mirror of
https://gitlab.com/libeigen/eigen.git
synced 2025-01-18 14:34:17 +08:00
bring the modern comfort also to ColPivotingHouseholderQR
+ some fixes in FullPivotingHouseholderQR
This commit is contained in:
Benoit Jacob
parent
3288e5157a
commit
0eb142f559
@ -31,14 +31,14 @@
|
||||
*
|
||||
* \class ColPivotingHouseholderQR
|
||||
*
|
||||
* \brief Householder rank-revealing QR decomposition of a matrix
|
||||
* \brief Householder rank-revealing QR decomposition of a matrix with column-pivoting
|
||||
*
|
||||
* \param MatrixType the type of the matrix of which we are computing the QR decomposition
|
||||
*
|
||||
* This class performs a rank-revealing QR decomposition using Householder transformations.
|
||||
*
|
||||
* This decomposition performs full-pivoting in order to be rank-revealing and achieve optimal
|
||||
* numerical stability.
|
||||
* This decomposition performs column pivoting in order to be rank-revealing and improve
|
||||
* numerical stability. It is slower than HouseholderQR, and faster than FullPivotingHouseholderQR.
|
||||
*
|
||||
* \sa MatrixBase::colPivotingHouseholderQr()
|
||||
*/
|
||||
@ -82,6 +82,8 @@ template<typename MatrixType> class ColPivotingHouseholderQR
|
||||
/** This method finds a solution x to the equation Ax=b, where A is the matrix of which
|
||||
* *this is the QR decomposition, if any exists.
|
||||
*
|
||||
* \returns \c true if a solution exists, \c false if no solution exists.
|
||||
*
|
||||
* \param b the right-hand-side of the equation to solve.
|
||||
*
|
||||
* \param result a pointer to the vector/matrix in which to store the solution, if any exists.
|
||||
@ -95,7 +97,7 @@ template<typename MatrixType> class ColPivotingHouseholderQR
|
||||
* Output: \verbinclude ColPivotingHouseholderQR_solve.out
|
||||
*/
|
||||
template<typename OtherDerived, typename ResultType>
|
||||
void solve(const MatrixBase<OtherDerived>& b, ResultType *result) const;
|
||||
bool solve(const MatrixBase<OtherDerived>& b, ResultType *result) const;
|
||||
|
||||
MatrixType matrixQ(void) const;
|
||||
|
||||
@ -111,12 +113,122 @@ template<typename MatrixType> class ColPivotingHouseholderQR
|
||||
return m_cols_permutation;
|
||||
}
|
||||
|
||||
/** \returns the absolute value of the determinant of the matrix of which
|
||||
* *this is the QR decomposition. It has only linear complexity
|
||||
* (that is, O(n) where n is the dimension of the square matrix)
|
||||
* as the QR decomposition has already been computed.
|
||||
*
|
||||
* \note This is only for square matrices.
|
||||
*
|
||||
* \warning a determinant can be very big or small, so for matrices
|
||||
* of large enough dimension, there is a risk of overflow/underflow.
|
||||
* One way to work around that is to use logAbsDeterminant() instead.
|
||||
*
|
||||
* \sa logAbsDeterminant(), MatrixBase::determinant()
|
||||
*/
|
||||
typename MatrixType::RealScalar absDeterminant() const;
|
||||
|
||||
/** \returns the natural log of the absolute value of the determinant of the matrix of which
|
||||
* *this is the QR decomposition. It has only linear complexity
|
||||
* (that is, O(n) where n is the dimension of the square matrix)
|
||||
* as the QR decomposition has already been computed.
|
||||
*
|
||||
* \note This is only for square matrices.
|
||||
*
|
||||
* \note This method is useful to work around the risk of overflow/underflow that's inherent
|
||||
* to determinant computation.
|
||||
*
|
||||
* \sa absDeterminant(), MatrixBase::determinant()
|
||||
*/
|
||||
typename MatrixType::RealScalar logAbsDeterminant() const;
|
||||
|
||||
/** \returns the rank of the matrix of which *this is the QR decomposition.
