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// Copyright (c) 1997-2007 ETH Zurich (Switzerland). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/QP_solver/include/CGAL/QP_solver/QP_basis_inverse_impl.h $ // $Id: include/CGAL/QP_solver/QP_basis_inverse_impl.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Sven Schoenherr // Bernd Gaertner // Franz Wessendorp // Kaspar Fischer #ifndef CGAL_QP_SOLVER_QP_BASIS_INVERSE_IMPL_H #define CGAL_QP_SOLVER_QP_BASIS_INVERSE_IMPL_H #include namespace CGAL { // ============================= // class implementation (cont'd) // ============================= // creation and initialization // --------------------------- // set-up template < class ET_, class Is_LP_ > void QP_basis_inverse:: set( int n, int m, int nr_equalities) { CGAL_qpe_assertion( n >= 0); CGAL_qpe_assertion( m >= 0); b = s = 0; // l is the maximum size of the basis in phase I l = (std::min)( n+nr_equalities+1, m); if ( ! M.empty()) M.clear(); set( Is_LP()); if ( ! x_l.empty()) x_l.clear(); if ( ! x_x.empty()) x_x.clear(); x_l.insert( x_l.end(), l, et0); x_x.insert( x_x.end(), l, et0); // has to grow later QP-case if ( ! tmp_l.empty()) tmp_l.clear(); if ( ! tmp_x.empty()) tmp_x.clear(); tmp_l.insert( tmp_l.end(), l, et0); tmp_x.insert( tmp_x.end(), l, et0); // has to grow later QP-case } // update functions // ---------------- // leaving of original variable (update type U2) template < class ET_, class Is_LP_ > void QP_basis_inverse:: leave_original( ) { // assert QP case Assert_compile_time_tag( Tag_false(), Is_LP()); // determine new denominator (`z') --b; ET z = M[ l+b][ l+b]; bool z_neg = ( z < et0); CGAL_qpe_assertion( z != et0); // update matrix in place update_inplace_QP( M[ l+b].begin(), M[ l+b].begin()+l, -z, ( z_neg ? d : -d)); // store new denominator d = ( z_neg ? -z : z); CGAL_qpe_assertion( d > et0); CGAL_qpe_debug { if ( vout.verbose()) print(); } } // entering of slack variable (update type U3) template < class ET_, class Is_LP_ > void QP_basis_inverse:: enter_slack( ) { // assert QP case Assert_compile_time_tag( Tag_false(), Is_LP()); // determine new denominator (`z') --s; ET z = M[ s][ s]; bool z_neg = ( z < et0); CGAL_qpe_assertion( z != et0); // update matrix in place typename Matrix::iterator col_it; typename Row ::iterator x_it; unsigned int col; for ( col = 0, col_it = M.begin()+l, x_it = x_x.begin(); col < b; ++col, ++col_it, ++x_it ) { *x_it = (*col_it)[ s]; } update_inplace_QP( M[ s].begin(), x_x.begin(), -z, ( z_neg ? d : -d)); // store new denominator d = ( z_neg ? -z : z); CGAL_qpe_assertion( d > et0); CGAL_qpe_debug { if ( vout.verbose()) print(); } } // replacing of original by slack variable (update type U8) template < class ET_, class Is_LP_ > void QP_basis_inverse:: enter_slack_leave_original( ) { // assert LP case or phase I CGAL_qpe_assertion( is_LP || is_phaseI); // update matrix in-place // ---------------------- typename Matrix::iterator matrix_it; typename Row ::iterator x_it; unsigned int row; // QP (in phase I)? matrix_it = M.begin(); if ( is_QP) matrix_it += l; // get last column of basis inverse (store it in 'x_x') --s; --b; for ( row = 0, x_it = x_x.begin(); row < s; ++row, ++x_it, ++matrix_it) { *x_it = (*matrix_it)[ b]; } ET z = (*matrix_it)[ b]; bool z_neg = ( z < et0); CGAL_qpe_assertion( z != et0); // update