//determine the most likely symbol
template <class GF_q, class real> void linear_code_utils<GF_q, real>::get_most_likely_received_word(
const array1dv_t& received_likelihoods, array1d_t & received_word_sd,
array1gfq_t& received_word_hd)
{
//some helper variables
int length_n = received_likelihoods.size();
real mostlikely_sofar = real(0.0);
int indx = 0;
array1d_t tmp_vec;
int num_of_symbs;
received_word_sd.init(length_n);
received_word_hd.init(length_n);
for (int loop_n = 0; loop_n < length_n; loop_n++)
{
mostlikely_sofar = 0;
indx = 0;
tmp_vec = received_likelihoods(loop_n);
num_of_symbs = tmp_vec.size();
for (int loop_q = 0; loop_q < num_of_symbs; loop_q++)
{
if (mostlikely_sofar <= tmp_vec(loop_q))
{
mostlikely_sofar = tmp_vec(loop_q);
indx = loop_q;
}
}
received_word_sd(loop_n) = mostlikely_sofar;
received_word_hd(loop_n) = GF_q(indx);
}
}
vector<double> sub_vec(const vector<double>& vec, int first, int len) {
// obtain the sub vector with length len starting from the first element
vector<double>::const_iterator beg = vec.begin() + first;
vector<double>::const_iterator end = beg + len;
vector<double> tmp_vec(beg, end);
return tmp_vec;
}
void find_lis(const std::vector<int> &sequence, std::vector<int> &lis) {
lis.clear();
lis.push_back(0);
std::vector<int> tmp_vec(sequence.size());
int lower, upper;
for(size_t i = 0; i < sequence.size(); i++) {
// if next element is greater than last element of longest subseq
if( sequence[lis.back()] < sequence[i] ) {
tmp_vec[i] = lis.back();
lis.push_back(i);
continue;
}
// binary search to find smallest element
for(lower = 0, upper = lis.size()-1; lower < upper;) {
int bin_index = (lower + upper) / 2;
if(sequence[lis[bin_index]] < sequence[i])
lower = bin_index + 1;
else
upper = bin_index;
}
// update lis if new value is smaller then previously
if(sequence[i] < sequence[lis[lower]]) {
if(lower > 0)
tmp_vec[i] = lis[lower-1];
lis[lower] = i;
}
}
for(lower = lis.size(), upper = lis.back(); lower--; upper = tmp_vec[upper])
lis[lower] = upper;
}
inline
typename T1::elem_type
op_median::median_vec
(
const T1& X,
const typename arma_not_cx<typename T1::elem_type>::result* junk
)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
typedef typename T1::elem_type eT;
const Proxy<T1> P(X);
const uword n_elem = P.get_n_elem();
arma_debug_check( (n_elem == 0), "median(): given object has no elements" );
std::vector<eT> tmp_vec(n_elem);
if(Proxy<T1>::prefer_at_accessor == false)
{
typedef typename Proxy<T1>::ea_type ea_type;
ea_type A = P.get_ea();
for(uword i=0; i<n_elem; ++i)
{
tmp_vec[i] = A[i];
}
}
else
{
const uword n_rows = P.get_n_rows();
const uword n_cols = P.get_n_cols();
if(n_cols == 1)
{
for(uword row=0; row < n_rows; ++row)
{
tmp_vec[row] = P.at(row,0);
}
}
else
if(n_rows == 1)
{
for(uword col=0; col < n_cols; ++col)
{
tmp_vec[col] = P.at(0,col);
}
}
else
{
arma_stop("op_median::median_vec(): expected a vector" );
}
}
return op_median::direct_median(tmp_vec);
}
const ROL::Vector<Real> & dual() const {
uint dimension = std_vec_->size();
std::vector<Element> tmp_vec(*std_vec_);
for (uint i = 0; i < dimension; i++) {
tmp_vec[i] /= (*scaling_vec_)[i];
}
dual_vec_ = Teuchos::rcp( new PrimalScaledStdVector<Real>( Teuchos::rcp(new std::vector<Element>(tmp_vec)), scaling_vec_ ) );
