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z3-z3-4.12.6.src.test.karr.cpp Maven / Gradle / Ivy
/*++
Copyright (c) 2015 Microsoft Corporation
--*/
#include "util/rlimit.h"
#include "math/hilbert/hilbert_basis.h"
#include
/*
Test generation of linear congruences a la Karr.
*/
namespace karr {
struct matrix {
vector > A;
vector b;
unsigned size() const { return A.size(); }
void reset() {
A.reset();
b.reset();
}
matrix& operator=(matrix const& other) {
reset();
append(other);
return *this;
}
void append(matrix const& other) {
A.append(other.A);
b.append(other.b);
}
void display(std::ostream& out) {
for (unsigned i = 0; i < A.size(); ++i) {
for (unsigned j = 0; j < A[i].size(); ++j) {
out << A[i][j] << " ";
}
out << " = " << -b[i] << "\n";
}
}
};
// treat src as a homogeneous matrix.
void dualizeH(matrix& dst, matrix const& src) {
reslimit rl;
hilbert_basis hb(rl);
for (unsigned i = 0; i < src.size(); ++i) {
vector v(src.A[i]);
v.push_back(src.b[i]);
hb.add_eq(v, rational(0));
}
for (unsigned i = 0; i < 1 + src.A[0].size(); ++i) {
hb.set_is_int(i);
}
lbool is_sat = hb.saturate();
hb.display(std::cout);
VERIFY(is_sat == l_true);
dst.reset();
unsigned basis_size = hb.get_basis_size();
for (unsigned i = 0; i < basis_size; ++i) {
bool is_initial;
vector soln;
hb.get_basis_solution(i, soln, is_initial);
if (!is_initial) {
dst.b.push_back(soln.back());
soln.pop_back();
dst.A.push_back(soln);
}
}
}
// treat src as an inhomegeneous matrix.
void dualizeI(matrix& dst, matrix const& src) {
reslimit rl;
hilbert_basis hb(rl);
for (unsigned i = 0; i < src.size(); ++i) {
hb.add_eq(src.A[i], -src.b[i]);
}
for (unsigned i = 0; i < src.A[0].size(); ++i) {
hb.set_is_int(i);
}
lbool is_sat = hb.saturate();
hb.display(std::cout);
VERIFY(is_sat == l_true);
dst.reset();
unsigned basis_size = hb.get_basis_size();
bool first_initial = true;
for (unsigned i = 0; i < basis_size; ++i) {
bool is_initial;
vector soln;
hb.get_basis_solution(i, soln, is_initial);
if (is_initial && first_initial) {
dst.A.push_back(soln);
dst.b.push_back(rational(1));
first_initial = false;
}
else if (!is_initial) {
dst.A.push_back(soln);
dst.b.push_back(rational(0));
}
}
}
void juxtapose(matrix& dst, matrix const& M, matrix const& N) {
dst = M;
dst.append(N);
}
void join(matrix& dst, matrix const& M, matrix const& N) {
matrix MD, ND, dstD;
dualizeI(MD, M);
dualizeI(ND, N);
juxtapose(dstD, MD, ND);
dualizeH(dst, dstD);
}
void joinD(matrix& dst, matrix const& MD, matrix const& ND) {
matrix dstD;
juxtapose(dstD, MD, ND);
dualizeH(dst, dstD);
}
void transition(
matrix& dst,
matrix const& src,
matrix const& Ab) {
matrix T;
// length of rows in Ab are twice as long as
// length of rows in src.
