Filters.cc

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#include "Filters.h"
 
void Filters::Convolute(double*& result, double* first, double* second, int size) {
 
    // FFT real -> im
    auto fft_re_im = [&size](double* orig, double*& re, double*& im) {
        TVirtualFFT* fft = TVirtualFFT::FFT(1, &size, "R2C ES");
        fft->SetPoints(orig);
        fft->Transform();
        fft->GetPointsComplex(re, im);
        delete fft;
        };
 
    double* refirst = new double[size];
    double* imfirst = new double[size];
    double* resecond = new double[size];
    double* imsecond = new double[size];
    double* reres = new double[size];
    double* imres = new double[size];
 
    fft_re_im(first, refirst, imfirst);
    fft_re_im(second, resecond, imsecond);
 
    TComplex cofirst;
    TComplex cosecond;
    TComplex cores;
    double i_size = 1. / static_cast<double>(max(1, size));
 
    for (int i = 0; i < size; i++) {
        cofirst(refirst[i], imfirst[i]);
        cosecond(resecond[i], imsecond[i]);
 
        cores = cofirst * cosecond * i_size;
 
        reres[i] = cores.Re();
        imres[i] = cores.Im();
    }
 
 
    //cout << "performing IFFT ... ";
    TVirtualFFT* fft_back = TVirtualFFT::FFT(1, &size, "C2R ES");
    fft_back->SetPointsComplex(reres, imres);
    fft_back->Transform();
    fft_back->GetPoints(result);
    delete fft_back;
    delete[] imres; delete[] reres; delete[] refirst; delete[] imfirst; delete[] resecond; delete[] imsecond;
}
 
void Filters::Convolute(double*& first, double* second, int size) {
    Convolute(first, first, second, size);
}
 
void Filters::Deconvolute(double*& result, double* first, double* second, int size, double sigma, double x0, double bin_size) {
 
    // FFT real -> im
    auto fft_re_im = [&size](double* orig, double*& re, double*& im) {
        TVirtualFFT* fft = TVirtualFFT::FFT(1, &size, "R2C ES");
        fft->SetPoints(orig);
        fft->Transform();
        fft->GetPointsComplex(re, im);
        delete fft;
        }; 
    
    double* refirst = new double[size];
    double* imfirst = new double[size];
    double* resecond = new double[size];
    double* imsecond = new double[size];
    double* regauss = new double[size];
    double* imgauss = new double[size];
    double* reres = new double[size];
    double* imres = new double[size];
    double* gauss = new double[size];
    
    fft_re_im(first, refirst, imfirst);
    fft_re_im(second, resecond, imsecond);
    if (sigma > 0.) {
        for (int i = 0; i < size; i++) {
            gauss[i] = TMath::Gaus(static_cast<double>(i) * bin_size, x0, sigma);
        }
        fft_re_im(gauss, regauss, imgauss);
    }
 
    TComplex cofirst;
    TComplex cosecond;
    TComplex cogauss;
    TComplex cores;
    double i_size = 1. / static_cast<double>(max(1, size));
 
    for (int i = 0; i < size; i++) {
        cofirst(refirst[i], imfirst[i]);
        cosecond(resecond[i], imsecond[i]);
        if (sigma > 0.) cogauss(regauss[i], imgauss[i]);
        else cogauss(1., 0.);
 
        cores = cofirst * cogauss / cosecond * i_size;
 
        reres[i] = cores.Re();
        imres[i] = cores.Im();
    }
 
    TVirtualFFT* fft_back = TVirtualFFT::FFT(1, &size, "C2R ES");
    fft_back->SetPointsComplex(reres, imres);
    fft_back->Transform();
    fft_back->GetPoints(result);
    delete fft_back;
 
    delete[] imres; delete[] reres; delete[] refirst; delete[] imfirst; 
    delete[] resecond; delete[] imsecond; delete[] regauss; delete[] imgauss; delete[] gauss;
}
 
void Filters::SmoothArray(double*& ar, int nbins, double sigma, string method, double bin_size, double sigma2) {
 
    if (method == "Box" || method == "Mean" || method == "Average") BoxFilter(ar, nbins, static_cast<int>(sigma));
    else if (method == "GausFFT")                                   GausFFTFilter(ar, nbins, sigma, bin_size);
    else if (method == "Gaus")                                      GausFilter(ar, nbins, sigma, bin_size);
    else if (method == "Bilateral")                                 BilateralFilter(ar, nbins, sigma, sigma2, bin_size);
    else if (method == "Bilateral2")                                Bilateral2Filter(ar, nbins, sigma, sigma2, .05, bin_size);
    else if (method == "Median")                                    MedianFilter(ar, nbins, static_cast<int>(sigma));
    else {
        cout << "Smooth method " << method << " not known. Using default Gaus method." << endl;
        GausFilter(ar, nbins, sigma, bin_size);
    }
}
 
