devtools/eigen
1
0
Fork 0
mirror of https://gitlab.com/libeigen/eigen.git synced 2026-04-10 11:34:33 +08:00
Code Issues Packages Projects Releases Wiki Activity

change the make householder algorithm so that the remaining coefficient

Browse Source 
is real, and make Tridiagonalization use it
This commit is contained in:
Gael Guennebaud
2009-08-17 17:04:32 +02:00
parent e125c199bb
commit ff0f005d4c
7 changed files with 75 additions and 105 deletions
Download Patch File Download Diff File Expand all files Collapse all files

80
Eigen/src/QR/Tridiagonalization.h
View File

@@ -198,65 +198,29 @@ void Tridiagonalization<MatrixType>::_compute(MatrixType& matA, CoeffVectorType&
{
assert(matA.rows()==matA.cols());
int n = matA.rows();
for (int i = 0; i<n-2; ++i)
Matrix<Scalar,1,Dynamic> aux(n);
for (int i = 0; i<n-1; ++i)
{
// let's consider the vector v = i-th column starting at position i+1
int remainingSize = n-i-1;
RealScalar beta;
Scalar h;
matA.col(i).end(remainingSize).makeHouseholderInPlace(&h, &beta);
// start of the householder transformation
// squared norm of the vector v skipping the first element
RealScalar v1norm2 = matA.col(i).end(n-(i+2)).squaredNorm();
// Apply similarity transformation to remaining columns,
// i.e., A = H A H' where H = I - h v v' and v = matA.col(i).end(n-i-1)
matA.col(i).coeffRef(i+1) = 1;
// FIXME comparing against 1
if (ei_isMuchSmallerThan(v1norm2,static_cast<Scalar>(1)))
{
hCoeffs.coeffRef(i) = 0.;
}
else
{
Scalar v0 = matA.col(i).coeff(i+1);
RealScalar beta = ei_sqrt(ei_abs2(v0)+v1norm2);
if (ei_real(v0)>=0.)
beta = -beta;
matA.col(i).end(n-(i+2)) *= (Scalar(1)/(v0-beta));
matA.col(i).coeffRef(i+1) = beta;
Scalar h = (beta - v0) / beta;
// end of the householder transformation
hCoeffs.end(n-i-1) = (matA.corner(BottomRight,remainingSize,remainingSize).template selfadjointView<LowerTriangular>()
* (ei_conj(h) * matA.col(i).end(remainingSize)));
// Apply similarity transformation to remaining columns,
// i.e., A = H' A H where H = I - h v v' and v = matA.col(i).end(n-i-1)
matA.col(i).coeffRef(i+1) = 1;
hCoeffs.end(n-i-1) += (ei_conj(h)*Scalar(-0.5)*(hCoeffs.end(remainingSize).dot(matA.col(i).end(remainingSize)))) * matA.col(i).end(n-i-1);
hCoeffs.end(n-i-1) = (matA.corner(BottomRight,n-i-1,n-i-1).template selfadjointView<LowerTriangular>()
* (h * matA.col(i).end(n-i-1)));
matA.corner(BottomRight, remainingSize, remainingSize).template selfadjointView<LowerTriangular>()
.rankUpdate(matA.col(i).end(remainingSize), hCoeffs.end(remainingSize), -1);
hCoeffs.end(n-i-1) += (h*Scalar(-0.5)*(hCoeffs.end(n-i-1).dot(matA.col(i).end(n-i-1)))) * matA.col(i).end(n-i-1);
matA.corner(BottomRight, n-i-1, n-i-1).template selfadjointView<LowerTriangular>()
.rankUpdate(matA.col(i).end(n-i-1), hCoeffs.end(n-i-1), -1);
// note: at that point matA(i+1,i+1) is the (i+1)-th element of the final diagonal
// note: the sequence of the beta values leads to the subdiagonal entries
matA.col(i).coeffRef(i+1) = beta;
hCoeffs.coeffRef(i) = h;
}
}
if (NumTraits<Scalar>::IsComplex)
{
// Householder transformation on the remaining single scalar
int i = n-2;
Scalar v0 = matA.col(i).coeff(i+1);
RealScalar beta = ei_abs(v0);
if (ei_real(v0)>=RealScalar(0))
beta = -beta;
matA.col(i).coeffRef(i+1) = beta;
// FIXME comparing against 1
if(ei_isMuchSmallerThan(beta, Scalar(1))) hCoeffs.coeffRef(i) = Scalar(0);
else hCoeffs.coeffRef(i) = (beta - v0) / beta;
}
else
{
hCoeffs.coeffRef(n-2) = 0;
hCoeffs.coeffRef(i) = h;
}
}
@@ -280,16 +244,8 @@ void Tridiagonalization<MatrixType>::matrixQInPlace(MatrixBase<QDerived>* q) con
Matrix<Scalar,1,Dynamic> aux(n);
for (int i = n-2; i>=0; i--)
{
Scalar tmp = m_matrix.coeff(i+1,i);
m_matrix.const_cast_derived().coeffRef(i+1,i) = 1;
aux.end(n-i-1) = (m_hCoeffs.coeff(i) * m_matrix.col(i).end(n-i-1).adjoint() * matQ.corner(BottomRight,n-i-1,n-i-1)).lazy();
// rank one update, TODO ! make it works efficiently as expected
for (int j=i+1;j<n;++j)
matQ.col(j).end(n-i-1) -= aux.coeff(j) * m_matrix.col(i).end(n-i-1);
// matQ.corner(BottomRight,n-i-1,n-i-1) -= (m_matrix.col(i).end(n-i-1) * aux.end(n-i-1)).lazy();
m_matrix.const_cast_derived().coeffRef(i+1,i) = tmp;
matQ.corner(BottomRight,n-i-1,n-i-1)
.applyHouseholderOnTheLeft(m_matrix.col(i).end(n-i-2), ei_conj(m_hCoeffs.coeff(i)), &aux.coeffRef(0,0));
}
}