void Annotator::update_color(MeshBundle<DefaultMesh>::Ptr m,const arma::uvec& label)
{
assert(m->mesh_.n_vertices()==label.size());
uint32_t* c = (uint32_t*)m->custom_color_.vertex_colors();
#pragma omp parallel for
for(int i=0;i<label.size();++i)
{
assert( l2c_.find(int(label(i))) != l2c_.end() );
c[i] = l2c_[ int(label(i)) ];
}
}
/**
* Add a random local matrix and rhs spanning over given rows and columns.
*
*/
void add(arma::uvec rows, arma::uvec cols) {
arma::mat loc_mat=arma::randu<arma::mat>(rows.size(), cols.size());
arma::vec loc_rhs=arma::randu<arma::vec>(rows.size());
// apply to full system
full_matrix_.submat(rows, cols)+=loc_mat;
full_rhs_.elem(rows)+=loc_rhs;
// apply to fixture system
arma::vec row_sol=dirichlet_values_.elem(rows);
arma::vec col_sol=dirichlet_values_.elem(cols);
auto i_rows=arma::conv_to<std::vector<int> >::from(
arma::conv_to<arma::ivec>::from(rows)%dirichlet_.elem(rows));
auto i_cols=arma::conv_to<std::vector<int> >::from(
arma::conv_to<arma::ivec>::from(cols)%dirichlet_.elem(cols));
//cout << "i_rows\n" << arma::ivec(i_rows);
//cout << "i_cols\n" << arma::ivec(i_cols);
this->set_values(i_rows, i_cols, loc_mat, loc_rhs, row_sol, col_sol);
// check consistency
double eps=4*arma::datum::eps;
// zero dirichlet rows and cols
//cout << "Dirich rows:\n" << dirichlet_rows_;
//cout << "matrix_:\n" << matrix_;
EXPECT_TRUE( arma::norm(matrix_.submat(dirichlet_rows_, non_dirichlet_rows_), "inf") < eps);
EXPECT_TRUE( arma::norm(matrix_.submat(non_dirichlet_rows_, dirichlet_rows_), "inf") < eps);
auto dirich_submat = matrix_.submat(dirichlet_rows_, dirichlet_rows_);
EXPECT_TRUE( arma::norm( dirich_submat - arma::diagmat(dirich_submat), "inf") < eps );
/*
// full check
arma::mat reduced_matrix_=full_matrix_;
auto dirich_cols=reduced_matrix_.submat(arma::span::all, dirichlet_rows_);
arma::vec reduced_rhs_=full_rhs_ - dirich_cols *dirichlet_values_;
dirich_cols.zeros();
reduced_matrix_.submat(dirichlet_rows_, arma::span::all).zeros();
reduced_matrix_.submat(dirichlet_rows_, dirichlet_rows_) = dirich_submat;
reduced_rhs_.subvec(dirichlet_rows_)=dirich_submat*dirichlet_values_;
EXPECT_TRUE( arma::all( abs(matrix_ - reduced_matrix_)<eps ) );
EXPECT_TRUE( arma::all( abs(rhs_ - reduced_rhs_)<eps ) );
*/
}
/**
* Obtains no more than maxNumSamples distinct samples. Each sample belongs to
* [loInclusive, hiExclusive).
*
* @param loInclusive The lower bound (inclusive).
* @param hiExclusive The high bound (exclusive).
* @param maxNumSamples The maximum number of samples to obtain.
* @param distinctSamples The samples that will be obtained.
