diff options
| -rw-r--r-- | Eigen/src/Householder/Householder.h | 2 | ||||
| -rw-r--r-- | Eigen/src/QR/FullPivotingHouseholderQR.h | 128 | ||||
| -rw-r--r-- | test/qr_fullpivoting.cpp | 15 |
3 files changed, 135 insertions, 10 deletions
diff --git a/Eigen/src/Householder/Householder.h b/Eigen/src/Householder/Householder.h index ea39e4c30..36f02d7ce 100644 --- a/Eigen/src/Householder/Householder.h +++ b/Eigen/src/Householder/Householder.h @@ -77,7 +77,7 @@ void MatrixBase<Derived>::makeHouseholder( RealScalar tailSqNorm = size()==1 ? 0 : tail.squaredNorm(); Scalar c0 = coeff(0); - if( tailSqNorm == RealScalar(0) && ei_imag(c0)==RealScalar(0)) + if(tailSqNorm == RealScalar(0) && ei_imag(c0)==RealScalar(0)) { *tau = 0; *beta = ei_real(c0); diff --git a/Eigen/src/QR/FullPivotingHouseholderQR.h b/Eigen/src/QR/FullPivotingHouseholderQR.h index f7b0f1cc1..0ffcfe88c 100644 --- a/Eigen/src/QR/FullPivotingHouseholderQR.h +++ b/Eigen/src/QR/FullPivotingHouseholderQR.h @@ -94,7 +94,7 @@ template<typename MatrixType> class FullPivotingHouseholderQR * Output: \verbinclude FullPivotingHouseholderQR_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; @@ -106,22 +106,117 @@ template<typename MatrixType> class FullPivotingHouseholderQR const IntRowVectorType& colsPermutation() const { - ei_assert(m_isInitialized && "FULLPIVOTINGHOUSEHOLDERQR is not initialized."); + ei_assert(m_isInitialized && "FullPivotingHouseholderQR is not initialized."); return m_cols_permutation; } const IntColVectorType& rowsTranspositions() const { - ei_assert(m_isInitialized && "FULLPIVOTINGHOUSEHOLDERQR is not initialized."); + ei_assert(m_isInitialized && "FullPivotingHouseholderQR is not initialized."); return m_rows_transpositions; } + /** \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. + * + * \sa MatrixBase::determinant() + */ + typename MatrixType::RealScalar absDeterminant() 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 && "FULLPIVOTINGHOUSEHOLDERQR is not initialized."); + ei_assert(m_isInitialized && "FullPivotingHouseholderQR 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 && "FullPivotingHouseholderQR 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 && "FullPivotingHouseholderQR 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 && "FullPivotingHouseholderQR 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 && "FullPivotingHouseholderQR 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 && "FullPivotingHouseholderQR 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; @@ -136,6 +231,14 @@ template<typename MatrixType> class FullPivotingHouseholderQR #ifndef EIGEN_HIDE_HEAVY_CODE template<typename MatrixType> +typename MatrixType::RealScalar FullPivotingHouseholderQR<MatrixType>::absDeterminant() const +{ + ei_assert(m_isInitialized && "FullPivotingHouseholderQR 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> FullPivotingHouseholderQR<MatrixType>& FullPivotingHouseholderQR<MatrixType>::compute(const MatrixType& matrix) { int rows = matrix.rows(); @@ -163,8 +266,8 @@ FullPivotingHouseholderQR<MatrixType>& FullPivotingHouseholderQR<MatrixType>::co RealScalar biggest_in_corner; biggest_in_corner = m_qr.corner(Eigen::BottomRight, rows-k, cols-k) - .cwise().abs() - .maxCoeff(&row_of_biggest_in_corner, &col_of_biggest_in_corner); + .cwise().abs() + .maxCoeff(&row_of_biggest_in_corner, &col_of_biggest_in_corner); row_of_biggest_in_corner += k; col_of_biggest_in_corner += k; if(k==0) biggest = biggest_in_corner; @@ -213,12 +316,14 @@ FullPivotingHouseholderQR<MatrixType>& FullPivotingHouseholderQR<MatrixType>::co template<typename MatrixType> template<typename OtherDerived, typename ResultType> -void FullPivotingHouseholderQR<MatrixType>::solve( +bool FullPivotingHouseholderQR<MatrixType>::solve( const MatrixBase<OtherDerived>& b, ResultType *result ) const { ei_assert(m_isInitialized && "FullPivotingHouseholderQR is not initialized."); + if(m_rank==0) return false; + const int rows = m_qr.rows(); const int cols = b.cols(); ei_assert(b.rows() == rows); @@ -234,6 +339,14 @@ void FullPivotingHouseholderQR<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())); @@ -241,6 +354,7 @@ void FullPivotingHouseholderQR<MatrixType>::solve( 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 */ diff --git a/test/qr_fullpivoting.cpp b/test/qr_fullpivoting.cpp index fcbf08e4c..1e0601a83 100644 --- a/test/qr_fullpivoting.cpp +++ b/test/qr_fullpivoting.cpp @@ -39,6 +39,11 @@ template<typename MatrixType> void qr() createRandomMatrixOfRank(rank,rows,cols,m1); FullPivotingHouseholderQR<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 @@ -54,8 +59,10 @@ 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() @@ -74,8 +81,12 @@ template<typename MatrixType> void qr_invertible() } FullPivotingHouseholderQR<MatrixType> qr(m1); + VERIFY(qr.isInjective()); + VERIFY(qr.isInvertible()); + VERIFY(qr.isSurjective()); + m3 = MatrixType::Random(size,size); - qr.solve(m3, &m2); + VERIFY(qr.solve(m3, &m2)); VERIFY_IS_APPROX(m3, m1*m2); } |