livetrax/libs/qm-dsp/dsp/tempotracking/TempoTrackV2.cpp

/* -*- c-basic-offset: 4 indent-tabs-mode: nil -*-  vi:set ts=8 sts=4 sw=4: */

/*
    QM DSP Library

    Centre for Digital Music, Queen Mary, University of London.
    This file copyright 2008-2009 Matthew Davies and QMUL.

    This program is free software; you can redistribute it and/or
    modify it under the terms of the GNU General Public License as
    published by the Free Software Foundation; either version 2 of the
    License, or (at your option) any later version.  See the file
    COPYING included with this distribution for more information.
*/

#include "TempoTrackV2.h"

#include <cmath>
#include <cstdlib>
#include <iostream>

#include "maths/MathUtilities.h"

#define   EPS 0.0000008 // just some arbitrary small number

TempoTrackV2::TempoTrackV2(float rate, size_t increment) :
    m_rate(rate), m_increment(increment) { }
TempoTrackV2::~TempoTrackV2() { }

void
TempoTrackV2::filter_df(d_vec_t &df)
{
    d_vec_t a(3);
    d_vec_t b(3);
    d_vec_t	lp_df(df.size());

    //equivalent in matlab to [b,a] = butter(2,0.4);
    a[0] = 1.0000;
    a[1] = -0.3695;
    a[2] = 0.1958;
    b[0] = 0.2066;
    b[1] = 0.4131;
    b[2] = 0.2066;
    
    double inp1 = 0.;
    double inp2 = 0.;
    double out1 = 0.;
    double out2 = 0.;


    // forwards filtering
    for (unsigned int i = 0;i < df.size();i++)
    {
        lp_df[i] =  b[0]*df[i] + b[1]*inp1 + b[2]*inp2 - a[1]*out1 - a[2]*out2;
        inp2 = inp1;
        inp1 = df[i];
        out2 = out1;
        out1 = lp_df[i];
    }

    // copy forwards filtering to df...
    // but, time-reversed, ready for backwards filtering
    for (unsigned int i = 0;i < df.size();i++)
    {
        df[i] = lp_df[df.size()-i-1];
    }

    for (unsigned int i = 0;i < df.size();i++)
    {
        lp_df[i] = 0.;    
    }

    inp1 = 0.; inp2 = 0.;
    out1 = 0.; out2 = 0.;

  // backwards filetering on time-reversed df
    for (unsigned int i = 0;i < df.size();i++)
    {
        lp_df[i] =  b[0]*df[i] + b[1]*inp1 + b[2]*inp2 - a[1]*out1 - a[2]*out2;
        inp2 = inp1;
        inp1 = df[i];
        out2 = out1;
        out1 = lp_df[i];
    }

  // write the re-reversed (i.e. forward) version back to df
    for (unsigned int i = 0;i < df.size();i++)
    {
        df[i] = lp_df[df.size()-i-1];
    }
}


void
TempoTrackV2::calculateBeatPeriod(const vector<double> &df,
                                  vector<double> &beat_period,
                                  vector<double> &tempi)
{
    // to follow matlab.. split into 512 sample frames with a 128 hop size
    // calculate the acf,
    // then the rcf.. and then stick the rcfs as columns of a matrix
    // then call viterbi decoding with weight vector and transition matrix
    // and get best path

    unsigned int wv_len = 128;
    double rayparam = 43.;

    // make rayleigh weighting curve
    d_vec_t wv(wv_len);
    for (unsigned int i=0; i<wv.size(); i++)
    {
        wv[i] = (static_cast<double> (i) / pow(rayparam,2.)) * exp((-1.*pow(-static_cast<double> (i),2.)) / (2.*pow(rayparam,2.)));
    }

    // beat tracking frame size (roughly 6 seconds) and hop (1.5 seconds)
    unsigned int winlen = 512;
    unsigned int step = 128;

    // matrix to store output of comb filter bank, increment column of matrix at each frame
    d_mat_t rcfmat;
    int col_counter = -1;

    // main loop for beat period calculation
    for (unsigned int i=0; i+winlen<df.size(); i+=step)
    {
        // get dfframe
        d_vec_t dfframe(winlen);
        for (unsigned int k=0; k<winlen; k++)
        {
            dfframe[k] = df[i+k];
        }
        // get rcf vector for current frame
        d_vec_t rcf(wv_len);    
        get_rcf(dfframe,wv,rcf);
  
        rcfmat.push_back( d_vec_t() ); // adds a new column
        col_counter++;
        for (unsigned int j=0; j<rcf.size(); j++)
        {
            rcfmat[col_counter].push_back( rcf[j] );
        }
    }
  
    // now call viterbi decoding function
    viterbi_decode(rcfmat,wv,beat_period,tempi);
}


void
TempoTrackV2::get_rcf(const d_vec_t &dfframe_in, const d_vec_t &wv, d_vec_t &rcf)
{
    // calculate autocorrelation function
    // then rcf
    // just hard code for now... don't really need separate functions to do this

    // make acf

    d_vec_t dfframe(dfframe_in);