*/
inline void ObtainDistinctSamples(const size_t loInclusive,
const size_t hiExclusive,
const size_t maxNumSamples,
arma::uvec& distinctSamples)
{
const size_t samplesRangeSize = hiExclusive - loInclusive;
if (samplesRangeSize > maxNumSamples)
{
arma::Col<size_t> samples;
samples.zeros(samplesRangeSize);
for (size_t i = 0; i < maxNumSamples; i++)
samples [ (size_t) math::RandInt(samplesRangeSize) ]++;
distinctSamples = arma::find(samples > 0);
if (loInclusive > 0)
distinctSamples += loInclusive;
}
else
{
distinctSamples.set_size(samplesRangeSize);
for (size_t i = 0; i < samplesRangeSize; i++)
distinctSamples[i] = loInclusive + i;
}
}
void SAC_Parallel_Plane::selectWithinDistance(arma::vec& coeff,double threshold,arma::uvec& inliers)
{
// Check if the model is valid given the user constraints
if (!isModelValid (coeff))
{
inliers.reset();
return;
}
SAC_Plane::selectWithinDistance(coeff,threshold,inliers);
}
void SVMConfiguration::setSparseData(
arma::uvec rowptr,
arma::uvec colind,
arma::vec values,
size_t nrow,
size_t ncol,
bool one_indexed
) {
// rowind and colptr are one-indexed -- we are sad
if (one_indexed) {
for (size_t i=0; i < rowptr.size(); ++i) {
rowptr[i] -= 1;
}
for (size_t i=0; i < colind.size(); ++i) {
colind[i] -= 1;
}
}
// THIS IS TRICKY:
// we are using fact that CSR format for A is CSC format for A^T
this->sparse_data = arma::sp_mat(colind, rowptr, values, ncol, nrow);
}
void InPatchGraphCut::applyToFrame(const arma::uvec& gc_label,const arma::uvec& label_indices)
{
MeshBundle<DefaultMesh>& mesh = *meshes_[current_frame_];
arma::uvec& label = labels_[current_frame_];
arma::uvec patch_label;
current_patch_graph_->sv2pix(gc_label,patch_label);
if(patch_label.size()!=label_indices.size())std::logic_error("gc_label.size()!=label_indices.size()");
arma::uvec new_patch_indices = arma::find( patch_label==0 );
arma::uvec new_patch_value = label(label_indices);
new_patch_value(new_patch_indices).fill(0);
label(label_indices) = new_patch_value;
mesh.custom_color_.fromlabel(label);
}
///
/// \brief Vespucci::Math::DimensionReduction::VCA
/// Vertex Component Analysis
/// \param R The dataset
/// \param endmembers Number of endmembers to compute
/// \param indices Row indices of pure components.
/// \param endmember_spectra Spectra of pure components (note that these are in
/// columns, not rows as in spectra_)
/// \param projected_data Projected data
/// \param fractional_abundances Purity of a given spectrum relative to endmember
/// \return Convergeance (no actual test implemented...)
///
bool Vespucci::Math::DimensionReduction::VCA(const arma::mat &R, arma::uword p,
arma::uvec &indices, arma::mat &endmember_spectra,
arma::mat &projected_data, arma::mat &fractional_abundances)
{
//Initializations
arma::uword L = R.n_rows;
arma::uword N = R.n_cols;
if (L == 0 || N == 0){
std::cerr << "No data!" << std::endl;
return false;
}
if (p > L){
std::cerr << "wrong number of endmembers (" << p << ")!"<< std::endl;
std::cerr << "set to 5 or one less than number of spectra" << std::endl;
p = (L < 5? 5: L-1);
}
//mat of SNR
arma::mat r_m = mean(R, 1);
arma::mat R_m = arma::repmat(r_m, 1, N); //the mean of each spectral band
arma::mat R_o = R - R_m; //mean-center the data
arma::mat Ud;
arma::vec Sd;
arma::mat Vd;
//arma::svds(Ud, Sd, Vd, arma::sp_mat(R_o * R_o.t()/N), p);
Vespucci::Math::DimensionReduction::svds(R_o*R_o.t()/N, p, Ud, Sd, Vd);
arma::mat x_p;
try{
x_p = Ud.t() * R_o;
}catch(std::exception e){
std::cout << "Ud.t() * R_o" << std::endl;
}
double SNR = Vespucci::Math::DimensionReduction::estimate_snr(R, r_m, x_p);
double SNR_th = 15 + 10*log10(p);
//Choose projective projection or projection to p-1 subspace
arma::mat y;
if (SNR < SNR_th){
arma::uword d = p - 1;
Ud = Ud.cols(0, d-1);
projected_data = Ud * x_p.rows(0, d-1) + R_m; //in dimension L
arma::mat x = x_p.rows(0, d-1);//x_p = trans(Ud)*R_o, p-dimensional subspace
//following three lines are one in arma::matlab...
arma::mat sum_squares = sum(pow(x, 2));
double c = sum_squares.max();
c = std::sqrt(c);
y = arma::join_vert(x, c*arma::ones(1, N));
}
else{
arma::uword d = p;
Vespucci::Math::DimensionReduction::svds(R*R.t()/N, p, Ud, Sd, Vd);
arma::svds(Ud, Sd, Vd, arma::sp_mat(R*R.t()/N), d);//R_o is a mean centered version...
