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-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra. Eigen itself is part of the KDE project.
-//
-// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
-//
-// 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_CHOLESKY_H
-#define EIGEN_CHOLESKY_H
-
-/** \ingroup Cholesky_Module
- *
- * \class Cholesky
- *
- * \deprecated this class has been renamed LLT
- */
-template<typename MatrixType> class Cholesky
-{
- private:
- typedef typename MatrixType::Scalar Scalar;
- typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
- typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
-
- enum {
- PacketSize = ei_packet_traits<Scalar>::size,
- AlignmentMask = int(PacketSize)-1
- };
-
- public:
-
- Cholesky(const MatrixType& matrix)
- : m_matrix(matrix.rows(), matrix.cols())
- {
- compute(matrix);
- }
-
- /** \deprecated */
- inline Part<MatrixType, LowerTriangular> matrixL(void) const { return m_matrix; }
-
- /** \deprecated */
- inline bool isPositiveDefinite(void) const { return m_isPositiveDefinite; }
-
- template<typename Derived>
- EIGEN_DEPRECATED typename MatrixBase<Derived>::PlainMatrixType_ColMajor solve(const MatrixBase<Derived> &b) const;
-
- template<typename RhsDerived, typename ResDerived>
- bool solve(const MatrixBase<RhsDerived> &b, MatrixBase<ResDerived> *result) const;
-
- template<typename Derived>
- bool solveInPlace(MatrixBase<Derived> &bAndX) const;
-
- void compute(const MatrixType& matrix);
-
- protected:
- /** \internal
- * Used to compute and store L
- * The strict upper part is not used and even not initialized.
- */
- MatrixType m_matrix;
- bool m_isPositiveDefinite;
-};
-
-/** \deprecated */
-template<typename MatrixType>
-void Cholesky<MatrixType>::compute(const MatrixType& a)
-{
- assert(a.rows()==a.cols());
- const int size = a.rows();
- m_matrix.resize(size, size);
- const RealScalar eps = ei_sqrt(precision<Scalar>());
-
- RealScalar x;
- x = ei_real(a.coeff(0,0));
- m_isPositiveDefinite = x > eps && ei_isMuchSmallerThan(ei_imag(a.coeff(0,0)), RealScalar(1));
- m_matrix.coeffRef(0,0) = ei_sqrt(x);
- m_matrix.col(0).end(size-1) = a.row(0).end(size-1).adjoint() / ei_real(m_matrix.coeff(0,0));
- for (int j = 1; j < size; ++j)
- {
- Scalar tmp = ei_real(a.coeff(j,j)) - m_matrix.row(j).start(j).squaredNorm();
- x = ei_real(tmp);
- if (x < eps || (!ei_isMuchSmallerThan(ei_imag(tmp), RealScalar(1))))
- {
- m_isPositiveDefinite = false;
- return;
- }
- m_matrix.coeffRef(j,j) = x = ei_sqrt(x);
-
- int endSize = size-j-1;
- if (endSize>0) {
- // Note that when all matrix columns have good alignment, then the following
- // product is guaranteed to be optimal with respect to alignment.
- m_matrix.col(j).end(endSize) =
- (m_matrix.block(j+1, 0, endSize, j) * m_matrix.row(j).start(j).adjoint()).lazy();
-
- // FIXME could use a.col instead of a.row
- m_matrix.col(j).end(endSize) = (a.row(j).end(endSize).adjoint()
- - m_matrix.col(j).end(endSize) ) / x;
- }
- }
-}
-
-/** \deprecated */
-template<typename MatrixType>
-template<typename Derived>
-typename MatrixBase<Derived>::PlainMatrixType_ColMajor Cholesky<MatrixType>::solve(const MatrixBase<Derived> &b) const
-{
- const int size = m_matrix.rows();
- ei_assert(size==b.rows());
- typename MatrixBase<Derived>::PlainMatrixType_ColMajor x(b);
- solveInPlace(x);
- return x;
-}
-
-/** \deprecated */
-template<typename MatrixType>
-template<typename RhsDerived, typename ResDerived>
-bool Cholesky<MatrixType>::solve(const MatrixBase<RhsDerived> &b, MatrixBase<ResDerived> *result) const
-{
- const int size = m_matrix.rows();
- ei_assert(size==b.rows() && "Cholesky::solve(): invalid number of rows of the right hand side matrix b");
- return solveInPlace((*result) = b);
-}
-
-/** \deprecated */
-template<typename MatrixType>
-template<typename Derived>
-bool Cholesky<MatrixType>::solveInPlace(MatrixBase<Derived> &bAndX) const
-{
- const int size = m_matrix.rows();
- ei_assert(size==bAndX.rows());
- if (!m_isPositiveDefinite)
- return false;
- matrixL().solveTriangularInPlace(bAndX);
- m_matrix.adjoint().template part<UpperTriangular>().solveTriangularInPlace(bAndX);
- return true;
-}
-
-/** \cholesky_module
- * \deprecated has been renamed llt()
- */
-template<typename Derived>
-inline const Cholesky<typename MatrixBase<Derived>::PlainMatrixType>
-MatrixBase<Derived>::cholesky() const
-{
- return Cholesky<PlainMatrixType>(derived());
-}
-
-#endif // EIGEN_CHOLESKY_H