bool gaussian_elimination(vvd &matrix, vd &output) {
for (int i = 0; i < matrix.size(); i++) {
int pivot = find_pivot(matrix, i);
if (fabs(matrix[pivot][i]) < EPS) {
return false;
}
swap_row(matrix, pivot, i);
double factor = matrix[i][i];
for (int j = 0; j < matrix[i].size(); j++) {
matrix[i][j] /= factor;
}
for (int j = 0; j < matrix.size(); j++) {
if (j == i) {
continue;
}
factor = matrix[j][i];
for (int k = 0; k < matrix[j].size(); k++) {
matrix[j][k] -= factor*matrix[i][k];
}
}
}
output.clear();
for (int i = 0; i < matrix.size(); i++) {
output.push_back(matrix[i][matrix[i].size() - 1]);
}
return true;
}
int find_pivot(const vvd &matrix, int index) {
double max_value = fabs(matrix[index][index]);
int max_index = index;
for (int i = index + 1; i < matrix.size(); i++) {
if (fabs(matrix[i][index]) > max_value) {
max_value = fabs(matrix[i][index]);
max_index = i;
}
}
return max_index;
}
void printTask(const vvd& a, const vd& b, const vd& c, const std::string& filename = "task.txt")
{
size_t n = c.size();
size_t m = a.size();
std::ofstream out(filename);
for (size_t i = 0; i < n; ++i)
{
auto& t = c[i];
if (std::abs(t) < EPS)
{
continue;
}
if (t > 0)
{
out << "+\t" << t;
}
if (t < 0)
{
out << "-\t" << -t;
}
out << " * x" << i + 1 << "\t";
}
out << "-----> MAX\n";
for (size_t i = 0; i < m; ++i)
{
out << "x" << n + i + 1 << "\t=\t" << b[i] << "\t";
for (size_t j = 0; j < n; ++j)
{
auto t = -a[i][j];
if (std::abs(t) < EPS)
{
continue;
}
if (t > 0)
{
out << "+\t" << t;
}
if (t < 0)
{
out << "-\t" << -t;
}
out << " * x" << j + 1 << "\t";
}
out << endl;
}
}
void getDualProblem(const vvd& a, vd& b, vd& c, vvd& dual_a, vd& dual_b, vd& dual_c)
{
for (auto x : b)
{
dual_c.push_back(-x);
}
for (auto x : c)
{
dual_b.push_back(-x);
}
dual_a.assign(a[0].size(), vd());
for (size_t i = 0; i < a.size(); ++i)
{
for (size_t j = 0; j < a[i].size(); ++j)
{
dual_a[j].push_back(-a[i][j]);
}
}
}
bool gaussian(vvd& A) { int m=A.size(), n=A[0].size()-1; vector<bool> used(m,0);
for (int c = 0; c < n; ++c) for (int r = 0; r < m; ++r)
if (!used[r] && !ISZERO(A[r][c]) ) { pivot(A, r, c); used[r] = true; }
for (int r = 0; r < m; ++r) if(!used[r] && !ISZERO(A[r].back())) return false;
return true; }
void pivot(vvd& A, int r, int c) { // A is A|b
int m = A.size(), n = A[0].size(); ld tmp = A[r][c];
for (int i = 0; i < n; ++i) A[r][i]/=tmp;
for (int i = 0; i < m; ++i) if (i != r) { ld k = A[i][c];
for(int j = 0; j < n; ++j) A[i][j] -= A[r][j]*k; } }