|
||||
*
|
||||
* \note This is computed at the time of the construction of the QR decomposition. This
|
||||
* method does not perform any further computation.
|
||||
*/
|
||||
inline int rank() const
|
||||
{
|
||||
ei_assert(m_isInitialized && "ColPivotingHouseholderQR is not initialized.");
|
||||
return m_rank;
|
||||
}
|
||||
|
||||
/** \returns the dimension of the kernel of the matrix of which *this is the QR decomposition.
|
||||
*
|
||||
* \note Since the rank is computed at the time of the construction of the QR decomposition, this
|
||||
* method almost does not perform any further computation.
|
||||
*/
|
||||
inline int dimensionOfKernel() const
|
||||
{
|
||||
ei_assert(m_isInitialized && "ColPivotingHouseholderQR is not initialized.");
|
||||
return m_qr.cols() - m_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 at the time of the construction of the QR decomposition, this
|
||||
* method almost does not perform any further computation.
|
||||
*/
|
||||
inline bool isInjective() const
|
||||
{
|
||||
ei_assert(m_isInitialized && "ColPivotingHouseholderQR is not initialized.");
|
||||
return m_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 at the time of the construction of the QR decomposition, this
|
||||
* method almost does not perform any further computation.
|
||||
*/
|
||||
inline bool isSurjective() const
|
||||
{
|
||||
ei_assert(m_isInitialized && "ColPivotingHouseholderQR is not initialized.");
|
||||
return m_rank == m_qr.rows();
|
||||
}
|
||||
|
||||
/** \returns true if the matrix of which *this is the QR decomposition is invertible.
|
||||
*
|
||||
* \note Since the rank is computed at the time of the construction of the QR decomposition, this
|
||||
* method almost does not perform any further computation.
|
||||
*/
|
||||
inline bool isInvertible() const
|
||||
{
|
||||
ei_assert(m_isInitialized && "ColPivotingHouseholderQR is not initialized.");
|
||||
return isInjective() && isSurjective();
|
||||
}
|
||||
|
||||
/** Computes the inverse of the matrix of which *this is the QR decomposition.
|
||||
*
|
||||
* \param result a pointer to the matrix into which to store the inverse. Resized if needed.
|
||||
*
|
||||
* \note If this matrix is not invertible, *result is left with undefined coefficients.
|
||||
* Use isInvertible() to first determine whether this matrix is invertible.
|
||||
*
|
||||
* \sa inverse()
|
||||
*/
|
||||
inline void computeInverse(MatrixType *result) const
|
||||
{
|
||||
ei_assert(m_isInitialized && "ColPivotingHouseholderQR is not initialized.");
|
||||
ei_assert(m_qr.rows() == m_qr.cols() && "You can't take the inverse of a non-square matrix!");
|
||||
solve(MatrixType::Identity(m_qr.rows(), m_qr.cols()), result);
|
||||
}
|
||||
|
||||
/** \returns the inverse of the matrix of which *this is the QR decomposition.
|
||||
*
|
||||
* \note If this matrix is not invertible, the returned matrix has undefined coefficients.
|
||||
* Use isInvertible() to first determine whether this matrix is invertible.