x_p = Ud.t() * R;
projected_data = Ud * x_p.rows(0, d-1);
arma::mat x = Ud.t() * R;
arma::mat u = arma::mean(x, 1);
y = x / arma::repmat(sum(x % arma::repmat(u, 1, N)), d, 1);
}
// The VCA algorithm
arma::vec w;
w.set_size(p);
arma::vec f;
arma::rowvec v;
indices.set_size(p);
//there are no fill functions for arma::uvecs
for (arma::uword i = 0; i < p; ++i)
indices(i) = 0;
arma::mat A = arma::zeros(p, p);
double v_max;
double sum_squares;
arma::uvec q1;
A(p-1, 0) = 1;
for (arma::uword i = 0; i < p; ++i){
w.randu();
f = w - A*arma::pinv(A)*w;
sum_squares = sqrt(sum(square(f)));
f /= sum_squares;
v = f.t() * y;
v_max = arma::max(abs(v));
q1 = arma::find(abs(v) == v_max, 1);
indices(i) = q1(0);
A.col(i) = y.col(indices(i)); //same as x.col(indices(i));
}
endmember_spectra = projected_data.cols(indices);
fractional_abundances = arma::trans(pinv(endmember_spectra) * projected_data);
return true;
}
/* Metropolis-Hastings updates of mu
* Updates are implemented simulateaneously for all biological genes
*/
arma::mat muUpdateNoSpikes(
arma::vec const& mu0,
arma::vec const& prop_var,
arma::mat const& Counts,
arma::vec const& invdelta,
arma::vec const& nu,
arma::vec const& sum_bycell_all,
double const& s2_mu,
int const& q0,
int const& n,
arma::vec & mu1,
arma::vec & u,
arma::vec & ind,
double const& Constrain,
int const& RefGene,
arma::uvec const& ConstrainGene,
arma::uvec const& NotConstrainGene,
int const& ConstrainType)
{
using arma::span;
int nConstrainGene = ConstrainGene.size();
int nNotConstrainGene = NotConstrainGene.size();
// PROPOSAL STEP
mu1 = exp(arma::randn(q0) % sqrt(prop_var) + log(mu0));
u = arma::randu(q0);
// INITIALIZE MU
double aux; double iAux;
double sumAux = sum(log(mu0.elem(ConstrainGene))) - log(mu0(RefGene));
// ACCEPT/REJECT STEP
// Step 1: Computing the likelihood contribution of the acceptance rate
// Calculated in the same way for all genes,
// but the reference one (no need to be sequential)
arma::vec log_aux = (log(mu1) - log(mu0)) % sum_bycell_all;
for (int i=0; i < q0; i++) {
if(i != RefGene) {
for (int j=0; j < n; j++) {
log_aux(i) -= ( Counts(i,j) + invdelta(i) ) *
log( ( nu(j)*mu1(i) + invdelta(i) ) /
( nu(j)*mu0(i) + invdelta(i) ));
}
}
}
// Step 2: Computing prior component of the acceptance rate
// Step 2.1: For genes that are under the constrain (excluding the reference one)
for (int i=0; i < nConstrainGene; i++) {
iAux = ConstrainGene(i);
if(iAux != RefGene) {
aux = 0.5 * (ConstrainGene.size() * Constrain - (sumAux - log(mu0(iAux))));
log_aux(iAux) -= (0.5 * 2 /s2_mu) * (pow(log(mu1(iAux)) - aux,2));
log_aux(iAux) += (0.5 * 2 /s2_mu) * (pow(log(mu0(iAux)) - aux,2));
// ACCEPT REJECT
if((log(u(iAux)) < log_aux(iAux)) & (mu1(iAux) > 1e-3)) {
ind(iAux) = 1; sumAux += log(mu1(iAux)) - log(mu0(iAux));
}
else{ind(iAux) = 0; mu1(iAux) = mu0(iAux); }
}
}
// Step 2.2: For the reference gene
ind(RefGene) = 1;
mu1(RefGene) = exp(ConstrainGene.size() * Constrain - sumAux);
// Step 2.3: For genes that are *not* under the constrain
// Only relevant for a trimmed constrain
if(ConstrainType == 2) {
for (int i=0; i < nNotConstrainGene; i++) {
iAux = NotConstrainGene(i);
log_aux(iAux) -= (0.5/s2_mu) * (pow(log(mu1(iAux)),2) - pow(log(mu0(iAux)),2));
// ACCEPT REJECT
if((log(u(iAux)) < log_aux(iAux)) & (mu1(iAux) > 1e-3)) { ind(iAux) = 1; }
else{ind(iAux) = 0; mu1(iAux) = mu0(iAux);}
}
}
// OUTPUT
return join_rows(mu1, ind);
}
List objectivex(const arma::mat& transition, const arma::cube& emission,
const arma::vec& init, const arma::ucube& obs, const arma::umat& ANZ,
const arma::ucube& BNZ, const arma::uvec& INZ, const arma::uvec& nSymbols,
