diff options
| -rw-r--r-- | Eigen/src/Core/TriangularMatrix.h | 93 | ||||
| -rw-r--r-- | test/triangular.cpp | 183 |
2 files changed, 193 insertions, 83 deletions
diff --git a/Eigen/src/Core/TriangularMatrix.h b/Eigen/src/Core/TriangularMatrix.h index e60d57e70..ed26683ea 100644 --- a/Eigen/src/Core/TriangularMatrix.h +++ b/Eigen/src/Core/TriangularMatrix.h @@ -26,22 +26,11 @@ #ifndef EIGEN_TRIANGULARMATRIX_H #define EIGEN_TRIANGULARMATRIX_H -/** \nonstableyet - * \class TriangularBase - * - * \brief Expression of a triangular matrix extracted from a given matrix - * - * \param MatrixType the type of the object in which we are taking the triangular part - * \param Mode the kind of triangular matrix expression to construct. Can be UpperTriangular, - * LowerTriangular, UpperSelfadjoint, or LowerSelfadjoint. This is in fact a bit field; - * it must have either UpperBit or LowerBit, and additionnaly it may have either - * TraingularBit or SelfadjointBit. +/** \internal * - * This class represents an expression of the upper or lower triangular part of - * a square matrix, possibly with a further assumption on the diagonal. It is the return type - * of MatrixBase::part() and most of the time this is the only way it is used. + * \class TriangularBase * - * \sa MatrixBase::part() + * \brief Base class for triangular part in a matrix */ template<typename Derived> class TriangularBase : public AnyMatrixBase<Derived> { @@ -115,19 +104,21 @@ template<typename Derived> class TriangularBase : public AnyMatrixBase<Derived> }; - /** \class TriangularView - * \nonstableyet * - * \brief Expression of a triangular part of a dense matrix + * \brief Base class for triangular part in a matrix * - * \param MatrixType the type of the dense matrix storing the coefficients + * \param MatrixType the type of the object in which we are taking the triangular part + * \param Mode the kind of triangular matrix expression to construct. Can be UpperTriangular, + * LowerTriangular, UpperSelfadjoint, or LowerSelfadjoint. This is in fact a bit field; + * it must have either UpperBit or LowerBit, and additionnaly it may have either + * TraingularBit or SelfadjointBit. * - * This class is an expression of a triangular part of a matrix with given dense - * storage of the coefficients. It is the return type of MatrixBase::triangularPart() - * and most of the time this is the only way that it is used. + * This class represents a triangular part of a matrix, not necessarily square. Strictly speaking, for rectangular + * matrices one should speak ok "trapezoid" parts. This class is the return type + * of MatrixBase::triangularView() and most of the time this is the only way it is used. * - * \sa class TriangularBase, MatrixBase::triangularPart(), class DiagonalWrapper + * \sa MatrixBase::triangularView() */ template<typename MatrixType, unsigned int _Mode> struct ei_traits<TriangularView<MatrixType, _Mode> > : ei_traits<MatrixType> @@ -155,7 +146,7 @@ template<typename _MatrixType, unsigned int _Mode> class TriangularView typedef TriangularBase<TriangularView> Base; typedef typename ei_traits<TriangularView>::Scalar Scalar; typedef _MatrixType MatrixType; - typedef typename MatrixType::PlainMatrixType PlainMatrixType; + typedef typename MatrixType::PlainMatrixType DenseMatrixType; typedef typename MatrixType::Nested MatrixTypeNested; typedef typename ei_cleantype<MatrixTypeNested>::type _MatrixTypeNested; @@ -244,9 +235,9 @@ template<typename _MatrixType, unsigned int _Mode> class TriangularView inline const TriangularView<NestByValue<Transpose<MatrixType> >,TransposeMode> transpose() const { return m_matrix.transpose().nestByValue(); } - PlainMatrixType toDense() const + DenseMatrixType toDenseMatrix() const { - PlainMatrixType res(rows(), cols()); + DenseMatrixType res(rows(), cols()); res = *this; return res; } @@ -351,6 +342,7 @@ struct ei_triangular_assignment_selector } } }; + template<typename Derived1, typename Derived2, unsigned int Mode, bool ClearOpposite> struct ei_triangular_assignment_selector<Derived1, Derived2, Mode, 1, ClearOpposite> { @@ -365,6 +357,7 @@ struct ei_triangular_assignment_selector<Derived1, Derived2, Mode, 1, ClearOppos dst.copyCoeff(0, 0, src); } }; + // prevent buggy user code from causing an infinite recursion template<typename Derived1, typename Derived2, unsigned int Mode, bool ClearOpposite> struct ei_triangular_assignment_selector<Derived1, Derived2, Mode, 0, ClearOpposite> @@ -379,14 +372,16 @@ struct ei_triangular_assignment_selector<Derived1, Derived2, UpperTriangular, Dy { for(int j = 0; j < dst.cols(); ++j) { - for(int i = 0; i <= j; ++i) + int maxi = std::min(j, dst.rows()-1); + for(int i = 0; i <= maxi; ++i) dst.copyCoeff(i, j, src); if (ClearOpposite) - for(int i = j+1; i < dst.rows(); ++i) + for(int i = maxi+1; i < dst.rows(); ++i) dst.coeffRef(i, j) = 0; } } }; + template<typename Derived1, typename Derived2, bool ClearOpposite> struct ei_triangular_assignment_selector<Derived1, Derived2, LowerTriangular, Dynamic, ClearOpposite> { @@ -396,8 +391,9 @@ struct ei_triangular_assignment_selector<Derived1, Derived2, LowerTriangular, Dy { for(int i = j; i < dst.rows(); ++i) dst.copyCoeff(i, j, src); + int maxi = std::min(j, dst.rows()); if (ClearOpposite) - for(int i = 0; i < j; ++i) + for(int i = 0; i < maxi; ++i) dst.coeffRef(i, j) = 0; } } @@ -410,14 +406,16 @@ struct ei_triangular_assignment_selector<Derived1, Derived2, StrictlyUpperTriang { for(int j = 0; j < dst.cols(); ++j) { - for(int i = 0; i < j; ++i) + int maxi = std::min(j, dst.rows()); + for(int i = 0; i < maxi; ++i) dst.copyCoeff(i, j, src); if (ClearOpposite) - for(int i = j; i < dst.rows(); ++i) + for(int i = maxi; i < dst.rows(); ++i) dst.coeffRef(i, j) = 0; } } }; + template<typename Derived1, typename Derived2, bool ClearOpposite> struct ei_triangular_assignment_selector<Derived1, Derived2, StrictlyLowerTriangular, Dynamic, ClearOpposite> { @@ -427,8 +425,9 @@ struct ei_triangular_assignment_selector<Derived1, Derived2, StrictlyLowerTriang { for(int i = j+1; i < dst.rows(); ++i) dst.copyCoeff(i, j, src); + int maxi = std::min(j, dst.rows()); if (ClearOpposite) - for(int i = 0; i <= j; ++i) + for(int i = 0; i <= maxi; ++i) dst.coeffRef(i, j) = 0; } } @@ -441,11 +440,12 @@ struct ei_triangular_assignment_selector<Derived1, Derived2, UnitUpperTriangular { for(int j = 0; j < dst.cols(); ++j) { - for(int i = 0; i < j; ++i) + int maxi = std::min(j, dst.rows()); + for(int i = 0; i < maxi; ++i) dst.copyCoeff(i, j, src); if (ClearOpposite) { - for(int i = j+1; i < dst.rows(); ++i) + for(int i = maxi+1; i < dst.rows(); ++i) dst.coeffRef(i, j) = 0; dst.coeffRef(j, j) = 1; } @@ -459,11 +459,12 @@ struct ei_triangular_assignment_selector<Derived1, Derived2, UnitLowerTriangular { for(int j = 0; j < dst.cols(); ++j) { - for(int i = j+1; i < dst.rows(); ++i) + int maxi = std::min(j, dst.rows()); + for(int i = maxi+1; i < dst.rows(); ++i) dst.copyCoeff(i, j, src); if (ClearOpposite) { - for(int i = 0; i < j; ++i) + for(int i = 0; i < maxi; ++i) dst.coeffRef(i, j) = 0; dst.coeffRef(j, j) = 1; } @@ -514,7 +515,7 @@ TriangularView<MatrixType, Mode>::operator=(const TriangularBase<OtherDerived>& ei_assert(Mode == OtherDerived::Mode); if(ei_traits<OtherDerived>::Flags & EvalBeforeAssigningBit) { - typename OtherDerived::PlainMatrixType other_evaluated(other.rows(), other.cols()); + typename OtherDerived::DenseMatrixType other_evaluated(other.rows(), other.cols()); other_evaluated.template triangularView<Mode>().lazyAssign(other.derived()); lazyAssign(other_evaluated); } @@ -633,17 +634,20 @@ const TriangularView<Derived, Mode> MatrixBase<Derived>::triangularView() const template<typename Derived> bool MatrixBase<Derived>::isUpperTriangular(RealScalar prec) const { - if(cols() != rows()) return false; RealScalar maxAbsOnUpperTriangularPart = static_cast<RealScalar>(-1); for(int j = 0; j < cols(); ++j) - for(int i = 0; i <= j; ++i) + { + int maxi = std::min(j, rows()-1); + for(int i = 0; i <= maxi; ++i) { RealScalar absValue = ei_abs(coeff(i,j)); if(absValue > maxAbsOnUpperTriangularPart) maxAbsOnUpperTriangularPart = absValue; } - for(int j = 0; j < cols()-1; ++j) + } + RealScalar threshold = maxAbsOnUpperTriangularPart * prec; + for(int j = 0; j < cols(); ++j) for(int i = j+1; i < rows(); ++i) - if(!ei_isMuchSmallerThan(coeff(i, j), maxAbsOnUpperTriangularPart, prec)) return false; + if(ei_abs(coeff(i, j)) > threshold) return false; return true; } @@ -655,7 +659,6 @@ bool MatrixBase<Derived>::isUpperTriangular(RealScalar prec) const template<typename Derived> bool MatrixBase<Derived>::isLowerTriangular(RealScalar prec) const { - if(cols() != rows()) return false; RealScalar maxAbsOnLowerTriangularPart = static_cast<RealScalar>(-1); for(int j = 0; j < cols(); ++j) for(int i = j; i < rows(); ++i) @@ -663,9 +666,13 @@ bool MatrixBase<Derived>::isLowerTriangular(RealScalar prec) const RealScalar absValue = ei_abs(coeff(i,j)); if(absValue > maxAbsOnLowerTriangularPart) maxAbsOnLowerTriangularPart = absValue; } + RealScalar threshold = maxAbsOnLowerTriangularPart * prec; for(int j = 1; j < cols(); ++j) - for(int i = 0; i < j; ++i) - if(!ei_isMuchSmallerThan(coeff(i, j), maxAbsOnLowerTriangularPart, prec)) return false; + { + int maxi = std::min(j, rows()-1); + for(int i = 0; i < maxi; ++i) + if(ei_abs(coeff(i, j)) > threshold) return false; + } return true; } diff --git a/test/triangular.cpp b/test/triangular.cpp index ee02c0022..3c89a8abb 100644 --- a/test/triangular.cpp +++ b/test/triangular.cpp @@ -24,7 +24,9 @@ #include "main.h" -template<typename MatrixType> void triangular(const MatrixType& m) + + +template<typename MatrixType> void triangular_square(const MatrixType& m) { typedef typename MatrixType::Scalar Scalar; typedef typename NumTraits<Scalar>::Real RealScalar; @@ -51,8 +53,8 @@ template<typename MatrixType> void triangular(const MatrixType& m) v2 = VectorType::Random(rows), vzero = VectorType::Zero(rows); - MatrixType m1up = m1.template triangularView<Eigen::UpperTriangular>(); - MatrixType m2up = m2.template triangularView<Eigen::UpperTriangular>(); + MatrixType m1up = m1.template triangularView<UpperTriangular>(); + MatrixType m2up = m2.template triangularView<UpperTriangular>(); if (rows*cols>1) { @@ -66,20 +68,20 @@ template<typename