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*port the Cholesky module to the new solve() API
*improve documentation
This commit is contained in:
Benoit Jacob
parent
e8dd552257
commit
6b48e932e9
@ -27,6 +27,8 @@
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#ifndef EIGEN_LDLT_H
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#define EIGEN_LDLT_H
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template<typename MatrixType, typename Rhs> struct ei_ldlt_solve_impl;
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/** \ingroup cholesky_Module
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*
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* \class LDLT
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@ -43,8 +45,8 @@
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* zeros in the bottom right rank(A) - n submatrix. Avoiding the square root
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* on D also stabilizes the computation.
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*
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* Remember that Cholesky decompositions are not rank-revealing. Also, do not use a Cholesky decomposition to determine
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* whether a system of equations has a solution.
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* Remember that Cholesky decompositions are not rank-revealing. Also, do not use a Cholesky
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* decomposition to determine whether a system of equations has a solution.
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*
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* \sa MatrixBase::ldlt(), class LLT
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*/
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@ -117,14 +119,37 @@ template<typename MatrixType> class LDLT
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return m_sign == -1;
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}
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template<typename RhsDerived, typename ResultType>
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bool solve(const MatrixBase<RhsDerived> &b, ResultType *result) const;
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/** \returns a solution x of \f$ A x = b \f$ using the current decomposition of A.
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*
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* \note_about_checking_solutions
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*
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* \sa solveInPlace(), MatrixBase::ldlt()
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*/
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template<typename Rhs>
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inline const ei_ldlt_solve_impl<MatrixType, Rhs>
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solve(const MatrixBase<Rhs>& b) const
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{
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ei_assert(m_isInitialized && "LDLT is not initialized.");
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ei_assert(m_matrix.rows()==b.rows()
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&& "LDLT::solve(): invalid number of rows of the right hand side matrix b");
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return ei_ldlt_solve_impl<MatrixType, Rhs>(*this, b.derived());
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}
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template<typename Derived>
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bool solveInPlace(MatrixBase<Derived> &bAndX) const;
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LDLT& compute(const MatrixType& matrix);
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/** \returns the LDLT decomposition matrix
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*
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* TODO: document the storage layout
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*/
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inline const MatrixType& matrixLDLT() const
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{
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ei_assert(m_isInitialized && "LDLT is not initialized.");
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return m_matrix;
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}
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protected:
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/** \internal
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* Used to compute and store the Cholesky decomposition A = L D L^* = U^* D U.
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@ -134,7 +159,7 @@ template<typename MatrixType> class LDLT
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*/
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MatrixType m_matrix;
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IntColVectorType m_p;
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IntColVectorType m_transpositions;
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IntColVectorType m_transpositions; // FIXME do we really need to store permanently the transpositions?
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int m_sign;
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bool m_isInitialized;
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};
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@ -238,27 +263,38 @@ LDLT<MatrixType>& LDLT<MatrixType>::compute(const MatrixType& a)
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return *this;
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}
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/** Computes the solution x of \f$ A x = b \f$ using the current decomposition of A.
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* The result is stored in \a result
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*
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* \returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD.
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*
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* In other words, it computes \f$ b = A^{-1} b \f$ with
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* \f$ P^T{L^{*}}^{-1} D^{-1} L^{-1} P b \f$ from right to left.
