mirror of
https://github.com/Z3Prover/z3
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991 lines
32 KiB
C++
991 lines
32 KiB
C++
/*++
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Copyright (c) 2017 Microsoft Corporation
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Module Name:
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<name>
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Abstract:
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<abstract>
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Author:
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Lev Nachmanson (levnach)
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Revision History:
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--*/
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#include <string>
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#include <algorithm>
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#include <set>
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#include "util/vector.h"
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#include <utility>
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#include "util/debug.h"
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#include "math/lp/lu.h"
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namespace lp {
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template <typename T, typename X, typename M> // print the nr x nc submatrix at the top left corner
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void print_submatrix(square_sparse_matrix<T, X> & m, unsigned mr, unsigned nc, std::ostream & out) {
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vector<vector<std::string>> A;
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vector<unsigned> widths;
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for (unsigned i = 0; i < m.row_count() && i < mr ; i++) {
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A.push_back(vector<std::string>());
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for (unsigned j = 0; j < m.column_count() && j < nc; j++) {
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A[i].push_back(T_to_string(static_cast<T>(m(i, j))));
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}
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}
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for (unsigned j = 0; j < m.column_count() && j < nc; j++) {
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widths.push_back(get_width_of_column(j, A));
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}
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print_matrix_with_widths(A, widths, out);
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}
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template<typename M>
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void print_matrix(M &m, std::ostream & out) {
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vector<vector<std::string>> A;
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vector<unsigned> widths;
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for (unsigned i = 0; i < m.row_count(); i++) {
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A.push_back(vector<std::string>());
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for (unsigned j = 0; j < m.column_count(); j++) {
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A[i].push_back(T_to_string(m[i][j]));
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}
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}
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for (unsigned j = 0; j < m.column_count(); j++) {
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widths.push_back(get_width_of_column(j, A));
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}
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print_matrix_with_widths(A, widths, out);
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}
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template <typename T, typename X>
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one_elem_on_diag<T, X>::one_elem_on_diag(const one_elem_on_diag & o) {
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m_i = o.m_i;
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m_val = o.m_val;
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#ifdef Z3DEBUG
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m_m = m_n = o.m_m;
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m_one_over_val = numeric_traits<T>::one() / o.m_val;
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#endif
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}
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#ifdef Z3DEBUG
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template <typename T, typename X>
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T one_elem_on_diag<T, X>::get_elem(unsigned i, unsigned j) const {
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if (i == j){
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if (j == m_i) {
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return m_one_over_val;
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}
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return numeric_traits<T>::one();
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}
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return numeric_traits<T>::zero();
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}
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#endif
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template <typename T, typename X>
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void one_elem_on_diag<T, X>::apply_from_left_to_T(indexed_vector<T> & w, lp_settings & settings) {
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T & t = w[m_i];
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if (numeric_traits<T>::is_zero(t)) {
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return;
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}
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t /= m_val;
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if (numeric_traits<T>::precise()) return;
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if (settings.abs_val_is_smaller_than_drop_tolerance(t)) {
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w.erase_from_index(m_i);
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t = numeric_traits<T>::zero();
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}
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}
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// This class supports updates of the columns of B, and solves systems Bx=b,and yB=c
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// Using Suhl-Suhl method described in the dissertation of Achim Koberstein, Chapter 5
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template <typename M>
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lu<M>::lu(const M& A,
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vector<unsigned>& basis,
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lp_settings & settings):
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m_status(LU_status::OK),
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m_dim(A.row_count()),
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m_A(A),
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m_Q(m_dim),
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m_R(m_dim),
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m_r_wave(m_dim),
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m_U(A, basis), // create the square matrix that eventually will be factorized
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m_settings(settings),
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m_failure(false),
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m_row_eta_work_vector(A.row_count()),
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m_refactor_counter(0) {
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lp_assert(!(numeric_traits<T>::precise() && settings.use_tableau()));
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#ifdef Z3DEBUG
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debug_test_of_basis(A, basis);
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#endif
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++m_settings.st().m_num_factorizations;
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create_initial_factorization();
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#ifdef Z3DEBUG
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// lp_assert(check_correctness());
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#endif
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}
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template <typename M>
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lu<M>::lu(const M& A,
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lp_settings & settings):
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m_status(LU_status::OK),
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m_dim(A.row_count()),
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m_A(A),
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m_Q(m_dim),
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m_R(m_dim),
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m_r_wave(m_dim),
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m_U(A), // create the square matrix that eventually will be factorized
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m_settings(settings),
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m_failure(false),
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m_row_eta_work_vector(A.row_count()),
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m_refactor_counter(0) {
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lp_assert(A.row_count() == A.column_count());
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create_initial_factorization();
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#ifdef Z3DEBUG
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lp_assert(is_correct());
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#endif
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}
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template <typename M>
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void lu<M>::debug_test_of_basis( M const & A, vector<unsigned> & basis) {
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std::set<unsigned> set;
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for (unsigned i = 0; i < A.row_count(); i++) {
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lp_assert(basis[i]< A.column_count());
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set.insert(basis[i]);
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}
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lp_assert(set.size() == A.row_count());
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}
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template <typename M>
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void lu<M>::solve_By(indexed_vector<X> & y) {
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lp_assert(false); // not implemented