 
void Filters::SmoothArray(double*& ar, int nbins, double sigma, int method, double bin_size, double sigma2) {
 
    switch (method) {
    case 0:
        SmoothArray(ar, nbins, sigma, "Box");
        break;
    case 1:
        SmoothArray(ar, nbins, sigma, "GausFFT", bin_size);
        break;
    case 3:         
        SmoothArray(ar, nbins, sigma, "Bilateral", bin_size, sigma2);
        break;
    case 4:
        SmoothArray(ar, nbins, sigma, "Bilateral2", bin_size, sigma2);
        break;
    case 5: 
        SmoothArray(ar, nbins, sigma, "Median");
        break;
    default:
        SmoothArray(ar, nbins, sigma, "Gaus", bin_size);
        break;
    }
}
 
void Filters::BoxFilter(double*& ar, int nbins, int sigma) {
    // calculate running average from -sigma until +sigma (sigma = number of bins)
    if (sigma == 0) sigma = 1.;
 
    double* result = new double[nbins];
    double w_sum = .0;
    int w_nbins = 2 * sigma + 1;
 
    // init
    for (int i = 0; i <= min(nbins - 1, sigma); i++) w_sum += ar[i];
    // start
    for (int i = 0; i < sigma && i < nbins; i++) {
        result[i] = w_sum / static_cast<double>(i + sigma + 1);
        if (i + sigma + 1 < nbins) w_sum += ar[i + sigma + 1];
    }
    // center (full window)
    for (int i = sigma; i < nbins - sigma; i++) {
        if (i - sigma - 1 >= 0) w_sum -= ar[i - sigma - 1];
        if (i + sigma < nbins) w_sum += ar[i + sigma];
        result[i] = w_sum / static_cast<double>(w_nbins);
    }
    // end
    for (int i = max(nbins - sigma, 0); i < nbins; i++) {
        int nmean = nbins - (i - sigma);
        result[i] = w_sum / static_cast<double>(nmean);
        if (i - sigma >= 0) w_sum -= ar[i - sigma];
    }
    for (int i = 0; i < nbins; i++) ar[i] = result[i];
    delete[] result;
}
 
void Filters::GausFilter(double*& ar, int nbins, double sigma, double bin_size) {
    // gauss kernel +/-3*sigma
    if (sigma <= 0 || bin_size <= 0) return;
    
    double* artmp = new double[nbins];
    for (int i = 0; i < nbins; i++) artmp[i] = ar[i];
 
    // calculate running average from -sigma until +sigma (sigma = number of bins)
    int nbins_6sigma = static_cast<int>(ceil(6. * sigma / bin_size));
    if (nbins_6sigma % 2 == 0) nbins_6sigma++;
    
    if (nbins_6sigma > 1) {
        int half_window = nbins_6sigma * 0.5;
        double gauss_offset = static_cast<double>(half_window) * bin_size;
        double* gauss = new double[nbins_6sigma];
        for (int i = 0; i < nbins_6sigma; i++) {
            gauss[i] = TMath::Gaus(static_cast<double>(i) * bin_size, gauss_offset, sigma, true);
        }
 
        double res = 0, norm = 0;
        for (int i = 0; i < nbins; i++) {
            res = 0., norm = 0.;
            int start = max(0, half_window - i);
            int end = min(nbins - i + half_window, nbins_6sigma);
 
            for (int j = start; j < end; j++) {
                res += gauss[j] * artmp[i + j - half_window];
                norm += gauss[j];
            }
            if (norm != 0.) ar[i] = res / norm;
        }
        delete[] gauss;
    }
    delete[] artmp;
}
 
void Filters::GausFFTFilter(double*& ar, int nbins, double sigma, double bin_size) {
    // convolution with gauss clipped at +-5 sigma (very inefficient and slow)
    double* gauss = new double[nbins];
 
    double sum = 0.;
    double five_sigma = 5 * sigma;
    double i_denom1 = -1. / (2. * sigma * sigma);
    double i_denom2 = 1. / sigma * 2.506628;
 
    for (int i = 0; i < nbins; i++) {
        double position = static_cast<double>(i) * bin_size;
        if (position < five_sigma) gauss[i] = exp(pow((position - five_sigma), 2) * i_denom1) * i_denom2;
        else gauss[i] = 0.;
        sum += gauss[i];
    }
 
    double i_sum = (sum == 0.) ? 1. : 1. / sum;
    for (int i = 0; i < nbins; i++) {
        gauss[i] *= i_sum;
    }
 
