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tidy, initial polysat
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
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Nikolaj Bjorner
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fc60690742
8 changed files with 496 additions and 32 deletions
264
src/math/polysat/fixplex_def.h
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264
src/math/polysat/fixplex_def.h
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/*++
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Copyright (c) 2021 Microsoft Corporation
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Module Name:
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fixplex_def.h
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Abstract:
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Fixed-precision unsigned integer simplex tableau.
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Author:
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Nikolaj Bjorner (nbjorner) 2021-03-19
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Jakob Rath 2021-04-6
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--*/
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#pragma once
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#include "math/polysat/fixplex.h"
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#include "math/simplex/sparse_matrix_def.h"
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namespace polysat {
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template<typename Ext>
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fixplex<Ext>::~fixplex() {
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reset();
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}
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template<typename Ext>
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void fixplex<Ext>::ensure_var(var_t v) {
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while (v >= m_vars.size()) {
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M.ensure_var(m_vars.size());
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m_vars.push_back(var_info());
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}
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if (m_to_patch.get_bounds() <= v)
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m_to_patch.set_bounds(2*v+1);
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}
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template<typename Ext>
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void fixplex<Ext>::reset() {
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M.reset();
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m_to_patch.reset();
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m_vars.reset();
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m_row2base.reset();
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m_left_basis.reset();
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m_base_vars.reset();
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}
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template<typename Ext>
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lbool fixplex<Ext>::make_feasible() {
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++m_stats.m_num_checks;
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m_left_basis.reset();
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m_infeasible_var = null_var;
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unsigned num_iterations = 0;
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unsigned num_repeated = 0;
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var_t v = null_var;
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m_bland = false;
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SASSERT(well_formed());
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while ((v = select_var_to_fix()) != null_var) {
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TRACE("simplex", display(tout << "v" << v << "\n"););
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if (!m_limit.inc() || num_iterations > m_max_iterations) {
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return l_undef;
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}
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check_blands_rule(v, num_repeated);
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if (!make_var_feasible(v)) {
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m_to_patch.insert(v);
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m_infeasible_var = v;
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++m_stats.m_num_infeasible;
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return l_false;
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}
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++num_iterations;
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}
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SASSERT(well_formed());
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return l_true;
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}
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template<typename Ext>
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typename fixplex<Ext>::row
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fixplex<Ext>::add_row(var_t base_var, unsigned num_vars, var_t const* vars, numeral const* coeffs) {
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row r = M.mk_row();
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for (unsigned i = 0; i < num_vars; ++i)
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if (coeffs[i] != 0)
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M.add_var(r, coeffs[i], vars[i]);
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numeral base_coeff = 0;
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numeral value = 0;
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bool has_base = false;
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for (auto const& e : M.row_entries(r)) {
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var_t v = e.m_var;
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if (v == base_var)
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base_coeff = e.m_coeff;
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else {
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has_base |= is_base(v);
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value += e.m_coeff * m_vars[v].m_value;
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}
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}
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SASSERT(base_coeff != 0);
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SASSERT(!is_base(base_var));
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while (m_row2base.size() <= r.id())
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m_row2base.push_back(null_var);
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m_row2base[r.id()] = base_var;
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m_vars[base_var].m_base2row = r.id();
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m_vars[base_var].m_is_base = true;
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m_vars[base_var].m_base_coeff = base_coeff;
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m_vars[base_vars].m_value = value / base_coeff;
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// TBD: record when base_coeff does not divide value
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add_patch(base_var);
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if (has_base) {
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m_to_fix_base.push_back(r.id());
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gauss_jordan();
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}
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SASSERT(well_formed_row(r));
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SASSERT(well_formed());
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return r;
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}
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template<typename Ext>
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void fixplex<Ext>::gauss_jordan() {
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while (!m_to_fix_base.empty()) {
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auto rid = m_to_fix_base.back();
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if (gauss_jordan(m_rows[rid])) {
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m_to_fix_base.pop_back();
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}
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}
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}
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template<typename Ext>
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bool fixplex<Ext>::gauss_jordan(row const& r) {
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auto base_var = m_row2base[r.id()];
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unsigned other_base = null_var;
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numeral c1;
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for (auto const& e : M.row_entries(r)) {
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var_t v = e.m_var;
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if (is_base(v) && v != base_var) {
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other_base = v;
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c1 = e.m_coeff;
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break;
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}
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}
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if (null_var == other_base)
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return true;
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auto c2 = m_vars[other_base].m_base_coeff;
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auto r2 = m_vars[other_base].m_base2row;
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unsigned exp1 = trailing_zeros(c1); // exponent of two for v in r
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unsigned exp2 = trailing_zeros(c2); // exponent of two for v in r2
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if (exp1 >= exp2) {
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// eliminate v from r
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}
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else {
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// eliminate v from r2,
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// make v the new base for r
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// perform gauss-jordan for both r and r2 (add to queue)
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}
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NOT_IMPLEMENTED_YET();
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return false;
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}
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#if 0
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/**
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\brief Make x_j the new base variable for row of x_i.