|
||||
*
|
||||
* \sa computeInverse()
|
||||
*/
|
||||
inline MatrixType inverse() const
|
||||
{
|
||||
MatrixType result;
|
||||
computeInverse(&result);
|
||||
return result;
|
||||
}
|
||||
|
||||
protected:
|
||||
MatrixType m_qr;
|
||||
HCoeffsType m_hCoeffs;
|
||||
@ -129,6 +241,22 @@ template<typename MatrixType> class ColPivotingHouseholderQR
|
||||
|
||||
#ifndef EIGEN_HIDE_HEAVY_CODE
|
||||
|
||||
template<typename MatrixType>
|
||||
typename MatrixType::RealScalar ColPivotingHouseholderQR<MatrixType>::absDeterminant() const
|
||||
{
|
||||
ei_assert(m_isInitialized && "ColPivotingHouseholderQR is not initialized.");
|
||||
ei_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
|
||||
return ei_abs(m_qr.diagonal().prod());
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
typename MatrixType::RealScalar ColPivotingHouseholderQR<MatrixType>::logAbsDeterminant() const
|
||||
{
|
||||
ei_assert(m_isInitialized && "ColPivotingHouseholderQR is not initialized.");
|
||||
ei_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
|
||||
return m_qr.diagonal().cwise().abs().cwise().log().sum();
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
ColPivotingHouseholderQR<MatrixType>& ColPivotingHouseholderQR<MatrixType>::compute(const MatrixType& matrix)
|
||||
{
|
||||
@ -199,12 +327,23 @@ ColPivotingHouseholderQR<MatrixType>& ColPivotingHouseholderQR<MatrixType>::comp
|
||||
|
||||
template<typename MatrixType>
|
||||
template<typename OtherDerived, typename ResultType>
|
||||
void ColPivotingHouseholderQR<MatrixType>::solve(
|
||||
bool ColPivotingHouseholderQR<MatrixType>::solve(
|
||||
const MatrixBase<OtherDerived>& b,
|
||||
ResultType *result
|
||||
) const
|
||||
{
|
||||
ei_assert(m_isInitialized && "ColPivotingHouseholderQR is not initialized.");
|
||||
result->resize(m_qr.cols(), b.cols());
|
||||
if(m_rank==0)
|
||||
{
|
||||
if(b.squaredNorm() == RealScalar(0))
|
||||
{
|
||||
result->setZero();
|
||||
return true;
|
||||
}
|
||||
else return false;
|
||||
}
|
||||
|
||||
const int rows = m_qr.rows();
|
||||
const int cols = b.cols();
|
||||
ei_assert(b.rows() == rows);
|
||||
@ -219,13 +358,21 @@ void ColPivotingHouseholderQR<MatrixType>::solve(
|
||||
.applyHouseholderOnTheLeft(m_qr.col(k).end(remainingSize-1), m_hCoeffs.coeff(k), &temp.coeffRef(0));
|
||||
}
|
||||
|
||||
if(!isSurjective())
|
||||
{
|
||||
// is c is in the image of R ?
|
||||
RealScalar biggest_in_upper_part_of_c = c.corner(TopLeft, m_rank, c.cols()).cwise().abs().maxCoeff();
|
||||
RealScalar biggest_in_lower_part_of_c = c.corner(BottomLeft, rows-m_rank, c.cols()).cwise().abs().maxCoeff();
|
||||
if(!ei_isMuchSmallerThan(biggest_in_lower_part_of_c, biggest_in_upper_part_of_c, m_precision))
|
||||
return false;
|
||||
}
|
||||
m_qr.corner(TopLeft, m_rank, m_rank)
|
||||
.template triangularView<UpperTriangular>()
|
||||
.solveInPlace(c.corner(TopLeft, m_rank, c.cols()));
|
||||
|
||||
result->resize(m_qr.cols(), b.cols());
|
||||
for(int i = 0; i < m_rank; ++i) result->row(m_cols_permutation.coeff(i)) = c.row(i);
|
||||
for(int i = m_rank; i < m_qr.cols(); ++i) result->row(m_cols_permutation.coeff(i)).setZero();
|
||||
return true;
|
||||
}
|
||||
|
||||
/** \returns the matrix Q */
|
||||
|
||||
@ -31,7 +31,7 @@
|
||||
*
|
||||
* \class FullPivotingHouseholderQR
|
||||
*
|
||||
* \brief Householder rank-revealing QR decomposition of a matrix
|
||||
* \brief Householder rank-revealing QR decomposition of a matrix with full pivoting
|
||||
*
|
||||
* \param MatrixType the type of the matrix of which we are computing the QR decomposition
|
||||
*
|
||||
@ -62,12 +62,11 @@ template<typename MatrixType> class FullPivotingHouseholderQR
|
||||
typedef Matrix<Scalar, 1, ColsAtCompileTime> RowVectorType;
|
||||
typedef Matrix<Scalar, RowsAtCompileTime, 1> ColVectorType;
|
||||
|
||||
/**
|
||||
* \brief Default Constructor.