    Convolute(ar, gauss, nbins);
    delete[] gauss;
}
 
void Filters::BilateralFilter(double*& ar, int nbins, double sigma_x, double sigma_y, double bin_size) {
    double* artmp = new double[nbins];
    for (int i = 0; i < nbins; i++) artmp[i] = ar[i];
 
    int nbins_3sigma = static_cast<int>(ceil(3 * sigma_x / bin_size));
 
    for (int i = 0; i < nbins; i++) {
        double weighted_sum = 0.0;
        double sum_of_weights = 0.0;
 
        for (int j = max(0, i - nbins_3sigma); j < min(nbins - 1, i + nbins_3sigma); j++) {
            // Calculate spatial and intensity distances
            double spatial_dist = abs(i - j) * bin_size;
            double intensity_dist = abs(artmp[i] - artmp[j]);
 
            // weights
            double w_x = exp(-0.5 * (spatial_dist * spatial_dist) / (sigma_x * sigma_x));
            double w_y = exp(-0.5 * (intensity_dist * intensity_dist) / (sigma_y * sigma_y));
            double weight = w_x * w_y;
 
            weighted_sum += artmp[j] * weight;
            sum_of_weights += weight;
        }
 
        if (sum_of_weights != 0.) ar[i] = weighted_sum / sum_of_weights;
    }
    delete[] artmp;
}
 
void Filters::Bilateral2Filter(double*& ar, int nbins, int sigma_x, double sigma_y, double sigma_slope, double bin_size) {
    // Asymmetric smoothing using a gauss of the change of the data relative to the central bin in a window for weighting
    double* artmp = new double[nbins]; 
    for (int i = 0; i < nbins; i++) artmp[i] = ar[i];
 
    double i_denom = -1. / (2. * sigma_y * sigma_y);
    int x_shift = static_cast<int>(sigma_x / bin_size);
 
    double weightedSum = 0.;
    double sumOfWeights = 0.;
 
    double* slope = new double[nbins - 1];
    double* slope_weight = new double[nbins - 1];
    for (int i = 0; i < nbins - 1; i++) {
        slope[i] = ar[i + 1] - ar[i];
        slope_weight[i] = 1. / (1. + pow(.5 * slope[i] / sigma_slope, 2.));
    }
 
    for (int i = 0; i < nbins; i++) {
        weightedSum = 0.;
        sumOfWeights = 0.;
        int start = max(0, i - x_shift);
        int end =   min(i + x_shift, nbins - 1);
 
        for (int j = start; j <= end; j++) {
            double diff = artmp[i] - artmp[j];
            double weight = exp(pow(diff, 2) * i_denom);
            if (j < nbins - 1) weight *= slope_weight[j];
            weightedSum += weight * artmp[j];
            sumOfWeights += weight;
        }
        if (sumOfWeights != 0) ar[i] = weightedSum / sumOfWeights;
    }
    delete[] artmp;
    delete[] slope;
    delete[] slope_weight;
}
 
void Filters::MedianFilter(double*& ar, int nbins, int window_size) {
    double* artmp = new double[nbins];
    for (int i = 0; i < nbins; i++) artmp[i] = ar[i];
 
    int half_window = window_size * 0.5;
 
    for (int i = 0; i < nbins; i++) {
        double* window = new double[window_size];
        int window_index = 0;
 
        for (int j = i - half_window; j <= i + half_window; j++) {
            if (j >= 0 && j < nbins) {
                window[window_index] = artmp[j];
                window_index++;
            }
        }
 
        // calculate the median
        sort(window, window + window_index);
        double median = (window_index % 2 == 0) ? 
            (window[window_index / 2 - 1] + window[window_index / 2]) * 0.5 :
            window[window_index / 2];
 
        ar[i] = median;
 
        delete[] window;
    }
    delete[] artmp;
}
 
void Filters::ResponseFilter(double*& ar, int nbins, double sigma1, double sigma2, double factor, double bin_size) {
 
    double* artmp = new double[nbins];
    for (int i = 0; i < nbins; i++) artmp[i] = ar[i];
 