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*
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* \sa LDLT::solveInPlace(), MatrixBase::ldlt()
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*/
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template<typename MatrixType>
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template<typename RhsDerived, typename ResultType>
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bool LDLT<MatrixType>
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::solve(const MatrixBase<RhsDerived> &b, ResultType *result) const
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template<typename MatrixType,typename Rhs>
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struct ei_traits<ei_ldlt_solve_impl<MatrixType,Rhs> >
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{
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ei_assert(m_isInitialized && "LDLT is not initialized.");
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const int size = m_matrix.rows();
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ei_assert(size==b.rows() && "LDLT::solve(): invalid number of rows of the right hand side matrix b");
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*result = b;
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return solveInPlace(*result);
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}
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typedef Matrix<typename Rhs::Scalar,
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MatrixType::ColsAtCompileTime,
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Rhs::ColsAtCompileTime,
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Rhs::PlainMatrixType::Options,
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MatrixType::MaxColsAtCompileTime,
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Rhs::MaxColsAtCompileTime> ReturnMatrixType;
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};
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template<typename MatrixType, typename Rhs>
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struct ei_ldlt_solve_impl : public ReturnByValue<ei_ldlt_solve_impl<MatrixType, Rhs> >
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{
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typedef typename ei_cleantype<typename Rhs::Nested>::type RhsNested;
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typedef LDLT<MatrixType> LDLTType;
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const LDLTType& m_ldlt;
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const typename Rhs::Nested m_rhs;
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ei_ldlt_solve_impl(const LDLTType& ldlt, const Rhs& rhs)
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: m_ldlt(ldlt), m_rhs(rhs)
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{}
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inline int rows() const { return m_ldlt.matrixLDLT().cols(); }
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inline int cols() const { return m_rhs.cols(); }
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template<typename Dest> void evalTo(Dest& dst) const
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{
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dst = m_rhs;
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m_ldlt.solveInPlace(dst);
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}
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};
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/** This is the \em in-place version of solve().
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*
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@ -26,6 +26,7 @@
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#define EIGEN_LLT_H
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template<typename MatrixType, int UpLo> struct LLT_Traits;
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template<typename MatrixType, int UpLo, typename Rhs> struct ei_llt_solve_impl;
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/** \ingroup cholesky_Module
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*
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@ -99,14 +100,41 @@ template<typename MatrixType, int _UpLo> class LLT
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return Traits::getL(m_matrix);
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}
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template<typename RhsDerived, typename ResultType>
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bool solve(const MatrixBase<RhsDerived> &b, ResultType *result) const;
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/** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
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*
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* Since this LLT class assumes anyway that the matrix A is invertible, the solution
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* theoretically exists and is unique regardless of b.
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*
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* Example: \include LLT_solve.cpp
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* Output: \verbinclude LLT_solve.out
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*
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* \sa solveInPlace(), MatrixBase::llt()
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*/
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template<typename Rhs>
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inline const ei_llt_solve_impl<MatrixType, UpLo, Rhs>
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solve(const MatrixBase<Rhs>& b) const
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{
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ei_assert(m_isInitialized && "LLT is not initialized.");
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ei_assert(m_matrix.rows()==b.rows()
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&& "LLT::solve(): invalid number of rows of the right hand side matrix b");
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return ei_llt_solve_impl<MatrixType, UpLo, Rhs>(*this, b.derived());
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}
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template<typename Derived>
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bool solveInPlace(MatrixBase<Derived> &bAndX) const;
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LLT& compute(const MatrixType& matrix);
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/** \returns the LLT decomposition matrix
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*
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* TODO: document the storage layout
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*/
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inline const MatrixType& matrixLLT() const
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{
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ei_assert(m_isInitialized && "LLT is not initialized.");
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return m_matrix;
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}
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protected:
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/** \internal
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* Used to compute and store L
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@ -229,28 +257,38 @@ LLT<MatrixType,_UpLo>& LLT<MatrixType,_UpLo>::compute(const MatrixType& a)
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return *this;
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}
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/** Computes the solution x of \f$ A x = b \f$ using the current decomposition of A.
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* The result is stored in \a result
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*
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* \returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD.
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*
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* In other words, it computes \f$ b = A^{-1} b \f$ with
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* \f$ {L^{*}}^{-1} L^{-1} b \f$ from right to left.
