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change the make householder algorithm so that the remaining coefficient

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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
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34
Eigen/src/Householder/Householder.h
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@@ -42,7 +42,7 @@ void makeTrivialHouseholder(
}
template<typename Derived>
void MatrixBase<Derived>::makeHouseholderInPlace(RealScalar *tau, Scalar *beta)
void MatrixBase<Derived>::makeHouseholderInPlace(Scalar *tau, RealScalar *beta)
{
VectorBlock<Derived, ei_decrement_size<SizeAtCompileTime>::ret> essentialPart(derived(), 1, size()-1);
makeHouseholder(&essentialPart, tau, beta);
@@ -67,33 +67,35 @@ template<typename Derived>
template<typename EssentialPart>
void MatrixBase<Derived>::makeHouseholder(
EssentialPart *essential,
RealScalar *tau,
Scalar *beta) const
Scalar *tau,
RealScalar *beta) const
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(EssentialPart)
RealScalar _squaredNorm = squaredNorm();
Scalar c0;
if(ei_abs2(coeff(0)) <= ei_abs2(precision<Scalar>()) * _squaredNorm)
VectorBlock<Derived, EssentialPart::SizeAtCompileTime> tail(derived(), 1, size()-1);
RealScalar tailSqNorm;
Scalar c0 = coeff(0);
if( (size()==1 || (tailSqNorm=tail.squaredNorm()) == RealScalar(0)) && ei_imag(c0)==RealScalar(0))
{
c0 = ei_sqrt(_squaredNorm);
*tau = 0;
*beta = ei_real(c0);
}
else
{
Scalar sign = coeff(0) / ei_abs(coeff(0));
c0 = coeff(0) + sign * ei_sqrt(_squaredNorm);
*beta = ei_sqrt(ei_abs2(c0) + tailSqNorm);
if (ei_real(c0)>=0.)
*beta = -*beta;
*essential = tail / (c0 - *beta);
*tau = ei_conj((*beta - c0) / *beta);
}
VectorBlock<Derived, EssentialPart::SizeAtCompileTime> tail(derived(), 1, size()-1);
*essential = tail / c0;
const RealScalar c0abs2 = ei_abs2(c0);
*tau = RealScalar(2) * c0abs2 / (c0abs2 + _squaredNorm - ei_abs2(coeff(0)));
*beta = coeff(0) - c0;
}
template<typename Derived>
template<typename EssentialPart>
void MatrixBase<Derived>::applyHouseholderOnTheLeft(
const EssentialPart& essential,
const RealScalar& tau,
const Scalar& tau,
Scalar* workspace)
{
Map<Matrix<Scalar, 1, ColsAtCompileTime, PlainMatrixType::Options, 1, MaxColsAtCompileTime> > tmp(workspace,cols());
@@ -108,7 +110,7 @@ template<typename Derived>
template<typename EssentialPart>
void MatrixBase<Derived>::applyHouseholderOnTheRight(
const EssentialPart& essential,
const RealScalar& tau,
const Scalar& tau,
Scalar* workspace)
{
Map<Matrix<Scalar, RowsAtCompileTime, 1, PlainMatrixType::Options, MaxRowsAtCompileTime, 1> > tmp(workspace,rows());