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z3/src/test/model_based_opt.cpp
Nikolaj Bjorner 813da35539 fix unit test 
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
2025-02-17 20:36:38 -08:00

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#include "math/simplex/model_based_opt.h"
#include "util/util.h"
#include "util/uint_set.h"
#include <iostream>
typedef opt::model_based_opt::var var;
static void add_ineq(opt::model_based_opt& mbo, unsigned x, int a, int k, opt::ineq_type rel) {
vector<var> vars;
vars.push_back(var(x, rational(a)));
mbo.add_constraint(vars, rational(k), rel);
}
static void add_ineq(opt::model_based_opt& mbo,
unsigned x, int a,
unsigned y, int b, int k,
opt::ineq_type rel) {
vector<var> vars;
vars.push_back(var(x, rational(a)));
vars.push_back(var(y, rational(b)));
mbo.add_constraint(vars, rational(k), rel);
}
#if 0
static void add_ineq(opt::model_based_opt& mbo,
unsigned x, int a,
unsigned y, int b,
unsigned z, int c, int k,
opt::ineq_type rel) {
vector<var> vars;
vars.push_back(var(x, rational(a)));
vars.push_back(var(y, rational(b)));
vars.push_back(var(z, rational(c)));
mbo.add_constraint(vars, rational(k), rel);
}
#endif
static void add_random_ineq(opt::model_based_opt& mbo,
random_gen& r,
svector<int> const& values,
unsigned max_vars,
unsigned max_coeff) {
unsigned num_vars = values.size();
uint_set used_vars;
vector<var> vars;
int value = 0;
for (unsigned i = 0; i < max_vars; ++i) {
unsigned x = r(num_vars);
if (used_vars.contains(x)) {
continue;
}
used_vars.insert(x);
int coeff = r(max_coeff + 1);
if (coeff == 0) {
continue;
}
unsigned sign = r(2);
coeff = sign == 0 ? coeff : -coeff;
vars.push_back(var(x, rational(coeff)));
value += coeff*values[x];
}
unsigned abs_value = value < 0 ? - value : value;
// value + k <= 0
// k <= - value
// range for k is 2*|value|
// k <= - value - range
opt::ineq_type rel = opt::t_le;
int coeff = 0;
if (r(4) == 0) {
rel = opt::t_eq;
coeff = -value;
}
else {
if (abs_value > 0) {
coeff = -value - r(2*abs_value);
}
else {
coeff = 0;
}
if (coeff != -value && r(3) == 0) {
rel = opt::t_lt;
}
}
mbo.add_constraint(vars, rational(coeff), rel);
}
static void check_random_ineqs(random_gen& r, unsigned num_vars, unsigned max_value, unsigned num_ineqs, unsigned max_vars, unsigned max_coeff) {
opt::model_based_opt mbo;
svector<int> values;
for (unsigned i = 0; i < num_vars; ++i) {
values.push_back(r(max_value + 1));
mbo.add_var(rational(values.back()));
}
for (unsigned i = 0; i < num_ineqs; ++i) {
add_random_ineq(mbo, r, values, max_vars, max_coeff);
}
vector<var> vars;
vars.reset();
vars.push_back(var(0, rational(2)));
vars.push_back(var(1, rational(-2)));
mbo.set_objective(vars, rational(0));
mbo.display(std::cout);
opt::inf_eps value = mbo.maximize();
std::cout << "optimal: " << value << "\n";
mbo.display(std::cout);
for (unsigned i = 0; i < values.size(); ++i) {
std::cout << i << ": " << values[i] << " -> " << mbo.get_value(i) << "\n";