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*
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* Example: \include LLT_solve.cpp
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* Output: \verbinclude LLT_solve.out
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*
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* \sa LLT::solveInPlace(), MatrixBase::llt()
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*/
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template<typename MatrixType, int _UpLo>
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template<typename RhsDerived, typename ResultType>
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bool LLT<MatrixType,_UpLo>::solve(const MatrixBase<RhsDerived> &b, ResultType *result) const
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template<typename MatrixType, int UpLo, typename Rhs>
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struct ei_traits<ei_llt_solve_impl<MatrixType,UpLo,Rhs> >
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{
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ei_assert(m_isInitialized && "LLT is not initialized.");
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const int size = m_matrix.rows();
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ei_assert(size==b.rows() && "LLT::solve(): invalid number of rows of the right hand side matrix b");
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return solveInPlace((*result) = b);
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}
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typedef Matrix<typename Rhs::Scalar,
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MatrixType::ColsAtCompileTime,
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Rhs::ColsAtCompileTime,
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Rhs::PlainMatrixType::Options,
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MatrixType::MaxColsAtCompileTime,
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Rhs::MaxColsAtCompileTime> ReturnMatrixType;
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};
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template<typename MatrixType, int UpLo, typename Rhs>
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struct ei_llt_solve_impl : public ReturnByValue<ei_llt_solve_impl<MatrixType,UpLo,Rhs> >
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{
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typedef typename ei_cleantype<typename Rhs::Nested>::type RhsNested;
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typedef LLT<MatrixType,UpLo> LLTType;
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const LLTType& m_llt;
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const typename Rhs::Nested m_rhs;
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ei_llt_solve_impl(const LLTType& llt, const Rhs& rhs)
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: m_llt(llt), m_rhs(rhs)
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{}
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inline int rows() const { return m_llt.matrixLLT().cols(); }
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inline int cols() const { return m_rhs.cols(); }
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template<typename Dest> void evalTo(Dest& dst) const
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{
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dst = m_rhs;
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m_llt.solveInPlace(dst);
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}
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};
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/** This is the \em in-place version of solve().
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*
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@ -25,9 +25,9 @@
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#ifndef EIGEN_LU_H
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#define EIGEN_LU_H
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template<typename MatrixType, typename Rhs> struct ei_lu_solve_impl;
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template<typename MatrixType> struct ei_lu_kernel_impl;
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template<typename MatrixType> struct ei_lu_image_impl;
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template<typename MatrixType, typename Rhs> struct ei_fullpivlu_solve_impl;
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template<typename MatrixType> struct ei_fullpivlu_kernel_impl;
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template<typename MatrixType> struct ei_fullpivlu_image_impl;
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/** \ingroup LU_Module
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*
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@ -167,10 +167,10 @@ template<typename MatrixType> class FullPivLU
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*
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* \sa image()
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*/
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inline const ei_lu_kernel_impl<MatrixType> kernel() const
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inline const ei_fullpivlu_kernel_impl<MatrixType> kernel() const
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{
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ei_assert(m_isInitialized && "LU is not initialized.");
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return ei_lu_kernel_impl<MatrixType>(*this);
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return ei_fullpivlu_kernel_impl<MatrixType>(*this);
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}
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/** \returns the image of the matrix, also called its column-space. The columns of the returned matrix
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@ -193,11 +193,11 @@ template<typename MatrixType> class FullPivLU