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// init_vector_y(y);
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// solve_By_when_y_is_ready(y);
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}
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template <typename M>
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void lu<M>::solve_By(vector<X> & y) {
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init_vector_y(y);
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solve_By_when_y_is_ready_for_X(y);
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}
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template <typename M>
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void lu<M>::solve_By_when_y_is_ready_for_X(vector<X> & y) {
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if (numeric_traits<T>::precise()) {
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m_U.solve_U_y(y);
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m_R.apply_reverse_from_left_to_X(y); // see 24.3 from Chvatal
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return;
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}
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m_U.double_solve_U_y(y);
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m_R.apply_reverse_from_left_to_X(y); // see 24.3 from Chvatal
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unsigned i = m_dim;
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while (i--) {
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if (is_zero(y[i])) continue;
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if (m_settings.abs_val_is_smaller_than_drop_tolerance(y[i])){
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y[i] = zero_of_type<X>();
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}
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}
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}
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template <typename M>
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void lu<M>::solve_By_when_y_is_ready_for_T(vector<T> & y, vector<unsigned> & index) {
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if (numeric_traits<T>::precise()) {
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m_U.solve_U_y(y);
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m_R.apply_reverse_from_left_to_T(y); // see 24.3 from Chvatal
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unsigned j = m_dim;
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while (j--) {
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if (!is_zero(y[j]))
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index.push_back(j);
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}
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return;
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}
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m_U.double_solve_U_y(y);
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m_R.apply_reverse_from_left_to_T(y); // see 24.3 from Chvatal
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unsigned i = m_dim;
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while (i--) {
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if (is_zero(y[i])) continue;
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if (m_settings.abs_val_is_smaller_than_drop_tolerance(y[i])){
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y[i] = zero_of_type<T>();
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} else {
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index.push_back(i);
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}
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}
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}
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template <typename M>
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void lu<M>::solve_By_for_T_indexed_only(indexed_vector<T> & y, const lp_settings & settings) {
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if (numeric_traits<T>::precise()) {
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vector<unsigned> active_rows;
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m_U.solve_U_y_indexed_only(y, settings, active_rows);
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m_R.apply_reverse_from_left(y); // see 24.3 from Chvatal
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return;
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}
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m_U.double_solve_U_y(y, m_settings);
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m_R.apply_reverse_from_left(y); // see 24.3 from Chvatal
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}
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template <typename M>
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void lu<M>::print_matrix_compact(std::ostream & f) {
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f << "matrix_start" << std::endl;
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f << "nrows " << m_A.row_count() << std::endl;
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f << "ncolumns " << m_A.column_count() << std::endl;
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for (unsigned i = 0; i < m_A.row_count(); i++) {
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auto & row = m_A.m_rows[i];
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f << "row " << i << std::endl;
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for (auto & t : row) {
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f << "column " << t.m_j << " value " << t.m_value << std::endl;
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}
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f << "row_end" << std::endl;
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}
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f << "matrix_end" << std::endl;
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}
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template <typename M>
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void lu< M>::print(indexed_vector<T> & w, const vector<unsigned>& basis) {
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std::string dump_file_name("/tmp/lu");
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remove(dump_file_name.c_str());
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std::ofstream f(dump_file_name);
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if (!f.is_open()) {
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LP_OUT(m_settings, "cannot open file " << dump_file_name << std::endl);
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return;
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}
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LP_OUT(m_settings, "writing lu dump to " << dump_file_name << std::endl);
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print_matrix_compact(f);
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print_vector(basis, f);
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print_indexed_vector(w, f);
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f.close();
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}
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template <typename M>
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void lu< M>::solve_Bd(unsigned a_column, indexed_vector<T> & d, indexed_vector<T> & w) {
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init_vector_w(a_column, w);
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if (w.m_index.size() * ratio_of_index_size_to_all_size<T>() < d.m_data.size()) { // this const might need some tuning
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d = w;
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solve_By_for_T_indexed_only(d, m_settings);
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} else {
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d.m_data = w.m_data;
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d.m_index.clear();
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solve_By_when_y_is_ready_for_T(d.m_data, d.m_index);
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}
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}
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template <typename M>
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void lu< M>::solve_Bd_faster(unsigned a_column, indexed_vector<T> & d) { // puts the a_column into d
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init_vector_w(a_column, d);
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solve_By_for_T_indexed_only(d, m_settings);
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}
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template <typename M>
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void lu< M>::solve_yB(vector<T>& y) {
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// first solve yU = cb*R(-1)
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m_R.apply_reverse_from_right_to_T(y); // got y = cb*R(-1)
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m_U.solve_y_U(y); // got y*U=cb*R(-1)
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m_Q.apply_reverse_from_right_to_T(y); //
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for (auto e = m_tail.rbegin(); e != m_tail.rend(); ++e) {
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#ifdef Z3DEBUG
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(*e)->set_number_of_columns(m_dim);
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#endif
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(*e)->apply_from_right(y);
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}
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}
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template <typename M>
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void lu< M>::solve_yB_indexed(indexed_vector<T>& y) {
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lp_assert(y.is_OK());
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// first solve yU = cb*R(-1)
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m_R.apply_reverse_from_right_to_T(y); // got y = cb*R(-1)
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lp_assert(y.is_OK());
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m_U.solve_y_U_indexed(y, m_settings); // got y*U=cb*R(-1)
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lp_assert(y.is_OK());
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m_Q.apply_reverse_from_right_to_T(y);
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lp_assert(y.is_OK());
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for (auto e = m_tail.rbegin(); e != m_tail.rend(); ++e) {
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#ifdef Z3DEBUG
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(*e)->set_number_of_columns(m_dim);
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#endif
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(*e)->apply_from_right(y);
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lp_assert(y.is_OK());
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}
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}
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template <typename M>
