static_matrix_def.h

/*++
Copyright (c) 2017 Microsoft Corporation

Module Name:

    <name>

Abstract:

    <abstract>

Author:

    Lev Nachmanson (levnach)

Revision History:


--*/
#pragma once

#include "util/vector.h"
#include <utility>
#include <set>
#include "math/lp/static_matrix.h"
namespace lp {
// each assignment for this matrix should be issued only once!!!

inline void addmul(double& r, double a, double b) { r += a*b; }
inline void addmul(mpq& r, mpq const& a, mpq const& b) { r.addmul(a, b); }

template <typename T, typename X>
void  static_matrix<T, X>::init_row_columns(unsigned m, unsigned n) {
    lp_assert(m_rows.size() == 0 && m_columns.size() == 0);
    for (unsigned i = 0; i < m; i++) {
        m_rows.push_back(row_strip<T>());
    }
    for (unsigned j = 0; j < n; j++) {
        m_columns.push_back(column_strip());
    }
}


template <typename T, typename X> void static_matrix<T, X>::scan_row_ii_to_offset_vector(const row_strip<T> & rvals) {
    for (unsigned j = 0; j < rvals.size(); j++)
        m_vector_of_row_offsets[rvals[j].var()] = j;
}


template <typename T, typename X> bool static_matrix<T, X>::pivot_row_to_row_given_cell(unsigned i, column_cell & c, unsigned pivot_col) {
    unsigned ii = c.var();
    lp_assert(i < row_count() && ii < column_count() && i != ii);
    T alpha = -get_val(c);
    lp_assert(!is_zero(alpha));
    auto & rowii = m_rows[ii];
    remove_element(rowii, rowii[c.offset()]);
    scan_row_ii_to_offset_vector(rowii);
    unsigned prev_size_ii = rowii.size();
    // run over the pivot row and update row ii
    for (const auto & iv : m_rows[i]) {
        unsigned j = iv.var();
        if (j == pivot_col) continue;
        lp_assert(!is_zero(iv.coeff()));
        int j_offs = m_vector_of_row_offsets[j];
        if (j_offs == -1) { // it is a new element
            T alv = alpha * iv.coeff();
            add_new_element(ii, j, alv);
        }
        else {
            addmul(rowii[j_offs].coeff(), iv.coeff(), alpha);
        }
    }
    // clean the work vector
    for (unsigned k = 0; k < prev_size_ii; k++) {
        m_vector_of_row_offsets[rowii[k].var()] = -1;
    }

    // remove zeroes
    for (unsigned k = rowii.size(); k-- > 0;  ) {
        if (is_zero(rowii[k].coeff()))
            remove_element(rowii, rowii[k]);
    }
    return !rowii.empty();
}


// constructor that copies columns of the basis from A
template <typename T, typename X>
static_matrix<T, X>::static_matrix(static_matrix const &A, unsigned * /* basis */) :
    m_vector_of_row_offsets(A.column_count(), numeric_traits<T>::zero()) {
    unsigned m = A.row_count();
    init_row_columns(m, m);
    for (; m-- > 0; ) 
        for (auto & col : A.m_columns[m]) 
            set(col.var(), m, A.get_column_cell(col));
}

template <typename T, typename X> void static_matrix<T, X>::clear() {
    m_vector_of_row_offsets.clear();
    m_rows.clear();
    m_columns.clear();
}

template <typename T, typename X> void static_matrix<T, X>::init_vector_of_row_offsets() {
    m_vector_of_row_offsets.clear();
    m_vector_of_row_offsets.resize(column_count(), -1);
}

template <typename T, typename X> void static_matrix<T, X>::init_empty_matrix(unsigned m, unsigned n) {
    init_vector_of_row_offsets();
    init_row_columns(m, n);
}

template <typename T, typename X> unsigned static_matrix<T, X>::lowest_row_in_column(unsigned col) {
    lp_assert(col < column_count());
    column_strip & colstrip = m_columns[col];
    lp_assert(colstrip.size() > 0);
    unsigned ret = 0;
    for (auto & t : colstrip) {
        if (t.var() > ret) {
            ret = t.var();
        }
    }
    return ret;
}

template <typename T, typename X> void static_matrix<T, X>::forget_last_columns(unsigned how_many_to_forget) {
    lp_assert(m_columns.size() >= how_many_to_forget);
    unsigned j = column_count() - 1;
    for (; how_many_to_forget-- > 0; ) {
        remove_last_column(j --);
    }
}