matrix update_inplace_LP( matrix_it->begin(), x_x.begin(), -z, ( z_neg ? d : -d)); // store new denominator // --------------------- d = ( z_neg ? -z : z); CGAL_qpe_assertion( d > et0); CGAL_qpe_debug { if ( vout.verbose()) print(); } } // replacing of original by original variable with precondition in QP-case // for phaseII (update type UZ_1) template < class ET_, class Is_LP_ > template < class ForwardIterator > void QP_basis_inverse:: z_replace_original_by_original(ForwardIterator y_l_it, ForwardIterator y_x_it, const ET& s_delta, const ET& s_nu, unsigned int k_i) { // assert QP case and phaseII CGAL_qpe_assertion(is_QP && is_phaseII); // prepare \hat{k}_{1} -scalar ET hat_k_1 = *(y_x_it + k_i); // prepare \hat{\rho} -vector in x_l, x_x copy_row_in_B_O(x_l.begin(), x_x.begin(), k_i); // prepare \hat{v} -vector in tmp_l, tmp_x // tmp_l -part std::transform(y_l_it, (y_l_it+s), x_l.begin(), tmp_l.begin(), [&s_delta](const ET& v1, const ET& v2){ return std::plus()(v1, s_delta * v2); }); // tmp_x -part std::transform(y_x_it, (y_x_it+b), x_x.begin(), tmp_x.begin(), [&s_delta](const ET& v1, const ET& v2){ return std::plus()(v1, s_delta * v2); }); tmp_x[k_i] -= d; // prepare \hat{k}_{2} -scalar ET hat_k_2 = s_nu - (et2 * s_delta * hat_k_1); CGAL_qpe_assertion( d != et0); // update matrix in place z_update_inplace(x_l.begin(), x_x.begin(), tmp_l.begin(), tmp_x.begin(), hat_k_1 * hat_k_1, -hat_k_2, -hat_k_1, d*d); // store new denominator d = CGAL::integral_division(hat_k_1 * hat_k_1, d); CGAL_qpe_assertion( d > et0); CGAL_qpe_debug { if ( vout.verbose()) print(); } } // replacing of original by slack variable with precondition in QP-case // for phaseII (update type UZ_2) template < class ET_, class Is_LP_ > void QP_basis_inverse:: z_replace_original_by_slack( ) { // assert QP case and phaseII CGAL_qpe_assertion(is_QP && is_phaseII); // adapt s and b --s; --b; // prepare \hat{\rho} -vector in x_l, x_x copy_row_in_B_O(x_l.begin(), x_x.begin(), b); // prepare \hat{\varrho} -vector in tmp_l, tmp_x copy_row_in_C(tmp_l.begin(), tmp_x.begin(), s); // prepare \hat{\kappa} -scalar ET hat_kappa = M[l+b][s]; // prepare \hat{\xi} -scalar ET hat_xi = M[s][s]; CGAL_qpe_assertion( d != et0); // update matrix in place z_update_inplace(x_l.begin(), x_x.begin(), tmp_l.begin(), tmp_x.begin(), hat_kappa * hat_kappa, hat_xi, -hat_kappa, d * d); // store new denominator d = CGAL::integral_division(hat_kappa * hat_kappa, d); CGAL_qpe_assertion( d > et0); CGAL_qpe_debug { if ( vout.verbose()) print(); } } // replacing of slack by original variable with precondition in QP-case // for phaseII (update type UZ_3) template < class ET_, class Is_LP_ > template < class ForwardIterator > void QP_basis_inverse:: z_replace_slack_by_original(ForwardIterator y_l_it, ForwardIterator y_x_it, ForwardIterator u_x_it, const ET& hat_kappa, const ET& hat_nu) { // assert QP case and phaseII CGAL_qpe_assertion(is_QP && is_phaseII); // get copies of y_l_it and y_x_it for later use ForwardIterator y_l_it_copy = y_l_it; ForwardIterator y_x_it_copy = y_x_it; CGAL_qpe_assertion( d != et0); // prepare \hat{\phi} // prepare \hat{\varphi} -vector in x_l, x_x multiply(u_x_it, u_x_it, x_l.begin(), x_x.begin(), Tag_false(), Tag_false()); // prepare \hat{\kappa} -scalar // prepare \hat{\nu} -scalar // update matrix in place