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void lu< M>::add_delta_to_solution(const vector<T>& yc, vector<T>& y){
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unsigned i = static_cast<unsigned>(y.size());
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while (i--)
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y[i]+=yc[i];
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}
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template <typename M>
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void lu< M>::add_delta_to_solution_indexed(indexed_vector<T>& y) {
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// the delta sits in m_y_copy, put result into y
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lp_assert(y.is_OK());
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lp_assert(m_y_copy.is_OK());
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m_ii.clear();
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m_ii.resize(y.data_size());
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for (unsigned i : y.m_index)
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m_ii.set_value(1, i);
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for (unsigned i : m_y_copy.m_index) {
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y.m_data[i] += m_y_copy[i];
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if (m_ii[i] == 0)
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m_ii.set_value(1, i);
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}
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lp_assert(m_ii.is_OK());
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y.m_index.clear();
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for (unsigned i : m_ii.m_index) {
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T & v = y.m_data[i];
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if (!lp_settings::is_eps_small_general(v, 1e-14))
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y.m_index.push_back(i);
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else if (!numeric_traits<T>::is_zero(v))
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v = zero_of_type<T>();
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}
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lp_assert(y.is_OK());
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}
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template <typename M>
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void lu< M>::find_error_of_yB(vector<T>& yc, const vector<T>& y, const vector<unsigned>& m_basis) {
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unsigned i = m_dim;
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while (i--) {
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yc[i] -= m_A.dot_product_with_column(y, m_basis[i]);
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}
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}
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template <typename M>
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void lu< M>::find_error_of_yB_indexed(const indexed_vector<T>& y, const vector<int>& heading, const lp_settings& settings) {
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#if 0 == 1
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// it is a non efficient version
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indexed_vector<T> yc = m_y_copy;
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yc.m_index.clear();
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lp_assert(!numeric_traits<T>::precise());
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{
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vector<unsigned> d_basis(y.m_data.size());
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for (unsigned j = 0; j < heading.size(); j++) {
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if (heading[j] >= 0) {
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d_basis[heading[j]] = j;
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}
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}
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unsigned i = m_dim;
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while (i--) {
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T & v = yc.m_data[i] -= m_A.dot_product_with_column(y.m_data, d_basis[i]);
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if (settings.abs_val_is_smaller_than_drop_tolerance(v))
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v = zero_of_type<T>();
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else
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yc.m_index.push_back(i);
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}
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}
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#endif
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lp_assert(m_ii.is_OK());
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m_ii.clear();
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m_ii.resize(y.data_size());
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lp_assert(m_y_copy.is_OK());
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// put the error into m_y_copy
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for (auto k : y.m_index) {
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auto & row = m_A.m_rows[k];
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const T & y_k = y.m_data[k];
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for (auto & c : row) {
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unsigned j = c.var();
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int hj = heading[j];
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if (hj < 0) continue;
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if (m_ii.m_data[hj] == 0)
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m_ii.set_value(1, hj);
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m_y_copy.m_data[hj] -= c.get_val() * y_k;
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}
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}
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// add the index of m_y_copy to m_ii
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for (unsigned i : m_y_copy.m_index) {
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if (m_ii.m_data[i] == 0)
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m_ii.set_value(1, i);
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}
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// there is no guarantee that m_y_copy is OK here, but its index
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// is contained in m_ii index
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m_y_copy.m_index.clear();
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// setup the index of m_y_copy
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for (auto k : m_ii.m_index) {
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T& v = m_y_copy.m_data[k];
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if (settings.abs_val_is_smaller_than_drop_tolerance(v))
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v = zero_of_type<T>();
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else {
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m_y_copy.set_value(v, k);
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}
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}
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lp_assert(m_y_copy.is_OK());
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}
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// solves y*B = y
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// y is the input
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template <typename M>
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void lu< M>::solve_yB_with_error_check_indexed(indexed_vector<T> & y, const vector<int>& heading, const vector<unsigned> & basis, const lp_settings & settings) {
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if (numeric_traits<T>::precise()) {
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if (y.m_index.size() * ratio_of_index_size_to_all_size<T>() * 3 < m_A.column_count()) {
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solve_yB_indexed(y);
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} else {
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solve_yB(y.m_data);
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y.restore_index_and_clean_from_data();
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}
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return;
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}
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lp_assert(m_y_copy.is_OK());
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lp_assert(y.is_OK());
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if (y.m_index.size() * ratio_of_index_size_to_all_size<T>() < m_A.column_count()) {
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m_y_copy = y;
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solve_yB_indexed(y);
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lp_assert(y.is_OK());
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if (y.m_index.size() * ratio_of_index_size_to_all_size<T>() >= m_A.column_count()) {
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find_error_of_yB(m_y_copy.m_data, y.m_data, basis);
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solve_yB(m_y_copy.m_data);
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add_delta_to_solution(m_y_copy.m_data, y.m_data);
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y.restore_index_and_clean_from_data();
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m_y_copy.clear_all();
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} else {
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find_error_of_yB_indexed(y, heading, settings); // this works with m_y_copy
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solve_yB_indexed(m_y_copy);
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add_delta_to_solution_indexed(y);
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}
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lp_assert(m_y_copy.is_OK());
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} else {
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solve_yB_with_error_check(y.m_data, basis);
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|
y.restore_index_and_clean_from_data();
|
|
}
|
|
}
|
|
|
|
|
|
// solves y*B = y
|
|
// y is the input
|
|
template <typename M>
|
|
void lu< M>::solve_yB_with_error_check(vector<T> & y, const vector<unsigned>& basis) {
|
|
if (numeric_traits<T>::precise()) {
|
|
solve_yB(y);
|
|
return;
|
|
}
|
|
auto & yc = m_y_copy.m_data;
|
|
yc =y; // copy y aside
|
|
solve_yB(y);
|
|
find_error_of_yB(yc, y, basis);
|
|
solve_yB(yc);
|
|
add_delta_to_solution(yc, y);
|
|
m_y_copy.clear_all();
|
|
}
|
|
template <typename M>
|
|
void lu< M>::apply_Q_R_to_U(permutation_matrix<T, X> & r_wave) {
|
|
m_U.multiply_from_right(r_wave);
|
|
m_U.multiply_from_left_with_reverse(r_wave);
|
|
}
|
|
|
|
|
|
// Solving yB = cb to find the entering variable,
|
|
// where cb is the cost vector projected to B.