ENSURE(2*src.A[0].size() == Ab.A[0].size());
vector zeros;
for (unsigned i = 0; i < src.A[0].size(); ++i) {
zeros.push_back(rational(0));
}
for (unsigned i = 0; i < src.size(); ++i) {
T.A.push_back(src.A[i]);
T.A.back().append(zeros);
}
T.b.append(src.b);
T.append(Ab);
T.display(std::cout << "T:\n");
matrix TD;
dualizeI(TD, T);
TD.display(std::cout << "TD:\n");
for (unsigned i = 0; i < TD.size(); ++i) {
vector v;
v.append(src.size(), TD.A[i].data() + src.size());
dst.A.push_back(v);
dst.b.push_back(TD.b[i]);
}
dst.display(std::cout << "dst\n");
}
static vector V(int i, int j) {
vector v;
v.push_back(rational(i));
v.push_back(rational(j));
return v;
}
static vector V(int i, int j, int k, int l) {
vector v;
v.push_back(rational(i));
v.push_back(rational(j));
v.push_back(rational(k));
v.push_back(rational(l));
return v;
}
#if 0
static vector V(int i, int j, int k, int l, int m) {
vector v;
v.push_back(rational(i));
v.push_back(rational(j));
v.push_back(rational(k));
v.push_back(rational(l));
v.push_back(rational(m));
return v;
}
#endif
static vector V(int i, int j, int k, int l, int x, int y, int z) {
vector v;
v.push_back(rational(i));
v.push_back(rational(j));
v.push_back(rational(k));
v.push_back(rational(l));
v.push_back(rational(x));
v.push_back(rational(y));
v.push_back(rational(z));
return v;
}
#define R(_x_) rational(_x_)
static void tst1() {
matrix Theta;
matrix Ab;
//
Theta.A.push_back(V(1, 0));
Theta.b.push_back(R(0));
Theta.A.push_back(V(0, 1));
Theta.b.push_back(R(-2));
Theta.display(std::cout << "Theta\n");
Ab.A.push_back(V(-1, 0, 1, 0));
Ab.b.push_back(R(1));
Ab.A.push_back(V(-1, -2, 0, 1));
Ab.b.push_back(R(1));
Ab.display(std::cout << "Ab\n");
matrix ThetaD;
dualizeI(ThetaD, Theta);
ThetaD.display(std::cout);
matrix t1D, e1;
transition(t1D, Theta, Ab);
joinD(e1, t1D, ThetaD);
t1D.display(std::cout << "t1D\n");
e1.display(std::cout << "e1\n");
matrix t2D, e2;
transition(t2D, e1, Ab);
joinD(e2, t2D, ThetaD);
t2D.display(std::cout << "t2D\n");
e2.display(std::cout << "e2\n");
}
void tst2() {
/**
0 0 0 0 0 0 0 = 0
0 0 0 0 0 0 0 = 0
0 0 0 0 0 0 0 = 0
0 0 0 0 0 0 0 = 0
0 0 0 0 1 0 0 = 0
0 0 0 0 -1 0 0 = 0
0 1 0 0 0 0 0 = 0
0 -1 0 0 0 0 0 = 0
0 0 0 2 0 0 0 = 0
0 0 0 -2 0 0 0 = 0
*/
matrix ND;
ND.A.push_back(V(0,0,0,0,1,0,0)); ND.b.push_back(R(0));
ND.A.push_back(V(0,0,0,0,-1,0,0)); ND.b.push_back(R(0));
ND.A.push_back(V(0,1,0,0,0,0,0)); ND.b.push_back(R(0));
ND.A.push_back(V(0,-1,0,0,0,0,0)); ND.b.push_back(R(0));
ND.A.push_back(V(0,0,0,2,0,0,0)); ND.b.push_back(R(0));
ND.A.push_back(V(0,0,0,-2,0,0,0)); ND.b.push_back(R(0));
ND.display(std::cout << "ND\n");
matrix N;
dualizeH(N, ND);
N.display(std::cout << "N\n");
}
void tst3() {
/**
0 0 0 0 1 0 0 = 0
0 0 0 0 -1 0 0 = 0
0 1 0 0 0 0 0 = 0
0 -1 0 0 0 0 0 = 0
0 0 0 2 0 0 0 = 0
0 0 0 -2 0 0 0 = 0
*/
matrix ND;
ND.A.push_back(V(1,0)); ND.b.push_back(R(0));
ND.A.push_back(V(0,2)); ND.b.push_back(R(0));
ND.display(std::cout << "ND\n");
matrix N;
dualizeH(N, ND);
N.display(std::cout << "N\n");
}
};
void tst_karr() {
karr::tst3();
return;
karr::tst1();
}