    // shifted difference of two gauss functions (~smoothed derivative)
    int nbins_23sigma = static_cast<int>(ceil((2. * sigma1 + 3. * sigma2) / bin_size));
    int nbins_3sigma = static_cast<int>(ceil(3. * sigma2 / bin_size));
    double* sdog = new double[nbins_23sigma];
 
    double i_denom1 = 1. / (2. * sigma1 * sigma1);
    double i_denom2 = 1. / (2. * sigma2 * sigma2);
    double norm = 0.;
    for (int i = 0; i < nbins_23sigma; i++) {
        sdog[i] = exp(-1. * pow(static_cast<double>(i) * bin_size - 3. * sigma2, 2.) * i_denom1) -
            factor * exp(-1. * pow(static_cast<double>(i) * bin_size - 2. * sigma2, 2.) * i_denom2);
        if (sdog[i] > 0.) norm += sdog[i];
    }
    if (norm == 0.) norm = 1.;
    double i_norm = 1. / norm;
 
    for (int i = 0; i < nbins; i++) {
        double res = 0.;
        for (int j = -1 * nbins_3sigma; j < nbins_23sigma - nbins_3sigma; j++) {
            if (i + j >= 0 && i + j < nbins) res += sdog[j + nbins_3sigma] * artmp[i + j];
            else if (i + j < 0) res += sdog[j + nbins_3sigma] * artmp[0];
            else res += sdog[j + nbins_3sigma] * artmp[nbins - 1];
        }
        ar[i] = res * i_norm;
    }
    delete[] artmp;
    delete[] sdog;
}
 
void Filters::SecondOrderUnderdampedFilter(double*& ar, int nbins, double period, double damping, double shift, double bin_size, bool do_plot) {
 
    double* artmp = new double[nbins];
    for (int i = 0; i < nbins; i++) artmp[i] = ar[i];
 
    int shift_n = static_cast<int>(ceil(shift / bin_size));
    int nbins_response = shift_n + static_cast<int>(3. * period / bin_size);
    
    if (nbins_response > nbins) {
        cout << "ERROR: nbins_response > nbins. Reduce shift or period." << endl;
        nbins_response = nbins - 1;
    }
    if (damping <= 0) {
        cout << "ERROR: damping <= 0. Setting to 1 ns" << endl;
        damping = 1;
    }
 
    if (nbins_response % 2 == 0) nbins_response++;
    double* souf = new double[nbins_response];
 
    double exp_factor = -1. / damping;
    double omega = 2. * M_PI / period;
    double sum_norm = 0.;
    for (int i = 0; i < nbins_response; i++) {
        double position = static_cast<double>(i) * bin_size;
        
        if (i < shift_n) souf[i] = 0.;
        else {
            souf[i] = exp(exp_factor * (position - shift)) * sin(omega * (position - shift));
            sum_norm += souf[i];
        }
    }
    if (sum_norm == 0.) sum_norm = 1.;
    double i_sum_norm = 1. / sum_norm;
 
    for (int i = 0; i < nbins; i++) {
        double res = 0.;
        for (int j = max(0, nbins_response / 2 - i); j < min(nbins_response, nbins + nbins_response / 2 - i); j++) {
            res += souf[nbins_response - j - 1] * artmp[i + j - nbins_response / 2];
        }
        ar[i] = res * i_sum_norm;
    }
 
    // plot the results
    if (do_plot) {
        double* x = new double[nbins_response];
        double* x_full = new double[nbins];
        for (int i = 0; i < nbins; i++) {
            x_full[i] = static_cast<double>(i) * bin_size;
            if (i < nbins_response) x[i] = static_cast<double>(i) * bin_size;
        }
 
        TCanvas* c_response = new TCanvas("response", "response", 800, 600);
        TGraph* g_original = new TGraph(nbins, x_full, artmp);
        g_original->SetTitle("original");
        g_original->SetMarkerStyle(34);
        g_original->Draw("AP");
 
        TGraph* g_response = new TGraph(nbins_response, x, souf);
        g_response->SetTitle("response");
        g_response->SetLineColor(kBlue);
        g_response->SetLineWidth(5); 
        g_response->SetLineStyle(7);
        g_response->Draw("L same");
 
        TGraph* g_result = new TGraph(nbins, x_full, ar);
        g_result->SetTitle("result");
        g_result->SetLineColor(kRed);
        g_result->SetLineWidth(3);
        g_result->Draw("L same");
 
        g_response->Scale(TMath::MaxElement(nbins, ar) / TMath::MaxElement(nbins_response, souf));
        c_response->Update(); c_response->Modified();
        gPad->BuildLegend(.5, .7, .9, .9);
        c_response->SaveAs("response.png");
        
        delete[] x;
        delete[] x_full;
    }
    delete[] artmp;
    delete[] souf;
}
 
void Filters::SecondOrderUnderdampedFilter(TH1F*& his, int nbins, double period, double damping, double shift, double bin_size, bool do_plot) {
    double* yvals = Helpers::gety(his);
    SecondOrderUnderdampedFilter(yvals, nbins, period, damping, shift, bin_size, do_plot);
    for (int i = 1; i <= his->GetNbinsX(); i++) his->SetBinContent(i, yvals[i - 1]);
    delete[] yvals;
}