// Implementation of class Matrix
#include <cmath>
#include <iostream>
// #include "Matrix.h"
#include "stdMatrix.h"

using namespace std;

// Row echelon form
int Matrix::gauss(double eps /* = 1e-8 */) { // Return rank of matrix
    int i = 0;
    int j = 0;
    while (i < m && j < n) {
        // Find the maximal element in j-th column
        int indMax = i;
        for (int k = i+1; k < m; ++k) {
            if (fabs(at(k, j)) > fabs(at(indMax, j))) {
                indMax = k;
            }
        }
        if (fabs(at(indMax, j)) <= eps) {
            // Zero column
            for (int k = i; k < m; ++k)
                at(k, j) = 0.;
            ++j;
            continue;
        }
        
        // Maximal element is in row indMax
        if (indMax != i) {
            // Swap rows i, indMax
            for (int k = j; k < n; ++k) {
                double tmp = at(i, k);
                at(i, k) = at(indMax, k);
                at(indMax, k) = (-tmp);
            }
        }
        // Now, the maximal element in j-th column is a_ij
        for (int k = i+1; k < m; ++k) {
            // Subtract i-th row from k-th row
            double r = at(k, j)/at(i, j);
            at(k, j) = 0.;
            for (int l = j+1; l < n; ++l) {
                at(k, l) -= at(i, l)*r;
            }
        }
        ++i; ++j;
    }
    // i == rank of matrix
    return i;
}

ostream& operator<<(ostream& s, const Matrix& matrix) {
    for (int i = 0; i < matrix.rows(); ++i) {
        for (int j = 0; j < matrix.cols(); ++j) {
            if (j > 0)
                s << " ";
            s << matrix.at(i, j);
        }
        s << endl;
    }
    return s;
}

istream& operator>>(istream& s, Matrix& matrix) {
    for (int i = 0; i < matrix.rows(); ++i) {
        for (int j = 0; j < matrix.cols(); ++j) {
            s >> matrix.at(i, j);
            if (!s.good())
                return s;
        }
    }
    return s;
}