z_update_inplace(x_l.begin(), x_x.begin(), y_l_it, y_x_it, hat_kappa * hat_kappa, -hat_nu, hat_kappa, d * d); // append new rows and columns // --------------------------- typename Row ::iterator row_it, x_l_it, x_x_it; typename Matrix::iterator matrix_it; unsigned int count; // insert new row and column at the end of block P CGAL_qpe_assertion(M.size()>=s+1); if (M[s].size()==0) { // row has to be filled first M[s].insert(M[s].end(), s+1, et0); } // P-block: left of diagonal (including element on diagonal) y_l_it = y_l_it_copy; for ( row_it = M[s].begin(), x_l_it = x_l.begin(); row_it != M[s].end() - 1; ++row_it, ++x_l_it, ++y_l_it ) { *row_it = CGAL::integral_division((hat_nu * *x_l_it)-(hat_kappa * *y_l_it), d); } *row_it = -hat_nu; // Q-block y_x_it = y_x_it_copy; for ( matrix_it = M.begin()+l, count = 0, x_x_it = x_x.begin(); count < b; ++matrix_it, ++count, ++x_x_it, ++y_x_it ) { (*matrix_it)[s] = CGAL::integral_division((hat_nu * *x_x_it) - (hat_kappa * *y_x_it), d); } // insert new row and column at the end of blocks Q and R ensure_physical_row(l+b); // Q-block for ( row_it = M[l+b].begin(), count = 0, x_l_it = x_l.begin(); count < s; ++row_it, ++count, ++x_l_it ) { *row_it = CGAL::integral_division(-hat_kappa * *x_l_it, d); } *row_it = hat_kappa; // R-block for ( row_it = M[l+b].begin()+l, count = 0, x_x_it = x_x.begin(); count < b; ++row_it, ++count, ++x_x_it ) { *row_it = CGAL::integral_division(-hat_kappa * *x_x_it, d); } *row_it = et0; //adapt s and b ++s; ++b; // store new denominator d = CGAL::integral_division(hat_kappa * hat_kappa, d); CGAL_qpe_assertion( d > et0); CGAL_qpe_debug { if ( vout.verbose()) print(); } } // replacing of slack by slack variable with precondition in QP-case // for phaseII (update type UZ_4) template < class ET_, class Is_LP_ > template < class ForwardIterator > void QP_basis_inverse:: z_replace_slack_by_slack(ForwardIterator u_x_it, unsigned int k_j) { // assert QP case and phaseII CGAL_qpe_assertion(is_QP && is_phaseII); // prepare \hat{v} -vector in x_l, x_x multiply(u_x_it, u_x_it, x_l.begin(), x_x.begin(),Tag_false(), Tag_false()); x_l[k_j] -= d; // prepare \hat{\varrho} -vector in tmp_l, tmp_x copy_row_in_C(tmp_l.begin(), tmp_x.begin(), k_j); // prepare \hat{k}_{1} -scalar ET hat_k_1 = inner_product_x(tmp_x.begin(), u_x_it); // prepare \hat{k}_{3} -scalar ET hat_k_3 = -M[k_j][k_j]; CGAL_qpe_assertion( d != et0); // update matrix in place z_update_inplace(x_l.begin(), x_x.begin(), tmp_l.begin(), tmp_x.begin(), hat_k_1 * hat_k_1, -hat_k_3, -hat_k_1, d * d); // store new denominator d = CGAL::integral_division(hat_k_1 * hat_k_1, d); CGAL_qpe_assertion( d > et0); CGAL_qpe_debug { if ( vout.verbose()) print(); } } // copying of reduced basis inverse row in (upper) C-half template < class ET_, class Is_LP_ > template < class OutIt > void QP_basis_inverse:: copy_row_in_C(OutIt y_l_it, OutIt y_x_it, unsigned int r) { typename Matrix::const_iterator matrix_it; typename Row ::const_iterator row_it; unsigned int count; // P-block: left of diagonal (including element on diagonal) matrix_it = M.begin()+r; for ( row_it = matrix_it->begin(); row_it != matrix_it->end(); ++row_it, ++y_l_it ) { *y_l_it = *row_it; } // P-block: right of diagonal (excluding element on diagonal) for ( matrix_it = M.begin()+r+1, count = r+1; count < s; ++matrix_it, ++count, ++y_l_it ) { *y_l_it = (*matrix_it)[r]; } // Q-block for ( matrix_it = M.begin()+l, count = 0; count < b; ++matrix_it, ++count, ++y_x_it ) { *y_x_it = (*matrix_it)[r]; } } // copying of reduced basis inverse row in (lower) B_O-half template < class ET_, class Is_LP_ > template < class OutIt > void QP_basis_inverse:: copy_row_in_B_O(OutIt y_l_it, OutIt y_x_it, unsigned int r) { typename Matrix::const_iterator matrix_it; typename Row ::const_iterator row_it; unsigned int count; // Q-block matrix_it = M.begin()+l+r; for ( row_it = matrix_it->begin(), count = 0; count < s; ++row_it, ++count, ++y_l_it ) { *y_l_it = *row_it; } // R-block: left of diagonal (including element on diagonal) for ( row_it = matrix_it->begin()+l; row_it != matrix_it->end(); ++row_it, ++y_x_it ) { *y_x_it = *row_it; } // R-block: right of diagonal (excluding element on diagonal) for ( matrix_it = M.begin()+l+r+1, count = r+1; count < b; ++matrix_it, ++count, ++y_x_it ) { *y_x_it = (*matrix_it)[l+r]; } } template < class ET_, class Is_LP_ > template < class ForIt > void QP_basis_inverse:: z_update_inplace( ForIt psi1_l_it, ForIt psi1_x_it, ForIt psi2_l_it, ForIt psi2_x_it, const ET& omega0, const ET& omega1, const ET& omega2, const ET& omega3) { typename Matrix:: iterator matrix_it; typename Row :: iterator row_it; typename Row ::const_iterator y_it1_r, y_it1_c, y_it2_r, y_it2_c; unsigned int row, col, k = l+b; ET u_elem; // rows: 0..s-1 ( P ) for ( row = 0, matrix_it = M.begin(), y_it1_r = psi1_l_it, y_it2_r = psi2_l_it; row < s; ++row, ++matrix_it, ++y_it1_r, ++y_it2_r ) { // columns: 0..row ( P ) for ( row_it = matrix_it->begin(), y_it1_c = psi1_l_it, y_it2_c = psi2_l_it; row_it != matrix_it->end(); ++row_it, ++y_it1_c, ++y_it2_c ) { u_elem = (*y_it1_r * *y_it2_c) + (*y_it2_r * *y_it1_c); u_elem *= omega2; u_elem += omega1 * *y_it1_r * *y_it1_c; update_entry( *row_it, omega0, u_elem, omega3); } } // rows: l..k-1 ( Q R ) for ( row = l, matrix_it = M.begin()+l, y_it1_r = psi1_x_it, y_it2_r = psi2_x_it; row != k; ++row, ++matrix_it, ++y_it1_r, ++y_it2_r ) { // columns: 0..s-1 ( Q ) for ( col = 0, row_it = matrix_it->begin(), y_it1_c = psi1_l_it, y_it2_c = psi2_l_it; col < s; ++col, ++row_it, ++y_it1_c, ++y_it2_c ){ u_elem = (*y_it1_r * *y_it2_c) + (*y_it2_r * *y_it1_c); u_elem *= omega2; u_elem += omega1 * *y_it1_r * *y_it1_c; update_entry( *row_it, omega0, u_elem, omega3); } // columns: l..k-1 ( R ) for ( row_it = matrix_it->begin()+l, y_it1_c = psi1_x_it, y_it2_c = psi2_x_it; row_it != matrix_it->end(); ++row_it, ++y_it1_c, ++y_it2_c ){ u_elem = (*y_it1_r * *y_it2_c) + (*y_it2_r * *y_it1_c); u_elem *= omega2; u_elem += omega1 * *y_it1_r * *y_it1_c; update_entry( *row_it, omega0, u_elem, omega3); } } } // swap functions // -------------- // swap variable ``to the end'' of R template < class ET_, class Is_LP_ > // LP case void QP_basis_inverse:: swap_variable( unsigned int j, Tag_true) { unsigned int k = b-1; if ( j == k) return; // swap rows // --------- typename Row::iterator row_j_it = M[ j].begin(); typename Row::iterator row_k_it = M[ k].begin(); unsigned int count; // swap entries 0..b-1 (row <-> row) [in Q] for ( count = 0; count < b; ++count, ++row_j_it, ++row_k_it) { std::iter_swap( row_j_it, row_k_it); } } template < class ET_, class Is_LP_ > // QP case void QP_basis_inverse:: swap_variable( unsigned