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#include <Eigen/Core>
USING_PART_OF_NAMESPACE_EIGEN
namespace Eigen {
template<typename Derived>
void echelon(MatrixBase<Derived>& m)
{
const int N = std::min(m.rows(), m.cols());
for(int k = 0; k < N; k++)
{
int rowOfBiggest, colOfBiggest;
int cornerRows = m.rows()-k;
int cornerCols = m.cols()-k;
m.corner(BottomRight, cornerRows, cornerCols)
.findBiggestCoeff(&rowOfBiggest, &colOfBiggest);
m.row(k).swap(m.row(k+rowOfBiggest));
m.col(k).swap(m.col(k+colOfBiggest));
for(int r = k+1; r < m.rows(); r++)
m.row(r).end(cornerCols) -= m.row(k).end(cornerCols) * m(r,k) / m(k,k);
}
}
template<typename Derived>
void doSomeRankPreservingOperations(MatrixBase<Derived>& m)
{
for(int a = 0; a < 3*(m.rows()+m.cols()); a++)
{
double d = ei_random<double>(-1,1);
int i = ei_random<int>(0,m.rows()-1); // i is a random row number
int j;
do {
j = ei_random<int>(0,m.rows()-1);
} while (i==j); // j is another one (must be different)
m.row(i) += d * m.row(j);
i = ei_random<int>(0,m.cols()-1); // i is a random column number
do {
j = ei_random<int>(0,m.cols()-1);
} while (i==j); // j is another one (must be different)
m.col(i) += d * m.col(j);
}
}
} // namespace Eigen
using namespace std;
int main(int, char **)
{
srand((unsigned int)time(0));
const int Rows = 6, Cols = 4;
typedef Matrix<double, Rows, Cols> Mat;
const int N = Rows < Cols ? Rows : Cols;
// start with a matrix m that's obviously of rank N-1
Mat m = Mat::identity(Rows, Cols); // args just in case of dyn. size
m.row(0) = m.row(1) = m.row(0) + m.row(1);
doSomeRankPreservingOperations(m);
// now m is still a matrix of rank N-1
cout << "Here's the matrix m:" << endl << m << endl;
cout << "Now let's echelon m:" << endl;
echelon(m);
cout << "Now m is:" << endl << m << endl;
}
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