return *dual_vec_;
}
//! Construct
lcp_vlc(cache_config& config, std::string other_key="")
{
std::string lcp_key = conf::KEY_LCP;
if ("" != other_key) {
lcp_key = other_key;
}
int_vector_buffer<> lcp_buf(cache_file_name(lcp_key, config));
vlc_vec_type tmp_vec(lcp_buf);
m_vec.swap(tmp_vec);
}
int zimg_depth_process(zimg_depth_context *ctx, const void *src, void *dst, void *,
int width, int height, int src_stride, int dst_stride,
int pixel_in, int pixel_out, int depth_in, int depth_out, int fullrange_in, int fullrange_out, int chroma)
{
try {
const void *src_p[3] = { src, nullptr, nullptr };
void *dst_p[3] = { dst, nullptr, nullptr };
ptrdiff_t src_stride_[3] = { src_stride, 0, 0 };
ptrdiff_t dst_stride_[3] = { dst_stride, 0, 0 };
std::unique_ptr<zimg_filter> filter;
zimg_depth_params params;
size_t tmp_size;
int err;
zimg2_depth_params_default(¶ms, ZIMG_API_VERSION);
params.width = width;
params.height = height;
params.dither_type = ctx->type;
params.chroma = chroma;
params.pixel_in = pixel_in;
params.depth_in = depth_in;
params.range_in = fullrange_in;
params.pixel_out = pixel_out;
params.depth_out = depth_out;
params.range_out = fullrange_out;
filter.reset(zimg2_depth_create(¶ms));
if (!filter)
return g_last_error;
if ((err = zimg2_plane_filter_get_tmp_size(filter.get(), &tmp_size)))
return err;
zimg::AlignedVector<char> tmp_vec(tmp_size);
return zimg2_plane_filter_process(filter.get(), tmp_vec.data(), src_p, dst_p, src_stride_, dst_stride_);
} catch (const zimg::ZimgException &e) {
return handle_exception(e);
} catch (const std::bad_alloc &e) {
return handle_exception(e);
}
}
int _tmain(int argc, _TCHAR* argv[])
{
//1.06 9.2 151 54.4 1.6
//0.89 10.3 202 57.9 2.2
//1.43 15.4 113 53 3.4
//1.02 11.2 168 56 0.3
//1.49 8.8 192 51.2 1
//1.32 13.5 111 60 -2.2
//1.22 12.2 175 67.6 2.2
//1.1 9.2 245 57 3.3
//1.34 13 168 60.4 7.2
//1.12 12.4 197 53 2.7
//0.75 7.5 173 51.5 6.5
//1.13 10.9 178 62 3.7
//1.15 12.7 199 53.7 6.4
//1.09 12 96 49.8 1.4
//0.96 7.6 164 62.2 -0.1
//1.16 9.9 252 56 9.2
//0.76 6.4 136 61.9 9
//1.05 12.6 150 56.7 2.7
//1.16 11.7 104 54 -2.1
//1.2 11.8 148 59.9 3.5
//1.04 8.6 204 61 3.5
//1.07 9.3 174 54.3 5.9
UINT n = 22;
UINT k = 3;
UINT vec_dim = 5;
vector<ublas::vector<double>> coord_array;
ifstream dataset_stream("dataset.txt");
ublas::vector<double> tmp_vec(vec_dim);
for(UINT i = 0; i < n; i++)
{
for(UINT j = 0; j < vec_dim; j++)
dataset_stream >> tmp_vec(j);
coord_array.push_back(tmp_vec);
cout << tmp_vec << endl;
}
vector<ublas::vector<double>> the_centroid_vec;
vector<boost::unordered_set<UINT>> the_groups;
k_mean_cluster(k, n, vec_dim, coord_array, the_groups, the_centroid_vec);
vector<UINT> representatives;
for(UINT i = 0; i<k; i++) //for each group
{
//each group
double closest_distance_to_centroid = std::numeric_limits<double>::max();
UINT pixel_id_closest_distance_to_centroid = 0;
for(boost::unordered_set<UINT>::iterator it = the_groups[i].begin(); it!=the_groups[i].end(); ++it)
{
double distance = compute_distance(coord_array[*it], the_centroid_vec[i]);
if(distance < closest_distance_to_centroid)
{
closest_distance_to_centroid = distance;
pixel_id_closest_distance_to_centroid = *it;
}
}
representatives.push_back(pixel_id_closest_distance_to_centroid);