int j, Tag_false) { unsigned int i = l+j, k = l+b-1; if ( i == k) return; // swap rows and columns // --------------------- typename Row::iterator row_i_it = M[ i].begin(); typename Row::iterator row_k_it = M[ k].begin(); typename Matrix::iterator matrix_it = M.begin()+(i+1); unsigned int count; // swap entries 0..s-1 (row <-> row) [in Q] for ( count = 0; count < s; ++count, ++row_i_it, ++row_k_it) { std::iter_swap( row_i_it, row_k_it); } if ( is_phaseII) { // swap entries l..i-1 (row <-> row) [in R] for ( count = l, row_i_it += l-s, row_k_it += l-s; count < i; ++count, ++row_i_it, ++row_k_it ) { std::iter_swap( row_i_it, row_k_it); } // swap entries i+1..k-1 (column <-> row) [in R] for ( ++count, ++row_k_it; count < k; ++count, ++matrix_it, ++row_k_it) { std::swap( ( *matrix_it)[ i], *row_k_it); } // swap entries i,i with k,k (entry <-> entry) [in R] std::iter_swap( row_i_it, row_k_it); } } // swap constraint ``to the end'' of P template < class ET_, class Is_LP_ > // LP case void QP_basis_inverse:: swap_constraint( unsigned int i, Tag_true) { unsigned int k = s-1; if ( i == k) return; // swap columns // ------------ typename Matrix::iterator matrix_it = M.begin(); unsigned int count; // swap entries 0..s-1 (column <-> column) [in Q] for ( count = 0; count < s; ++count, ++matrix_it) { std::swap( ( *matrix_it)[ i], ( *matrix_it)[ k]); } } template < class ET_, class Is_LP_ > // QP case void QP_basis_inverse:: swap_constraint( unsigned int i, Tag_false) { if ( i == s-1) return; // swap rows and columns // --------------------- typename Row::iterator row_i_it = M[ i].begin(); typename Row::iterator row_k_it = M[ s-1].begin(); typename Matrix::iterator matrix_it = M.begin()+i; unsigned int count; if ( is_phaseI) { // skip empty P matrix_it =M.begin() + l; } else { // swap entries 0..i-1 (row <-> row) [in P] for ( count = 0; count < i; ++count, ++row_i_it, ++row_k_it) { std::iter_swap( row_i_it, row_k_it); } // swap entries i+1..s-2 (column <-> row) [in P] for ( count = i + 1, ++matrix_it, ++row_k_it; count < s-1; ++count, ++matrix_it, ++row_k_it) { std::swap( ( *matrix_it)[ i], *row_k_it); } // the remaining two entries to be swapped on the main diagonal std::swap(M[i][i], M[s-1][s-1]); // advance to Q matrix_it = M.begin() + l; } // swap entries l..l+b (column <-> column) [in Q] for ( count = 0; count < b; ++count, ++matrix_it) { std::swap( ( *matrix_it)[ i], ( *matrix_it)[ s-1]); } } // diagnostic output // ----------------- template < class ET_, class Is_LP_ > void QP_basis_inverse:: print( ) { // P if ( is_LP || is_phaseII) { for ( unsigned int row = 0; row < s; ++row) { std::copy( M[ row].begin(), M[ row].begin() + ( is_LP ? s : row+1), std::ostream_iterator( vout.out(), " ")); vout.out() << std::endl; } if ( is_QP) vout.out() << "= = = = = = = = = =" << std::endl; } // Q & R if ( is_QP) { for ( unsigned int row = l; row < l+b; ++row) { std::copy( M[ row].begin(), M[ row].begin()+s, std::ostream_iterator( vout.out(), " ")); if ( is_phaseII) { vout.out() << "|| "; std::copy( M[ row].begin()+l, M[ row].end(), std::ostream_iterator( vout.out(), " ")); } vout.out() << std::endl; } } vout.out() << "denominator = " << d << std::endl; } } //namespace CGAL // ===== EOF ================================================================== #endif //CGAL_QP_SOLVER_QP_BASIS_INVERSE_IMPL_H