}
}
static void check_random_ineqs() {
random_gen r(1);
for (unsigned i = 0; i < 1009; ++i) {
check_random_ineqs(r, 4, 5, 5, 3, 6);
}
}
// test with upper bounds
static void test1() {
opt::model_based_opt mbo;
vector<var> vars;
unsigned x = mbo.add_var(rational(2));
unsigned y = mbo.add_var(rational(3));
unsigned z = mbo.add_var(rational(4));
unsigned u = mbo.add_var(rational(5));
add_ineq(mbo, x, 1, y, -1, 0, opt::t_le);
add_ineq(mbo, x, 1, z, -1, 0, opt::t_le);
add_ineq(mbo, y, 1, u, -1, 0, opt::t_le);
add_ineq(mbo, z, 1, u, -1, 1, opt::t_le);
add_ineq(mbo, u, 1, -6, opt::t_le);
vars.reset();
vars.push_back(var(x, rational(2)));
mbo.set_objective(vars, rational(0));
opt::inf_eps value = mbo.maximize();
std::cout << value << "\n";
std::cout << "x: " << mbo.get_value(x) << "\n";
std::cout << "y: " << mbo.get_value(y) << "\n";
std::cout << "z: " << mbo.get_value(z) << "\n";
std::cout << "u: " << mbo.get_value(u) << "\n";
}
// test with lower bounds
static void test2() {
opt::model_based_opt mbo;
vector<var> vars;
unsigned x = mbo.add_var(rational(5));
unsigned y = mbo.add_var(rational(4));
unsigned z = mbo.add_var(rational(3));
unsigned u = mbo.add_var(rational(2));
add_ineq(mbo, x, -1, y, 1, 0, opt::t_le);
add_ineq(mbo, x, -1, z, 1, 0, opt::t_le);
add_ineq(mbo, y, -1, u, 1, 0, opt::t_le);
add_ineq(mbo, z, -1, u, 1, 1, opt::t_le);
add_ineq(mbo, u, -1, -6, opt::t_le);
vars.reset();
vars.push_back(var(x, rational(-2)));
mbo.set_objective(vars, rational(0));
opt::inf_eps value = mbo.maximize();
std::cout << value << "\n";
}
// test unbounded
static void test3() {
opt::model_based_opt mbo;
vector<var> vars;
unsigned x = mbo.add_var(rational(2));
unsigned y = mbo.add_var(rational(3));
unsigned z = mbo.add_var(rational(4));
unsigned u = mbo.add_var(rational(5));
add_ineq(mbo, x, 1, y, -1, 0, opt::t_le);
add_ineq(mbo, x, 1, z, -1, 0, opt::t_le);
add_ineq(mbo, y, 1, u, -1, 0, opt::t_le);
add_ineq(mbo, z, 1, u, -1, 1, opt::t_le);
vars.reset();
vars.push_back(var(x, rational(2)));
mbo.set_objective(vars, rational(0));
opt::inf_eps value = mbo.maximize();
std::cout << value << "\n";
}
// test strict
static void test4() {
opt::model_based_opt mbo;
vector<var> vars;
unsigned x = mbo.add_var(rational(2));
unsigned y = mbo.add_var(rational(3));
unsigned z = mbo.add_var(rational(4));
unsigned u = mbo.add_var(rational(5));
add_ineq(mbo, x, 1, y, -1, 0, opt::t_lt);
add_ineq(mbo, x, 1, z, -1, 0, opt::t_lt);
add_ineq(mbo, y, 1, u, -1, 0, opt::t_le);
add_ineq(mbo, z, 1, u, -1, 1, opt::t_le);
add_ineq(mbo, u, 1, -6, opt::t_le);
vars.reset();
vars.push_back(var(x, rational(2)));
mbo.set_objective(vars, rational(0));
opt::inf_eps value = mbo.maximize();
std::cout << value << "\n";
std::cout << "x: " << mbo.get_value(x) << "\n";
std::cout << "y: " << mbo.get_value(y) << "\n";
std::cout << "z: " << mbo.get_value(z) << "\n";
std::cout << "u: " << mbo.get_value(u) << "\n";