|
||||
*
|
||||
* The default constructor is useful in cases in which the user intends to
|
||||
* perform decompositions via FullPivotingHouseholderQR::compute(const MatrixType&).
|
||||
*/
|
||||
/** \brief Default Constructor.
|
||||
*
|
||||
* The default constructor is useful in cases in which the user intends to
|
||||
* perform decompositions via FullPivotingHouseholderQR::compute(const MatrixType&).
|
||||
*/
|
||||
FullPivotingHouseholderQR() : m_qr(), m_hCoeffs(), m_isInitialized(false) {}
|
||||
|
||||
FullPivotingHouseholderQR(const MatrixType& matrix)
|
||||
@ -81,6 +80,8 @@ template<typename MatrixType> class FullPivotingHouseholderQR
|
||||
/** This method finds a solution x to the equation Ax=b, where A is the matrix of which
|
||||
* *this is the QR decomposition, if any exists.
|
||||
*
|
||||
* \returns \c true if a solution exists, \c false if no solution exists.
|
||||
*
|
||||
* \param b the right-hand-side of the equation to solve.
|
||||
*
|
||||
* \param result a pointer to the vector/matrix in which to store the solution, if any exists.
|
||||
@ -345,7 +346,16 @@ bool FullPivotingHouseholderQR<MatrixType>::solve(
|
||||
) const
|
||||
{
|
||||
ei_assert(m_isInitialized && "FullPivotingHouseholderQR is not initialized.");
|
||||
if(m_rank==0) return false;
|
||||
result->resize(m_qr.cols(), b.cols());
|
||||
if(m_rank==0)
|
||||
{
|
||||
if(b.squaredNorm() == RealScalar(0))
|
||||
{
|
||||
result->setZero();
|
||||
return true;
|
||||
}
|
||||
else return false;
|
||||
}
|
||||
|
||||
const int rows = m_qr.rows();
|
||||
const int cols = b.cols();
|
||||
@ -374,7 +384,6 @@ bool FullPivotingHouseholderQR<MatrixType>::solve(
|
||||
.template triangularView<UpperTriangular>()
|
||||
.solveInPlace(c.corner(TopLeft, m_rank, c.cols()));
|
||||
|
||||
result->resize(m_qr.cols(), b.cols());
|
||||
for(int i = 0; i < m_rank; ++i) result->row(m_cols_permutation.coeff(i)) = c.row(i);
|
||||
for(int i = m_rank; i < m_qr.cols(); ++i) result->row(m_cols_permutation.coeff(i)).setZero();
|
||||
return true;
|
||||
|
||||
@ -28,7 +28,6 @@
|
||||
|
||||
template<typename MatrixType> void qr()
|
||||
{
|
||||
/* this test covers the following files: QR.h */
|
||||
int rows = ei_random<int>(20,200), cols = ei_random<int>(20,200), cols2 = ei_random<int>(20,200);
|
||||
int rank = ei_random<int>(1, std::min(rows, cols)-1);
|
||||
|
||||
@ -39,6 +38,10 @@ template<typename MatrixType> void qr()
|
||||
createRandomMatrixOfRank(rank,rows,cols,m1);
|
||||
ColPivotingHouseholderQR<MatrixType> qr(m1);
|
||||
VERIFY_IS_APPROX(rank, qr.rank());
|
||||
VERIFY(cols - qr.rank() == qr.dimensionOfKernel());
|
||||
VERIFY(!qr.isInjective());
|
||||
VERIFY(!qr.isInvertible());
|
||||
VERIFY(!qr.isSurjective());