MatrixType> void triangular(const MatrixType& m) // test overloaded operator+= r1.setZero(); r2.setZero(); - r1.template triangularView<Eigen::UpperTriangular>() += m1; + r1.template triangularView<UpperTriangular>() += m1; r2 += m1up; VERIFY_IS_APPROX(r1,r2); // test overloaded operator= m1.setZero(); - m1.template triangularView<Eigen::UpperTriangular>() = m2.transpose() + m2; + m1.template triangularView<UpperTriangular>() = m2.transpose() + m2; m3 = m2.transpose() + m2; - VERIFY_IS_APPROX(m3.template triangularView<Eigen::LowerTriangular>().transpose().toDense(), m1); + VERIFY_IS_APPROX(m3.template triangularView<LowerTriangular>().transpose().toDenseMatrix(), m1); // test overloaded operator= m1.setZero(); - m1.template triangularView<Eigen::LowerTriangular>() = m2.transpose() + m2; - VERIFY_IS_APPROX(m3.template triangularView<Eigen::LowerTriangular>().toDense(), m1); + m1.template triangularView<LowerTriangular>() = m2.transpose() + m2; + VERIFY_IS_APPROX(m3.template triangularView<LowerTriangular>().toDenseMatrix(), m1); m1 = MatrixType::Random(rows, cols); for (int i=0; i<rows; ++i) @@ -87,49 +89,143 @@ template<typename MatrixType> void triangular(const MatrixType& m) Transpose<MatrixType> trm4(m4); // test back and forward subsitution with a vector as the rhs - m3 = m1.template triangularView<Eigen::UpperTriangular>(); - VERIFY(v2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Eigen::LowerTriangular>().solve(v2)), largerEps)); - m3 = m1.template triangularView<Eigen::LowerTriangular>(); - VERIFY(v2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Eigen::UpperTriangular>().solve(v2)), largerEps)); - m3 = m1.template triangularView<Eigen::UpperTriangular>(); - VERIFY(v2.isApprox(m3 * (m1.template triangularView<Eigen::UpperTriangular>().solve(v2)), largerEps)); - m3 = m1.template triangularView<Eigen::LowerTriangular>(); - VERIFY(v2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Eigen::LowerTriangular>().solve(v2)), largerEps)); + m3 = m1.template triangularView<UpperTriangular>(); + VERIFY(v2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<LowerTriangular>().solve(v2)), largerEps)); + m3 = m1.template triangularView<LowerTriangular>(); + VERIFY(v2.isApprox(m3.transpose() * (m1.transpose().template triangularView<UpperTriangular>().solve(v2)), largerEps)); + m3 = m1.template triangularView<UpperTriangular>(); + VERIFY(v2.isApprox(m3 * (m1.template triangularView<UpperTriangular>().solve(v2)), largerEps)); + m3 = m1.template triangularView<LowerTriangular>(); + VERIFY(v2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<LowerTriangular>().solve(v2)), largerEps)); // test back and forward subsitution with a matrix as the rhs - m3 = m1.template triangularView<Eigen::UpperTriangular>(); - VERIFY(m2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Eigen::LowerTriangular>().solve(m2)), largerEps)); - m3 = m1.template triangularView<Eigen::LowerTriangular>(); - VERIFY(m2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Eigen::UpperTriangular>().solve(m2)), largerEps)); - m3 = m1.template triangularView<Eigen::UpperTriangular>(); - VERIFY(m2.isApprox(m3 * (m1.template triangularView<Eigen::UpperTriangular>().solve(m2)), largerEps)); - m3 = m1.template triangularView<Eigen::LowerTriangular>(); - VERIFY(m2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Eigen::LowerTriangular>().solve(m2)), largerEps)); + m3 = m1.template