}
return 0;
}
inline
void
op_median::apply(Mat< std::complex<T> >& out, const Op<T1,op_median>& in)
{
arma_extra_debug_sigprint();
typedef typename std::complex<T> eT;
arma_type_check(( is_same_type<eT, typename T1::elem_type>::value == false ));
const unwrap_check<T1> tmp(in.m, out);
const Mat<eT>& X = tmp.M;
const uword X_n_rows = X.n_rows;
const uword X_n_cols = X.n_cols;
const uword dim = in.aux_uword_a;
arma_debug_check( (dim > 1), "median(): incorrect usage. dim must be 0 or 1");
if(dim == 0) // in each column
{
arma_extra_debug_print("op_median::apply(), dim = 0");
arma_debug_check( (X_n_rows == 0), "median(): given object has zero rows" );
out.set_size(1, X_n_cols);
std::vector< arma_cx_median_packet<T> > tmp_vec(X_n_rows);
for(uword col=0; col<X_n_cols; ++col)
{
const eT* colmem = X.colptr(col);
for(uword row=0; row<X_n_rows; ++row)
{
tmp_vec[row].val = std::abs(colmem[row]);
tmp_vec[row].index = row;
}
uword index1;
uword index2;
op_median::direct_cx_median_index(index1, index2, tmp_vec);
out[col] = op_median::robust_mean(colmem[index1], colmem[index2]);
}
}
else
if(dim == 1) // in each row
{
arma_extra_debug_print("op_median::apply(), dim = 1");
arma_debug_check( (X_n_cols == 0), "median(): given object has zero columns" );
out.set_size(X_n_rows, 1);
std::vector< arma_cx_median_packet<T> > tmp_vec(X_n_cols);
for(uword row=0; row<X_n_rows; ++row)
{
for(uword col=0; col<X_n_cols; ++col)
{
tmp_vec[col].val = std::abs(X.at(row,col));
tmp_vec[row].index = col;
}
uword index1;
uword index2;
op_median::direct_cx_median_index(index1, index2, tmp_vec);
out[row] = op_median::robust_mean( X.at(row,index1), X.at(row,index2) );
}
}
}
inline
void
op_median::apply(Mat<typename T1::elem_type>& out, const Op<T1,op_median>& in)
{
arma_extra_debug_sigprint();
typedef typename T1::elem_type eT;
const unwrap_check<T1> tmp(in.m, out);
const Mat<eT>& X = tmp.M;
const uword X_n_rows = X.n_rows;
const uword X_n_cols = X.n_cols;
const uword dim = in.aux_uword_a;
arma_debug_check( (dim > 1), "median(): incorrect usage. dim must be 0 or 1");
if(dim == 0) // in each column
{
arma_extra_debug_print("op_median::apply(), dim = 0");
arma_debug_check( (X_n_rows == 0), "median(): given object has zero rows" );
out.set_size(1, X_n_cols);
std::vector<eT> tmp_vec(X_n_rows);
for(uword col=0; col<X_n_cols; ++col)
{
const eT* colmem = X.colptr(col);
for(uword row=0; row<X_n_rows; ++row)
{
tmp_vec[row] = colmem[row];
}
out[col] = op_median::direct_median(tmp_vec);
}
}
else
if(dim == 1) // in each row
{
arma_extra_debug_print("op_median::apply(), dim = 1");
arma_debug_check( (X_n_cols == 0), "median(): given object has zero columns" );
out.set_size(X_n_rows, 1);
std::vector<eT> tmp_vec(X_n_cols);
for(uword row=0; row<X_n_rows; ++row)
{
for(uword col=0; col<X_n_cols; ++col)
{
tmp_vec[col] = X.at(row,col);
}
out[row] = op_median::direct_median(tmp_vec);
}
}
}
inline
typename T1::elem_type
op_median::median_vec
(
const T1& X,
const typename arma_cx_only<typename T1::elem_type>::result* junk
)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
typedef typename T1::elem_type eT;
typedef typename T1::pod_type T;
const Proxy<T1> P(X);
const uword n_elem = P.get_n_elem();
if(n_elem == 0)
{
arma_debug_check(true, "median(): object has no elements");