|
||||
|
||||
MatrixType r = qr.matrixQR();
|
||||
// FIXME need better way to construct trapezoid
|
||||
@ -54,14 +57,17 @@ template<typename MatrixType> void qr()
|
||||
MatrixType m2 = MatrixType::Random(cols,cols2);
|
||||
MatrixType m3 = m1*m2;
|
||||
m2 = MatrixType::Random(cols,cols2);
|
||||
qr.solve(m3, &m2);
|
||||
VERIFY(qr.solve(m3, &m2));
|
||||
VERIFY_IS_APPROX(m3, m1*m2);
|
||||
m3 = MatrixType::Random(rows,cols2);
|
||||
VERIFY(!qr.solve(m3, &m2));
|
||||
}
|
||||
|
||||
template<typename MatrixType> void qr_invertible()
|
||||
{
|
||||
/* this test covers the following files: RRQR.h */
|
||||
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
|
||||
int size = ei_random<int>(10,50);
|
||||
|
||||
MatrixType m1(size, size), m2(size, size), m3(size, size);
|
||||
@ -78,6 +84,16 @@ template<typename MatrixType> void qr_invertible()
|
||||
m3 = MatrixType::Random(size,size);
|
||||
qr.solve(m3, &m2);
|
||||
VERIFY_IS_APPROX(m3, m1*m2);
|
||||
|
||||
// now construct a matrix with prescribed determinant
|
||||
m1.setZero();
|
||||
for(int i = 0; i < size; i++) m1(i,i) = ei_random<Scalar>();
|
||||
RealScalar absdet = ei_abs(m1.diagonal().prod());
|
||||
m3 = qr.matrixQ(); // get a unitary
|
||||
m1 = m3 * m1 * m3;
|
||||
qr.compute(m1);
|
||||
VERIFY_IS_APPROX(absdet, qr.absDeterminant());
|
||||
VERIFY_IS_APPROX(ei_log(absdet), qr.logAbsDeterminant());
|
||||
}
|
||||
|
||||
template<typename MatrixType> void qr_verify_assert()
|
||||
|
||||
@ -28,7 +28,6 @@
|
||||
|
||||
template<typename MatrixType> void qr()
|
||||
{
|
||||
/* this test covers the following files: QR.h */
|
||||
int rows = ei_random<int>(20,200), cols = ei_random<int>(20,200), cols2 = ei_random<int>(20,200);
|
||||
int rank = ei_random<int>(1, std::min(rows, cols)-1);
|
||||
|
||||
@ -44,7 +43,6 @@ template<typename MatrixType> void qr()
|
||||
VERIFY(!qr.isInvertible());
|
||||
VERIFY(!qr.isSurjective());
|
||||
|
||||
|
||||
MatrixType r = qr.matrixQR();
|
||||
// FIXME need better way to construct trapezoid
|
||||
for(int i = 0; i < rows; i++) for(int j = 0; j < cols; j++) if(i>j) r(i,j) = Scalar(0);
|
||||
@ -110,6 +108,12 @@ template<typename MatrixType> void qr_verify_assert()
|
||||
VERIFY_RAISES_ASSERT(qr.matrixR())
|
||||
VERIFY_RAISES_ASSERT(qr.solve(tmp,&tmp))
|
||||
VERIFY_RAISES_ASSERT(qr.matrixQ())
|
||||
VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())
|
||||
VERIFY_RAISES_ASSERT(qr.isInjective())
|
||||
VERIFY_RAISES_ASSERT(qr.isSurjective())
|
||||
VERIFY_RAISES_ASSERT(qr.isInvertible())
|
||||
VERIFY_RAISES_ASSERT(qr.computeInverse(&tmp))
|
||||
VERIFY_RAISES_ASSERT(qr.inverse())
|
||||
}
|
||||
|
||||
void test_qr_fullpivoting()
|
||||
|
||||
Loading…
Reference in New Issue
Block a user