triangularView<UpperTriangular>(); + VERIFY(m2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<LowerTriangular>().solve(m2)), largerEps)); + m3 = m1.template triangularView<LowerTriangular>(); + VERIFY(m2.isApprox(m3.transpose() * (m1.transpose().template triangularView<UpperTriangular>().solve(m2)), largerEps)); + m3 = m1.template triangularView<UpperTriangular>(); + VERIFY(m2.isApprox(m3 * (m1.template triangularView<UpperTriangular>().solve(m2)), largerEps)); + m3 = m1.template triangularView<LowerTriangular>(); + VERIFY(m2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<LowerTriangular>().solve(m2)), largerEps)); // check M * inv(L) using in place API m4 = m3; - m3.transpose().template triangularView<Eigen::UpperTriangular>().solveInPlace(trm4); + m3.transpose().template triangularView<UpperTriangular>().solveInPlace(trm4); VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>())); // check M * inv(U) using in place API - m3 = m1.template triangularView<Eigen::UpperTriangular>(); + m3 = m1.template triangularView<UpperTriangular>(); m4 = m3; - m3.transpose().template triangularView<Eigen::LowerTriangular>().solveInPlace(trm4); + m3.transpose().template triangularView<LowerTriangular>().solveInPlace(trm4); VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>())); // check solve with unit diagonal - m3 = m1.template triangularView<Eigen::UnitUpperTriangular>(); - VERIFY(m2.isApprox(m3 * (m1.template triangularView<Eigen::UnitUpperTriangular>().solve(m2)), largerEps)); + m3 = m1.template triangularView<UnitUpperTriangular>(); + VERIFY(m2.isApprox(m3 * (m1.template triangularView<UnitUpperTriangular>().solve(m2)), largerEps)); + +// VERIFY(( m1.template triangularView<UpperTriangular>() +// * m2.template triangularView<UpperTriangular>()).isUpperTriangular()); + + // test swap + m1.setOnes(); + m2.setZero(); + m2.template triangularView<UpperTriangular>().swap(m1); + m3.setZero(); + m3.template triangularView<UpperTriangular>().setOnes(); + VERIFY_IS_APPROX(m2,m3); + +} + + +template<typename MatrixType> void triangular_rect(const MatrixType& m) +{ + typedef typename MatrixType::Scalar Scalar; + typedef typename NumTraits<Scalar>::Real RealScalar; + typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType; + + int rows = m.rows(); + int cols = m.cols(); + + MatrixType m1 = MatrixType::Random(rows, cols), + m2 = MatrixType::Random(rows, cols), + m3(rows, cols), + m4(rows, cols), + r1(rows, cols), + r2(rows, cols), + mzero = MatrixType::Zero(rows, cols), + mones = MatrixType::Ones(rows, cols), + identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> + ::Identity(rows, rows), + square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> + ::Random(rows, rows); + VectorType v1 = VectorType::Random(rows), + v2 = VectorType::Random(rows), + vzero = VectorType::Zero(rows); + + MatrixType m1up = m1.template triangularView<UpperTriangular>(); + MatrixType m2up = m2.template triangularView<UpperTriangular>(); + + if (rows*cols>1) + { + VERIFY(m1up.isUpperTriangular()); + VERIFY(m2up.transpose().isLowerTriangular()); + VERIFY(!m2.isLowerTriangular()); + } + +// VERIFY_IS_APPROX(m1up.transpose() * m2, m1.upper().transpose().lower() * m2); -// VERIFY(( m1.template triangularView<Eigen::UpperTriangular>() -// * m2.template triangularView<Eigen::UpperTriangular>()).isUpperTriangular()); + // test overloaded operator+= + r1.setZero(); + r2.setZero(); + r1.template