return Datum<eT>::nan;
}
std::vector< arma_cx_median_packet<T> > tmp_vec(n_elem);
if(Proxy<T1>::prefer_at_accessor == false)
{
typedef typename Proxy<T1>::ea_type ea_type;
ea_type A = P.get_ea();
for(uword i=0; i<n_elem; ++i)
{
tmp_vec[i].val = std::abs( A[i] );
tmp_vec[i].index = i;
}
uword index1;
uword index2;
op_median::direct_cx_median_index(index1, index2, tmp_vec);
return op_mean::robust_mean( A[index1], A[index2] );
}
else
{
const uword n_rows = P.get_n_rows();
const uword n_cols = P.get_n_cols();
if(n_cols == 1)
{
for(uword row=0; row < n_rows; ++row)
{
tmp_vec[row].val = std::abs( P.at(row,0) );
tmp_vec[row].index = row;
}
uword index1;
uword index2;
op_median::direct_cx_median_index(index1, index2, tmp_vec);
return op_mean::robust_mean( P.at(index1,0), P.at(index2,0) );
}
else
if(n_rows == 1)
{
for(uword col=0; col < n_cols; ++col)
{
tmp_vec[col].val = std::abs( P.at(0,col) );
tmp_vec[col].index = col;
}
uword index1;
uword index2;
op_median::direct_cx_median_index(index1, index2, tmp_vec);
return op_mean::robust_mean( P.at(0,index1), P.at(0,index2) );
}
else
{
arma_stop("op_median::median_vec(): expected a vector" );
return eT(0);
}
}
}
inline
typename T1::elem_type
op_median::median_vec
(
const T1& X,
const typename arma_not_cx<typename T1::elem_type>::result* junk
)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
typedef typename T1::elem_type eT;
typedef typename Proxy<T1>::stored_type P_stored_type;
const Proxy<T1> P(X);
const uword n_elem = P.get_n_elem();
if(n_elem == 0)
{
arma_debug_check(true, "median(): object has no elements");
return Datum<eT>::nan;
}
std::vector<eT> tmp_vec(n_elem);
if(is_Mat<P_stored_type>::value == true)
{
const unwrap<P_stored_type> tmp(P.Q);
const typename unwrap<P_stored_type>::stored_type& Y = tmp.M;
arrayops::copy( &(tmp_vec[0]), Y.memptr(), n_elem );
}
else
{
if(Proxy<T1>::prefer_at_accessor == false)
{
typedef typename Proxy<T1>::ea_type ea_type;
ea_type A = P.get_ea();
for(uword i=0; i<n_elem; ++i) { tmp_vec[i] = A[i]; }
}
else
{
const uword n_rows = P.get_n_rows();
const uword n_cols = P.get_n_cols();
if(n_cols == 1)
{
for(uword row=0; row < n_rows; ++row) { tmp_vec[row] = P.at(row,0); }
}
else
if(n_rows == 1)
{
for(uword col=0; col < n_cols; ++col) { tmp_vec[col] = P.at(0,col); }
}
else
{
arma_stop("op_median::median_vec(): expected a vector" );
}
}
}
return op_median::direct_median(tmp_vec);
}
inline
void
op_median::apply(Mat<typename T1::elem_type>& out, const Op<T1,op_median>& in)
{
arma_extra_debug_sigprint();
typedef typename T1::elem_type eT;
const uword dim = in.aux_uword_a;
arma_debug_check( (dim > 1), "median(): parameter 'dim' must be 0 or 1" );
const Proxy<T1> P(in.m);
typedef typename Proxy<T1>::stored_type P_stored_type;
const bool is_alias = P.is_alias(out);
if( (is_Mat<P_stored_type>::value == true) || is_alias )
{
const unwrap_check<P_stored_type> tmp(P.Q, is_alias);
const typename unwrap_check<P_stored_type>::stored_type& X = tmp.M;
const uword X_n_rows = X.n_rows;
const uword X_n_cols = X.n_cols;
if(dim == 0) // in each column
{
arma_extra_debug_print("op_median::apply(): dim = 0");
out.set_size((X_n_rows > 0) ? 1 : 0, X_n_cols);
if(X_n_rows > 0)
{
std::vector<eT> tmp_vec(X_n_rows);