|
|
// The result is stored in cb.
|
|
|
|
// solving Bd = a ( to find the column d of B^{-1} A_N corresponding to the entering
|
|
// variable
|
|
template <typename M>
|
|
lu< M>::~lu(){
|
|
for (auto t : m_tail) {
|
|
delete t;
|
|
}
|
|
}
|
|
template <typename M>
|
|
void lu< M>::init_vector_y(vector<X> & y) {
|
|
apply_lp_list_to_y(y);
|
|
m_Q.apply_reverse_from_left_to_X(y);
|
|
}
|
|
|
|
template <typename M>
|
|
void lu< M>::perform_transformations_on_w(indexed_vector<T>& w) {
|
|
apply_lp_list_to_w(w);
|
|
m_Q.apply_reverse_from_left(w);
|
|
// TBD does not compile: lp_assert(numeric_traits<T>::precise() || check_vector_for_small_values(w, m_settings));
|
|
}
|
|
|
|
// see Chvatal 24.3
|
|
template <typename M>
|
|
void lu< M>::init_vector_w(unsigned entering, indexed_vector<T> & w) {
|
|
w.clear();
|
|
m_A.copy_column_to_indexed_vector(entering, w); // w = a, the column
|
|
perform_transformations_on_w(w);
|
|
}
|
|
template <typename M>
|
|
void lu< M>::apply_lp_list_to_w(indexed_vector<T> & w) {
|
|
for (unsigned i = 0; i < m_tail.size(); i++) {
|
|
m_tail[i]->apply_from_left_to_T(w, m_settings);
|
|
// TBD does not compile: lp_assert(check_vector_for_small_values(w, m_settings));
|
|
}
|
|
}
|
|
template <typename M>
|
|
void lu< M>::apply_lp_list_to_y(vector<X>& y) {
|
|
for (unsigned i = 0; i < m_tail.size(); i++) {
|
|
m_tail[i]->apply_from_left(y, m_settings);
|
|
}
|
|
}
|
|
template <typename M>
|
|
void lu< M>::swap_rows(int j, int k) {
|
|
if (j != k) {
|
|
m_Q.transpose_from_left(j, k);
|
|
m_U.swap_rows(j, k);
|
|
}
|
|
}
|
|
|
|
template <typename M>
|
|
void lu< M>::swap_columns(int j, int pivot_column) {
|
|
if (j == pivot_column)
|
|
return;
|
|
m_R.transpose_from_right(j, pivot_column);
|
|
m_U.swap_columns(j, pivot_column);
|
|
}
|
|
template <typename M>
|
|
bool lu< M>::pivot_the_row(int row) {
|
|
eta_matrix<T, X> * eta_matrix = get_eta_matrix_for_pivot(row);
|
|
if (get_status() != LU_status::OK) {
|
|
return false;
|
|
}
|
|
|
|
if (eta_matrix == nullptr) {
|
|
m_U.shorten_active_matrix(row, nullptr);
|
|
return true;
|
|
}
|
|
if (!m_U.pivot_with_eta(row, eta_matrix, m_settings))
|
|
return false;
|
|
eta_matrix->conjugate_by_permutation(m_Q);
|
|
push_matrix_to_tail(eta_matrix);
|
|
return true;
|
|
}
|
|
// we're processing the column j now
|
|
template <typename M>
|
|
eta_matrix<typename M::coefftype, typename M::argtype> * lu< M>::get_eta_matrix_for_pivot(unsigned j) {
|
|
eta_matrix<T, X> *ret;
|
|
if(!m_U.fill_eta_matrix(j, &ret)) {
|
|
set_status(LU_status::Degenerated);
|
|
}
|
|
return ret;
|
|
}
|
|
// we're processing the column j now
|
|
template <typename M>
|
|
eta_matrix<typename M::coefftype, typename M::argtype> * lu<M>::get_eta_matrix_for_pivot(unsigned j, square_sparse_matrix<T, X>& copy_of_U) {
|
|
eta_matrix<T, X> *ret;
|
|
copy_of_U.fill_eta_matrix(j, &ret);
|
|
return ret;
|
|
}
|
|
|
|
// see page 407 of Chvatal
|
|
template <typename M>
|
|
unsigned lu<M>::transform_U_to_V_by_replacing_column(indexed_vector<T> & w,
|
|
unsigned leaving_column) {
|
|
unsigned column_to_replace = m_R.apply_reverse(leaving_column);
|
|
m_U.replace_column(column_to_replace, w, m_settings);
|
|
return column_to_replace;
|
|
}
|
|
|
|
#ifdef Z3DEBUG
|
|
template <typename M>
|
|
void lu<M>::check_vector_w(unsigned entering) {
|
|
T * w = new T[m_dim];
|
|
m_A.copy_column_to_vector(entering, w);
|
|
check_apply_lp_lists_to_w(w);
|
|
delete [] w;
|
|
}
|
|
template <typename M>
|
|
void lu<M>::check_apply_matrix_to_vector(matrix<T, X> *lp, T *w) {
|
|
if (lp != nullptr) {
|
|
lp -> set_number_of_rows(m_dim);
|
|
lp -> set_number_of_columns(m_dim);
|
|
apply_to_vector(*lp, w);
|
