annotate src/CQKernel.cpp @ 132:c188cade44f8

Tests (not quite correct yet)

/* -*- c-basic-offset: 4 indent-tabs-mode: nil -*-  vi:set ts=8 sts=4 sw=4: */
/*
    Constant-Q library
    Copyright (c) 2013-2014 Queen Mary, University of London

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#include "CQKernel.h"

#include "dsp/MathUtilities.h"
#include "dsp/FFT.h"
#include "dsp/Window.h"

#include <cmath>
#include <cassert>
#include <vector>
#include <iostream>
#include <algorithm>

using std::vector;
using std::complex;
using std::cerr;
using std::endl;

typedef std::complex<double> C;

CQKernel::CQKernel(CQParameters params) :
    m_inparams(params),
    m_fft(0)
{
    m_p.sampleRate = params.sampleRate;
    m_p.maxFrequency = params.maxFrequency;
    m_p.binsPerOctave = params.binsPerOctave;
    generateKernel();
}

CQKernel::~CQKernel()
{
    delete m_fft;
}

vector<double>
CQKernel::makeWindow(int len) const
{
    // The MATLAB version uses a symmetric window, but our windows
    // are periodic. A symmetric window of size N is a periodic
    // one of size N-1 with the first element stuck on the end.

    WindowType wt(BlackmanHarrisWindow);

    switch (m_inparams.window) {
    case CQParameters::SqrtBlackmanHarris:
    case CQParameters::BlackmanHarris:
        wt = BlackmanHarrisWindow;
        break;
    case CQParameters::SqrtBlackman:
    case CQParameters::Blackman:
        wt = BlackmanWindow;
        break;
    case CQParameters::SqrtHann:
    case CQParameters::Hann:
        wt = HanningWindow;
        break;
    }

    Window<double> w(wt, len-1);
    vector<double> win = w.getWindowData();
    win.push_back(win[0]);

    switch (m_inparams.window) {
    case CQParameters::SqrtBlackmanHarris:
    case CQParameters::SqrtBlackman:
    case CQParameters::SqrtHann:
        for (int i = 0; i < (int)win.size(); ++i) {
            win[i] = sqrt(win[i]) / len;
        }
        break;
    case CQParameters::BlackmanHarris:
    case CQParameters::Blackman:
    case CQParameters::Hann:
        for (int i = 0; i < (int)win.size(); ++i) {
            win[i] = win[i] / len;
        }
        break;
    }

    return win;
}

void
CQKernel::generateKernel()
{
    double q = m_inparams.q;
    double atomHopFactor = m_inparams.atomHopFactor;
    double thresh = m_inparams.threshold;

    double bpo = m_p.binsPerOctave;

    m_p.minFrequency = (m_p.maxFrequency / 2) * pow(2, 1.0/bpo);
    m_p.Q = q / (pow(2, 1.0/bpo) - 1.0);

    double maxNK = round(m_p.Q * m_p.sampleRate / m_p.minFrequency);
    double minNK = round
        (m_p.Q * m_p.sampleRate /
         (m_p.minFrequency * pow(2, (bpo - 1.0) / bpo)));

    if (minNK == 0 || maxNK == 0) {
        // most likely pathological parameters of some sort
        cerr << "WARNING: CQKernel::generateKernel: minNK or maxNK is zero (minNK == " << minNK << ", maxNK == " << maxNK << "), not generating a kernel" << endl;
        m_p.atomSpacing = 0;
        m_p.firstCentre = 0;
        m_p.fftSize = 0;
        m_p.atomsPerFrame = 0;
        m_p.lastCentre = 0;
        m_p.fftHop = 0;
        return;
    }

    m_p.atomSpacing = round(minNK * atomHopFactor);
    m_p.firstCentre = m_p.atomSpacing * ceil(ceil(maxNK / 2.0) / m_p.atomSpacing);
    m_p.fftSize = MathUtilities::nextPowerOfTwo
        (m_p.firstCentre + ceil(maxNK / 2.0));