template <typename T, typename X> void static_matrix<T, X>::remove_last_column(unsigned j) {
    column_strip & col = m_columns.back();
    for (auto & it : col) {
        auto & row = m_rows[it.var()];
        unsigned offset = row.size() - 1;
        for (auto row_it = row.rbegin(); row_it != row.rend(); row_it ++) {
            if (row_it.var() == j) {
                row.erase(row.begin() + offset);
                break;
            }
            offset--;
        }
    }
    m_columns.pop_back();
    m_vector_of_row_offsets.pop_back();
}

template <typename T, typename X> void static_matrix<T, X>::set(unsigned row, unsigned col, T const & val) {
    if (numeric_traits<T>::is_zero(val)) return;
    lp_assert(row < row_count() && col < column_count());
    auto & r = m_rows[row];
    unsigned offs_in_cols = m_columns[col].size();
    m_columns[col].push_back(make_column_cell(row, r.size()));
    r.push_back(make_row_cell(col, offs_in_cols, val));
}

template <typename T, typename X>
std::set<std::pair<unsigned, unsigned>>  static_matrix<T, X>::get_domain() {
    std::set<std::pair<unsigned, unsigned>> ret;
    for (unsigned i = 0; i < m_rows.size(); i++) {
        for (auto &cell : m_rows[i]) {
            ret.insert(std::make_pair(i, cell.var()));
        }
    }
    return ret;
}


template <typename T, typename X> T static_matrix<T, X>::get_max_abs_in_row(unsigned row) const {
    T ret = numeric_traits<T>::zero();
    for (auto & t : m_rows[row]) {
        T a = abs(t.coeff());
        if (a > ret) {
            ret = a;
        }
    }
    return ret;
}

template <typename T, typename X> T static_matrix<T, X>::get_min_abs_in_row(unsigned row) const {
    bool first_time = true;
    T ret = numeric_traits<T>::zero();
    for (auto & t : m_rows[row]) {
        T a = abs(t.coeff());
        if (first_time) {
            ret = a;
            first_time = false;
        } else if (a < ret) {
            ret = a;
        }
    }
    return ret;
}


template <typename T, typename X> T static_matrix<T, X>::get_max_abs_in_column(unsigned column) const {
    T ret = numeric_traits<T>::zero();
    for (const auto & t : m_columns[column]) {
        T a = abs(get_val(t));
        if (a > ret) {
            ret = a;
        }
    }
    return ret;
}

template <typename T, typename X> T static_matrix<T, X>::get_min_abs_in_column(unsigned column) const {
    bool first_time = true;
    T ret = numeric_traits<T>::zero();
    for (auto & t : m_columns[column]) {
        T a = abs(get_val(t));
        if (first_time) {
            first_time = false;
            ret = a;
        } else if (a < ret) {
            ret = a;
        }
    }
    return ret;
}

#ifdef Z3DEBUG
template <typename T, typename X> void static_matrix<T, X>::check_consistency() {
    std::unordered_map<std::pair<unsigned, unsigned>, T> by_rows;
    for (unsigned i = 0; i < m_rows.size(); i++) {
        for (auto & t : m_rows[i]) {
            std::pair<unsigned, unsigned> p(i, t.var());
            lp_assert(by_rows.find(p) == by_rows.end());
            by_rows[p] = t.coeff();
        }
    }
    std::unordered_map<std::pair<unsigned, unsigned>, T> by_cols;
    for (unsigned i = 0; i < m_columns.size(); i++) {
        for (auto & t : m_columns[i]) {
            std::pair<unsigned, unsigned> p(t.var(), i);
            lp_assert(by_cols.find(p) == by_cols.end());
            by_cols[p] = get_val(t);
        }
    }
    lp_assert(by_rows.size() == by_cols.size());

    for (auto & t : by_rows) {
        auto ic = by_cols.find(t.first);
        lp_assert(ic != by_cols.end());
        lp_assert(t.second == ic->second);
    }
}
#endif


template <typename T, typename X> void static_matrix<T, X>::cross_out_row(unsigned k) {
#ifdef Z3DEBUG
    check_consistency();
#endif
    cross_out_row_from_columns(k, m_rows[k]);
    fix_row_indices_in_each_column_for_crossed_row(k);
    m_rows.erase(m_rows.begin() + k);
#ifdef Z3DEBUG
    regen_domain();
    check_consistency();
#endif
}