    MathUtilities::adaptiveThreshold(dfframe);

    d_vec_t acf(dfframe.size());

    
    for (unsigned int lag=0; lag<dfframe.size(); lag++)
    {
        double sum = 0.;
        double tmp = 0.;

        for (unsigned int n=0; n<(dfframe.size()-lag); n++)
        {
            tmp = dfframe[n] * dfframe[n+lag];    
            sum += tmp;
        }
        acf[lag] = static_cast<double> (sum/ (dfframe.size()-lag));
    }

    // now apply comb filtering
    int numelem = 4;
	
    for (unsigned int i = 2;i < rcf.size();i++) // max beat period
    {
        for (int a = 1;a <= numelem;a++) // number of comb elements
        {
            for (int b = 1-a;b <= a-1;b++) // general state using normalisation of comb elements
            {
                rcf[i-1] += ( acf[(a*i+b)-1]*wv[i-1] ) / (2.*a-1.);	// calculate value for comb filter row
            }
        }
    }
  
    // apply adaptive threshold to rcf
    MathUtilities::adaptiveThreshold(rcf);
  
    double rcfsum =0.;
    for (unsigned int i=0; i<rcf.size(); i++)
    {
        rcf[i] += EPS ;
        rcfsum += rcf[i];
    }

    // normalise rcf to sum to unity
    for (unsigned int i=0; i<rcf.size(); i++)
    {
        rcf[i] /= (rcfsum + EPS);
    }
}

void
TempoTrackV2::viterbi_decode(const d_mat_t &rcfmat, const d_vec_t &wv, d_vec_t &beat_period, d_vec_t &tempi)
{
    // following Kevin Murphy's Viterbi decoding to get best path of
    // beat periods through rfcmat

    // make transition matrix
    d_mat_t tmat;
    for (unsigned int i=0;i<wv.size();i++)
    {
        tmat.push_back ( d_vec_t() ); // adds a new column
        for (unsigned int j=0; j<wv.size(); j++)
        {	
            tmat[i].push_back(0.); // fill with zeros initially
        }
    }
    
    // variance of Gaussians in transition matrix
    // formed of Gaussians on diagonal - implies slow tempo change
    double sigma = 8.;
    // don't want really short beat periods, or really long ones
    for (unsigned int i=20;i <wv.size()-20; i++)
    {
        for (unsigned int j=20; j<wv.size()-20; j++)
        {	
            double mu = static_cast<double>(i);
            tmat[i][j] = exp( (-1.*pow((j-mu),2.)) / (2.*pow(sigma,2.)) );
        }
    }

    // parameters for Viterbi decoding... this part is taken from
    // Murphy's matlab

    d_mat_t delta;
    i_mat_t psi;
    for (unsigned int i=0;i <rcfmat.size(); i++)
    {
        delta.push_back( d_vec_t());
        psi.push_back( i_vec_t());
        for (unsigned int j=0; j<rcfmat[i].size(); j++)
        {	
            delta[i].push_back(0.); // fill with zeros initially
            psi[i].push_back(0); // fill with zeros initially
        }
    }


    unsigned int T = delta.size();

    if (T < 2) return; // can't do anything at all meaningful

    unsigned int Q = delta[0].size();

    // initialize first column of delta
    for (unsigned int j=0; j<Q; j++)
    {
        delta[0][j] = wv[j] * rcfmat[0][j];
        psi[0][j] = 0;
    }
    
    double deltasum = 0.;
    for (unsigned int i=0; i<Q; i++)
    {
        deltasum += delta[0][i];
    }      
    for (unsigned int i=0; i<Q; i++)
    {
        delta[0][i] /= (deltasum + EPS);
    }      


    for (unsigned int t=1; t<T; t++)
    {
        d_vec_t tmp_vec(Q);

        for (unsigned int j=0; j<Q; j++)
        {
            for (unsigned int i=0; i<Q; i++)
            {
                tmp_vec[i] = delta[t-1][i] * tmat[j][i];
            }      
   
            delta[t][j] = get_max_val(tmp_vec);    

            psi[t][j] = get_max_ind(tmp_vec);
 
            delta[t][j] *= rcfmat[t][j];
        }

        // normalise current delta column
        double deltasum = 0.;
        for (unsigned int i=0; i<Q; i++)
        {
            deltasum += delta[t][i];
        }      
        for (unsigned int i=0; i<Q; i++)
        {
            delta[t][i] /= (deltasum + EPS);
        }      
    }

    i_vec_t bestpath(T);
    d_vec_t tmp_vec(Q);
    for (unsigned int i=0; i<Q; i++)
    {  
        tmp_vec[i] = delta[T-1][i];
    }

    // find starting point - best beat period for "last" frame
    bestpath[T-1] = get_max_ind(tmp_vec);
 
    // backtrace through index of maximum values in psi
    for (unsigned int t=T-2; t>0 ;t--)
    {
        bestpath[t] = psi[t+1][bestpath[t+1]];
    }

