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#include <Eigen/Core>
USING_PART_OF_NAMESPACE_EIGEN
namespace Eigen {
template<typename Derived>
void echelon(MatrixBase<Derived>& m)
{
for(int k = 0; k < m.diagonal().size(); k++)
{
int rowOfBiggest, colOfBiggest;
int cornerRows = m.rows()-k, cornerCols = m.cols()-k;
m.corner(BottomRight, cornerRows, cornerCols)
.cwiseAbs()
.maxCoeff(&rowOfBiggest, &colOfBiggest);
m.row(k).swap(m.row(k+rowOfBiggest));
m.col(k).swap(m.col(k+colOfBiggest));
// important performance tip:
// in a complex expression such as below it can be very important to fine-tune
// exactly where evaluation occurs. The parentheses and .eval() below ensure
// that the quotient is computed only once, and that the evaluation caused
// by operator* occurs last.
m.corner(BottomRight, cornerRows-1, cornerCols)
-= m.col(k).end(cornerRows-1) * (m.row(k).end(cornerCols) / m(k,k)).eval();
}
}
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;
for(int i = 0; i < 1000000; i++)
echelon(m);
cout << "Now m is:" << endl << m << endl;
}
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