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x_i is assumed base variable of row r_i.
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x_j is assumed to have coefficient a_ij in r_i.
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a_ii*x_i + a_ij*x_j + r_i = 0
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current value of x_i is v_i
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new value of x_i is new_value
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a_ii*(x_i + new_value - x_i) + a_ij*((x_i - new_value)*a_ii/a_ij + x_j) + r_i = 0
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Let r_k be a row where x_j has coefficient x_kj != 0.
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r_k <- r_k * a_ij - r_i * a_kj
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*/
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template<typename Ext>
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void fixplex<Ext>::update_and_pivot(var_t x_i, var_t x_j, numeral const& a_ij, numeral const& new_value) {
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SASSERT(is_base(x_i));
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SASSERT(!is_base(x_j));
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var_info& x_iI = m_vars[x_i];
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numeral const& a_ii = x_iI.m_base_coeff;
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auto theta = x_iI.m_value - new_value;
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theta *= a_ii;
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theta /= a_ij;
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update_value(x_j, theta);
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SASSERT(new_value == x_iI.m_value);
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pivot(x_i, x_j, a_ij);
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}
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template<typename Ext>
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void fixplex<Ext>::pivot(var_t x_i, var_t x_j, numeral const& a_ij) {
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++m_stats.m_num_pivots;
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var_info& x_iI = m_vars[x_i];
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var_info& x_jI = m_vars[x_j];
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unsigned r_i = x_iI.m_base2row;
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m_row2base[r_i] = x_j;
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x_jI.m_base2row = r_i;
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x_jI.m_base_coeff = a_ij;
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x_jI.m_is_base = true;
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x_iI.m_is_base = false;
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add_patch(x_j);
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SASSERT(well_formed_row(row(r_i)));
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col_iterator it = M.col_begin(x_j), end = M.col_end(x_j);
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scoped_numeral a_kj(m), g(m);
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for (; it != end; ++it) {
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row r_k = it.get_row();
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if (r_k.id() != r_i) {
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a_kj = it.get_row_entry().m_coeff;
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a_kj.neg();
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M.mul(r_k, a_ij);
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M.add(r_k, a_kj, row(r_i));
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var_t s = m_row2base[r_k.id()];
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numeral& coeff = m_vars[s].m_base_coeff;
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m.mul(coeff, a_ij, coeff);
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M.gcd_normalize(r_k, g);
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if (!m.is_one(g)) {
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m.div(coeff, g, coeff);
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}
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SASSERT(well_formed_row(row(r_k)));
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}
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}
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SASSERT(well_formed());
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}
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template<typename Ext>
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void fixplex<Ext>::update_value(var_t v, eps_numeral const& delta) {
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if (em.is_zero(delta)) {
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return;
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}
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update_value_core(v, delta);
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col_iterator it = M.col_begin(v), end = M.col_end(v);
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// v <- v + delta
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// s*s_coeff + v*v_coeff + R = 0
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// ->
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// (v + delta)*v_coeff + (s - delta*v_coeff/s_coeff)*v + R = 0
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for (; it != end; ++it) {
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row r = it.get_row();
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var_t s = m_row2base[r.id()];
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var_info& si = m_vars[s];
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scoped_eps_numeral delta2(em);
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numeral const& coeff = it.get_row_entry().m_coeff;
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em.mul(delta, coeff, delta2);
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em.div(delta2, si.m_base_coeff, delta2);
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delta2.neg();
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update_value_core(s, delta2);
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}
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}
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template<typename Ext>
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void fixplex<Ext>::update_value_core(var_t v, eps_numeral const& delta) {
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eps_numeral& val = m_vars[v].m_value;
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em.add(val, delta, val);
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if (is_base(v)) {
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add_patch(v);
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}
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}
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#endif
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}
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