    // weird but necessary hack -- couldn't get above loop to terminate at t >= 0
    bestpath[0] = psi[1][bestpath[1]];

    unsigned int lastind = 0;
    for (unsigned int i=0; i<T; i++)
    {  
        unsigned int step = 128;
        for (unsigned int j=0; j<step; j++)
        {
            lastind = i*step+j;
            beat_period[lastind] = bestpath[i];
        }
//        std::cerr << "bestpath[" << i << "] = " << bestpath[i] << " (used for beat_periods " << i*step << " to " << i*step+step-1 << ")" << std::endl;
    }

    //fill in the last values...
    for (unsigned int i=lastind; i<beat_period.size(); i++)
    {
        beat_period[i] = beat_period[lastind];
    }

    for (unsigned int i = 0; i < beat_period.size(); i++)
    {
        tempi.push_back((60. * m_rate / m_increment)/beat_period[i]);
    }
}

double
TempoTrackV2::get_max_val(const d_vec_t &df)
{
    double maxval = 0.;
    for (unsigned int i=0; i<df.size(); i++)
    {
        if (maxval < df[i])
        {
            maxval = df[i];
        }
    }
    
    return maxval;
}

int
TempoTrackV2::get_max_ind(const d_vec_t &df)
{
    double maxval = 0.;
    int ind = 0;
    for (unsigned int i=0; i<df.size(); i++)
    {
        if (maxval < df[i])
        {
            maxval = df[i];
            ind = i;
        }
    }
    
    return ind;
}

void
TempoTrackV2::normalise_vec(d_vec_t &df)
{
    double sum = 0.;
    for (unsigned int i=0; i<df.size(); i++)
    {
        sum += df[i];
    }
    
    for (unsigned int i=0; i<df.size(); i++)
    {
        df[i]/= (sum + EPS);
    }
}

void
TempoTrackV2::calculateBeats(const vector<double> &df,
                             const vector<double> &beat_period,
                             vector<double> &beats)
{
    if (df.empty() || beat_period.empty()) return;

    d_vec_t cumscore(df.size()); // store cumulative score
    i_vec_t backlink(df.size()); // backlink (stores best beat locations at each time instant)
    d_vec_t localscore(df.size()); // localscore, for now this is the same as the detection function

    for (unsigned int i=0; i<df.size(); i++)
    {
        localscore[i] = df[i];
        backlink[i] = -1;
    }

    double tightness = 4.;
    double alpha = 0.9;

    // main loop
    for (unsigned int i=0; i<localscore.size(); i++)
    {
        int prange_min = -2*beat_period[i];
        int prange_max = round(-0.5*beat_period[i]);

        // transition range
        d_vec_t txwt (prange_max - prange_min + 1);
        d_vec_t scorecands (txwt.size());

        for (unsigned int j=0;j<txwt.size();j++)
        {
            double mu = static_cast<double> (beat_period[i]);
            txwt[j] = exp( -0.5*pow(tightness * log((round(2*mu)-j)/mu),2));

            // IF IN THE ALLOWED RANGE, THEN LOOK AT CUMSCORE[I+PRANGE_MIN+J
            // ELSE LEAVE AT DEFAULT VALUE FROM INITIALISATION:  D_VEC_T SCORECANDS (TXWT.SIZE());

            int cscore_ind = i+prange_min+j;
            if (cscore_ind >= 0)   
            {
                scorecands[j] = txwt[j] * cumscore[cscore_ind];
            }
        }

        // find max value and index of maximum value
        double vv = get_max_val(scorecands);
        int xx = get_max_ind(scorecands);

        cumscore[i] = alpha*vv + (1.-alpha)*localscore[i];
        backlink[i] = i+prange_min+xx;

//        std::cerr << "backlink[" << i << "] <= " << backlink[i] << std::endl;
    }

    // STARTING POINT, I.E. LAST BEAT.. PICK A STRONG POINT IN cumscore VECTOR
    d_vec_t tmp_vec;
    for (unsigned int i=cumscore.size() - beat_period[beat_period.size()-1] ; i<cumscore.size(); i++)
    {
        tmp_vec.push_back(cumscore[i]);
    }  

    int startpoint = get_max_ind(tmp_vec) + cumscore.size() - beat_period[beat_period.size()-1] ;

    // can happen if no results obtained earlier (e.g. input too short)
    if (startpoint >= backlink.size()) startpoint = backlink.size()-1;

    // USE BACKLINK TO GET EACH NEW BEAT (TOWARDS THE BEGINNING OF THE FILE)
    //  BACKTRACKING FROM THE END TO THE BEGINNING.. MAKING SURE NOT TO GO BEFORE SAMPLE 0
    i_vec_t ibeats;
    ibeats.push_back(startpoint);
//    std::cerr << "startpoint = " << startpoint << std::endl;
    while (backlink[ibeats.back()] > 0)
    {
//        std::cerr << "backlink[" << ibeats.back() << "] = " << backlink[ibeats.back()] << std::endl;
        int b = ibeats.back();
        if (backlink[b] == b) break; // shouldn't happen... haha
        ibeats.push_back(backlink[b]);
    }
  
    // REVERSE SEQUENCE OF IBEATS AND STORE AS BEATS
    for (unsigned int i=0; i<ibeats.size(); i++)
    { 
        beats.push_back( static_cast<double>(ibeats[ibeats.size()-i-1]) );
    }
}