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* add a HouseholderSequence class (not good enough yet for Triadiagonalization and HessenbergDecomposition)

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* rework a bit AnyMatrixBase, and mobe it to a separate file
This commit is contained in:
Gael Guennebaud
2009-09-16 14:35:42 +02:00
parent 77f858f6ab
commit 49dd5d7847
12 changed files with 339 additions and 103 deletions
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37
Eigen/src/QR/HouseholderQR.h
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@@ -56,12 +56,13 @@ template<typename MatrixType> class HouseholderQR
Options = MatrixType::Options,
DiagSizeAtCompileTime = EIGEN_ENUM_MIN(ColsAtCompileTime,RowsAtCompileTime)
};
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime> MatrixQType;
typedef Matrix<Scalar, DiagSizeAtCompileTime, 1> HCoeffsType;
typedef Matrix<Scalar, 1, ColsAtCompileTime> RowVectorType;
typedef typename HouseholderSequence<MatrixQType,HCoeffsType>::ConjugateReturnType HouseholderSequenceType;
/**
* \brief Default Constructor.
@@ -97,7 +98,12 @@ template<typename MatrixType> class HouseholderQR
template<typename OtherDerived, typename ResultType>
void solve(const MatrixBase<OtherDerived>& b, ResultType *result) const;
MatrixQType matrixQ(void) const;
MatrixQType matrixQ() const;
HouseholderSequenceType matrixQAsHouseholderSequence() const
{
return HouseholderSequenceType(m_qr, m_hCoeffs.conjugate());
}
/** \returns a reference to the matrix where the Householder QR decomposition is stored
* in a LAPACK-compatible way.
@@ -169,7 +175,7 @@ HouseholderQR<MatrixType>& HouseholderQR<MatrixType>::compute(const MatrixType&
int rows = matrix.rows();
int cols = matrix.cols();
int size = std::min(rows,cols);
m_qr = matrix;
m_hCoeffs.resize(size);
@@ -206,15 +212,7 @@ void HouseholderQR<MatrixType>::solve(
result->resize(rows, cols);
*result = b;
Matrix<Scalar,1,MatrixType::ColsAtCompileTime> temp(cols);
for (int k = 0; k < cols; ++k)
{
int remainingSize = rows-k;
result->corner(BottomRight, remainingSize, cols)
.applyHouseholderOnTheLeft(m_qr.col(k).end(remainingSize-1), m_hCoeffs.coeff(k), &temp.coeffRef(0));
}
result->applyOnTheLeft(matrixQAsHouseholderSequence().inverse());
const int rank = std::min(result->rows(), result->cols());
m_qr.corner(TopLeft, rank, rank)
@@ -227,20 +225,7 @@ template<typename MatrixType>
typename HouseholderQR<MatrixType>::MatrixQType HouseholderQR<MatrixType>::matrixQ() const
{
ei_assert(m_isInitialized && "HouseholderQR is not initialized.");
// compute the product H'_0 H'_1 ... H'_n-1,
// where H_k is the k-th Householder transformation I - h_k v_k v_k'
// and v_k is the k-th Householder vector [1,m_qr(k+1,k), m_qr(k+2,k), ...]
int rows = m_qr.rows();
int cols = m_qr.cols();
int size = std::min(rows,cols);
MatrixQType res = MatrixQType::Identity(rows, rows);
Matrix<Scalar,1,MatrixType::RowsAtCompileTime> temp(rows);
for (int k = size-1; k >= 0; k--)
{
res.block(k, k, rows-k, rows-k)
.applyHouseholderOnTheLeft(m_qr.col(k).end(rows-k-1), ei_conj(m_hCoeffs.coeff(k)), &temp.coeffRef(k));
}
return res;
return matrixQAsHouseholderSequence();
}
#endif // EIGEN_HIDE_HEAVY_CODE