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#include "../util.h"
constexpr double EPS = 1e-9;
constexpr int UNIQUE = 1;
constexpr int INCONSISTENT = 2;
constexpr int MULTIPLE = 3;
vector<vector<double>> mat;
#include <math/gauss.cpp>
vector<vector<double>> inverseMat(const vector<vector<double>>& m) {
int n = sz(m);
mat = m;
for (int i = 0; i < n; i++) {
if (sz(mat[i]) != n) cerr << "error: no square matrix" << FAIL;
mat[i].resize(2*n);
mat[i][n+i] = 1;
}
gauss(n); //the unique cetc. checks are not usefull since we dont solve an lgs...
vector<vector<double>> res(m);
for (int i = 0; i < n; i++) {
res[i] = vector<double>(mat[i].begin() + n, mat[i].end());
for (int j = 0; j < n; j++) {
if (j != i && mat[i][j] != 0) cerr << "error: not full rank?" << FAIL;
if (j == i && mat[i][j] == 0) cerr << "error: not full rank?" << FAIL;
}
}
return res;
}
vector<vector<double>> mul(const vector<vector<double>>& a, const vector<vector<double>>& b) {
int n = sz(a);
int m = sz(b[0]);
int x = sz(b);
if (sz(a[0]) != sz(b)) cerr << "error: wrong dimensions" << FAIL;
vector<vector<double>> res(n, vector<double>(m));
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
for (int k = 0; k < x; k++) {
res[i][j] += a[i][k] * b[k][j];
}
}
}
return res;
}
void test_tiny() {
mat = {
{1, 2, 3, 4},
{0, 5, 6, 7},
{0, 0, 8, 9},
};
if (gauss(sz(mat)) != UNIQUE) cerr << "error: 1" << FAIL;
mat = {
{-1, 1, 0, -1},
{ 2, 6, 0, 10},
{ 1, -2, 0, 0},
};
if (gauss(sz(mat)) != MULTIPLE) cerr << "error: 2" << FAIL;
mat = {
{-1, 1, 0, -1},
{ 2, 6, 0, 10},
{ 1, -2, 0, 1},
};
if (gauss(sz(mat)) != INCONSISTENT) cerr << "error: 3" << FAIL;
}
void stress_test_inv() {
ll queries = 0;
for (int tries = 0; tries < 20'000; tries++) {
int n = Random::integer<int>(1, 30);
vector<vector<double>> m(n);
for (auto& v : m) v = Random::reals<double>(n, 0, 1'000);
// m hopefully has full rank...
auto inv = inverseMat(m);
auto prod = mul(m, inv);
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (i == j && abs(prod[i][j] - 1) >= EPS) cerr << "error: not inverted " << prod[i][j] << FAIL;
if (i != j && abs(prod[i][j] - 0) >= EPS) cerr << "error: not inverted " << prod[i][j] << FAIL;
}
}
queries += n;
}
cerr << "tested random queries: " << queries << endl;
}
constexpr int N = 250;
void performance_test() {
timer t;
vector<vector<double>> m(N);
for (auto& v : m) v = Random::reals<double>(N, 0, 1'000);
mat = m;
t.start();
gauss(N);
t.stop();
hash_t hash = 0;
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
hash += mat[i][j];
}
}
if (t.time > 500) cerr << "too slow: " << t.time << FAIL;
cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl;
}
int main() {
test_tiny();
stress_test_inv();
performance_test();
}
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