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Gael Guennebaud
2009-07-14 23:06:25 +02:00
parent 279cedc1ce f5d2317b12
commit 8120a5cecd
46 changed files with 1241 additions and 966 deletions
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158
Eigen/src/QR/QR.h
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@@ -28,18 +28,20 @@
/** \ingroup QR_Module
* \nonstableyet
*
* \class QR
* \class HouseholderQR
*
* \brief QR decomposition of a matrix
* \brief Householder QR decomposition of a matrix
*
* \param MatrixType the type of the matrix of which we are computing the QR decomposition
*
* This class performs a QR decomposition using Householder transformations. The result is
* stored in a compact way compatible with LAPACK.
*
* Note that no pivoting is performed. This is \b not a rank-revealing decomposition.
*
* \sa MatrixBase::qr()
*/
template<typename MatrixType> class QR
template<typename MatrixType> class HouseholderQR
{
public:
@@ -53,88 +55,23 @@ template<typename MatrixType> class QR
* \brief Default Constructor.
*
* The default constructor is useful in cases in which the user intends to
* perform decompositions via QR::compute(const MatrixType&).
* perform decompositions via HouseholderQR::compute(const MatrixType&).
*/
QR() : m_qr(), m_hCoeffs(), m_isInitialized(false) {}
HouseholderQR() : m_qr(), m_hCoeffs(), m_isInitialized(false) {}
QR(const MatrixType& matrix)
HouseholderQR(const MatrixType& matrix)
: m_qr(matrix.rows(), matrix.cols()),
m_hCoeffs(matrix.cols()),
m_isInitialized(false)
{
compute(matrix);
}
/** \deprecated use isInjective()
* \returns whether or not the matrix is of full rank
*
* \note Since the rank is computed only once, i.e. the first time it is needed, this
* method almost does not perform any further computation.
*/
EIGEN_DEPRECATED bool isFullRank() const
{
ei_assert(m_isInitialized && "QR is not initialized.");
return rank() == m_qr.cols();
}
/** \returns the rank of the matrix of which *this is the QR decomposition.
*
* \note Since the rank is computed only once, i.e. the first time it is needed, this
* method almost does not perform any further computation.
*/
int rank() const;
/** \returns the dimension of the kernel of the matrix of which *this is the QR decomposition.
*
* \note Since the rank is computed only once, i.e. the first time it is needed, this
* method almost does not perform any further computation.
*/
inline int dimensionOfKernel() const
{
ei_assert(m_isInitialized && "QR is not initialized.");
return m_qr.cols() - rank();
}
/** \returns true if the matrix of which *this is the QR decomposition represents an injective
* linear map, i.e. has trivial kernel; false otherwise.
*
* \note Since the rank is computed only once, i.e. the first time it is needed, this
* method almost does not perform any further computation.
*/
inline bool isInjective() const
{
ei_assert(m_isInitialized && "QR is not initialized.");
return rank() == m_qr.cols();
}
/** \returns true if the matrix of which *this is the QR decomposition represents a surjective
* linear map; false otherwise.
*
* \note Since the rank is computed only once, i.e. the first time it is needed, this
* method almost does not perform any further computation.
*/
inline bool isSurjective() const
{
ei_assert(m_isInitialized && "QR is not initialized.");
return rank() == m_qr.rows();
}
/** \returns true if the matrix of which *this is the QR decomposition is invertible.
*
* \note Since the rank is computed only once, i.e. the first time it is needed, this
* method almost does not perform any further computation.
*/
inline bool isInvertible() const
{
ei_assert(m_isInitialized && "QR is not initialized.");
return isInjective() && isSurjective();
}
/** \returns a read-only expression of the matrix R of the actual the QR decomposition */
const TriangularView<NestByValue<MatrixRBlockType>, UpperTriangular>
matrixR(void) const
{
ei_assert(m_isInitialized && "QR is not initialized.");
ei_assert(m_isInitialized && "HouseholderQR is not initialized.");
int cols = m_qr.cols();
return MatrixRBlockType(m_qr, 0, 0, cols, cols).nestByValue().template part<UpperTriangular>();
}
@@ -148,58 +85,35 @@ template<typename MatrixType> class QR
* Resized if necessary, so that result->rows()==A.cols() and result->cols()==b.cols().
* If no solution exists, *result is left with undefined coefficients.
*
* \returns true if any solution exists, false if no solution exists.
*
* \note If there exist more than one solution, this method will arbitrarily choose one.
* If you need a complete analysis of the space of solutions, take the one solution obtained
* by this method and add to it elements of the kernel, as determined by kernel().