for(uword col=0; col < X_n_cols; ++col)
{
arrayops::copy( &(tmp_vec[0]), X.colptr(col), X_n_rows );
out[col] = op_median::direct_median(tmp_vec);
}
}
}
else // in each row
{
arma_extra_debug_print("op_median::apply(): dim = 1");
out.set_size(X_n_rows, (X_n_cols > 0) ? 1 : 0);
if(X_n_cols > 0)
{
std::vector<eT> tmp_vec(X_n_cols);
for(uword row=0; row < X_n_rows; ++row)
{
for(uword col=0; col < X_n_cols; ++col) { tmp_vec[col] = X.at(row,col); }
out[row] = op_median::direct_median(tmp_vec);
}
}
}
}
else
{
const uword P_n_rows = P.get_n_rows();
const uword P_n_cols = P.get_n_cols();
if(dim == 0) // in each column
{
arma_extra_debug_print("op_median::apply(): dim = 0");
out.set_size((P_n_rows > 0) ? 1 : 0, P_n_cols);
if(P_n_rows > 0)
{
std::vector<eT> tmp_vec(P_n_rows);
for(uword col=0; col < P_n_cols; ++col)
{
for(uword row=0; row < P_n_rows; ++row) { tmp_vec[row] = P.at(row,col); }
out[col] = op_median::direct_median(tmp_vec);
}
}
}
else // in each row
{
arma_extra_debug_print("op_median::apply(): dim = 1");
out.set_size(P_n_rows, (P_n_cols > 0) ? 1 : 0);
if(P_n_cols > 0)
{
std::vector<eT> tmp_vec(P_n_cols);
for(uword row=0; row < P_n_rows; ++row)
{
for(uword col=0; col < P_n_cols; ++col) { tmp_vec[col] = P.at(row,col); }
out[row] = op_median::direct_median(tmp_vec);
}
}
}
}
}
/*
* Fits a weighted cubic regression on predictor(s)
*
* @param contrast - want to predict this value per snp
* @param strength - covariate of choice
* @param weights - weight of data points for this genotype
* @param Predictor - output, prediction function coefficients
* @param Predicted - output, predicted contrast per snp
*/
void
FitWeightedCubic(const std::vector<double> &contrast,
const std::vector<double> &strength,
const std::vector<double> &weights,
std::vector<double> &Predictor,
std::vector<double> &Predicted) {
// Singular value decomposition method
unsigned int i;
unsigned int nobs;
unsigned int npred;
npred = 3+1;
nobs= contrast.size();
// convert double into doubles to match newmat
vector<Real> tmp_vec(nobs);
Real* tmp_ptr = &tmp_vec[0];
vector<Real> obs_vec(nobs);
Real *obs_ptr = &obs_vec[0];
vector<Real> weight_vec(nobs);
Matrix covarMat(nobs,npred);
ColumnVector observedVec(nobs);
// fill in the data
// modified by weights
for (i=0; i<nobs; i++)
weight_vec[i] = sqrt(weights[i]);
// load data - 1s into col 1 of matrix
for (i=0; i<nobs; i++)
tmp_vec[i] = weight_vec[i];
covarMat.Column(1) << tmp_ptr;
for (i=0; i<nobs; i++)
tmp_vec[i] *= strength[i];
covarMat.Column(2) << tmp_ptr;
for (i=0; i<nobs; i++)
tmp_vec[i] *= strength[i];
covarMat.Column(3) << tmp_ptr;
for (i=0; i<nobs; i++)
tmp_vec[i] *= strength[i];
covarMat.Column(4) << tmp_ptr;
for (i=0; i<nobs; i++)
obs_vec[i] = contrast[i]*weight_vec[i];
observedVec << obs_ptr;
// do SVD
Matrix U, V;
DiagonalMatrix D;
ColumnVector Fitted(nobs);
ColumnVector A(npred);
SVD(covarMat,D,U,V);
Fitted = U.t() * observedVec;
A = V * ( D.i() * Fitted );
// this predicts "0" for low weights
// because of weighted regression
Fitted = U * Fitted;
// this is the predictor
Predictor.resize(npred);
for (i=0; i<npred; i++)
Predictor[i] = A.element(i);
// export data back to doubles
// and therefore this predicts "0" for low-weighted points
// which is >not< the desired outcome!!!!