triangularView<UpperTriangular>() += m1; + r2 += m1up; + VERIFY_IS_APPROX(r1,r2); + // test overloaded operator= + m1.setZero(); + m1.template triangularView<UpperTriangular>() = 3 * m2; + m3 = 3 * m2; + VERIFY_IS_APPROX(m3.template triangularView<UpperTriangular>().toDenseMatrix(), m1); + + m1.setZero(); + m1.template triangularView<LowerTriangular>() = 3 * m2; + VERIFY_IS_APPROX(m3.template triangularView<LowerTriangular>().toDenseMatrix(), m1); + + m1.setZero(); + m1.template triangularView<StrictlyUpperTriangular>() = 3 * m2; + VERIFY_IS_APPROX(m3.template triangularView<StrictlyUpperTriangular>().toDenseMatrix(), m1); + + m1.setZero(); + m1.template triangularView<StrictlyLowerTriangular>() = 3 * m2; + VERIFY_IS_APPROX(m3.template triangularView<StrictlyLowerTriangular>().toDenseMatrix(), m1); + + m1.setRandom(); + m2 = m1.template triangularView<UpperTriangular>(); + VERIFY(m2.isUpperTriangular()); + VERIFY(!m2.isLowerTriangular()); + m2 = m1.template triangularView<StrictlyUpperTriangular>(); + VERIFY(m2.isUpperTriangular()); + VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1))); + m2 = m1.template triangularView<UnitUpperTriangular>(); + VERIFY(m2.isUpperTriangular()); + m2.diagonal().cwise() -= Scalar(1); + VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1))); + m2 = m1.template triangularView<LowerTriangular>(); + VERIFY(m2.isLowerTriangular()); + VERIFY(!m2.isUpperTriangular()); + m2 = m1.template triangularView<StrictlyLowerTriangular>(); + VERIFY(m2.isLowerTriangular()); + VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1))); + m2 = m1.template triangularView<UnitLowerTriangular>(); + VERIFY(m2.isLowerTriangular()); + m2.diagonal().cwise() -= Scalar(1); + VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1))); // test swap m1.setOnes(); m2.setZero(); - m2.template triangularView<Eigen::UpperTriangular>().swap(m1); + m2.template triangularView<UpperTriangular>().swap(m1); m3.setZero(); - m3.template triangularView<Eigen::UpperTriangular>().setOnes(); + m3.template triangularView<UpperTriangular>().setOnes(); VERIFY_IS_APPROX(m2,m3); } @@ -137,12 +233,19 @@ template<typename MatrixType> void triangular(const MatrixType& m) void test_triangular() { for(int i = 0; i < g_repeat ; i++) { - CALL_SUBTEST_1( triangular(Matrix<float, 1, 1>()) ); - CALL_SUBTEST_2( triangular(Matrix<float, 2, 2>()) ); - CALL_SUBTEST_3( triangular(Matrix3d()) ); - CALL_SUBTEST_4( triangular(MatrixXcf(4, 4)) ); - CALL_SUBTEST_5( triangular(Matrix<std::complex<float>,8, 8>()) ); - CALL_SUBTEST_6( triangular(MatrixXcd(17,17)) ); - CALL_SUBTEST_7( triangular(Matrix<float,Dynamic,Dynamic,RowMajor>(5, 5)) ); + CALL_SUBTEST_1( triangular_square(Matrix<float, 1, 1>()) ); + CALL_SUBTEST_2( triangular_square(Matrix<float, 2, 2>()) ); + CALL_SUBTEST_3( triangular_square(Matrix3d()) ); + CALL_SUBTEST_4( triangular_square(MatrixXcf(4, 4)) ); + CALL_SUBTEST_5( triangular_square(Matrix<std::complex<float>,8, 8>()) ); + CALL_SUBTEST_6( triangular_square(MatrixXcd(17,17)) ); + CALL_SUBTEST_7( triangular_square(Matrix<float,Dynamic,Dynamic,RowMajor>(5, 5)) ); + + CALL_SUBTEST_8( triangular_rect(Matrix<float, 4, 5>()) ); + CALL_SUBTEST_9( triangular_rect(Matrix<double, 6, 2>()) ); + CALL_SUBTEST_4( triangular_rect(MatrixXcf(4, 10)) ); + CALL_SUBTEST_6( triangular_rect(MatrixXcd(11, 3)) ); + CALL_SUBTEST_7( triangular_rect(Matrix<float,Dynamic,Dynamic,RowMajor>(7, 6)) ); + } } |