|
}
|
|
}
|
|
|
|
template <typename M>
|
|
void lu<M>::check_apply_lp_lists_to_w(T * w) {
|
|
for (unsigned i = 0; i < m_tail.size(); i++) {
|
|
check_apply_matrix_to_vector(m_tail[i], w);
|
|
}
|
|
permutation_matrix<T, X> qr = m_Q.get_reverse();
|
|
apply_to_vector(qr, w);
|
|
for (int i = m_dim - 1; i >= 0; i--) {
|
|
lp_assert(abs(w[i] - w[i]) < 0.0000001);
|
|
}
|
|
}
|
|
|
|
#endif
|
|
template <typename M>
|
|
void lu<M>::process_column(int j) {
|
|
unsigned pi, pj;
|
|
bool success = m_U.get_pivot_for_column(pi, pj, m_settings.c_partial_pivoting, j);
|
|
if (!success) {
|
|
// LP_OUT(m_settings, "get_pivot returned false: cannot find the pivot for column " << j << std::endl);
|
|
m_failure = true;
|
|
return;
|
|
}
|
|
|
|
if (static_cast<int>(pi) == -1) {
|
|
// LP_OUT(m_settings, "cannot find the pivot for column " << j << std::endl);
|
|
m_failure = true;
|
|
return;
|
|
}
|
|
swap_columns(j, pj);
|
|
swap_rows(j, pi);
|
|
if (!pivot_the_row(j)) {
|
|
// LP_OUT(m_settings, "pivot_the_row(" << j << ") failed" << std::endl);
|
|
m_failure = true;
|
|
}
|
|
}
|
|
template <typename M>
|
|
bool lu<M>::is_correct(const vector<unsigned>& basis) {
|
|
#ifdef Z3DEBUG
|
|
if (get_status() != LU_status::OK) {
|
|
return false;
|
|
}
|
|
dense_matrix<T, X> left_side = get_left_side(basis);
|
|
dense_matrix<T, X> right_side = get_right_side();
|
|
return left_side == right_side;
|
|
#else
|
|
return true;
|
|
#endif
|
|
}
|
|
|
|
template <typename M>
|
|
bool lu<M>::is_correct() {
|
|
#ifdef Z3DEBUG
|
|
if (get_status() != LU_status::OK) {
|
|
return false;
|
|
}
|
|
dense_matrix<T, X> left_side = get_left_side();
|
|
dense_matrix<T, X> right_side = get_right_side();
|
|
return left_side == right_side;
|
|
#else
|
|
return true;
|
|
#endif
|
|
}
|
|
|
|
|
|
#ifdef Z3DEBUG
|
|
template <typename M>
|
|
dense_matrix<typename M::coefftype, typename M::argtype> lu<M>::tail_product() {
|
|
lp_assert(tail_size() > 0);
|
|
dense_matrix<T, X> left_side = permutation_matrix<T, X>(m_dim);
|
|
for (unsigned i = 0; i < tail_size(); i++) {
|
|
matrix<T, X>* lp = get_lp_matrix(i);
|
|
lp->set_number_of_rows(m_dim);
|
|
lp->set_number_of_columns(m_dim);
|
|
left_side = ((*lp) * left_side);
|
|
}
|
|
return left_side;
|
|
}
|
|
template <typename M>
|
|
dense_matrix<typename M::coefftype, typename M::argtype> lu<M>::get_left_side(const vector<unsigned>& basis) {
|
|
dense_matrix<T, X> left_side = get_B(*this, basis);
|
|
for (unsigned i = 0; i < tail_size(); i++) {
|
|
matrix<T, X>* lp = get_lp_matrix(i);
|
|
lp->set_number_of_rows(m_dim);
|
|
lp->set_number_of_columns(m_dim);
|
|
left_side = ((*lp) * left_side);
|
|
}
|
|
return left_side;
|
|
}
|
|
template <typename M>
|
|
dense_matrix<typename M::coefftype, typename M::argtype> lu<M>::get_left_side() {
|
|
dense_matrix<T, X> left_side = get_B(*this);
|
|
for (unsigned i = 0; i < tail_size(); i++) {
|
|
matrix<T, X>* lp = get_lp_matrix(i);
|
|
lp->set_number_of_rows(m_dim);
|
|
lp->set_number_of_columns(m_dim);
|
|
left_side = ((*lp) * left_side);
|
|
}
|
|
return left_side;
|
|
}
|
|
template <typename M>
|
|
dense_matrix<typename M::coefftype, typename M::argtype> lu<M>::get_right_side() {
|
|
auto ret = U() * R();
|
|
ret = Q() * ret;
|
|
return ret;
|
|
}
|
|
#endif
|
|
|
|
// needed for debugging purposes
|
|
template <typename M>
|
|
void lu<M>::copy_w(T *buffer, indexed_vector<T> & w) {
|
|
unsigned i = m_dim;
|
|
while (i--) {
|
|
buffer[i] = w[i];
|
|
}
|
|
}
|
|
|
|
// needed for debugging purposes
|
|
template <typename M>
|
|
void lu<M>::restore_w(T *buffer, indexed_vector<T> & w) {
|
|
unsigned i = m_dim;
|
|
while (i--) {
|
|
w[i] = buffer[i];
|
|
}
|
|
}
|
|