const arma::mat& coef, const arma::mat& X, arma::uvec& numberOfStates,
unsigned int threads) {
unsigned int q = coef.n_rows;
arma::vec grad(
arma::accu(ANZ) + arma::accu(BNZ) + arma::accu(INZ) + (numberOfStates.n_elem- 1) * q,
arma::fill::zeros);
arma::mat weights = exp(X * coef).t();
if (!weights.is_finite()) {
grad.fill(-arma::datum::inf);
return List::create(Named("objective") = arma::datum::inf, Named("gradient") = wrap(grad));
}
weights.each_row() /= sum(weights, 0);
arma::mat initk(emission.n_rows, obs.n_slices);
for (unsigned int k = 0; k < obs.n_slices; k++) {
initk.col(k) = init % reparma(weights.col(k), numberOfStates);
}
arma::uvec cumsumstate = arma::cumsum(numberOfStates);
unsigned int error = 0;
double ll = 0;
#pragma omp parallel for if(obs.n_slices >= threads) schedule(static) reduction(+:ll) num_threads(threads) \
default(none) shared(q, grad, nSymbols, ANZ, BNZ, INZ, \
numberOfStates, cumsumstate, obs, init, initk, X, weights, transition, emission, error)
for (unsigned int k = 0; k < obs.n_slices; k++) {
if (error == 0) {
arma::mat alpha(emission.n_rows, obs.n_cols); //m,n
arma::vec scales(obs.n_cols); //n
arma::sp_mat sp_trans(transition);
uvForward(sp_trans.t(), emission, initk.col(k), obs.slice(k), alpha, scales);
arma::mat beta(emission.n_rows, obs.n_cols); //m,n
uvBackward(sp_trans, emission, obs.slice(k), beta, scales);
int countgrad = 0;
arma::vec grad_k(grad.n_elem, arma::fill::zeros);
// transitionMatrix
if (arma::accu(ANZ) > 0) {
for (unsigned int jj = 0; jj < numberOfStates.n_elem; jj++) {
arma::vec gradArow(numberOfStates(jj));
arma::mat gradA(numberOfStates(jj), numberOfStates(jj));
int ind_jj = cumsumstate(jj) - numberOfStates(jj);
for (unsigned int i = 0; i < numberOfStates(jj); i++) {
arma::uvec ind = arma::find(ANZ.row(ind_jj + i).subvec(ind_jj, cumsumstate(jj) - 1));
if (ind.n_elem > 0) {
gradArow.zeros();
gradA.eye();
gradA.each_row() -= transition.row(ind_jj + i).subvec(ind_jj, cumsumstate(jj) - 1);
gradA.each_col() %= transition.row(ind_jj + i).subvec(ind_jj, cumsumstate(jj) - 1).t();
for (unsigned int j = 0; j < numberOfStates(jj); j++) {
for (unsigned int t = 0; t < (obs.n_cols - 1); t++) {
double tmp = alpha(ind_jj + i, t);
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(ind_jj + j, obs(r, t + 1, k), r);
}
gradArow(j) += tmp * beta(ind_jj + j, t + 1);
}
}
gradArow = gradA * gradArow;
grad_k.subvec(countgrad, countgrad + ind.n_elem - 1) = gradArow.rows(ind);
countgrad += ind.n_elem;
}
}
}
}
if (arma::accu(BNZ) > 0) {
// emissionMatrix
for (unsigned int r = 0; r < obs.n_rows; r++) {
arma::vec gradBrow(nSymbols(r));
arma::mat gradB(nSymbols(r), nSymbols(r));
for (unsigned int i = 0; i < emission.n_rows; i++) {
arma::uvec ind = arma::find(BNZ.slice(r).row(i));
if (ind.n_elem > 0) {
gradBrow.zeros();
gradB.eye();
gradB.each_row() -= emission.slice(r).row(i).subvec(0, nSymbols(r) - 1);
gradB.each_col() %= emission.slice(r).row(i).subvec(0, nSymbols(r) - 1).t();
for (unsigned int j = 0; j < nSymbols(r); j++) {
if (obs(r, 0, k) == j) {
double tmp = initk(i, k);
for (unsigned int r2 = 0; r2 < obs.n_rows; r2++) {
if (r2 != r) {
tmp *= emission(i, obs(r2, 0, k), r2);
}
}
gradBrow(j) += tmp * beta(i, 0);
}
for (unsigned int t = 0; t < (obs.n_cols - 1); t++) {
if (obs(r, t + 1, k) == j) {
double tmp = beta(i, t + 1);
for (unsigned int r2 = 0; r2 < obs.n_rows; r2++) {
if (r2 != r) {
tmp *= emission(i, obs(r2, t + 1, k), r2);
}
}
gradBrow(j) += arma::dot(alpha.col(t), transition.col(i)) * tmp;
}
}
}
gradBrow = gradB * gradBrow;
grad_k.subvec(countgrad, countgrad + ind.n_elem - 1) = gradBrow.rows(ind);
countgrad += ind.n_elem;
}
}
}
}