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* \sa kernel()
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*/
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template<typename OriginalMatrixType>
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inline const ei_lu_image_impl<MatrixType>
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inline const ei_fullpivlu_image_impl<MatrixType>
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image(const MatrixBase<OriginalMatrixType>& originalMatrix) const
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{
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ei_assert(m_isInitialized && "LU is not initialized.");
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return ei_lu_image_impl<MatrixType>(*this, originalMatrix.derived());
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return ei_fullpivlu_image_impl<MatrixType>(*this, originalMatrix.derived());
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}
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/** This method returns a solution x to the equation Ax=b, where A is the matrix of which
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@ -220,11 +220,11 @@ template<typename MatrixType> class FullPivLU
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* \sa TriangularView::solve(), kernel(), inverse()
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*/
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template<typename Rhs>
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inline const ei_lu_solve_impl<MatrixType, Rhs>
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inline const ei_fullpivlu_solve_impl<MatrixType, Rhs>
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solve(const MatrixBase<Rhs>& b) const
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{
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ei_assert(m_isInitialized && "LU is not initialized.");
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return ei_lu_solve_impl<MatrixType, Rhs>(*this, b.derived());
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return ei_fullpivlu_solve_impl<MatrixType, Rhs>(*this, b.derived());
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}
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/** \returns the determinant of the matrix of which
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@ -365,11 +365,11 @@ template<typename MatrixType> class FullPivLU
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*
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* \sa MatrixBase::inverse()
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*/
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inline const ei_lu_solve_impl<MatrixType,NestByValue<typename MatrixType::IdentityReturnType> > inverse() const
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inline const ei_fullpivlu_solve_impl<MatrixType,NestByValue<typename MatrixType::IdentityReturnType> > inverse() const
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{
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ei_assert(m_isInitialized && "LU is not initialized.");
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ei_assert(m_lu.rows() == m_lu.cols() && "You can't take the inverse of a non-square matrix!");
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return ei_lu_solve_impl<MatrixType,NestByValue<typename MatrixType::IdentityReturnType> >
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return ei_fullpivlu_solve_impl<MatrixType,NestByValue<typename MatrixType::IdentityReturnType> >
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(*this, MatrixType::Identity(m_lu.rows(), m_lu.cols()).nestByValue());
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}
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@ -493,7 +493,7 @@ typename ei_traits<MatrixType>::Scalar FullPivLU<MatrixType>::determinant() cons
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/********* Implementation of kernel() **************************************************/
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template<typename MatrixType>
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struct ei_traits<ei_lu_kernel_impl<MatrixType> >
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struct ei_traits<ei_fullpivlu_kernel_impl<MatrixType> >
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{
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typedef Matrix<
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typename MatrixType::Scalar,
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@ -509,7 +509,7 @@ struct ei_traits<ei_lu_kernel_impl<MatrixType> >
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};
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template<typename MatrixType>
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struct ei_lu_kernel_impl : public ReturnByValue<ei_lu_kernel_impl<MatrixType> >
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struct ei_fullpivlu_kernel_impl : public ReturnByValue<ei_fullpivlu_kernel_impl<MatrixType> >
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{
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typedef FullPivLU<MatrixType> LUType;
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typedef typename MatrixType::Scalar Scalar;
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@ -517,7 +517,7 @@ struct ei_lu_kernel_impl : public ReturnByValue<ei_lu_kernel_impl<MatrixType> >
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const LUType& m_lu;
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int m_rank, m_cols;
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ei_lu_kernel_impl(const LUType& lu)
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ei_fullpivlu_kernel_impl(const LUType& lu)
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: m_lu(lu),
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m_rank(lu.rank()),
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m_cols(m_rank==lu.matrixLU().cols() ? 1 : lu.matrixLU().cols() - m_rank){}
