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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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23
Eigen/src/QR/QR.h
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@@ -53,7 +53,7 @@ template<typename MatrixType> class HouseholderQR
typedef typename MatrixType::RealScalar RealScalar;
typedef Block<MatrixType, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> MatrixRBlockType;
typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> MatrixTypeR;
typedef Matrix<RealScalar, MinSizeAtCompileTime, 1> HCoeffsType;
typedef Matrix<Scalar, MinSizeAtCompileTime, 1> HCoeffsType;
/**
* \brief Default Constructor.
@@ -132,11 +132,13 @@ HouseholderQR<MatrixType>& HouseholderQR<MatrixType>::compute(const MatrixType&
int remainingRows = rows - k;
int remainingCols = cols - k -1;
m_qr.col(k).end(remainingRows).makeHouseholderInPlace(&m_hCoeffs.coeffRef(k), &m_qr.coeffRef(k,k));
if (remainingRows>1 && remainingCols>0)
m_qr.corner(BottomRight, remainingRows, remainingCols)
.applyHouseholderOnTheLeft(m_qr.col(k).end(remainingRows-1), m_hCoeffs.coeffRef(k), &temp.coeffRef(k+1));
RealScalar beta;
m_qr.col(k).end(remainingRows).makeHouseholderInPlace(&m_hCoeffs.coeffRef(k), &beta);
m_qr.coeffRef(k,k) = beta;
// apply H to remaining part of m_qr from the left
m_qr.corner(BottomRight, remainingRows, remainingCols)
.applyHouseholderOnTheLeft(m_qr.col(k).end(remainingRows-1), m_hCoeffs.coeffRef(k), &temp.coeffRef(k+1));
}
m_isInitialized = true;
return *this;
@@ -163,7 +165,7 @@ void HouseholderQR<MatrixType>::solve(
int remainingSize = rows-k;
result->corner(BottomRight, remainingSize, cols)
.applyHouseholderOnTheLeft(m_qr.col(k).end(remainingSize-1), ei_real(m_hCoeffs.coeff(k)), &temp.coeffRef(0));
.applyHouseholderOnTheLeft(m_qr.col(k).end(remainingSize-1), m_hCoeffs.coeff(k), &temp.coeffRef(0));
}
const int rank = std::min(result->rows(), result->cols());
@@ -177,8 +179,8 @@ template<typename MatrixType>
MatrixType HouseholderQR<MatrixType>::matrixQ() const
{
ei_assert(m_isInitialized && "HouseholderQR is not initialized.");
// compute the product Q_0 Q_1 ... Q_n-1,
// where Q_k is the k-th Householder transformation I - h_k v_k v_k'
// 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();
@@ -187,9 +189,8 @@ MatrixType HouseholderQR<MatrixType>::matrixQ() const
for (int k = cols-1; k >= 0; k--)
{
int remainingSize = rows-k;
res.corner(BottomRight, remainingSize, cols-k)
.applyHouseholderOnTheLeft(m_qr.col(k).end(remainingSize-1), ei_real(m_hCoeffs.coeff(k)), &temp.coeffRef(k));
.applyHouseholderOnTheLeft(m_qr.col(k).end(remainingSize-1), ei_conj(m_hCoeffs.coeff(k)), &temp.coeffRef(k));
}
return res;
}