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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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103
Eigen/src/QR/QR.h
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@@ -45,11 +45,15 @@ template<typename MatrixType> class HouseholderQR
{
public:
enum {
MinSizeAtCompileTime = EIGEN_ENUM_MIN(MatrixType::ColsAtCompileTime,MatrixType::RowsAtCompileTime)
};
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef Block<MatrixType, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> MatrixRBlockType;
typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> MatrixTypeR;
typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
typedef Matrix<RealScalar, MinSizeAtCompileTime, 1> HCoeffsType;
/**
* \brief Default Constructor.
@@ -61,7 +65,7 @@ template<typename MatrixType> class HouseholderQR
HouseholderQR(const MatrixType& matrix)
: m_qr(matrix.rows(), matrix.cols()),
m_hCoeffs(matrix.cols()),
m_hCoeffs(std::min(matrix.rows(),matrix.cols())),
m_isInitialized(false)
{
compute(matrix);
@@ -105,7 +109,7 @@ template<typename MatrixType> class HouseholderQR
protected:
MatrixType m_qr;
VectorType m_hCoeffs;
HCoeffsType m_hCoeffs;
bool m_isInitialized;
};
@@ -114,65 +118,25 @@ template<typename MatrixType> class HouseholderQR
template<typename MatrixType>
HouseholderQR<MatrixType>& HouseholderQR<MatrixType>::compute(const MatrixType& matrix)
{
m_qr = matrix;
m_hCoeffs.resize(matrix.cols());
int rows = matrix.rows();
int cols = matrix.cols();
RealScalar eps2 = precision<RealScalar>()*precision<RealScalar>();
int size = std::min(rows,cols);
m_qr = matrix;
m_hCoeffs.resize(size);
Matrix<Scalar,1,MatrixType::ColsAtCompileTime> temp(cols);
for (int k = 0; k < cols; ++k)
for (int k = 0; k < size; ++k)
{
int remainingSize = rows-k;
int remainingRows = rows - k;
int remainingCols = cols - k -1;
RealScalar beta;
Scalar v0 = m_qr.col(k).coeff(k);
if (remainingSize==1)
{
if (NumTraits<Scalar>::IsComplex)
{
// Householder transformation on the remaining single scalar
beta = ei_abs(v0);
if (ei_real(v0)>0)
beta = -beta;
m_qr.coeffRef(k,k) = beta;
m_hCoeffs.coeffRef(k) = (beta - v0) / beta;
}
else
{
m_hCoeffs.coeffRef(k) = 0;
}
}
else if ((beta=m_qr.col(k).end(remainingSize-1).squaredNorm())>eps2)
// FIXME what about ei_imag(v0) ??
{
// form k-th Householder vector
beta = ei_sqrt(ei_abs2(v0)+beta);
if (ei_real(v0)>=0.)
beta = -beta;
m_qr.col(k).end(remainingSize-1) /= v0-beta;
m_qr.coeffRef(k,k) = beta;
Scalar h = m_hCoeffs.coeffRef(k) = (beta - v0) / beta;
// apply the Householder transformation (I - h v v') to remaining columns, i.e.,
// R <- (I - h v v') * R where v = [1,m_qr(k+1,k), m_qr(k+2,k), ...]
int remainingCols = cols - k -1;
if (remainingCols>0)
{
m_qr.coeffRef(k,k) = Scalar(1);
temp.end(remainingCols) = (m_qr.col(k).end(remainingSize).adjoint()
* m_qr.corner(BottomRight, remainingSize, remainingCols)).lazy();
m_qr.corner(BottomRight, remainingSize, remainingCols) -= (ei_conj(h) * m_qr.col(k).end(remainingSize)
* temp.end(remainingCols)).lazy();
m_qr.coeffRef(k,k) = beta;
}
}
else
{
m_hCoeffs.coeffRef(k) = 0;
}
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));
}
m_isInitialized = true;
return *this;
@@ -187,12 +151,20 @@ void HouseholderQR<MatrixType>::solve(
{
ei_assert(m_isInitialized && "HouseholderQR is not initialized.");
const int rows = m_qr.rows();
const int cols = b.cols();
ei_assert(b.rows() == rows);
result->resize(rows, b.cols());
result->resize(rows, cols);
// TODO(keir): There is almost certainly a faster way to multiply by
// Q^T without explicitly forming matrixQ(). Investigate.
*result = matrixQ().transpose()*b;
*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), ei_real(m_hCoeffs.coeff(k)), &temp.coeffRef(0));
}
const int rank = std::min(result->rows(), result->cols());
m_qr.corner(TopLeft, rank, rank)
@@ -214,15 +186,10 @@ MatrixType HouseholderQR<MatrixType>::matrixQ() const
Matrix<Scalar,1,MatrixType::ColsAtCompileTime> temp(cols);
for (int k = cols-1; k >= 0; k--)
{
// to make easier the computation of the transformation, let's temporarily
// overwrite m_qr(k,k) such that the end of m_qr.col(k) is exactly our Householder vector.
Scalar beta = m_qr.coeff(k,k);
m_qr.const_cast_derived().coeffRef(k,k) = 1;
int endLength = rows-k;
int remainingSize = rows-k;
temp.end(cols-k) = (m_qr.col(k).end(endLength).adjoint() * res.corner(BottomRight,endLength, cols-k)).lazy();
res.corner(BottomRight,endLength, cols-k) -= ((m_hCoeffs.coeff(k) * m_qr.col(k).end(endLength)) * temp.end(cols-k)).lazy();
m_qr.const_cast_derived().coeffRef(k,k) = beta;
res.corner(BottomRight, remainingSize, cols-k)
.applyHouseholderOnTheLeft(m_qr.col(k).end(remainingSize-1), ei_real(m_hCoeffs.coeff(k)), &temp.coeffRef(k));
}
return res;
}