diff options
author | Benoit Jacob <jacob.benoit.1@gmail.com> | 2009-08-24 13:46:14 -0400 |
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committer | Benoit Jacob <jacob.benoit.1@gmail.com> | 2009-08-24 13:46:14 -0400 |
commit | 191d5275a7c59f1a8bcf590479c337a68543f3ad (patch) | |
tree | 1e77beb2a9dc6f396688533dc87e5cbc17ff9b6c | |
parent | 7e4bd70157465c9ed26dffdffe84e890b05cb975 (diff) |
modernize HouseholderQR too, uniformize all that stuff, update tests
-rw-r--r-- | Eigen/QR | 2 | ||||
-rw-r--r-- | Eigen/src/QR/ColPivotingHouseholderQR.h | 15 | ||||
-rw-r--r-- | Eigen/src/QR/FullPivotingHouseholderQR.h | 12 | ||||
-rw-r--r-- | Eigen/src/QR/HouseholderQR.h (renamed from Eigen/src/QR/QR.h) | 93 | ||||
-rw-r--r-- | test/qr.cpp | 25 | ||||
-rw-r--r-- | test/qr_colpivoting.cpp | 10 | ||||
-rw-r--r-- | test/qr_fullpivoting.cpp | 4 |
7 files changed, 121 insertions, 40 deletions
@@ -35,7 +35,7 @@ namespace Eigen { * \endcode */ -#include "src/QR/QR.h" +#include "src/QR/HouseholderQR.h" #include "src/QR/FullPivotingHouseholderQR.h" #include "src/QR/ColPivotingHouseholderQR.h" #include "src/QR/Tridiagonalization.h" diff --git a/Eigen/src/QR/ColPivotingHouseholderQR.h b/Eigen/src/QR/ColPivotingHouseholderQR.h index 0aec6a607..8024e3b9d 100644 --- a/Eigen/src/QR/ColPivotingHouseholderQR.h +++ b/Eigen/src/QR/ColPivotingHouseholderQR.h @@ -99,11 +99,15 @@ template<typename MatrixType> class ColPivotingHouseholderQR template<typename OtherDerived, typename ResultType> bool solve(const MatrixBase<OtherDerived>& b, ResultType *result) const; - MatrixType matrixQ(void) const; + MatrixQType matrixQ(void) const; /** \returns a reference to the matrix where the Householder QR decomposition is stored */ - const MatrixType& matrixQR() const { return m_qr; } + const MatrixType& matrixQR() const + { + ei_assert(m_isInitialized && "ColPivotingHouseholderQR is not initialized."); + return m_qr; + } ColPivotingHouseholderQR& compute(const MatrixType& matrix); @@ -363,9 +367,10 @@ bool ColPivotingHouseholderQR<MatrixType>::solve( // 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)) + if(!ei_isMuchSmallerThan(biggest_in_lower_part_of_c, biggest_in_upper_part_of_c, m_precision*4)) return false; } + m_qr.corner(TopLeft, m_rank, m_rank) .template triangularView<UpperTriangular>() .solveInPlace(c.corner(TopLeft, m_rank, c.cols())); @@ -377,7 +382,7 @@ bool ColPivotingHouseholderQR<MatrixType>::solve( /** \returns the matrix Q */ template<typename MatrixType> -MatrixType ColPivotingHouseholderQR<MatrixType>::matrixQ() const +typename ColPivotingHouseholderQR<MatrixType>::MatrixQType ColPivotingHouseholderQR<MatrixType>::matrixQ() const { ei_assert(m_isInitialized && "ColPivotingHouseholderQR is not initialized."); // compute the product H'_0 H'_1 ... H'_n-1, @@ -386,7 +391,7 @@ MatrixType ColPivotingHouseholderQR<MatrixType>::matrixQ() const int rows = m_qr.rows(); int cols = m_qr.cols(); int size = std::min(rows,cols); - MatrixType res = MatrixType::Identity(rows, rows); + MatrixQType res = MatrixQType::Identity(rows, rows); Matrix<Scalar,1,MatrixType::RowsAtCompileTime> temp(rows); for (int k = size-1; k >= 0; k--) { diff --git a/Eigen/src/QR/FullPivotingHouseholderQR.h b/Eigen/src/QR/FullPivotingHouseholderQR.h index 77b664f6e..cee41b152 100644 --- a/Eigen/src/QR/FullPivotingHouseholderQR.h +++ b/Eigen/src/QR/FullPivotingHouseholderQR.h @@ -97,11 +97,15 @@ template<typename MatrixType> class FullPivotingHouseholderQR template<typename OtherDerived, typename ResultType> bool solve(const MatrixBase<OtherDerived>& b, ResultType *result) const; - MatrixType matrixQ(void) const; + MatrixQType matrixQ(void) const; /** \returns a reference to the matrix where the Householder QR decomposition is stored */ - const MatrixType& matrixQR() const { return m_qr; } + const MatrixType& matrixQR() const + { + ei_assert(m_isInitialized && "FullPivotingHouseholderQR is not initialized."); + return m_qr; + } FullPivotingHouseholderQR& compute(const MatrixType& matrix); @@ -391,7 +395,7 @@ bool FullPivotingHouseholderQR<MatrixType>::solve( /** \returns the matrix Q */ template<typename MatrixType> -MatrixType FullPivotingHouseholderQR<MatrixType>::matrixQ() const +typename FullPivotingHouseholderQR<MatrixType>::MatrixQType FullPivotingHouseholderQR<MatrixType>::matrixQ() const { ei_assert(m_isInitialized && "FullPivotingHouseholderQR is not initialized."); // compute the product H'_0 H'_1 ... H'_n-1, @@ -400,7 +404,7 @@ MatrixType FullPivotingHouseholderQR<MatrixType>::matrixQ() const int rows = m_qr.rows(); int cols = m_qr.cols(); int size = std::min(rows,cols); - MatrixType res = MatrixType::Identity(rows, rows); + MatrixQType res = MatrixQType::Identity(rows, rows); Matrix<Scalar,1,MatrixType::RowsAtCompileTime> temp(rows); for (int k = size-1; k >= 0; k--) { diff --git a/Eigen/src/QR/QR.h b/Eigen/src/QR/HouseholderQR.h index e5da6d691..a89305869 100644 --- a/Eigen/src/QR/QR.h +++ b/Eigen/src/QR/HouseholderQR.h @@ -2,6 +2,7 @@ // for linear algebra. // // Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr> +// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com> // // Eigen is free software; you can redistribute it and/or // modify it under the terms of the GNU Lesser General Public @@ -38,6 +39,10 @@ * stored in a compact way compatible with LAPACK. * * Note that no pivoting is performed. This is \b not a rank-revealing decomposition. + * If you want that feature, use FullPivotingHouseholderQR or ColPivotingHouseholderQR instead. + * + * This Householder QR decomposition is faster, but less numerically stable and less feature-full than + * FullPivotingHouseholderQR or ColPivotingHouseholderQR. * * \sa MatrixBase::householderQr() */ @@ -46,15 +51,17 @@ template<typename MatrixType> class HouseholderQR public: enum { - MinSizeAtCompileTime = EIGEN_ENUM_MIN(MatrixType::ColsAtCompileTime,MatrixType::RowsAtCompileTime) + RowsAtCompileTime = MatrixType::RowsAtCompileTime, + ColsAtCompileTime = MatrixType::ColsAtCompileTime, + Options = MatrixType::Options, + DiagSizeAtCompileTime = EIGEN_ENUM_MIN(ColsAtCompileTime,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, MinSizeAtCompileTime, 1> HCoeffsType; - typedef Matrix<Scalar, 1, MatrixType::ColsAtCompileTime> RowVectorType; + typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime> MatrixQType; + typedef Matrix<Scalar, DiagSizeAtCompileTime, 1> HCoeffsType; + typedef Matrix<Scalar, 1, ColsAtCompileTime> RowVectorType; /** * \brief Default Constructor. @@ -72,15 +79,6 @@ template<typename MatrixType> class HouseholderQR compute(matrix); } - /** \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 && "HouseholderQR is not initialized."); - int cols = m_qr.cols(); - return MatrixRBlockType(m_qr, 0, 0, cols, cols).nestByValue().template triangularView<UpperTriangular>(); - } - /** 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. * @@ -99,15 +97,48 @@ template<typename MatrixType> class HouseholderQR template<typename OtherDerived, typename ResultType> void solve(const MatrixBase<OtherDerived>& b, ResultType *result) const; - MatrixType matrixQ(void) const; + MatrixQType 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; } + const MatrixType& matrixQR() const + { + ei_assert(m_isInitialized && "HouseholderQR is not initialized."); + return m_qr; + } HouseholderQR& compute(const MatrixType& matrix); + /** \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; + protected: MatrixType m_qr; HCoeffsType m_hCoeffs; @@ -117,6 +148,22 @@ template<typename MatrixType> class HouseholderQR #ifndef EIGEN_HIDE_HEAVY_CODE template<typename MatrixType> +typename MatrixType::RealScalar HouseholderQR<MatrixType>::absDeterminant() const +{ + ei_assert(m_isInitialized && "HouseholderQR 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 HouseholderQR<MatrixType>::logAbsDeterminant() const +{ + ei_assert(m_isInitialized && "HouseholderQR 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> HouseholderQR<MatrixType>& HouseholderQR<MatrixType>::compute(const MatrixType& matrix) { int