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@ -599,7 +599,7 @@ struct ei_lu_kernel_impl : public ReturnByValue<ei_lu_kernel_impl<MatrixType> >
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/***** Implementation of image() *****************************************************/
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template<typename MatrixType>
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struct ei_traits<ei_lu_image_impl<MatrixType> >
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struct ei_traits<ei_fullpivlu_image_impl<MatrixType> >
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{
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typedef Matrix<
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typename MatrixType::Scalar,
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@ -613,7 +613,7 @@ struct ei_traits<ei_lu_image_impl<MatrixType> >
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};
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template<typename MatrixType>
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struct ei_lu_image_impl : public ReturnByValue<ei_lu_image_impl<MatrixType> >
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struct ei_fullpivlu_image_impl : public ReturnByValue<ei_fullpivlu_image_impl<MatrixType> >
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{
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typedef FullPivLU<MatrixType> LUType;
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typedef typename MatrixType::RealScalar RealScalar;
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@ -621,7 +621,7 @@ struct ei_lu_image_impl : public ReturnByValue<ei_lu_image_impl<MatrixType> >
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int m_rank, m_cols;
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const MatrixType& m_originalMatrix;
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ei_lu_image_impl(const LUType& lu, const MatrixType& originalMatrix)
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ei_fullpivlu_image_impl(const LUType& lu, const MatrixType& originalMatrix)
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: m_lu(lu), m_rank(lu.rank()),
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m_cols(m_rank == 0 ? 1 : m_rank),
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m_originalMatrix(originalMatrix) {}
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@ -656,7 +656,7 @@ struct ei_lu_image_impl : public ReturnByValue<ei_lu_image_impl<MatrixType> >
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/***** Implementation of solve() *****************************************************/
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template<typename MatrixType,typename Rhs>
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struct ei_traits<ei_lu_solve_impl<MatrixType,Rhs> >
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struct ei_traits<ei_fullpivlu_solve_impl<MatrixType,Rhs> >
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{
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typedef Matrix<typename Rhs::Scalar,
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MatrixType::ColsAtCompileTime,
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@ -667,14 +667,14 @@ struct ei_traits<ei_lu_solve_impl<MatrixType,Rhs> >
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};
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template<typename MatrixType, typename Rhs>
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struct ei_lu_solve_impl : public ReturnByValue<ei_lu_solve_impl<MatrixType, Rhs> >
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struct ei_fullpivlu_solve_impl : public ReturnByValue<ei_fullpivlu_solve_impl<MatrixType, Rhs> >
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{
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typedef typename ei_cleantype<typename Rhs::Nested>::type RhsNested;
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typedef FullPivLU<MatrixType> LUType;
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const LUType& m_lu;
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const typename Rhs::Nested m_rhs;
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ei_lu_solve_impl(const LUType& lu, const Rhs& rhs)
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ei_fullpivlu_solve_impl(const LUType& lu, const Rhs& rhs)
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: m_lu(lu), m_rhs(rhs)
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{}
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@ -26,7 +26,7 @@
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#ifndef EIGEN_PARTIALLU_H
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#define EIGEN_PARTIALLU_H
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template<typename MatrixType, typename Rhs> struct ei_partiallu_solve_impl;
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template<typename MatrixType, typename Rhs> struct ei_partialpivlu_solve_impl;
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/** \ingroup LU_Module
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*
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@ -116,7 +116,7 @@ template<typename MatrixType> class PartialPivLU
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return m_p;
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}
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/** This method returns a solution x to the equation Ax=b, where A is the matrix of which
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/** This method returns the solution x to the equation Ax=b, where A is the matrix of which
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* *this is the LU decomposition.
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*
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* \param b the right-hand-side of the equation to solve. Can be a vector or a matrix,
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@ -131,16 +131,14 @@ template<typename MatrixType> class PartialPivLU