template <typename M>
|
|
bool lu<M>::all_columns_and_rows_are_active() {
|
|
unsigned i = m_dim;
|
|
while (i--) {
|
|
lp_assert(m_U.col_is_active(i));
|
|
lp_assert(m_U.row_is_active(i));
|
|
}
|
|
return true;
|
|
}
|
|
template <typename M>
|
|
bool lu<M>::too_dense(unsigned j) const {
|
|
unsigned r = m_dim - j;
|
|
if (r < 5)
|
|
return false;
|
|
// if (j * 5 < m_dim * 4) // start looking for dense only at the bottom of the rows
|
|
// return false;
|
|
// return r * r * m_settings.density_threshold <= m_U.get_number_of_nonzeroes_below_row(j);
|
|
return r * r * m_settings.density_threshold <= m_U.get_n_of_active_elems();
|
|
}
|
|
template <typename M>
|
|
void lu<M>::pivot_in_dense_mode(unsigned i) {
|
|
int j = m_dense_LU->find_pivot_column_in_row(i);
|
|
if (j == -1) {
|
|
m_failure = true;
|
|
return;
|
|
}
|
|
if (i != static_cast<unsigned>(j)) {
|
|
swap_columns(i, j);
|
|
m_dense_LU->swap_columns(i, j);
|
|
}
|
|
m_dense_LU->pivot(i, m_settings);
|
|
}
|
|
template <typename M>
|
|
void lu<M>::create_initial_factorization(){
|
|
m_U.prepare_for_factorization();
|
|
unsigned j;
|
|
for (j = 0; j < m_dim; j++) {
|
|
process_column(j);
|
|
if (m_failure) {
|
|
set_status(LU_status::Degenerated);
|
|
return;
|
|
}
|
|
if (too_dense(j)) {
|
|
break;
|
|
}
|
|
}
|
|
if (j == m_dim) {
|
|
// TBD does not compile: lp_assert(m_U.is_upper_triangular_and_maximums_are_set_correctly_in_rows(m_settings));
|
|
// lp_assert(is_correct());
|
|
// lp_assert(m_U.is_upper_triangular_and_maximums_are_set_correctly_in_rows(m_settings));
|
|
return;
|
|
}
|
|
j++;
|
|
m_dense_LU = new square_dense_submatrix<T, X>(&m_U, j);
|
|
for (; j < m_dim; j++) {
|
|
pivot_in_dense_mode(j);
|
|
if (m_failure) {
|
|
set_status(LU_status::Degenerated);
|
|
return;
|
|
}
|
|
}
|
|
m_dense_LU->update_parent_matrix(m_settings);
|
|
lp_assert(m_dense_LU->is_L_matrix());
|
|
m_dense_LU->conjugate_by_permutation(m_Q);
|
|
push_matrix_to_tail(m_dense_LU);
|
|
m_refactor_counter = 0;
|
|
// lp_assert(is_correct());
|
|
// lp_assert(m_U.is_upper_triangular_and_maximums_are_set_correctly_in_rows(m_settings));
|
|
}
|
|
|
|
template <typename M>
|
|
void lu<M>::calculate_r_wave_and_update_U(unsigned bump_start, unsigned bump_end, permutation_matrix<T, X> & r_wave) {
|
|
if (bump_start > bump_end) {
|
|
set_status(LU_status::Degenerated);
|
|
return;
|
|
}
|
|
if (bump_start == bump_end) {
|
|
return;
|
|
}
|
|
|
|
r_wave[bump_start] = bump_end; // sending the offensive column to the end of the bump
|
|
|
|
for ( unsigned i = bump_start + 1 ; i <= bump_end; i++ ) {
|
|
r_wave[i] = i - 1;
|
|
}
|
|
|
|
m_U.multiply_from_right(r_wave);
|
|
m_U.multiply_from_left_with_reverse(r_wave);
|
|
}
|
|
template <typename M>
|
|
void lu<M>::scan_last_row_to_work_vector(unsigned lowest_row_of_the_bump) {
|
|
vector<indexed_value<T>> & last_row_vec = m_U.get_row_values(m_U.adjust_row(lowest_row_of_the_bump));
|
|
for (auto & iv : last_row_vec) {
|
|
if (is_zero(iv.m_value)) continue;
|
|
lp_assert(!m_settings.abs_val_is_smaller_than_drop_tolerance(iv.m_value));
|
|
unsigned adjusted_col = m_U.adjust_column_inverse(iv.m_index);
|
|
if (adjusted_col < lowest_row_of_the_bump) {
|
|
m_row_eta_work_vector.set_value(-iv.m_value, adjusted_col);
|
|
} else {
|
|
m_row_eta_work_vector.set_value(iv.m_value, adjusted_col); // preparing to calculate the real value in the matrix
|
|
}
|
|
}
|
|
}
|
|
|
|
template <typename M>
|
|
void lu<M>::pivot_and_solve_the_system(unsigned replaced_column, unsigned lowest_row_of_the_bump) {
|
|
// we have the system right side at m_row_eta_work_vector now
|
|
// solve the system column wise
|
|
for (unsigned j = replaced_column; j < lowest_row_of_the_bump; j++) {