if (arma::accu(INZ) > 0) {
for (unsigned int i = 0; i < numberOfStates.n_elem; i++) {
int ind_i = cumsumstate(i) - numberOfStates(i);
arma::uvec ind = arma::find(
INZ.subvec(ind_i, cumsumstate(i) - 1));
if (ind.n_elem > 0) {
arma::vec gradIrow(numberOfStates(i), arma::fill::zeros);
for (unsigned int j = 0; j < numberOfStates(i); j++) {
double tmp = weights(i, k);
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(ind_i + j, obs(r, 0, k), r);
}
gradIrow(j) += tmp * beta(ind_i + j, 0);
}
arma::mat gradI(numberOfStates(i), numberOfStates(i), arma::fill::zeros);
gradI.eye();
gradI.each_row() -= init.subvec(ind_i, cumsumstate(i) - 1).t();
gradI.each_col() %= init.subvec(ind_i, cumsumstate(i) - 1);
gradIrow = gradI * gradIrow;
grad_k.subvec(countgrad, countgrad + ind.n_elem - 1) = gradIrow.rows(ind);
countgrad += ind.n_elem;
}
}
}
for (unsigned int jj = 1; jj < numberOfStates.n_elem; jj++) {
unsigned int ind_jj = (cumsumstate(jj) - numberOfStates(jj));
for (unsigned int j = 0; j < emission.n_rows; j++) {
double tmp = 1.0;
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(j, obs(r, 0, k), r);
}
if ((j >= ind_jj) & (j < cumsumstate(jj))) {
grad_k.subvec(countgrad + q * (jj - 1), countgrad + q * jj - 1) += tmp
* beta(j, 0) * initk(j, k) * X.row(k).t() * (1.0 - weights(jj, k));
} else {
grad_k.subvec(countgrad + q * (jj - 1), countgrad + q * jj - 1) -= tmp
* beta(j, 0) * initk(j, k) * X.row(k).t() * weights(jj, k);
}
}
}
if (!scales.is_finite() || !beta.is_finite()) {
#pragma omp atomic
error++;
} else {
ll -= arma::sum(log(scales));
#pragma omp critical
grad += grad_k;
}
}
}
if(error > 0){
ll = -arma::datum::inf;
grad.fill(-arma::datum::inf);
}
return List::create(Named("objective") = -ll, Named("gradient") = wrap(-grad));
}
inline TR TrX(const T1& rho1, arma::uvec sys, arma::uvec dim) {
const auto& p = as_Mat(rho1);
bool checkV = true;
if (p.n_cols == 1)
checkV = false;
#ifndef QICLIB_NO_DEBUG
if (p.n_elem == 0)
throw Exception("qic::TrX", Exception::type::ZERO_SIZE);
if (checkV)
if (p.n_rows != p.n_cols)
throw Exception("qic::TrX",
Exception::type::MATRIX_NOT_SQUARE_OR_CVECTOR);
if (dim.n_elem == 0 || arma::any(dim == 0))
throw Exception("qic::TrX", Exception::type::INVALID_DIMS);
if (arma::prod(dim) != p.n_rows)
throw Exception("qic::TrX", Exception::type::DIMS_MISMATCH_MATRIX);
if (dim.n_elem < sys.n_elem || arma::any(sys == 0) ||
arma::any(sys > dim.n_elem) ||
sys.n_elem != arma::find_unique(sys, false).eval().n_elem)
throw Exception("qic::TrX", Exception::type::INVALID_SUBSYS);
#endif
if (sys.n_elem == dim.n_elem)
return {arma::trace(p)};
_internal::dim_collapse_sys(dim, sys);
const arma::uword n = dim.n_elem;
const arma::uword m = sys.n_elem;
arma::uvec keep(n - m);
arma::uword keep_count(0);
for (arma::uword run = 0; run < n; ++run) {
if (!arma::any(sys == run + 1)) {
keep.at(keep_count) = run + 1;
++keep_count;
}
}
arma::uword dimtrace = arma::prod(dim(sys - 1));
arma::uword dimkeep = p.n_rows / dimtrace;
arma::uvec product(n, arma::fill::ones);
for (arma::sword i = n - 2; i > -1; --i)
product.at(i) = product.at(i + 1) * dim.at(i + 1);
arma::uvec productr(n - m, arma::fill::ones);
for (arma::sword i = n - m - 2; i > -1; --i)
productr.at(i) = productr.at(i + 1) * dim.at(keep.at(i + 1) - 1);
arma::Mat<trait::eT<T1> > tr_p(dimkeep, dimkeep, arma::fill::zeros);
const arma::uword loop_no = 2 * n;
arma::uword* loop_counter = new arma::uword[loop_no + 1];
arma::uword* MAX = new arma::uword[loop_no + 1];
for (arma::uword i = 0; i < n; ++i) {
MAX[i] = dim.at(i);
if (arma::any(sys == (i + 1)))
MAX[i + n] = 1;
else
MAX[i + n] = dim.at(i);
}
MAX[loop_no] = 2;