template <typename T, typename X> void static_matrix<T, X>::fix_row_indices_in_each_column_for_crossed_row(unsigned k) {
    for (auto & column : m_columns) 
        for (auto& cell : column)
            if (cell.var() > k) 
                cell.var()--;
}

template <typename T, typename X> void static_matrix<T, X>::cross_out_row_from_columns(unsigned k, row_strip<T> & row) {
    for (auto & t : row) {
        cross_out_row_from_column(t.var(), k);
    }
}

template <typename T, typename X> void static_matrix<T, X>::cross_out_row_from_column(unsigned col, unsigned k) {
    auto & s = m_columns[col];
    for (unsigned i = 0; i < s.size(); i++) {
        if (s[i].var() == k) {
            s.erase(s.begin() + i);
            break;
        }
    }
}

template <typename T, typename X> T static_matrix<T, X>::get_elem(unsigned i, unsigned j) const { // should not be used in efficient code !!!!
    for (auto & t : m_rows[i]) {
        if (t.var() == j) {
            return t.coeff();
        }
    }
    return numeric_traits<T>::zero();
}

template <typename T, typename X> T static_matrix<T, X>::get_balance() const {
    T ret = zero_of_type<T>();
    for (unsigned i = 0; i < row_count();  i++) {
        ret += get_row_balance(i);
    }
    return ret;
}

template <typename T, typename X> T static_matrix<T, X>::get_row_balance(unsigned row) const {
    T ret = zero_of_type<T>();
    for (auto & t : m_rows[row]) {
        if (numeric_traits<T>::is_zero(t.coeff())) continue;
        T a = abs(t.coeff());
        numeric_traits<T>::log(a);
        ret += a * a;
    }
    return ret;
}

template <typename T, typename X> bool static_matrix<T, X>::is_correct() const {
    for (auto & row : m_rows) {
        std::unordered_set<unsigned> s;
        for (auto & rc : row) {
            if (s.find(rc.var()) != s.end()) 
                return false;
            s.insert(rc.var());
            if (rc.var() >= m_columns.size())
                return false;
            if (rc.offset() >= m_columns[rc.var()].size())
                return false;
            if (rc.coeff() != get_val(m_columns[rc.var()][rc.offset()]))
                return false;
            if (is_zero(rc.coeff())) 
                return false;            
        }
    }
    
    for (auto & column : m_columns) {
        std::unordered_set<unsigned> s;
        for (auto & cc : column) {
            if (s.find(cc.var()) != s.end()) 
                return false;
            s.insert(cc.var());
            if (cc.var() >= m_rows.size())
                return false;
            if (cc.offset() >= m_rows[cc.var()].size())
                return false;
            if (get_val(cc) != m_rows[cc.var()][cc.offset()].coeff())
                return false;
        }
    }    
    return true;
}

template <typename T, typename X>
void static_matrix<T, X>::remove_element(vector<row_cell<T>> & row_vals, row_cell<T> & row_el_iv) {
    unsigned column_offset = row_el_iv.offset();
    auto & column_vals = m_columns[row_el_iv.var()];
    column_cell& cs = m_columns[row_el_iv.var()][column_offset];
    unsigned row_offset = cs.offset();
    if (column_offset != column_vals.size() - 1) {
        auto & cc = column_vals[column_offset] = column_vals.back(); // copy from the tail
        m_rows[cc.var()][cc.offset()].offset() = column_offset;
    }
    
    if (row_offset != row_vals.size() - 1) {
        auto & rc = row_vals[row_offset] = row_vals.back(); // copy from the tail
        m_columns[rc.var()][rc.offset()].offset() = row_offset;
    }

    column_vals.pop_back();
    row_vals.pop_back();
}

template <typename T, typename X>
void static_matrix<T, X>::add_new_element(unsigned row, unsigned col, const T& val) {
    auto & row_vals = m_rows[row];
    auto & col_vals = m_columns[col];
    unsigned row_el_offs = row_vals.size();
    unsigned col_el_offs = col_vals.size();
    row_vals.push_back(row_cell<T>(col, col_el_offs, val));
    col_vals.push_back(column_cell(row, row_el_offs));
}

}