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make HouseholderQR uses the Householder module

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This commit is contained in:
Gael Guennebaud
2009-08-16 19:22:15 +02:00
parent ef13c3e754
commit 737bed19c1
7 changed files with 96 additions and 102 deletions
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50
Eigen/src/Householder/Householder.h
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@@ -41,11 +41,34 @@ void makeTrivialHouseholder(
essential->setZero();
}
template<typename Derived>
void MatrixBase<Derived>::makeHouseholderInPlace(RealScalar *tau, Scalar *beta)
{
VectorBlock<Derived, ei_decrement_size<SizeAtCompileTime>::ret> essentialPart(derived(), 1, size()-1);
makeHouseholder(&essentialPart, tau, beta);
}
/** Computes the elementary reflector H such that:
* \f$ H *this = [ beta 0 ... 0]^T \f$
* where the transformation H is:
* \f$ H = I - tau v v^*\f$
* and the vector v is:
* \f$ v^T = [1 essential^T] \f$
*
* On output:
* \param essential the essential part of the vector \c v
* \param tau the scaling factor of the householder transformation
* \param beta the result of H * \c *this
*
* \sa MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft(),
* MatrixBase::applyHouseholderOnTheRight()
*/
template<typename Derived>
template<typename EssentialPart>
void MatrixBase<Derived>::makeHouseholder(
EssentialPart *essential,
RealScalar *beta) const
RealScalar *tau,
Scalar *beta) const
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(EssentialPart)
RealScalar _squaredNorm = squaredNorm();
@@ -62,35 +85,38 @@ void MatrixBase<Derived>::makeHouseholder(
VectorBlock<Derived, EssentialPart::SizeAtCompileTime> tail(derived(), 1, size()-1);
*essential = tail / c0;
const RealScalar c0abs2 = ei_abs2(c0);
*beta = RealScalar(2) * c0abs2 / (c0abs2 + _squaredNorm - ei_abs2(coeff(0)));
*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& beta)
const RealScalar& tau,
Scalar* workspace)
{
Matrix<Scalar, 1, ColsAtCompileTime, PlainMatrixType::Options, 1, MaxColsAtCompileTime> tmp(cols());
Map<Matrix<Scalar, 1, ColsAtCompileTime, PlainMatrixType::Options, 1, MaxColsAtCompileTime> > tmp(workspace,cols());
Block<Derived, EssentialPart::SizeAtCompileTime, Derived::ColsAtCompileTime> bottom(derived(), 1, 0, rows()-1, cols());
tmp = (essential.adjoint() * bottom).lazy();
tmp.noalias() = essential.adjoint() * bottom;
tmp += row(0);
row(0) -= beta * tmp;
bottom -= beta * essential * tmp;
row(0) -= tau * tmp;
bottom.noalias() -= tau * essential * tmp;
}
template<typename Derived>
template<typename EssentialPart>
void MatrixBase<Derived>::applyHouseholderOnTheRight(
const EssentialPart& essential,
const RealScalar& beta)
const RealScalar& tau,
Scalar* workspace)
{
Matrix<Scalar, RowsAtCompileTime, 1, PlainMatrixType::Options, MaxRowsAtCompileTime, 1> tmp(rows());
Map<Matrix<Scalar, RowsAtCompileTime, 1, PlainMatrixType::Options, MaxRowsAtCompileTime, 1> > tmp(workspace,rows());
Block<Derived, Derived::RowsAtCompileTime, EssentialPart::SizeAtCompileTime> right(derived(), 0, 1, rows(), cols()-1);
tmp = (right * essential.conjugate()).lazy();
tmp.noalias() = right * essential.conjugate();
tmp += col(0);
col(0) -= beta * tmp;
right -= beta * tmp * essential.transpose();
col(0) -= tau * tmp;
right.noalias() -= tau * tmp * essential.transpose();
}
#endif // EIGEN_HOUSEHOLDER_H