// instead we need to predict all points at once
// >unweighted< as output
vector<double> Goofy;
Predicted.resize(nobs);
for (i = 0; i < nobs; ++i) {
Goofy.resize(npred);
Goofy[0] = 1;
Goofy[1] = strength[i];
Goofy[2] = strength[i]*Goofy[1];
Goofy[3] = strength[i]*Goofy[2];
Predicted[i] = vprod(Goofy,Predictor);
}
}
int cPCA2::computePC(std::vector<float>& x,
size_t nrow,
size_t ncol,
bool is_center,
bool is_scale,
bool is_corr)
{
_ncol = ncol;
_nrow = nrow;
_is_center = is_center;
_is_scale = is_scale;
_is_corr = is_corr;
if (x.size() != _nrow*_ncol) { return -1; }
if ((1 == _ncol) || (1 == nrow)) { return -1; }
// convert vector to Eigen 2-dimensional matrix
_xXf.resize(_nrow, _ncol);
for (size_t i = 0; i < _nrow; ++i) {
for (size_t j = 0; j < _ncol; ++j) {
_xXf(i, j) = x[j + i*_ncol];
}
}
// mean and standard deviation for each column
Eigen::VectorXf mean_vector(_ncol),
sd_vector(_ncol);
size_t zero_sd_num = 0;
float denom = static_cast<float>((_nrow > 1) ? _nrow - 1 : 1);
mean_vector = _xXf.colwise().mean();
Eigen::VectorXf curr_col;
for (size_t i = 0; i < _ncol; ++i) {
curr_col = Eigen::VectorXf::Constant(_nrow, mean_vector(i)); // mean(x) for column x
curr_col = _xXf.col(i) - curr_col; // x - mean(x)
curr_col = curr_col.array().square(); // (x-mean(x))^2
sd_vector(i) = std::sqrt((curr_col.sum())/denom);
if (0 == sd_vector(i)) {
zero_sd_num++;
}
}
// if colums with sd == 0 are too many, don't continue calculation
if (1 > _ncol-zero_sd_num) {
return -1;
}
// delete columns with sd == 0
Eigen::MatrixXf tmp(_nrow, _ncol-zero_sd_num);
Eigen::VectorXf tmp_mean_vector(_ncol-zero_sd_num);
size_t curr_col_num = 0;
for (size_t i = 0; i < _ncol; ++i) {
if (0 != sd_vector(i)) {
tmp.col(curr_col_num) = _xXf.col(i);
tmp_mean_vector(curr_col_num) = mean_vector(i);
curr_col_num++;
}
else {
_eliminated_columns.push_back(i);
}
}
_ncol -= zero_sd_num;
_xXf = tmp;
mean_vector = tmp_mean_vector;
tmp.resize(0, 0);
tmp_mean_vector.resize(0);
// shift to zero
if (true == _is_center) {
for (size_t i = 0; i < _ncol; ++i) {
_xXf.col(i) -= Eigen::VectorXf::Constant(_nrow, mean_vector(i));
}
}
// scale to unit variance
if ( (false == _is_corr) || (true == _is_scale)) {
for (size_t i = 0; i < _ncol; ++i) {
_xXf.col(i) /= std::sqrt(_xXf.col(i).array().square().sum()/denom);
}
}
#ifndef NDEBUG
std::cout << "\nScaled matrix:\n";
std::cout << _xXf << std::endl;
std::cout << "\nMean before scaling:\n" << mean_vector.transpose();
std::cout << "\nStandard deviation before scaling:\n" << sd_vector.transpose();
#endif
// when _nrow < _ncol then svd will be used
// if corr is true and _nrow > _ncol then correlation matrix will be used
// (TODO): What about covariance?