}
static void display_project(vector<opt::model_based_opt::def_ref> const& defs) {
for (auto const& d : defs) {
if (d)
std::cout << *d << "\n";
}
}
static void test5() {
opt::model_based_opt mbo;
unsigned x = mbo.add_var(rational(2));
unsigned y = mbo.add_var(rational(3));
unsigned z = mbo.add_var(rational(4));
unsigned u = mbo.add_var(rational(5));
add_ineq(mbo, x, 1, y, -1, 0, opt::t_le);
add_ineq(mbo, x, 1, z, -1, 0, opt::t_le);
add_ineq(mbo, y, 1, u, -1, 0, opt::t_le);
add_ineq(mbo, z, 1, u, -1, 1, opt::t_le);
unsigned vars[2] = { y, z };
display_project(mbo.project(1, vars, true));
mbo.display(std::cout);
display_project(mbo.project(1, vars, true));
mbo.display(std::cout);
display_project(mbo.project(1, vars+1, true));
mbo.display(std::cout);
vector<opt::model_based_opt::row> rows;
mbo.get_live_rows(rows);
}
static void test6() {
opt::model_based_opt mbo;
unsigned x0 = mbo.add_var(rational(1));
unsigned x = mbo.add_var(rational(2));
unsigned y = mbo.add_var(rational(3));
unsigned z = mbo.add_var(rational(4));
unsigned u = mbo.add_var(rational(5));
unsigned v = mbo.add_var(rational(6));
unsigned w = mbo.add_var(rational(6));
add_ineq(mbo, x0, 1, y, -1, 0, opt::t_le);
add_ineq(mbo, x, 1, y, -1, 0, opt::t_le);
add_ineq(mbo, y, 1, u, -1, 0, opt::t_le);
add_ineq(mbo, y, 1, z, -1, 1, opt::t_le);
add_ineq(mbo, y, 1, v, -1, 1, opt::t_le);
add_ineq(mbo, y, 1, w, -1, 1, opt::t_le);
mbo.display(std::cout);
display_project(mbo.project(1, &y, true));
mbo.display(std::cout);
}
static void test7() {
opt::model_based_opt mbo;
unsigned x0 = mbo.add_var(rational(2));
unsigned x = mbo.add_var(rational(1));
unsigned y = mbo.add_var(rational(3));
unsigned z = mbo.add_var(rational(4));
unsigned u = mbo.add_var(rational(5));
unsigned v = mbo.add_var(rational(6));
unsigned w = mbo.add_var(rational(6));
add_ineq(mbo, x0, 1, y, -1, 0, opt::t_le);
add_ineq(mbo, x, 1, y, -1, 0, opt::t_lt);
add_ineq(mbo, y, 1, u, -1, 0, opt::t_le);
add_ineq(mbo, y, 1, z, -1, 1, opt::t_le);
add_ineq(mbo, y, 1, v, -1, 1, opt::t_le);
add_ineq(mbo, y, 1, w, -1, 1, opt::t_lt);
mbo.display(std::cout);
display_project(mbo.project(1, &y, true));
mbo.display(std::cout);
}
static void test8() {
opt::model_based_opt mbo;
unsigned x0 = mbo.add_var(rational(2));
unsigned x = mbo.add_var(rational(1));
unsigned y = mbo.add_var(rational(3));
unsigned z = mbo.add_var(rational(4));
unsigned u = mbo.add_var(rational(5));
unsigned v = mbo.add_var(rational(6));
// unsigned w = mbo.add_var(rational(6));
add_ineq(mbo, x0, 1, y, -1, 0, opt::t_le);
add_ineq(mbo, x, 1, y, -1, 0, opt::t_lt);
add_ineq(mbo, y, 1, u, -1, 0, opt::t_le);
add_ineq(mbo, y, 1, z, -1, 1, opt::t_le);
add_ineq(mbo, y, 1, v, -1, 1, opt::t_le);
mbo.display(std::cout);
display_project(mbo.project(1, &y, true));
mbo.display(std::cout);
}
static void test9() {
opt::model_based_opt mbo;
unsigned x0 = mbo.add_var(rational(2), true);
unsigned x = mbo.add_var(rational(1), true);
