diff options
| -rw-r--r-- | Eigen/QR | 3 | ||||
| -rw-r--r-- | Eigen/src/Core/MatrixBase.h | 2 | ||||
| -rw-r--r-- | Eigen/src/Core/util/ForwardDeclarations.h | 2 | ||||
| -rw-r--r-- | Eigen/src/QR/ColPivotingHouseholderQR.h | 266 | ||||
| -rw-r--r-- | Eigen/src/QR/FullPivotingHouseholderQR.h (renamed from Eigen/src/QR/RRQR.h) | 53 | ||||
| -rw-r--r-- | test/CMakeLists.txt | 3 | ||||
| -rw-r--r-- | test/qr_colpivoting.cpp (renamed from test/rrqr.cpp) | 8 | ||||
| -rw-r--r-- | test/qr_fullpivoting.cpp | 115 |
8 files changed, 417 insertions, 35 deletions
@@ -36,7 +36,8 @@ namespace Eigen { */ #include "src/QR/QR.h" -#include "src/QR/RRQR.h" +#include "src/QR/FullPivotingHouseholderQR.h" +#include "src/QR/ColPivotingHouseholderQR.h" #include "src/QR/Tridiagonalization.h" #include "src/QR/EigenSolver.h" #include "src/QR/SelfAdjointEigenSolver.h" diff --git a/Eigen/src/Core/MatrixBase.h b/Eigen/src/Core/MatrixBase.h index 1f4c6bf7a..7cb8853e6 100644 --- a/Eigen/src/Core/MatrixBase.h +++ b/Eigen/src/Core/MatrixBase.h @@ -745,6 +745,8 @@ template<typename Derived> class MatrixBase /////////// QR module /////////// const HouseholderQR<PlainMatrixType> householderQr() const; + const ColPivotingHouseholderQR<PlainMatrixType> colPivotingHouseholderQr() const; + const FullPivotingHouseholderQR<PlainMatrixType> fullPivotingHouseholderQr() const; EigenvaluesReturnType eigenvalues() const; RealScalar operatorNorm() const; diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h index 6f3e6a788..414aaceca 100644 --- a/Eigen/src/Core/util/ForwardDeclarations.h +++ b/Eigen/src/Core/util/ForwardDeclarations.h @@ -117,6 +117,8 @@ template<typename MatrixType, int Direction = BothDirections> class Reverse; template<typename MatrixType> class LU; template<typename MatrixType> class PartialLU; template<typename MatrixType> class HouseholderQR; +template<typename MatrixType> class ColPivotingHouseholderQR; +template<typename MatrixType> class FullPivotingHouseholderQR; template<typename MatrixType> class SVD; template<typename MatrixType, int UpLo = LowerTriangular> class LLT; template<typename MatrixType> class LDLT; diff --git a/Eigen/src/QR/ColPivotingHouseholderQR.h b/Eigen/src/QR/ColPivotingHouseholderQR.h new file mode 100644 index 000000000..ed4b84f63 --- /dev/null +++ b/Eigen/src/QR/ColPivotingHouseholderQR.h @@ -0,0 +1,266 @@ +// This file is part of Eigen, a lightweight C++ template library +// 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 +// License as published by the Free Software Foundation; either +// version 3 of the License, or (at your option) any later version. +// +// Alternatively, you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of +// the License, or (at your option) any later version. +// +// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY +// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS +// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the +// GNU General Public License for more details. +// +// You should have received a copy of the GNU Lesser General Public +// License and a copy of the GNU General Public License along with +// Eigen. If not, see <http://www.gnu.org/licenses/>. + +#ifndef EIGEN_COLPIVOTINGHOUSEHOLDERQR_H +#define EIGEN_COLPIVOTINGHOUSEHOLDERQR_H + +/** \ingroup QR_Module + * \nonstableyet + * + * \class ColPivotingHouseholderQR + * + * \brief Householder rank-revealing QR decomposition of a matrix + * + * \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. + * + * \sa MatrixBase::colPivotingHouseholderQr() + */ +template<typename MatrixType> class ColPivotingHouseholderQR +{ + public: + + enum { + 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 Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime> MatrixQType; + typedef Matrix<Scalar, DiagSizeAtCompileTime, 1> HCoeffsType; + typedef Matrix<int, 1, ColsAtCompileTime> IntRowVectorType; + typedef Matrix<int, RowsAtCompileTime, 1> IntColVectorType; + typedef Matrix<Scalar, 1, ColsAtCompileTime> RowVectorType; + typedef Matrix<Scalar, RowsAtCompileTime, 1> ColVectorType; + typedef Matrix<RealScalar, 1, ColsAtCompileTime> RealRowVectorType; + + /** + * \brief Default Constructor. + * + * The default constructor is useful in cases in which the user intends to + * perform decompositions via ColPivotingHouseholderQR::compute(const MatrixType&). + */ + ColPivotingHouseholderQR() : m_qr(), m_hCoeffs(), m_isInitialized(false) {} + + ColPivotingHouseholderQR(const MatrixType& matrix) + : m_qr(matrix.rows(), matrix.cols()), + m_hCoeffs(std::min(matrix.rows(),matrix.cols())), + m_isInitialized(false) + { + compute(matrix); + } + + /** 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. + * + * \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. + * Resized if necessary, so that result->rows()==A.cols() and result->cols()==b.cols(). + * If no solution exists, *result is left with undefined coefficients. + * + * \note The case where b is a matrix is not yet implemented. Also, this + * code is space inefficient. + * + * Example: \include ColPivotingHouseholderQR_solve.cpp + * Output: \verbinclude ColPivotingHouseholderQR_solve.out + */ + template<typename OtherDerived, typename ResultType> + 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 + */ + const MatrixType& matrixQR() const { return m_qr; } + + ColPivotingHouseholderQR& compute(const MatrixType& matrix); + + const IntRowVectorType& colsPermutation() const + { + ei_assert(m_isInitialized && "ColPivotingHouseholderQR is not initialized."); + return m_cols_permutation; + } + + inline int rank() const + { + ei_assert(m_isInitialized && "ColPivotingHouseholderQR is not initialized."); + return m_rank; + } + + protected: + MatrixType m_qr; + HCoeffsType m_hCoeffs; + IntRowVectorType m_cols_permutation; + bool m_isInitialized; + RealScalar m_precision; + int m_rank; + int m_det_pq; +}; + +#ifndef EIGEN_HIDE_HEAVY_CODE + +template<typename MatrixType> +ColPivotingHouseholderQR<MatrixType>& ColPivotingHouseholderQR<MatrixType>::compute(const MatrixType& matrix) +{ + int rows = matrix.rows(); + int cols = matrix.cols(); + int size = std::min(rows,cols); + m_rank = size; + + m_qr = matrix; + m_hCoeffs.resize(size); + + RowVectorType temp(cols); + + m_precision = epsilon<Scalar>() * size; + + IntRowVectorType cols_transpositions(matrix.cols()); + m_cols_permutation.resize(matrix.cols()); + int number_of_transpositions = 0; + + RealRowVectorType colSqNorms(cols); + for(int k = 0; k < cols; ++k) + colSqNorms.coeffRef(k) = m_qr.col(k).squaredNorm(); + RealScalar biggestColSqNorm = colSqNorms.maxCoeff(); + + for (int k = 0; k < size; ++k) + { + int biggest_col_in_corner; + RealScalar biggestColSqNormInCorner = colSqNorms.end(cols-k).maxCoeff(&biggest_col_in_corner); + biggest_col_in_corner += k; + + // if the corner is negligible, then we have less than full rank, and we can finish early + if(ei_isMuchSmallerThan(biggestColSqNormInCorner, biggestColSqNorm, m_precision)) + { + m_rank = k; + for(int i = k; i < size; i++) + { + cols_transpositions.coeffRef(i) = i; + m_hCoeffs.coeffRef(i) = Scalar(0); + } + break; + } + + cols_transpositions.coeffRef(k) = biggest_col_in_corner; + if(k != biggest_col_in_corner) { + m_qr.col(k).swap(m_qr.col(biggest_col_in_corner)); + ++number_of_transpositions; + } + + RealScalar beta; + m_qr.col(k).end(rows-k).makeHouseholderInPlace(&m_hCoeffs.coeffRef(k), &beta); + m_qr.coeffRef(k,k) = beta; + + m_qr.corner(BottomRight, rows-k, cols-k-1) + .applyHouseholderOnTheLeft(m_qr.col(k).end(rows-k-1), m_hCoeffs.coeffRef(k), &temp.coeffRef(k+1)); + + colSqNorms.end(cols-k-1) -= m_qr.row(k).end(cols-k-1).cwise().abs2(); + } + + for(int k = 0; k < matrix.cols(); ++k) m_cols_permutation.coeffRef(k) = k; + for(int k = 0; k < size; ++k) + std::swap(m_cols_permutation.coeffRef(k), m_cols_permutation.coeffRef(cols_transpositions.coeff(k))); + + m_det_pq = (number_of_transpositions%2) ? -1 : 1; + m_isInitialized = true; + + return *this; +} + +template<typename MatrixType> +template<typename OtherDerived, typename ResultType> +void ColPivotingHouseholderQR<MatrixType>::solve( + const MatrixBase<OtherDerived>& b, + ResultType *result +) const +{ + ei_assert(m_isInitialized && "ColPivotingHouseholderQR is not initialized."); + const int rows = m_qr.rows(); + const int cols = b.cols(); + ei_assert(b.rows() == rows); + + typename OtherDerived::PlainMatrixType c(b); + + Matrix<Scalar,1,MatrixType::ColsAtCompileTime> temp(cols); + for (int k = 0; k < m_rank; ++k) + { + int remainingSize = rows-k; + c.corner(BottomRight, remainingSize, cols) + .applyHouseholderOnTheLeft(m_qr.col(k).end(remainingSize-1), m_hCoeffs.coeff(k), &temp.coeffRef(0)); + } + + 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(); +} + +/** \returns the matrix Q */ +template<typename MatrixType> +MatrixType ColPivotingHouseholderQR<MatrixType>::matrixQ() const +{ + ei_assert(m_isInitialized && "ColPivotingHouseholderQR is not initialized."); + // compute the product H'_0 H'_1 ... H'_n-1, + // where H_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), ...] + int rows = m_qr.rows(); + int cols = m_qr.cols(); + int size = std::min(rows,cols); + MatrixType res = MatrixType::Identity(rows, rows); + Matrix<Scalar,1,MatrixType::RowsAtCompileTime> temp(rows); + for (int k = size-1; k >= 0; 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; +} + +#endif // EIGEN_HIDE_HEAVY_CODE + +/** \return the column-pivoting Householder QR decomposition of \c *this. + * + * \sa class ColPivotingHouseholderQR + */ +template<typename Derived> +const ColPivotingHouseholderQR<typename MatrixBase<Derived>::PlainMatrixType> +MatrixBase<Derived>::colPivotingHouseholderQr() const +{ + return ColPivotingHouseholderQR<PlainMatrixType>(eval()); +} + + +#endif // EIGEN_COLPIVOTINGHOUSEHOLDERQR_H diff --git a/Eigen/src/QR/RRQR.h b/Eigen/src/QR/FullPivotingHouseholderQR.h index 5e4f009dd..f7b0f1cc1 100644 --- a/Eigen/src/QR/RRQR.h +++ b/Eigen/src/QR/FullPivotingHouseholderQR.h @@ -23,13 +23,13 @@ // License and a copy of the GNU General Public License along with // Eigen. If not, see <http://www.gnu.org/licenses/>. -#ifndef EIGEN_RRQR_H -#define EIGEN_RRQR_H +#ifndef EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H +#define EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H /** \ingroup QR_Module * \nonstableyet * - * \class HouseholderRRQR + * \class FullPivotingHouseholderQR * * \brief Householder rank-revealing QR decomposition of a matrix * @@ -42,7 +42,7 @@ * * \sa MatrixBase::householderRrqr() */ -template<typename MatrixType> class HouseholderRRQR +template<typename MatrixType> class FullPivotingHouseholderQR { public: @@ -66,11 +66,11 @@ template<typename MatrixType> class HouseholderRRQR * \brief Default Constructor. * * The default constructor is useful in cases in which the user intends to - * perform decompositions via HouseholderRRQR::compute(const MatrixType&). + * perform decompositions via FullPivotingHouseholderQR::compute(const MatrixType&). */ - HouseholderRRQR() : m_qr(), m_hCoeffs(), m_isInitialized(false) {} + FullPivotingHouseholderQR() : m_qr(), m_hCoeffs(), m_isInitialized(false) {} - HouseholderRRQR(const MatrixType& matrix) + FullPivotingHouseholderQR(const MatrixType& matrix) : m_qr(matrix.rows(), matrix.cols()), m_hCoeffs(std::min(matrix.rows(),matrix.cols())), m_isInitialized(false) @@ -90,8 +90,8 @@ template<typename MatrixType> class HouseholderRRQR * \note The case where b is a matrix is not yet implemented. Also, this * code is space inefficient. * - * Example: \include HouseholderRRQR_solve.cpp - * Output: \verbinclude HouseholderRRQR_solve.out + * Example: \include FullPivotingHouseholderQR_solve.cpp + * Output: \verbinclude FullPivotingHouseholderQR_solve.out */ template<typename OtherDerived, typename ResultType> void solve(const MatrixBase<OtherDerived>& b, ResultType *result) const; @@ -102,23 +102,23 @@ template<typename MatrixType> class HouseholderRRQR */ const MatrixType& matrixQR() const { return m_qr; } - HouseholderRRQR& compute(const MatrixType& matrix); + FullPivotingHouseholderQR& compute(const MatrixType& matrix); const IntRowVectorType& colsPermutation() const { - ei_assert(m_isInitialized && "RRQR is not initialized."); + ei_assert(m_isInitialized && "FULLPIVOTINGHOUSEHOLDERQR is not initialized."); return m_cols_permutation; } const IntColVectorType& rowsTranspositions() const { - ei_assert(m_isInitialized && "RRQR is not initialized."); + ei_assert(m_isInitialized && "FULLPIVOTINGHOUSEHOLDERQR is not initialized."); return m_rows_transpositions; } inline int rank() const { - ei_assert(m_isInitialized && "RRQR is not initialized."); + ei_assert(m_isInitialized && "FULLPIVOTINGHOUSEHOLDERQR is not initialized."); return m_rank; } @@ -136,7 +136,7 @@ template<typename MatrixType> class HouseholderRRQR #ifndef EIGEN_HIDE_HEAVY_CODE template<typename MatrixType> -HouseholderRRQR<MatrixType>& HouseholderRRQR<MatrixType>::compute(const MatrixType& matrix) +FullPivotingHouseholderQR<MatrixType>& FullPivotingHouseholderQR<MatrixType>::compute(const MatrixType& matrix) { int rows = matrix.rows(); int cols = matrix.cols(); @@ -148,7 +148,6 @@ HouseholderRRQR<MatrixType>& HouseholderRRQR<MatrixType>::compute(const MatrixTy RowVectorType temp(cols); - // TODO: experiment to see the best formula m_precision = epsilon<Scalar>() * size; m_rows_transpositions.resize(matrix.rows()); @@ -198,7 +197,6 @@ HouseholderRRQR<MatrixType>& HouseholderRRQR<MatrixType>::compute(const MatrixTy m_qr.col(k).end(rows-k).makeHouseholderInPlace(&m_hCoeffs.coeffRef(k), &beta); m_qr.coeffRef(k,k) = beta; - // apply H to remaining part of m_qr from the left m_qr.corner(BottomRight, rows-k, cols-k-1) .applyHouseholderOnTheLeft(m_qr.col(k).end(rows-k-1), m_hCoeffs.coeffRef(k), &temp.coeffRef(k+1)); } @@ -215,12 +213,12 @@ HouseholderRRQR<MatrixType>& HouseholderRRQR<MatrixType>::compute(const MatrixTy template<typename MatrixType> template<typename OtherDerived, typename ResultType> -void HouseholderRRQR<MatrixType>::solve( +void FullPivotingHouseholderQR<MatrixType>::solve( const MatrixBase<OtherDerived>& b, ResultType *result ) const { - ei_assert(m_isInitialized && "HouseholderRRQR is not initialized."); + ei_assert(m_isInitialized && "FullPivotingHouseholderQR is not initialized."); const int rows = m_qr.rows(); const int cols = b.cols(); ei_assert(b.rows() == rows); @@ -247,9 +245,9 @@ void HouseholderRRQR<MatrixType>::solve( /** \returns the matrix Q */ template<typename MatrixType> -MatrixType HouseholderRRQR<MatrixType>::matrixQ() const +MatrixType FullPivotingHouseholderQR<MatrixType>::matrixQ() const { - ei_assert(m_isInitialized && "HouseholderRRQR is not initialized."); + ei_assert(m_isInitialized && "FullPivotingHouseholderQR is not initialized."); // compute the product H'_0 H'_1 ... H'_n-1, // where H_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), ...] @@ -269,18 +267,15 @@ MatrixType HouseholderRRQR<MatrixType>::matrixQ() const #endif // EIGEN_HIDE_HEAVY_CODE -#if 0 -/** \return the Householder QR decomposition of \c *this. +/** \return the full-pivoting Householder QR decomposition of \c *this. * - * \sa class HouseholderRRQR + * \sa class FullPivotingHouseholderQR */ template<typename Derived> -const HouseholderRRQR<typename MatrixBase<Derived>::PlainMatrixType> -MatrixBase<Derived>::householderQr() const +const FullPivotingHouseholderQR<typename MatrixBase<Derived>::PlainMatrixType> +MatrixBase<Derived>::fullPivotingHouseholderQr() const { - return HouseholderRRQR<PlainMatrixType>(eval()); + return FullPivotingHouseholderQR<PlainMatrixType>(eval()); } -#endif - -#endif // EIGEN_QR_H +#endif // EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt index b79e069b7..fc43bbb1d 100644 --- a/test/CMakeLists.txt +++ b/test/CMakeLists.txt @@ -121,7 +121,8 @@ ei_add_test(lu ${EI_OFLAG}) ei_add_test(determinant) ei_add_test(inverse ${EI_OFLAG}) ei_add_test(qr) -ei_add_test(rrqr) +ei_add_test(qr_colpivoting) +ei_add_test(qr_fullpivoting) ei_add_test(eigensolver_selfadjoint " " "${GSL_LIBRARIES}") ei_add_test(eigensolver_generic " " "${GSL_LIBRARIES}") ei_add_test(svd) diff --git a/test/rrqr.cpp b/test/qr_colpivoting.cpp index b6cc75d17..3a07c7131 100644 --- a/test/rrqr.cpp +++ b/test/qr_colpivoting.cpp @@ -37,7 +37,7 @@ template<typename MatrixType> void qr() typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType; MatrixType m1; createRandomMatrixOfRank(rank,rows,cols,m1); - HouseholderRRQR<MatrixType> qr(m1); + ColPivotingHouseholderQR<MatrixType> qr(m1); VERIFY_IS_APPROX(rank, qr.rank()); MatrixType r = qr.matrixQR(); @@ -74,7 +74,7 @@ template<typename MatrixType> void qr_invertible() m1 += a * a.adjoint(); } - HouseholderRRQR<MatrixType> qr(m1); + ColPivotingHouseholderQR<MatrixType> qr(m1); m3 = MatrixType::Random(size,size); qr.solve(m3, &m2); VERIFY_IS_APPROX(m3, m1*m2); @@ -84,13 +84,13 @@ template<typename MatrixType> void qr_verify_assert() { MatrixType tmp; - HouseholderRRQR<MatrixType> qr; + ColPivotingHouseholderQR<MatrixType> qr; VERIFY_RAISES_ASSERT(qr.matrixR()) VERIFY_RAISES_ASSERT(qr.solve(tmp,&tmp)) VERIFY_RAISES_ASSERT(qr.matrixQ()) } -void test_rrqr() +void test_qr_colpivoting() { for(int i = 0; i < 1; i++) { // FIXME : very weird bug here diff --git a/test/qr_fullpivoting.cpp b/test/qr_fullpivoting.cpp new file mode 100644 index 000000000..fcbf08e4c --- /dev/null +++ b/test/qr_fullpivoting.cpp @@ -0,0 +1,115 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 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 +// License as published by the Free Software Foundation; either +// version 3 of the License, or (at your option) any later version. +// +// Alternatively, you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of +// the License, or (at your option) any later version. +// +// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY +// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS +// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the +// GNU General Public License for more details. +// +// You should have received a copy of the GNU Lesser General Public +// License and a copy of the GNU General Public License along with +// Eigen. If not, see <http://www.gnu.org/licenses/>. + +#include "main.h" +#include <Eigen/QR> + +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); + + typedef typename MatrixType::Scalar Scalar; + typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> SquareMatrixType; + typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType; + MatrixType m1; + createRandomMatrixOfRank(rank,rows,cols,m1); + FullPivotingHouseholderQR<MatrixType> qr(m1); + VERIFY_IS_APPROX(rank, qr.rank()); + + 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); + + MatrixType b = qr.matrixQ() * r; + + MatrixType c = MatrixType::Zero(rows,cols); + + for(int i = 0; i < cols; ++i) c.col(qr.colsPermutation().coeff(i)) = b.col(i); + VERIFY_IS_APPROX(m1, c); + + MatrixType m2 = MatrixType::Random(cols,cols2); + MatrixType m3 = m1*m2; + m2 = MatrixType::Random(cols,cols2); + qr.solve(m3, &m2); + VERIFY_IS_APPROX(m3, m1*m2); +} + +template<typename MatrixType> void qr_invertible() +{ + typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar; + int size = ei_random<int>(10,50); + + MatrixType m1(size, size), m2(size, size), m3(size, size); + m1 = MatrixType::Random(size,size); + + if (ei_is_same_type<RealScalar,float>::ret) + { + // let's build a matrix more stable to inverse + MatrixType a = MatrixType::Random(size,size*2); + m1 += a * a.adjoint(); + } + + FullPivotingHouseholderQR<MatrixType> qr(m1); + m3 = MatrixType::Random(size,size); + qr.solve(m3, &m2); + VERIFY_IS_APPROX(m3, m1*m2); +} + +template<typename MatrixType> void qr_verify_assert() +{ + MatrixType tmp; + + FullPivotingHouseholderQR<MatrixType> qr; + VERIFY_RAISES_ASSERT(qr.matrixR()) + VERIFY_RAISES_ASSERT(qr.solve(tmp,&tmp)) + VERIFY_RAISES_ASSERT(qr.matrixQ()) +} + +void test_qr_fullpivoting() +{ + for(int i = 0; i < 1; i++) { + // FIXME : very weird bug here +// CALL_SUBTEST( qr(Matrix2f()) ); + CALL_SUBTEST( qr<MatrixXf>() ); + CALL_SUBTEST( qr<MatrixXd>() ); + CALL_SUBTEST( qr<MatrixXcd>() ); + } + + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST( qr_invertible<MatrixXf>() ); + CALL_SUBTEST( qr_invertible<MatrixXd>() ); + CALL_SUBTEST( qr_invertible<MatrixXcf>() ); + CALL_SUBTEST( qr_invertible<MatrixXcd>() ); + } + + CALL_SUBTEST(qr_verify_assert<Matrix3f>()); + CALL_SUBTEST(qr_verify_assert<Matrix3d>()); + CALL_SUBTEST(qr_verify_assert<MatrixXf>()); + CALL_SUBTEST(qr_verify_assert<MatrixXd>()); + CALL_SUBTEST(qr_verify_assert<MatrixXcf>()); + CALL_SUBTEST(qr_verify_assert<MatrixXcd>()); +} |