for (arma::uword i = 0; i < loop_no + 1; ++i) loop_counter[i] = 0;
arma::uword p1 = 0;
while (loop_counter[loop_no] == 0) {
arma::uword I(0), J(0), K(0), L(0), n_to_k(0);
for (arma::uword i = 0; i < n; ++i) {
if (arma::any(sys == i + 1)) {
I += product.at(i) * loop_counter[i];
J += product.at(i) * loop_counter[i];
} else {
I += product.at(i) * loop_counter[i];
J += product.at(i) * loop_counter[i + n];
}
if (arma::any(keep == i + 1)) {
K += productr.at(n_to_k) * loop_counter[i];
L += productr.at(n_to_k) * loop_counter[i + n];
++n_to_k;
}
}
tr_p.at(K, L) += checkV ? p.at(I, J) : p.at(I) * std::conj(p.at(J));
++loop_counter[0];
while (loop_counter[p1] == MAX[p1]) {
loop_counter[p1] = 0;
loop_counter[++p1]++;
if (loop_counter[p1] != MAX[p1])
p1 = 0;
}
}
delete[] loop_counter;
delete[] MAX;
return tr_p;
}
inline TR sysperm(const T1& rho1, const arma::uvec& sys,
const arma::uvec& dim) {
const auto& p = as_Mat(rho1);
const arma::uword n = dim.n_elem;
bool checkV = true;
if (p.n_cols == 1)
checkV = false;
#ifndef QICLIB_NO_DEBUG
if (p.n_elem == 0)
throw Exception("qic::sysperm", Exception::type::ZERO_SIZE);
if (checkV)
if (p.n_rows != p.n_cols)
throw Exception("qic::sysperm",
Exception::type::MATRIX_NOT_SQUARE_OR_CVECTOR);
if (dim.n_elem == 0 || arma::any(dim == 0))
throw Exception("qic::sysperm", Exception::type::INVALID_DIMS);
if (arma::prod(dim) != p.n_rows)
throw Exception("qic::sysperm", Exception::type::DIMS_MISMATCH_MATRIX);
if (n != sys.n_elem || arma::any(sys == 0) || arma::any(sys > n) ||
sys.n_elem != arma::unique(sys).eval().n_elem)
throw Exception("qic::sysperm", Exception::type::PERM_INVALID);
#endif
arma::uword product[_internal::MAXQDIT];
product[n-1] = 1;
for (arma::sword i = n - 2; i >= 0; --i)
product[i] = product[i + 1] * dim.at(i + 1);
arma::uword productr[_internal::MAXQDIT];
productr[n-1] = 1;
for (arma::sword i = n - 2; i >= 0; --i)
productr[i] = productr[i + 1] * dim.at(sys.at(i + 1) - 1);
if (checkV) {
arma::Mat<trait::eT<T1> > p_r(p.n_rows, p.n_cols, arma::fill::zeros);
const arma::uword loop_no = 2 * n;
constexpr auto loop_no_buffer = 2 * _internal::MAXQDIT + 1;
arma::uword loop_counter[loop_no_buffer] = {0};
arma::uword MAX[loop_no_buffer];
for (arma::uword i = 0; i < n; ++i) {
MAX[i] = dim.at(i);
MAX[i + n] = dim.at(i);
}
MAX[loop_no] = 2;
arma::uword p1 = 0;
while (loop_counter[loop_no] == 0) {
arma::uword I(0), J(0), K(0), L(0);
for (arma::uword i = 0; i < n; ++i) {
I += product[i] * loop_counter[i];
J += product[i] * loop_counter[i + n];
K += productr[i] * loop_counter[sys.at(i) - 1];
L += productr[i] * loop_counter[sys.at(i) + n - 1];
}
p_r.at(K, L) = p.at(I, J);
++loop_counter[0];
while (loop_counter[p1] == MAX[p1]) {
loop_counter[p1] = 0;
loop_counter[++p1]++;
if (loop_counter[p1] != MAX[p1])
p1 = 0;
}
}
return p_r;
} else {
arma::Col<trait::eT<T1> > p_r(p.n_rows, arma::fill::zeros);
const arma::uword loop_no = n;
constexpr auto loop_no_buffer = _internal::MAXQDIT + 1;
arma::uword loop_counter[loop_no_buffer] = {0};
arma::uword MAX[loop_no_buffer];
for (arma::uword i = 0; i < n; ++i) MAX[i] = dim.at(i);
MAX[loop_no] = 2;
for (arma::uword i = 0; i < loop_no + 1; ++i) loop_counter[i] = 0;
arma::uword p1 = 0;
while (loop_counter[loop_no] == 0) {
arma::uword I(0), K(0);
for (arma::uword i = 0; i < n; ++i) {
I += product[i] * loop_counter[i];
K += productr[i] * loop_counter[sys.at(i) - 1];
}
p_r.at(K) = p.at(I);
++loop_counter[0];
while (loop_counter[p1] == MAX[p1]) {
loop_counter[p1] = 0;
loop_counter[++p1]++;
if (loop_counter[p1] != MAX[p1])
p1 = 0;
}
}
return p_r;
}
}
TR discord3_reg(const T1& rho1, arma::uword nodal, arma::uvec dim) {
const auto& rho = as_Mat(rho1);