if ((_nrow < _ncol) || (false == _is_corr)) {
_method = "svd";
Eigen::JacobiSVD<Eigen::MatrixXf> svd(_xXf, Eigen::ComputeThinV);
Eigen::VectorXf eigen_singular_values = svd.singularValues();
Eigen::VectorXf tmp_vec = eigen_singular_values.array().square();
float tmp_sum = tmp_vec.sum();
size_t lim = (_nrow < _ncol)? _nrow : _ncol;
tmp_vec /= tmp_sum;
// PC's standard deviation and
// PC's proportion of variance
_kaiser = 0;
for (size_t i = 0; i < lim; ++i) {
_sd.push_back(eigen_singular_values(i)/std::sqrt(denom));
if (_sd[i] >= 1) {
_kaiser = (unsigned int) i + 1;
}
_prop_of_var.push_back(tmp_vec(i));
}
tmp_vec.resize(0);
#ifndef NDEBUG
std::cout << "\n\nStandard deviations for PCs:\n";
copy(_sd.begin(), _sd.end(),std::ostream_iterator<float>(std::cout," "));
std::cout << "\n\nKaiser criterion: PC #" << _kaiser << std::endl;
#endif
// PC's cumulative proportion
_thresh95 = 1;
_cum_prop.push_back(_prop_of_var[0]);
for (size_t i = 1; i < _prop_of_var.size(); ++i) {
_cum_prop.push_back(_cum_prop[i-1]+_prop_of_var[i]);
if (_cum_prop[i] < 0.95) {
_thresh95 = (unsigned int) i + 1;
}
}
#ifndef NDEBUG
std::cout << "\nCumulative proportion:\n";
copy(_cum_prop.begin(), _cum_prop.end(),std::ostream_iterator<float>(std::cout," "));
std::cout << "\n\nThresh95 criterion: PC #" << _thresh95 << std::endl;
#endif
// scores
Eigen::MatrixXf eigen_scores = _xXf * svd.matrixV();
#ifndef NDEBUG
std::cout << "\n\nRotated values (scores):\n" << eigen_scores;
#endif
_scores.reserve(lim*lim);
for (size_t i = 0; i < lim; ++i) {
for (size_t j = 0; j < lim; ++j) {
_scores.push_back(eigen_scores(i, j));
}
}
eigen_scores.resize(0, 0);
#ifndef NDEBUG
std::cout << "\n\nScores in vector:\n";
copy(_scores.begin(), _scores.end(),std::ostream_iterator<float>(std::cout," "));
std::cout << "\n";
#endif
}
else { // COR OR COV MATRICES ARE HERE
_method = "cor";
// calculate covariance matrix
Eigen::MatrixXf eigen_cov; // = MatrixXf::Zero(_ncol, _ncol);
Eigen::VectorXf sds;
// (TODO) should be weighted cov matrix, even if is_center == false
eigen_cov = (1.0f /((float) _nrow/*-1*/)) * _xXf.transpose() * _xXf;
sds = eigen_cov.diagonal().array().sqrt();
Eigen::MatrixXf outer_sds = sds * sds.transpose();
eigen_cov = eigen_cov.array() / outer_sds.array();
outer_sds.resize(0, 0);
// ?if data matrix is scaled, covariance matrix is equal to correlation matrix
Eigen::EigenSolver<Eigen::MatrixXf> edc(eigen_cov);
Eigen::VectorXf eigen_eigenvalues = edc.eigenvalues().real();
Eigen::MatrixXf eigen_eigenvectors = edc.eigenvectors().real();
#ifndef NDEBUG
std::cout << eigen_cov << std::endl;
std::cout << std::endl << eigen_eigenvalues.transpose() << std::endl;
std::cout << std::endl << eigen_eigenvectors << std::endl;
#endif
// the eigenvalues and eigenvectors are not sorted
// so, we should sort them