    m_p.atomsPerFrame = floor
        (1.0 + (m_p.fftSize - ceil(maxNK / 2.0) - m_p.firstCentre) / m_p.atomSpacing);

    cerr << "atomsPerFrame = " << m_p.atomsPerFrame << " (q = " << q << ", Q = " << m_p.Q << ", atomHopFactor = " << atomHopFactor << ", atomSpacing = " << m_p.atomSpacing << ", fftSize = " << m_p.fftSize << ", maxNK = " << maxNK << ", firstCentre = " << m_p.firstCentre << ")" << endl;

    m_p.lastCentre = m_p.firstCentre + (m_p.atomsPerFrame - 1) * m_p.atomSpacing;

    m_p.fftHop = (m_p.lastCentre + m_p.atomSpacing) - m_p.firstCentre;

    cerr << "fftHop = " << m_p.fftHop << endl;

    m_fft = new FFT(m_p.fftSize);

    for (int k = 1; k <= m_p.binsPerOctave; ++k) {
        
        int nk = round(m_p.Q * m_p.sampleRate /
                       (m_p.minFrequency * pow(2, ((k-1.0) / bpo))));

        vector<double> win = makeWindow(nk);

        double fk = m_p.minFrequency * pow(2, ((k-1.0) / bpo));

        vector<double> reals, imags;
        
        for (int i = 0; i < nk; ++i) {
            double arg = (2.0 * M_PI * fk * i) / m_p.sampleRate;
            reals.push_back(win[i] * cos(arg));
            imags.push_back(win[i] * sin(arg));
        }

        int atomOffset = m_p.firstCentre - int(ceil(nk/2.0));

        for (int i = 0; i < m_p.atomsPerFrame; ++i) {

            int shift = atomOffset + (i * m_p.atomSpacing);

            vector<double> rin(m_p.fftSize, 0.0);
            vector<double> iin(m_p.fftSize, 0.0);

            for (int j = 0; j < nk; ++j) {
                rin[j + shift] = reals[j];
                iin[j + shift] = imags[j];
            }

            vector<double> rout(m_p.fftSize, 0.0);
            vector<double> iout(m_p.fftSize, 0.0);

            m_fft->process(false,
                           rin.data(), iin.data(),
                           rout.data(), iout.data());

            // Keep this dense for the moment (until after
            // normalisation calculations)

            vector<C> row;

            for (int j = 0; j < m_p.fftSize; ++j) {
                if (sqrt(rout[j] * rout[j] + iout[j] * iout[j]) < thresh) {
                    row.push_back(C(0, 0));
                } else {
                    row.push_back(C(rout[j] / m_p.fftSize,
                                    iout[j] / m_p.fftSize));
                }
            }

            m_kernel.origin.push_back(0);
            m_kernel.data.push_back(row);
        }
    }

    assert((int)m_kernel.data.size() == m_p.binsPerOctave * m_p.atomsPerFrame);

    // print density as diagnostic

    int nnz = 0;
    for (int i = 0; i < (int)m_kernel.data.size(); ++i) {
        for (int j = 0; j < (int)m_kernel.data[i].size(); ++j) {
            if (m_kernel.data[i][j] != C(0, 0)) {
                ++nnz;
            }
        }
    }

    cerr << "size = " << m_kernel.data.size() << "*" << m_kernel.data[0].size() << " (fft size = " << m_p.fftSize << ")" << endl;

    assert((int)m_kernel.data.size() == m_p.binsPerOctave * m_p.atomsPerFrame);
    assert((int)m_kernel.data[0].size() == m_p.fftSize);

    cerr << "density = " << double(nnz) / double(m_p.binsPerOctave * m_p.atomsPerFrame * m_p.fftSize) << " (" << nnz << " of " << m_p.binsPerOctave * m_p.atomsPerFrame * m_p.fftSize << ")" << endl;

    finaliseKernel();
}

static bool ccomparator(C &c1, C &c2)
{
    return abs(c1) < abs(c2);
}

static int maxidx(vector<C> &v)
{
    return std::max_element(v.begin(), v.end(), ccomparator) - v.begin();
}

