std::ptrdiff_t max_index;
VectorXcd fft_atom = VectorXcd::Zero(current_resid.rows());
FixDictAtom best_matching;
qreal max_scalar_product = 0;
for(qint32 i = 0; i < current_pdict.atoms.length(); i++)
{
VectorXd fitted_atom = VectorXd::Zero(current_resid.rows());
qint32 p = floor(current_resid.rows() / 2);//translation
VectorXd resized_atom = VectorXd::Zero(current_resid.rows());
if(current_pdict.atoms.at(i).atom_samples.rows() > current_resid.rows())
for(qint32 k = 0; k < current_resid.rows(); k++)
resized_atom[k] = current_pdict.atoms.at(i).atom_samples[k + floor(current_pdict.atoms.at(i).atom_samples.rows() / 2) - floor(current_resid.rows() / 2)];
else resized_atom = current_pdict.atoms.at(i).atom_samples;
if(resized_atom.rows() < current_resid.rows())
for(qint32 k = 0; k < resized_atom.rows(); k++)
fitted_atom[(k + p - floor(resized_atom.rows() / 2))] = resized_atom[k];
else fitted_atom = resized_atom;
//normalization
qreal norm = 0;
norm = fitted_atom.norm();
if(norm != 0) fitted_atom /= norm;
fft.fwd(fft_atom, fitted_atom);
for(qint32 chn = 0; chn < channel_count; chn++)
{
p = floor(current_resid.rows() / 2);//translation
VectorXd corr_coeffs = VectorXd::Zero(current_resid.rows());
VectorXcd fft_signal = VectorXcd::Zero(current_resid.rows());
VectorXcd fft_sig_atom = VectorXcd::Zero(current_resid.rows());
fft.fwd(fft_signal, current_resid.col(chn));
for( qint32 m = 0; m < current_resid.rows(); m++)
fft_sig_atom[m] = fft_signal[m] * conj(fft_atom[m]);
fft.inv(corr_coeffs, fft_sig_atom);
//find index of maximum correlation-coefficient to use in translation
max_scalar_product = corr_coeffs.maxCoeff(&max_index);
if(i == 0)
{
best_matching = current_pdict.atoms.at(i);
best_matching.max_scalar_product = max_scalar_product;
//adapting translation p to create atomtranslation correctly
if(max_index >= p && current_resid.rows() % (2) == 0) p = max_index - p;
else if(max_index >= p && current_resid.rows() % (2) != 0) p = max_index - p - 1;
else p = max_index + p;
best_matching.translation = p;
}
else if(abs(max_scalar_product) > abs(best_matching.max_scalar_product))
{
best_matching = current_pdict.atoms.at(i);
best_matching.max_scalar_product = max_scalar_product;
//adapting translation p to create atomtranslation correctly
if(max_index >= p && current_resid.rows() % (2) == 0) p = max_index - p;
else if(max_index >= p && current_resid.rows() % (2) != 0) p = max_index - p - 1;
else p = max_index + p;
best_matching.translation = p;
}
}
}
best_matching.atom_formula = current_pdict.atom_formula;
best_matching.dict_source = current_pdict.source;
best_matching.type = current_pdict.type;
best_matching.sample_count = current_pdict.sample_count;
return best_matching;
}