int btLemkeAlgorithm::findLexicographicMinimum(const btMatrixXu& A, const int & pivotColIndex) {
int RowIndex = 0;
int dim = A.rows();
btAlignedObjectArray<btVectorXu> Rows;
for (int row = 0; row < dim; row++)
{
btVectorXu vec(dim + 1);
vec.setZero();//, INIT, 0.)
Rows.push_back(vec);
btScalar a = A(row, pivotColIndex);
if (a > 0) {
Rows[row][0] = A(row, 2 * dim + 1) / a;
Rows[row][1] = A(row, 2 * dim) / a;
for (int j = 2; j < dim + 1; j++)
Rows[row][j] = A(row, j - 1) / a;
#ifdef BT_DEBUG_OSTREAM
// if (DEBUGLEVEL) {
// cout << "Rows(" << row << ") = " << Rows[row] << endl;
// }
#endif
}
}
for (int i = 0; i < Rows.size(); i++)
{
if (Rows[i].nrm2() > 0.) {
int j = 0;
for (; j < Rows.size(); j++)
{
if(i != j)
{
if(Rows[j].nrm2() > 0.)
{
btVectorXu test(dim + 1);
for (int ii=0;ii<dim+1;ii++)
{
test[ii] = Rows[j][ii] - Rows[i][ii];
}
//=Rows[j] - Rows[i]
if (! LexicographicPositive(test))
break;
}
}
}
if (j == Rows.size())
{
RowIndex += i;
break;
}
}
}
return RowIndex;
}
void btLemkeAlgorithm::GaussJordanEliminationStep(btMatrixXu& A, int pivotRowIndex, int pivotColumnIndex, const btAlignedObjectArray<int>& basis)
{
btScalar a = -1 / A(pivotRowIndex, pivotColumnIndex);
#ifdef BT_DEBUG_OSTREAM
cout << A << std::endl;
#endif
for (int i = 0; i < A.rows(); i++)
{
if (i != pivotRowIndex)
{
for (int j = 0; j < A.cols(); j++)
{
if (j != pivotColumnIndex)
{
btScalar v = A(i, j);
v += A(pivotRowIndex, j) * A(i, pivotColumnIndex) * a;
A.setElem(i, j, v);
}
}
}
}
#ifdef BT_DEBUG_OSTREAM
cout << A << std::endl;
#endif //BT_DEBUG_OSTREAM
for (int i = 0; i < A.cols(); i++)
{
A.mulElem(pivotRowIndex, i,-a);
}
#ifdef BT_DEBUG_OSTREAM
cout << A << std::endl;
#endif //#ifdef BT_DEBUG_OSTREAM
for (int i = 0; i < A.rows(); i++)
{
if (i != pivotRowIndex)
{
A.setElem(i, pivotColumnIndex,0);
}
}
#ifdef BT_DEBUG_OSTREAM
cout << A << std::endl;
#endif //#ifdef BT_DEBUG_OSTREAM
}