void NeighborColSwap
( Matrix<F>& Q,
Matrix<F>& R,
Int j )
{
DEBUG_CSE
typedef Base<F> Real;
const Int m = Q.Height();
ColSwap( R, j, j+1 );
if( j < m-1 )
{
Real c; F s;
Givens( R(j,j), R(j+1,j), c, s );
auto RBR = R( IR(j,END), IR(j,END) );
// RBR((0,1),:) := | c, s | RBR((0,1),:)
// | -conj(s), c |
RotateRows( c, s, RBR, 0, 1 );
// Since | c, s |^H = | c, -s |, the transformation
// | -conj(s), c | | conj(s), c |
//
// s |-> -s inverts a Givens rotation matrix.
//
// We therefore update
//
// Q(:,(j,j+1)) := Q(:,(j,j+1)) | c, -s |.
// | conj(s), c |
RotateCols( c, -s, Q, j, j+1 );
}
}
void NeighborColSwap
( Matrix<F>& Q,
Matrix<F>& R,
Int j )
{
DEBUG_CSE
typedef Base<F> Real;
const Int m = Q.Height();
ColSwap( R, j, j+1 );
if( j < m-1 )
{
Real c; F s;
Givens( R.Get(j,j), R.Get(j+1,j), c, s );
auto RBR = R( IR(j,END), IR(j,END) );
RotateRows( c, s, RBR, 0, 1 );
auto col1 = Q( ALL, IR(j) );
auto col2 = Q( ALL, IR(j+1) );
RotateCols( c, Conj(s), Q, j, j+1 );
}
}