unsigned y = mbo.add_var(rational(3), true);
unsigned z = mbo.add_var(rational(4), true);
unsigned u = mbo.add_var(rational(5), true);
unsigned v = mbo.add_var(rational(6), true);
add_ineq(mbo, x0, 1, y, -1, 0, opt::t_le);
add_ineq(mbo, x, 1, y, -1, 0, opt::t_lt);
add_ineq(mbo, y, 1, u, -1, 0, opt::t_le);
add_ineq(mbo, y, 1, z, -1, 1, opt::t_le);
add_ineq(mbo, y, 1, v, -1, 1, opt::t_le);
mbo.display(std::cout);
display_project(mbo.project(1, &y, true));
mbo.display(std::cout);
}
static void test10() {
opt::model_based_opt mbo;
unsigned x0 = mbo.add_var(rational(2), true);
unsigned x = mbo.add_var(rational(1), true);
unsigned y = mbo.add_var(rational(3), true);
unsigned z = mbo.add_var(rational(4), true);
unsigned u = mbo.add_var(rational(5), true);
unsigned v = mbo.add_var(rational(6), true);
add_ineq(mbo, x0, 1, y, -2, 0, opt::t_le);
add_ineq(mbo, x, 1, y, -2, 0, opt::t_lt);
add_ineq(mbo, y, 3, u, -4, 0, opt::t_le);
add_ineq(mbo, y, 3, z, -5, 1, opt::t_le);
add_ineq(mbo, y, 3, v, -6, 1, opt::t_le);
mbo.display(std::cout);
display_project(mbo.project(1, &y, true));
mbo.display(std::cout);
display_project(mbo.project(1, &x0, true));
mbo.display(std::cout);
}
static void test11() {
{
opt::model_based_opt mbo;
unsigned s = mbo.add_var(rational(2), true);
unsigned a = mbo.add_var(rational(1), true);
unsigned t = mbo.add_var(rational(3), true);
add_ineq(mbo, s, 1, a, -2, 0, opt::t_le); // s - 2a <= 0
add_ineq(mbo, a, 2, t, -1, 0, opt::t_le); // 2a - t <= 0
mbo.display(std::cout);
display_project(mbo.project(1, &a, true));
mbo.display(std::cout);
}
{
opt::model_based_opt mbo;
unsigned s = mbo.add_var(rational(3), true);
unsigned a = mbo.add_var(rational(2), true);
unsigned t = mbo.add_var(rational(4), true);
add_ineq(mbo, s, 1, a, -2, 0, opt::t_le); // s - 2a <= 0
add_ineq(mbo, a, 2, t, -1, 0, opt::t_le); // 2a - t <= 0
mbo.display(std::cout);
display_project(mbo.project(1, &a, true));
mbo.display(std::cout);
}
}
static void test12() {
opt::model_based_opt::def_ref d1(nullptr), d2(nullptr), d3(nullptr), d4(nullptr);
typedef opt::model_based_opt::var var;
d1 = alloc(opt::model_based_opt::var_def, var(1, rational(4)));
d1 = *d1 + *alloc(opt::model_based_opt::var_def, var(2, rational(3)));
d1 = *d1 + *alloc(opt::model_based_opt::var_def, var(3, rational(5)));
d1 = *d1 + rational(8);
d1 = *d1 / rational(7);
std::cout << *d1 << "\n";
d2 = alloc(opt::model_based_opt::var_def, var(3, rational(2)));
d2 = *d2 + *alloc(opt::model_based_opt::var_def, var(4, rational(2)));
d2 = *d2 + rational(5);
d2 = *d2 / rational(3);
d2 = *d2 / rational(3);
std::cout << *d2 << "\n";
d1 = d1->substitute(2, *d2);
std::cout << *d1 << "\n";
}
// test with mix of upper and lower bounds
void tst_model_based_opt() {
test12();
return;
test10();
check_random_ineqs();
test1();
test2();
test3();
test4();
test5();
test6();
test7();
test8();
test9();
test11();
}
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