rows = matrix.rows(); @@ -177,7 +224,7 @@ void HouseholderQR<MatrixType>::solve( /** \returns the matrix Q */ template<typename MatrixType> -MatrixType HouseholderQR<MatrixType>::matrixQ() const +typename HouseholderQR<MatrixType>::MatrixQType HouseholderQR<MatrixType>::matrixQ() const { ei_assert(m_isInitialized && "HouseholderQR is not initialized."); // compute the product H'_0 H'_1 ... H'_n-1, @@ -185,13 +232,13 @@ MatrixType HouseholderQR<MatrixType>::matrixQ() const // 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(); - MatrixType res = MatrixType::Identity(rows, cols); - Matrix<Scalar,1,MatrixType::ColsAtCompileTime> temp(cols); - for (int k = cols-1; k >= 0; k--) + int size = std::min(rows,cols); + MatrixQType res = MatrixQType::Identity(rows, rows); + Matrix<Scalar,1,MatrixType::RowsAtCompileTime> temp(rows); + for (int k = size-1; k >= 0; k--) { - int remainingSize = rows-k; - res.corner(BottomRight, remainingSize, cols-k) - .applyHouseholderOnTheLeft(m_qr.col(k).end(remainingSize-1), ei_conj(m_hCoeffs.coeff(k)), &temp.coeffRef(k)); + res.block(k, k, rows-k, rows-k) + .applyHouseholderOnTheLeft(m_qr.col(k).end(rows-k-1), ei_conj(m_hCoeffs.coeff(k)), &temp.coeffRef(k)); } return res; } diff --git a/test/qr.cpp b/test/qr.cpp index f004a36ca..f2e2eda61 100644 --- a/test/qr.cpp +++ b/test/qr.cpp @@ -27,7 +27,6 @@ template<typename MatrixType> void qr(const MatrixType& m) { - /* this test covers the following files: QR.h */ int rows = m.rows(); int cols = m.cols(); @@ -37,8 +36,11 @@ template<typename MatrixType> void qr(const MatrixType& m) MatrixType a = MatrixType::Random(rows,cols); HouseholderQR<MatrixType> qrOfA(a); - VERIFY_IS_APPROX(a, qrOfA.matrixQ() * qrOfA.matrixR().toDense()); - VERIFY_IS_NOT_APPROX(a+MatrixType::Identity(rows, cols), qrOfA.matrixQ() * qrOfA.matrixR().toDense()); + MatrixType r = qrOfA.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); + + VERIFY_IS_APPROX(a, qrOfA.matrixQ() * r); SquareMatrixType b = a.adjoint() * a; @@ -57,8 +59,9 @@ template<typename MatrixType> void qr(const MatrixType& m) template<typename MatrixType> void qr_invertible() { - /* this test covers the following files: QR.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); @@ -75,6 +78,16 @@ 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() @@ -82,9 +95,11 @@ template<typename MatrixType> void qr_verify_assert() MatrixType tmp; HouseholderQR<MatrixType> qr; - VERIFY_RAISES_ASSERT(qr.matrixR()) + VERIFY_RAISES_ASSERT(qr.matrixQR()) VERIFY_RAISES_ASSERT(qr.solve(tmp,&tmp)) VERIFY_RAISES_ASSERT(qr.matrixQ()) + VERIFY_RAISES_ASSERT(qr.absDeterminant()) + VERIFY_RAISES_ASSERT(qr.logAbsDeterminant()) } void test_qr() diff --git a/test/qr_colpivoting.cpp b/test/qr_colpivoting.cpp index d190bce73..283855451 100644 --- a/test/qr_colpivoting.cpp +++ b/test/qr_colpivoting.cpp @@ -101,9 +101,17 @@ template<typename MatrixType> void qr_verify_assert() MatrixType tmp; ColPivotingHouseholderQR<MatrixType> qr; - VERIFY_RAISES_ASSERT(qr.matrixR()) + VERIFY_RAISES_ASSERT(qr.matrixQR()) 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()) + VERIFY_RAISES_ASSERT(qr.absDeterminant()) + VERIFY_RAISES_ASSERT(qr.logAbsDeterminant()) } void test_qr_colpivoting() diff --git a/test/qr_fullpivoting.cpp b/test/qr_fullpivoting.cpp index bdebea7cc..525c669a5 100644 --- a/test/qr_fullpivoting.cpp +++ b/test/qr_fullpivoting.cpp @@ -105,7 +105,7 @@ template<typename MatrixType> void qr_verify_assert() MatrixType tmp; FullPivotingHouseholderQR<MatrixType> qr; - VERIFY_RAISES_ASSERT(qr.matrixR()) + VERIFY_RAISES_ASSERT(qr.matrixQR()) VERIFY_RAISES_ASSERT(qr.solve(tmp,&tmp)) VERIFY_RAISES_ASSERT(qr.matrixQ()) VERIFY_RAISES_ASSERT(qr.dimensionOfKernel()) @@ -114,6 +114,8 @@ template<typename MatrixType> void qr_verify_assert() VERIFY_RAISES_ASSERT(qr.isInvertible()) VERIFY_RAISES_ASSERT(qr.computeInverse(&tmp)) VERIFY_RAISES_ASSERT(qr.inverse()) + VERIFY_RAISES_ASSERT(qr.absDeterminant()) + VERIFY_RAISES_ASSERT(qr.logAbsDeterminant()) } void test_qr_fullpivoting() |