arma::uword party_no = dim.n_elem;
arma::uword dim1 = arma::prod(dim);
#ifndef QICLIB_NO_DEBUG
if (rho.n_elem == 0)
throw Exception("qic::discord3_reg", Exception::type::ZERO_SIZE);
if (rho.n_rows != rho.n_cols)
throw Exception("qic::discord3_reg", Exception::type::MATRIX_NOT_SQUARE);
if (any(dim == 0))
throw Exception("qic::discord3_reg", Exception::type::INVALID_DIMS);
if (dim1 != rho.n_rows)
throw Exception("qic::discord3_reg", Exception::type::DIMS_MISMATCH_MATRIX);
if (nodal <= 0 || nodal > party_no)
throw Exception("qic::discord3_reg", "Invalid measured party index");
if (dim(nodal - 1) != 3)
throw Exception("qic::discord3_reg", "Measured party is not qutrit");
#endif
arma::uvec party = arma::zeros<arma::uvec>(party_no);
for (arma::uword i = 0; i < party_no; ++i) party.at(i) = i + 1;
arma::uvec rest = party;
rest.shed_row(nodal - 1);
auto rho_A = TrX(rho, rest, dim);
auto rho_B = TrX(rho, {nodal}, dim);
auto S_A = entropy(rho_A);
auto S_B = entropy(rho_B);
auto S_A_B = entropy(rho);
auto I1 = S_A + S_B - S_A_B;
dim1 /= 3;
arma::uword dim2(1);
for (arma::uword i = 0; i < nodal - 1; ++i) dim2 *= dim.at(i);
arma::uword dim3(1);
for (arma::uword i = nodal; i < party_no; ++i) dim3 *= dim.at(i);
arma::Mat<trait::pT<T1> > eye2 =
arma::eye<arma::Mat<trait::pT<T1> > >(dim1, dim1);
arma::Mat<trait::pT<T1> > eye3 =
arma::eye<arma::Mat<trait::pT<T1> > >(dim2, dim2);
arma::Mat<trait::pT<T1> > eye4 =
arma::eye<arma::Mat<trait::pT<T1> > >(dim3, dim3);
typename arma::Col<trait::pT<T1> >::template fixed<3> disc;
for (arma::uword i = 0; i < 3; ++i) {
arma::Mat<std::complex<trait::pT<T1> > > proj1 =
SPM<trait::pT<T1> >::get_instance().proj3.at(0, i + 1);
arma::Mat<std::complex<trait::pT<T1> > > proj2 =
SPM<trait::pT<T1> >::get_instance().proj3.at(1, i + 1);
arma::Mat<std::complex<trait::pT<T1> > > proj3 =
SPM<trait::pT<T1> >::get_instance().proj3.at(2, i + 1);
if (nodal == 1) {
proj1 = kron(proj1, eye2);
proj2 = kron(proj2, eye2);
proj3 = kron(proj3, eye2);
} else if (party_no == nodal) {
proj1 = kron(eye2, proj1);
proj2 = kron(eye2, proj2);
proj3 = kron(eye2, proj3);
} else {
proj1 = kron(kron(eye3, proj1), eye4);
proj2 = kron(kron(eye3, proj2), eye4);
proj3 = kron(kron(eye3, proj3), eye4);
}
arma::Mat<std::complex<trait::pT<T1> > > rho_1 = (proj1 * rho * proj1);
arma::Mat<std::complex<trait::pT<T1> > > rho_2 = (proj2 * rho * proj2);
arma::Mat<std::complex<trait::pT<T1> > > rho_3 = (proj3 * rho * proj3);
trait::pT<T1> p1 = std::real(arma::trace(rho_1));
trait::pT<T1> p2 = std::real(arma::trace(rho_2));
trait::pT<T1> p3 = std::real(arma::trace(rho_3));
trait::pT<T1> S_max = 0.0;
if (p1 > _precision::eps<trait::pT<T1> >::value) {
rho_1 /= p1;
S_max += p1 * entropy(rho_1);
}
if (p2 > _precision::eps<trait::pT<T1> >::value) {
rho_2 /= p2;
S_max += p2 * entropy(rho_2);
}
if (p3 > _precision::eps<trait::pT<T1> >::value) {
rho_3 /= p3;
S_max += p3 * entropy(rho_3);
}
disc.at(i) = I1 - (S_B - S_max);
}
return disc;
}
void PZStability::real_imag_idx(arma::uvec & idxr, arma::uvec & idxi) const {
if(!cplx) {
ERROR_INFO();
throw std::runtime_error("Should not call real_imag_idx for purely real calculation!\n");
}
// Count amount of parameters
size_t nreal=0, nimag=0;
if(cancheck) {
nreal+=oa*va;
nimag+=oa*va;
if(!restr) {
nreal+=ob*vb;
nimag+=ob*vb;
}
}
if(oocheck) {
nreal+=oa*(oa-1)/2;
if(cplx)
nimag+=oa*(oa+1)/2;
if(!restr) {
nreal+=ob*(ob-1)/2;
if(cplx)
nimag+=ob*(ob+1)/2;
}
}
// Sanity check
if(nreal+nimag != count_params()) {
ERROR_INFO();
throw std::runtime_error("Parameter count is wrong!\n");
}
// Parameter indices
idxr.zeros(nreal);
idxi.zeros(nimag);
// Fill indices.