|
|
T v = m_row_eta_work_vector[j];
|
|
if (numeric_traits<T>::is_zero(v)) continue; // this column does not contribute to the solution
|
|
unsigned aj = m_U.adjust_row(j);
|
|
vector<indexed_value<T>> & row = m_U.get_row_values(aj);
|
|
for (auto & iv : row) {
|
|
unsigned col = m_U.adjust_column_inverse(iv.m_index);
|
|
lp_assert(col >= j || numeric_traits<T>::is_zero(iv.m_value));
|
|
if (col == j) continue;
|
|
if (numeric_traits<T>::is_zero(iv.m_value)) {
|
|
continue;
|
|
}
|
|
// the -v is for solving the system ( to zero the last row), and +v is for pivoting
|
|
T delta = col < lowest_row_of_the_bump? -v * iv.m_value: v * iv.m_value;
|
|
lp_assert(numeric_traits<T>::is_zero(delta) == false);
|
|
|
|
|
|
|
|
// m_row_eta_work_vector.add_value_at_index_with_drop_tolerance(col, delta);
|
|
if (numeric_traits<T>::is_zero(m_row_eta_work_vector[col])) {
|
|
if (!m_settings.abs_val_is_smaller_than_drop_tolerance(delta)){
|
|
m_row_eta_work_vector.set_value(delta, col);
|
|
}
|
|
} else {
|
|
T t = (m_row_eta_work_vector[col] += delta);
|
|
if (m_settings.abs_val_is_smaller_than_drop_tolerance(t)){
|
|
m_row_eta_work_vector[col] = numeric_traits<T>::zero();
|
|
auto it = std::find(m_row_eta_work_vector.m_index.begin(), m_row_eta_work_vector.m_index.end(), col);
|
|
if (it != m_row_eta_work_vector.m_index.end())
|
|
m_row_eta_work_vector.m_index.erase(it);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
// see Achim Koberstein's thesis page 58, but here we solve the system and pivot to the last
|
|
// row at the same time
|
|
template <typename M>
|
|
row_eta_matrix<typename M::coefftype, typename M::argtype> *lu<M>::get_row_eta_matrix_and_set_row_vector(unsigned replaced_column, unsigned lowest_row_of_the_bump, const T & pivot_elem_for_checking) {
|
|
if (replaced_column == lowest_row_of_the_bump) return nullptr;
|
|
scan_last_row_to_work_vector(lowest_row_of_the_bump);
|
|
pivot_and_solve_the_system(replaced_column, lowest_row_of_the_bump);
|
|
if (numeric_traits<T>::precise() == false && !is_zero(pivot_elem_for_checking)) {
|
|
T denom = std::max(T(1), abs(pivot_elem_for_checking));
|
|
if (
|
|
!m_settings.abs_val_is_smaller_than_pivot_tolerance((m_row_eta_work_vector[lowest_row_of_the_bump] - pivot_elem_for_checking) / denom)) {
|
|
set_status(LU_status::Degenerated);
|
|
// LP_OUT(m_settings, "diagonal element is off" << std::endl);
|
|
return nullptr;
|
|
}
|
|
}
|
|
#ifdef Z3DEBUG
|
|
auto ret = new row_eta_matrix<typename M::coefftype, typename M::argtype>(replaced_column, lowest_row_of_the_bump, m_dim);
|
|
#else
|
|
auto ret = new row_eta_matrix<typename M::coefftype, typename M::argtype>(replaced_column, lowest_row_of_the_bump);
|
|
#endif
|
|
|
|
for (auto j : m_row_eta_work_vector.m_index) {
|
|
if (j < lowest_row_of_the_bump) {
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|
auto & v = m_row_eta_work_vector[j];
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|
if (!is_zero(v)) {
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|
if (!m_settings.abs_val_is_smaller_than_drop_tolerance(v)){
|
|
ret->push_back(j, v);
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|
}
|
|
v = numeric_traits<T>::zero();
|
|
}
|
|
}
|
|
} // now the lowest_row_of_the_bump contains the rest of the row to the right of the bump with correct values
|
|
return ret;
|
|
}
|
|
|
|
template <typename M>
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|
void lu<M>::replace_column(T pivot_elem_for_checking, indexed_vector<T> & w, unsigned leaving_column_of_U){
|
|
m_refactor_counter++;
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|