typedef std::pair<float,int> eigen_pair;
std::vector<eigen_pair> ep;
for (size_t i = 0 ; i < _ncol; ++i) {
ep.push_back(std::make_pair(eigen_eigenvalues(i), i));
}
sort(ep.begin(), ep.end()); // ascending order by default
// sort them all in descending order
Eigen::MatrixXf eigen_eigenvectors_sorted = Eigen::MatrixXf::Zero(eigen_eigenvectors.rows(), eigen_eigenvectors.cols());
Eigen::VectorXf eigen_eigenvalues_sorted = Eigen::VectorXf::Zero(_ncol);
int colnum = 0;
for (int i = (int) ep.size()-1; i > -1; i--) {
eigen_eigenvalues_sorted(colnum) = ep[i].first;
eigen_eigenvectors_sorted.col(colnum++) += eigen_eigenvectors.col(ep[i].second);
}
#ifndef NDEBUG
std::cout << std::endl << eigen_eigenvalues_sorted.transpose() << std::endl;
std::cout << std::endl << eigen_eigenvectors_sorted << std::endl;
#endif
// we don't need not sorted arrays anymore
eigen_eigenvalues.resize(0);
eigen_eigenvectors.resize(0, 0);
_sd.clear();
_prop_of_var.clear();
_kaiser = 0;
float tmp_sum = eigen_eigenvalues_sorted.sum();
for (size_t i = 0; i < _ncol; ++i) {
_sd.push_back(std::sqrt(eigen_eigenvalues_sorted(i)));
if (_sd[i] >= 1) {
_kaiser = (unsigned int) i + 1;
}
_prop_of_var.push_back(eigen_eigenvalues_sorted(i)/tmp_sum);
}
#ifndef NDEBUG
std::cout << "\nStandard deviations for PCs:\n";
copy(_sd.begin(), _sd.end(), std::ostream_iterator<float>(std::cout," "));
std::cout << "\nProportion of variance:\n";
copy(_prop_of_var.begin(), _prop_of_var.end(), std::ostream_iterator<float>(std::cout," "));
std::cout << "\nKaiser criterion: PC #" << _kaiser << std::endl;
#endif
// PC's cumulative proportion
_cum_prop.clear();
_thresh95 = 1;
_cum_prop.push_back(_prop_of_var[0]);
for (size_t i = 1; i < _prop_of_var.size(); ++i) {
_cum_prop.push_back(_cum_prop[i-1]+_prop_of_var[i]);
if (_cum_prop[i] < 0.95) {
_thresh95 = (unsigned int) i + 1;
}
}
#ifndef NDEBUG
std::cout << "\n\nCumulative proportions:\n";
copy(_cum_prop.begin(), _cum_prop.end(), std::ostream_iterator<float>(std::cout," "));
std::cout << "\n\n95% threshold: PC #" << _thresh95 << std::endl;
#endif
// scores for PCA with correlation matrix
// scale before calculating new values
for (size_t i = 0; i < _ncol; ++i) {
_xXf.col(i) /= sds(i);
}
sds.resize(0);
Eigen::MatrixXf eigen_scores = _xXf * eigen_eigenvectors_sorted;
#ifndef NDEBUG
std::cout << "\n\nRotated values (scores):\n" << eigen_scores;
#endif
_scores.clear();
_scores.reserve(_ncol*_nrow);
for (size_t i = 0; i < _nrow; ++i) {
for (size_t j = 0; j < _ncol; ++j) {
_scores.push_back(eigen_scores(i, j));
}
}
eigen_scores.resize(0, 0);
#ifndef NDEBUG
std::cout << "\n\nScores in vector:\n";
copy(_scores.begin(), _scores.end(), std::ostream_iterator<float>(std::cout," "));
std::cout << "\n";
#endif
}
return 0;
}
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]);
}
}