size_t ir=0, ii=0;
// Offset
size_t ioff=0;
if(cancheck) {
// First are the real parameters
for(size_t irot=0;irot<oa*va;irot++) {
idxr(ir++)=irot;
}
ioff+=oa*va;
// followed by the imaginary parameters
for(size_t irot=0;irot<oa*va;irot++)
idxi(ii++)=irot+ioff;
ioff+=oa*va;
if(!restr) {
// and then again the real parameters
for(size_t irot=0;irot<ob*vb;irot++)
idxr(ir++)=irot + ioff;
ioff+=ob*vb;
// followed by the imaginary parameters
for(size_t irot=0;irot<ob*vb;irot++)
idxi(ii++)=irot + ioff;
ioff+=ob*vb;
}
}
if(oocheck) {
// First are the real parameters
for(size_t irot=0;irot<oa*(oa-1)/2;irot++) {
idxr(ir++)=irot+ioff;
}
ioff+=oa*(oa-1)/2;
// and then the imaginary parameters
for(size_t irot=0;irot<oa*(oa+1)/2;irot++)
idxi(ii++)=irot + ioff;
ioff+=oa*(oa+1)/2;
if(!restr) {
// First are the real parameters
for(size_t irot=0;irot<ob*(ob-1)/2;irot++) {
idxr(ir++)=irot+ioff;
}
ioff+=ob*(ob-1)/2;
// and then the imaginary parameters
for(size_t irot=0;irot<ob*(ob+1)/2;irot++)
idxi(ii++)=irot + ioff;
ioff+=ob*(ob+1)/2;
}
}
// Sanity check
arma::uvec idx(nreal+nimag);
idx.subvec(0,nreal-1)=idxr;
idx.subvec(nreal,nreal+nimag-1)=idxi;
idx=arma::sort(idx,"ascending");
for(size_t i=0;i<idx.n_elem;i++)
if(idx(i)!=i) {
std::ostringstream oss;
oss << "Element " << i << " of compound index is wrong: " << idx(i) << "!\n";
throw std::runtime_error(oss.str());
}
}
bool Partition(arma::mat &A, arma::uvec &label, int &nGroups){
// to do
int N = A.n_rows;
arma::uvec parent(N);
arma::uvec rank;
for (int i = 0; i < N; i++){
parent(i) = i;
}
rank.zeros(N, 1);
arma::uvec ori_parent(parent);
for (int i = 0; i < N; i++){
// check equal items
for (int j = 0; j < N; j++){
if (A(i, j) == 0){
continue;
}
// find root of node i and compress path
int root_i = Find(parent, i);
// find root of node j and compress path
int root_j = Find(parent, j);
// union both trees
if (root_j != root_i){
if (rank(root_j) < rank(root_i)){
parent(root_j) = root_i;
}
else if (rank(root_i) < rank(root_j)){
parent(root_i) = root_j;
}
else{
parent(root_j) = root_i;
rank(root_i) = rank(root_i) + 1;
}
}
}
}
//parent.print("parent:");
//rank.print("rank:");
// label each element
arma::uvec flag = parent == ori_parent;
nGroups = arma::sum(flag);
label.zeros(N,1);
// matlab: label(flag) = 1:nGroups
int t = 1;
for (int i = 0; i < N; i++){
if (flag(i)){
label(i) = t++;
}
}
//label.print("label");
int root_i;
for (int i = 0; i < N; i++){
if (parent(i) == i){
continue;
}
// find root of node i
root_i = Find(parent, i);
label(i) = label(root_i);
}
//label.print("label:");
//cout << "nGroups:" << nGroups << endl;
return true;
}
