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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__filtered_base_impl.h $ // $Id: include/CGAL/QP_solver/QP__filtered_base_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_FILTERED_BASE_IMPL_H #define CGAL_QP_FILTERED_BASE_IMPL_H #include namespace CGAL { // ============================= // class implementation (cont'd) // ============================= // set-up template < typename Q, typename ET, typename Tags, class NT_, class ET2NT_ > void QP__filtered_base:: set( ) { // reserve memory for NT versions of current solution //int l = (std::min)( this->solver().number_of_variables(), // this->solver().number_of_constraints()); int l = this->solver().get_l(); lambda_NT.resize( l, nt0); set( l, Is_linear()); } // initialization; BG: who calls this??? template < typename Q, typename ET, typename Tags, class NT_, class ET2NT_ > void QP__filtered_base:: init( ) { // get properties of quadratic program n = this->solver().number_of_variables(); int m = this->solver().number_of_constraints(); int s = this->solver().number_of_slack_variables(); // clear row and column maxima, if necessary if ( ! row_max_A.empty()) row_max_A.clear(); if ( ! handled_A.empty()) handled_A.clear(); if ( ! col_max .empty()) col_max .clear(); init( Is_linear()); // initialize row and column maxima // assuming nonneg coefficients row_max_c = nt0; C_auxiliary_iterator v_it; for ( v_it = this->solver().c_auxiliary_value_iterator_begin(); v_it != this->solver().c_auxiliary_value_iterator_end(); ++v_it) { if (*v_it > row_max_c) row_max_c = (*v_it); } handled_A.insert( handled_A.end(), m, false); row_max_A.insert( row_max_A.end(), m, nt0); col_max.insert( col_max.end(), n, nt0); // original col_max.insert( col_max.end(), s, nt1); // slack //auxiliary for ( v_it = this->solver().c_auxiliary_value_iterator_begin(); v_it != this->solver().c_auxiliary_value_iterator_end(); ++v_it) { col_max.insert( col_max.end(), (*v_it)); } } // operations template < typename Q, typename ET, typename Tags, class NT_, class ET2NT_ > void QP__filtered_base:: init_NT( ) { // ToDo: scale 'x_B_O', 'lambda', and 'd' if necessary // get inexact version of 'lambda' std::transform( this->solver().get_lambda_begin(), this->solver().get_lambda_end(), lambda_NT.begin(), et2nt_obj); // get inexact version of 'x_B_O' init_NT( Is_linear()); // get inexact version of 'd' d_NT = et2nt_obj( this->solver().variables_common_denominator()); } // Here is how it works (Sven's thesis, page 99): // ---------------------------------------------- // R_0 := max_j |c_j| (largest objective function coefficient) // R_i^A := max_j |A_ij| (largest entry in row i of A) // R_i^D := max_j 2|D_ij| (largest entry in row i of D) // C_j := max_j (|c_j|, max_i |A_ij|, max_i |D_ij|) // // U := max( // d_NT * R_0, // max_{i basic} |lambda_NT[i]| * R_i^A, // max_{j basic} |x_NT[j]| * R_j^D // ) // W := max( // d_NT, // max_{i basic} |lambda_NT[i]|, // max_{j basic} |x_NT[j]| // ) // Note: all max_{j basic} are over basic ORIGINAL variables only // // q := (1+1/64) * // (#basic constraints + #basic original variables + 1) * // (#basic constraints + #basic original variables + 2) * 2^(-53) // // the actual error bound for mu_j_NT is then // // min (U * q, W * q * C_j) // // the code maintains and manipulates: // // row_max_c = R_0 (set in init() for phase I, transition() for phase II) // row_max_A[i] = R_i^A (set in update_maxima()) // row_max_D[i] = R_i^D (set in update_maxima(Tag_false)) // col_max[j] = C_j (set in update_maxima() + Tag_false variant) // bound1 = U * q (computed in update_maxima() + Tag_true/Tag_false ) // bound2_wq = W * q (computed in update_maxima() + Tag_true/Tag_false ) // // Changes for upper-bounded case: // ------------------------------- // in the scalar product considered on p.100, we have another term: // d * w_j, where w_j is the correction term 2 x_N^T D_Nj that shows // up additionally in the pricing and that the QP_solver maintains in // the vector w. The first bound on p.101 yields U, while the second // bound yields W. This means that // - C_j = max_y|y_i| has an additional term |w_NT[j]| in the maximum, // - U has an additional term d_NT * R_w in the maximum, where // // R_w = max_j |w_j| // // The problem is that R_w is not a static quantity like max_j|c_j|, // so it has to be handled per j in certify_mu_j_NT: // --> for q: (c+b)*(c+b+1) -> (c+b+1)*(c+b+2) // --> for bound1: take d_NT * |w_NT[j]| into account for U // --> for bound2: take |w_NT[j]| into account for C_j template < typename Q, typename ET, typename Tags, class NT_, class ET2NT_ > void QP__filtered_base:: update_maxima( ) { // get properties of quadratic program int c = this->solver().number_of_basic_constraints(); int b = this->solver().number_of_basic_original_variables(); // initialize error bounds bound1 = d_NT * row_max_c; bound2_wq = d_NT; // update row and column maxima of 'A' A_iterator a_it = this->solver().a_begin(); R_iterator r_it = this->solver().row_type_begin(); int row, col; NT row_max, z; Basic_constraint_index_iterator it; Values_NT_iterator v_it = lambda_NT.begin(); for ( it = this->solver().basic_constraint_indices_begin(); it != this->solver().basic_constraint_indices_end(); ++it, ++v_it) { row = *it; // row not handled yet? if ( ! handled_A[ row]) { // slack variable (or artificial in phase I) involved? row_max = ( ( r_it[ row] != CGAL::EQUAL) || ( this->solver().phase() == 1) ? nt1 : nt0); // scan row and update maxima for ( col = 0; col < n; ++col) { z = CGAL::abs( *((*(a_it + col))+row)); if ( z > row_max ) row_max = z; if ( z > col_max[ col]) col_max[ col] = z; } row_max_A[ row] = row_max; handled_A[ row] = true; } // update bounds z = CGAL::abs( *v_it); if ( z > bound2_wq) bound2_wq = z; z *= row_max_A[ row]; if ( z > bound1) bound1 = z; } // update row and column maxima of 'D', if necessary if (this->solver().phase() == 1) { update_maxima( Tag_true()); } else { update_maxima( Is_linear()); } // finalize error bounds // ToDo: use std::numeric_limits for 'machine epsilon' to // support types different from double set_q(c, b); bound1 *= q; bound2_wq *= q; CGAL_qpe_debug { this->vout() << std::endl << "first bound for certification: " << bound1 << std::endl; } } template < typename Q, typename ET, typename Tags, class NT_, class ET2NT_ > // QP case void QP__filtered_base:: update_maxima( Tag_false) { // update row and column maxima of 'D' D_row_iterator d_row_it; int row, col; NT row_max, z; Basic_variable_index_iterator it; Values_NT_iterator v_it = x_B_O_NT.begin(); for ( it = this->solver().basic_original_variable_indices_begin(); it != this->solver().basic_original_variable_indices_end(); ++it, ++v_it) { row = *it; // row not handled yet? if ( ! handled_D[ row]) { d_row_it = this->solver().d_begin()[ row]; // scan row and update maxima row_max = nt0; for ( col = 0; col < n; ++col, ++d_row_it) { z = CGAL::abs( *d_row_it); if ( z > row_max ) row_max = z; if ( z > col_max[ col]) col_max[ col] = z; } row_max_D[ row] = row_max; handled_D[ row] = true; } // update bounds z = CGAL::abs( (*v_it)); if ( z > bound2_wq) bound2_wq = z; z *= row_max_D[ row]; if ( z > bound1) bound1 = z; } } template < typename Q, typename ET, typename Tags, class NT_, class ET2NT_ > // LP case void QP__filtered_base:: update_maxima( Tag_true) { // update basic original variables maxima NT z; Values_NT_iterator v_it; for ( v_it = x_B_O_NT.begin(); v_it != x_B_O_NT.end(); ++v_it) { // update bounds z = CGAL::abs( (*v_it)); if ( z > bound2_wq) bound2_wq = z; } } template < typename Q, typename ET, typename Tags, class NT_, class ET2NT_ > bool QP__filtered_base:: certify_mu_j_NT( int j, Tag_true) const // standard form { // compute 'mu_j' with inexact arithmetic again NT mu = mu_j_NT( j); CGAL_qpe_debug { this->vout() << "mu_" << j << " [NT]: " << mu; } // check against first bound if ( mu >= bound1) { CGAL_qpe_debug { this->vout() << " ok [1]" << std::endl; } return true; } // compute and check against second bound NT bound2 = bound2_wq * col_max[ j]; if ( mu >= bound2) { CGAL_qpe_debug { this->vout() << " ok [2: " << bound2 << "]" << std::endl; } return true; } // compute and check exact 'mu_j' ET mu_et = this->mu_j( j); CGAL_qpe_debug { this->vout() << " " << ( mu_et >= this->et0 ? "ok" : "MISSED") << " [exact: " << mu_et << "]" << std::endl; } return ( mu_et >= this->et0); } template < typename Q, typename ET, typename Tags, class NT_, class ET2NT_ > bool QP__filtered_base:: certify_mu_j_NT( int j, Tag_false) const // case with bounds { // compute 'mu_j' with inexact arithmetic again; this call sets w_j_NT NT mu = CGAL::abs(mu_j_NT( j)); // may have both signs in bounded case NT w_j_NT_abs = CGAL::abs(w_j_NT); CGAL_qpe_debug { this->vout() << "|mu_|" << j << " [NT]: " << mu; } // check against first bound, taking w_j_NT into account // q has been set in previous call to update_maxima() // bound1_with_w = (U + d_NT*|w_j|) * q NT bound1_with_w = bound1 + (d_NT * w_j_NT_abs * q); if ( mu >= bound1_with_w) { CGAL_qpe_debug { this->vout() << " ok [1]" << std::endl; } return true; } // compute and check against second bound, taking w_j_NT into account // bound2_with_w = max (W, |w_j|) NT bound2_with_w = bound2_wq * (std::max)(col_max[ j], w_j_NT_abs); if ( mu >= bound2_with_w) { CGAL_qpe_debug { this->vout() << " ok [2: " << bound2_with_w << "]" << std::endl; } return true; } // the bounds are insufficient: compute and check exact 'mu_j' ET mu_et = this->mu_j( j); bool improving = is_improving(j, mu_et, this->et0); CGAL_qpe_debug { this->vout() << " " << (!improving ? "ok" : "MISSED") << " [exact: " << mu_et << "]" << std::endl; } return ( !improving); } // transition template < typename Q, typename ET, typename Tags, class NT_, class ET2NT_ > void QP__filtered_base:: transition( ) { // update row and column maxima with original objective vector 'c' C_iterator c_it = this->solver().c_begin(); NT z; row_max_c = nt0; for ( int i = 0; i < n; ++i, ++c_it) { z = CGAL::abs( *c_it); if ( z > row_max_c ) row_max_c = z; if ( z > col_max[ i]) col_max[ i] = z; } // initialize row maxima of 'D', if necessary transition( n, Is_linear()); } } //namespace CGAL // ===== EOF ================================================================== #endif // CGAL_QP_FILTERED_BASE_IMPL_H