unsigned replaced_column = transform_U_to_V_by_replacing_column( w, leaving_column_of_U);
|
|
unsigned lowest_row_of_the_bump = m_U.lowest_row_in_column(replaced_column);
|
|
m_r_wave.init(m_dim);
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|
calculate_r_wave_and_update_U(replaced_column, lowest_row_of_the_bump, m_r_wave);
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|
auto row_eta = get_row_eta_matrix_and_set_row_vector(replaced_column, lowest_row_of_the_bump, pivot_elem_for_checking);
|
|
|
|
if (get_status() == LU_status::Degenerated) {
|
|
m_row_eta_work_vector.clear_all();
|
|
return;
|
|
}
|
|
m_Q.multiply_by_permutation_from_right(m_r_wave);
|
|
m_R.multiply_by_permutation_reverse_from_left(m_r_wave);
|
|
if (row_eta != nullptr) {
|
|
row_eta->conjugate_by_permutation(m_Q);
|
|
push_matrix_to_tail(row_eta);
|
|
}
|
|
calculate_Lwave_Pwave_for_bump(replaced_column, lowest_row_of_the_bump);
|
|
// lp_assert(m_U.is_upper_triangular_and_maximums_are_set_correctly_in_rows(m_settings));
|
|
// lp_assert(w.is_OK() && m_row_eta_work_vector.is_OK());
|
|
}
|
|
template <typename M>
|
|
void lu<M>::calculate_Lwave_Pwave_for_bump(unsigned replaced_column, unsigned lowest_row_of_the_bump){
|
|
T diagonal_elem;
|
|
if (replaced_column < lowest_row_of_the_bump) {
|
|
diagonal_elem = m_row_eta_work_vector[lowest_row_of_the_bump];
|
|
// lp_assert(m_row_eta_work_vector.is_OK());
|
|
m_U.set_row_from_work_vector_and_clean_work_vector_not_adjusted(m_U.adjust_row(lowest_row_of_the_bump), m_row_eta_work_vector, m_settings);
|
|
} else {
|
|
diagonal_elem = m_U(lowest_row_of_the_bump, lowest_row_of_the_bump); // todo - get it more efficiently
|
|
}
|
|
if (m_settings.abs_val_is_smaller_than_pivot_tolerance(diagonal_elem)) {
|
|
set_status(LU_status::Degenerated);
|
|
return;
|
|
}
|
|
|
|
calculate_Lwave_Pwave_for_last_row(lowest_row_of_the_bump, diagonal_elem);
|
|
// lp_assert(m_U.is_upper_triangular_and_maximums_are_set_correctly_in_rows(m_settings));
|
|
}
|
|
|
|
template <typename M>
|
|
void lu<M>::calculate_Lwave_Pwave_for_last_row(unsigned lowest_row_of_the_bump, T diagonal_element) {
|
|
auto l = new one_elem_on_diag<T, X>(lowest_row_of_the_bump, diagonal_element);
|
|
#ifdef Z3DEBUG
|
|
l->set_number_of_columns(m_dim);
|
|
#endif
|
|
push_matrix_to_tail(l);
|
|
m_U.divide_row_by_constant(lowest_row_of_the_bump, diagonal_element, m_settings);
|
|
l->conjugate_by_permutation(m_Q);
|
|
}
|
|
|
|
template <typename M>
|
|
void init_factorization(lu<M>* & factorization, M & m_A, vector<unsigned> & m_basis, lp_settings &m_settings) {
|
|
if (factorization != nullptr)
|
|
delete factorization;
|
|
factorization = new lu<M>(m_A, m_basis, m_settings);
|
|
// if (factorization->get_status() != LU_status::OK)
|
|
// LP_OUT(m_settings, "failing in init_factorization" << std::endl);
|
|
}
|
|
|
|
#ifdef Z3DEBUG
|
|
template <typename M>
|
|
dense_matrix<typename M::coefftype, typename M::argtype> get_B(lu<M>& f, const vector<unsigned>& basis) {
|
|
lp_assert(basis.size() == f.dimension());
|
|
lp_assert(basis.size() == f.m_U.dimension());
|
|
dense_matrix<typename M::coefftype, typename M::argtype> B(f.dimension(), f.dimension());
|
|
for (unsigned i = 0; i < f.dimension(); i++)
|
|
for (unsigned j = 0; j < f.dimension(); j++)
|
|
B.set_elem(i, j, f.B_(i, j, basis));
|
|
|
|
return B;
|
|
}
|
|
template <typename M>
|
|
dense_matrix<typename M::coefftype, typename M::argtype> get_B(lu<M>& f) {
|
|
dense_matrix<typename M::coefftype, typename M::argtype> B(f.dimension(), f.dimension());
|
|
for (unsigned i = 0; i < f.dimension(); i++)
|
|
for (unsigned j = 0; j < f.dimension(); j++)
|
|
B.set_elem(i, j, f.m_A[i][j]);
|
|
|
|
return B;
|
|
}
|
|
#endif
|
|
}
|