void
CQKernel::finaliseKernel()
{
    // calculate weight for normalisation

    int wx1 = maxidx(m_kernel.data[0]);
    int wx2 = maxidx(m_kernel.data[m_kernel.data.size()-1]);

    vector<vector<C> > subset(m_kernel.data.size());
    for (int j = wx1; j <= wx2; ++j) {
        for (int i = 0; i < (int)m_kernel.data.size(); ++i) {
            subset[i].push_back(m_kernel.data[i][j]);
        }
    }

    int nrows = subset.size();
    int ncols = subset[0].size();
    vector<vector<C> > square(ncols); // conjugate transpose of subset * subset

    for (int i = 0; i < nrows; ++i) {
        assert((int)subset[i].size() == ncols);
    }

    for (int j = 0; j < ncols; ++j) {
        for (int i = 0; i < ncols; ++i) {
            C v(0, 0);
            for (int k = 0; k < nrows; ++k) {
                v += subset[k][i] * conj(subset[k][j]);
            }
            square[i].push_back(v);
        }
    }

    vector<double> wK;
    double q = m_inparams.q;
    for (int i = round(1.0/q); i < ncols - round(1.0/q) - 2; ++i) {
        wK.push_back(abs(square[i][i]));
    }

    double weight = double(m_p.fftHop) / m_p.fftSize;
    weight /= MathUtilities::mean(wK.data(), wK.size());
    weight = sqrt(weight);
    
    cerr << "weight = " << weight << endl;

    // apply normalisation weight, make sparse, and store conjugate
    // (we use the adjoint or conjugate transpose of the kernel matrix
    // for the forward transform, the plain kernel for the inverse
    // which we expect to be less common)

    KernelMatrix sk;

    for (int i = 0; i < (int)m_kernel.data.size(); ++i) {

        sk.origin.push_back(0);
        sk.data.push_back(vector<C>());

        int lastNZ = 0;
        for (int j = (int)m_kernel.data[i].size()-1; j >= 0; --j) {
            if (abs(m_kernel.data[i][j]) != 0.0) {
                lastNZ = j;
                break;
            }
        }

        bool haveNZ = false;
        for (int j = 0; j <= lastNZ; ++j) {
            if (haveNZ || abs(m_kernel.data[i][j]) != 0.0) {
                if (!haveNZ) sk.origin[i] = j;
                haveNZ = true;
                sk.data[i].push_back(conj(m_kernel.data[i][j]) * weight);
            }
        }
    }

    m_kernel = sk;
}

vector<C>
CQKernel::processForward(const vector<C> &cv)
{
    // straightforward matrix multiply (taking into account m_kernel's
    // slightly-sparse representation)

    if (m_kernel.data.empty()) return vector<C>();

    int nrows = m_p.binsPerOctave * m_p.atomsPerFrame;

    vector<C> rv(nrows, C());

    for (int i = 0; i < nrows; ++i) {
        int len = m_kernel.data[i].size();
        for (int j = 0; j < len; ++j) {
            rv[i] += cv[j + m_kernel.origin[i]] * m_kernel.data[i][j];
        }
    }

    return rv;
}

vector<C>
CQKernel::processInverse(const vector<C> &cv)
{
    // matrix multiply by conjugate transpose of m_kernel. This is
    // actually the original kernel as calculated, we just stored the
    // conjugate-transpose of the kernel because we expect to be doing
    // more forward transforms than inverse ones.

    if (m_kernel.data.empty()) return vector<C>();

    int ncols = m_p.binsPerOctave * m_p.atomsPerFrame;
    int nrows = m_p.fftSize;

    vector<C> rv(nrows, C());

    for (int j = 0; j < ncols; ++j) {
        int i0 = m_kernel.origin[j];
        int i1 = i0 + m_kernel.data[j].size();
        for (int i = i0; i < i1; ++i) {
            rv[i] += cv[j] * conj(m_kernel.data[j][i - i0]);
        }
    }

    return rv;
}