*
* \note The case where b is a matrix is not yet implemented. Also, this
* code is space inefficient.
*
* Example: \include QR_solve.cpp
* Output: \verbinclude QR_solve.out
*
* \sa MatrixBase::solveTriangular(), kernel(), computeKernel(), inverse(), computeInverse()
* Example: \include HouseholderQR_solve.cpp
* Output: \verbinclude HouseholderQR_solve.out
*/
template<typename OtherDerived, typename ResultType>
bool solve(const MatrixBase<OtherDerived>& b, ResultType *result) const;
void solve(const MatrixBase<OtherDerived>& b, ResultType *result) const;
MatrixType matrixQ(void) const;
/** \returns a reference to the matrix where the Householder QR decomposition is stored
* in a LAPACK-compatible way.
*/
const MatrixType& matrixQR() const { return m_qr; }
void compute(const MatrixType& matrix);
protected:
MatrixType m_qr;
VectorType m_hCoeffs;
mutable int m_rank;
mutable bool m_rankIsUptodate;
bool m_isInitialized;
};
/** \returns the rank of the matrix of which *this is the QR decomposition. */
template<typename MatrixType>
int QR<MatrixType>::rank() const
{
ei_assert(m_isInitialized && "QR is not initialized.");
if (!m_rankIsUptodate)
{
RealScalar maxCoeff = m_qr.diagonal().cwise().abs().maxCoeff();
int n = m_qr.cols();
m_rank = 0;
while(m_rank<n && !ei_isMuchSmallerThan(m_qr.diagonal().coeff(m_rank), maxCoeff))
++m_rank;
m_rankIsUptodate = true;
}
return m_rank;
}
#ifndef EIGEN_HIDE_HEAVY_CODE
template<typename MatrixType>
void QR<MatrixType>::compute(const MatrixType& matrix)
void HouseholderQR<MatrixType>::compute(const MatrixType& matrix)
{
m_rankIsUptodate = false;
m_qr = matrix;
m_hCoeffs.resize(matrix.cols());
@@ -262,12 +176,12 @@ void QR<MatrixType>::compute(const MatrixType& matrix)
template<typename MatrixType>
template<typename OtherDerived, typename ResultType>
bool QR<MatrixType>::solve(
void HouseholderQR<MatrixType>::solve(
const MatrixBase<OtherDerived>& b,
ResultType *result
) const
{
ei_assert(m_isInitialized && "QR is not initialized.");
ei_assert(m_isInitialized && "HouseholderQR is not initialized.");
const int rows = m_qr.rows();
ei_assert(b.rows() == rows);
result->resize(rows, b.cols());
@@ -276,27 +190,17 @@ bool QR<MatrixType>::solve(
// Q^T without explicitly forming matrixQ(). Investigate.
*result = matrixQ().transpose()*b;
if(!isSurjective())
{
// is result is in the image of R ?
RealScalar biggest_in_res = result->corner(TopLeft, m_rank, result->cols()).cwise().abs().maxCoeff();
for(int col = 0; col < result->cols(); ++col)
for(int row = m_rank; row < result->rows(); ++row)
if(!ei_isMuchSmallerThan(result->coeff(row,col), biggest_in_res))
return false;
}
m_qr.corner(TopLeft, m_rank, m_rank)
const int rank = std::min(result->rows(), result->cols());
m_qr.corner(TopLeft, rank, rank)
.template marked<UpperTriangular>()
.solveTriangularInPlace(result->corner(TopLeft, m_rank, result->cols()));
return true;
.solveTriangularInPlace(result->corner(TopLeft, rank, result->cols()));
}
/** \returns the matrix Q */
template<typename MatrixType>
MatrixType QR<MatrixType>::matrixQ() const
MatrixType HouseholderQR<MatrixType>::matrixQ() const
{
ei_assert(m_isInitialized && "QR is not initialized.");
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'
// and v_k is the k-th Householder vector [1,m_qr(k+1,k), m_qr(k+2,k), ...]
@@ -319,15 +223,15 @@ MatrixType QR<MatrixType>::matrixQ() const
#endif // EIGEN_HIDE_HEAVY_CODE
/** \return the QR decomposition of \c *this.
/** \return the Householder QR decomposition of \c *this.
*
* \sa class QR
* \sa class HouseholderQR
*/
template<typename Derived>
const QR<typename MatrixBase<Derived>::PlainMatrixType>
MatrixBase<Derived>::qr() const
const HouseholderQR<typename MatrixBase<Derived>::PlainMatrixType>
MatrixBase<Derived>::householderQr() const
{
return QR<PlainMatrixType>(eval());
return HouseholderQR<PlainMatrixType>(eval());
}