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* Since this PartialPivLU class assumes anyway that the matrix A is invertible, the solution
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* theoretically exists and is unique regardless of b.
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*
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* \note_about_checking_solutions
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*
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* \sa TriangularView::solve(), inverse(), computeInverse()
|
||||
*/
|
||||
template<typename Rhs>
|
||||
inline const ei_partiallu_solve_impl<MatrixType, Rhs>
|
||||
inline const ei_partialpivlu_solve_impl<MatrixType, Rhs>
|
||||
solve(const MatrixBase<Rhs>& b) const
|
||||
{
|
||||
ei_assert(m_isInitialized && "LU is not initialized.");
|
||||
return ei_partiallu_solve_impl<MatrixType, Rhs>(*this, b.derived());
|
||||
ei_assert(m_isInitialized && "PartialPivLU is not initialized.");
|
||||
return ei_partialpivlu_solve_impl<MatrixType, Rhs>(*this, b.derived());
|
||||
}
|
||||
|
||||
/** \returns the inverse of the matrix of which *this is the LU decomposition.
|
||||
@ -150,10 +148,10 @@ template<typename MatrixType> class PartialPivLU
|
||||
*
|
||||
* \sa MatrixBase::inverse(), LU::inverse()
|
||||
*/
|
||||
inline const ei_partiallu_solve_impl<MatrixType,NestByValue<typename MatrixType::IdentityReturnType> > inverse() const
|
||||
inline const ei_partialpivlu_solve_impl<MatrixType,NestByValue<typename MatrixType::IdentityReturnType> > inverse() const
|
||||
{
|
||||
ei_assert(m_isInitialized && "LU is not initialized.");
|
||||
return ei_partiallu_solve_impl<MatrixType,NestByValue<typename MatrixType::IdentityReturnType> >
|
||||
ei_assert(m_isInitialized && "PartialPivLU is not initialized.");
|
||||
return ei_partialpivlu_solve_impl<MatrixType,NestByValue<typename MatrixType::IdentityReturnType> >
|
||||
(*this, MatrixType::Identity(m_lu.rows(), m_lu.cols()).nestByValue());
|
||||
}
|
||||
|
||||
@ -200,7 +198,7 @@ PartialPivLU<MatrixType>::PartialPivLU(const MatrixType& matrix)
|
||||
|
||||
|
||||
|
||||
/** This is the blocked version of ei_lu_unblocked() */
|
||||
/** This is the blocked version of ei_fullpivlu_unblocked() */
|
||||
template<typename Scalar, int StorageOrder>
|
||||
struct ei_partial_lu_impl
|
||||
{
|
||||
@ -410,7 +408,7 @@ typename ei_traits<MatrixType>::Scalar PartialPivLU<MatrixType>::determinant() c
|
||||
/***** Implementation of solve() *****************************************************/
|
||||
|
||||
template<typename MatrixType,typename Rhs>
|
||||
struct ei_traits<ei_partiallu_solve_impl<MatrixType,Rhs> >
|
||||
struct ei_traits<ei_partialpivlu_solve_impl<MatrixType,Rhs> >
|
||||
{
|
||||
typedef Matrix<typename Rhs::Scalar,
|
||||
MatrixType::ColsAtCompileTime,
|
||||
@ -421,14 +419,14 @@ struct ei_traits<ei_partiallu_solve_impl<MatrixType,Rhs> >
|
||||
};
|
||||
|
||||
template<typename MatrixType, typename Rhs>
|
||||
struct ei_partiallu_solve_impl : public ReturnByValue<ei_partiallu_solve_impl<MatrixType, Rhs> >
|
||||
struct ei_partialpivlu_solve_impl : public ReturnByValue<ei_partialpivlu_solve_impl<MatrixType, Rhs> >
|
||||
{
|
||||
typedef typename ei_cleantype<typename Rhs::Nested>::type RhsNested;
|
||||
typedef PartialPivLU<MatrixType> LUType;
|
||||
const LUType& m_lu;
|
||||
const typename Rhs::Nested m_rhs;
|
||||
|
||||
ei_partiallu_solve_impl(const LUType& lu, const Rhs& rhs)
|
||||
ei_partialpivlu_solve_impl(const LUType& lu, const Rhs& rhs)
|
||||
: m_lu(lu), m_rhs(rhs)
|
||||
{}
|
||||
|
||||
|
||||
@ -218,7 +218,7 @@ ALIASES = "only_for_vectors=This is only for vectors (either row-
|
||||
"nonstableyet=\warning This is not considered to be part of the stable public API yet. Changes may happen in future releases. See \ref Experimental \"Experimental parts of Eigen\"" \
|
||||
"note_about_arbitrary_choice_of_solution=If there exists more than one solution, this method will arbitrarily choose one." \
|
||||
"note_about_using_kernel_to_study_multiple_solutions=If you need a complete analysis of the space of solutions, take the one solution obtained by this method and add to it elements of the kernel, as determined by kernel()." \
|
||||
"note_about_checking_solutions=This method just tries to find as good a solution as possible. If you want to check whether a solution "exists" or if it is accurate, just call this function to get a solution and then compute the error margin, or use MatrixBase::isApprox() directly, for instance like this: \code bool a_solution_exists = (A*result).isApprox(b, precision); \endcode The non-existence of a solution doesn't by itself mean that you'll get \c inf or \c nan values."
|
||||
"note_about_checking_solutions=This method just tries to find as good a solution as possible. If you want to check whether a solution exists or if it is accurate, just call this function to get a result and then compute the error of this result, or use MatrixBase::isApprox() directly, for instance like this: \code bool a_solution_exists = (A*result).isApprox(b, precision); \endcode This method avoids dividing by zero, so that the non-existence of a solution doesn't by itself mean that you'll get \c inf or \c nan values."
|
||||
|
||||
# Set the OPTIMIZE_OUTPUT_FOR_C tag to YES if your project consists of C
|
||||
# sources only. Doxygen will then generate output that is more tailored for C.
|
||||
|
||||
@ -3,6 +3,6 @@ typedef Matrix<float,Dynamic,2> DataMatrix;
|
||||
DataMatrix samples = DataMatrix::Random(12,2);
|
||||
VectorXf elevations = 2*samples.col(0) + 3*samples.col(1) + VectorXf::Random(12)*0.1;
|
||||
// and let's solve samples * [x y]^T = elevations in least square sense:
|
||||
Matrix<float,2,1> xy;
|
||||
(samples.adjoint() * samples).llt().solve((samples.adjoint()*elevations), &xy);
|
||||
Matrix<float,2,1> xy
|
||||
= (samples.adjoint() * samples).llt().solve((samples.adjoint()*elevations));
|
||||
cout << xy << endl;
|
||||
|
||||
@ -93,17 +93,17 @@ template<typename MatrixType> void cholesky(const MatrixType& m)
|
||||
{
|
||||
LLT<SquareMatrixType,LowerTriangular> chollo(symmLo);
|
||||
VERIFY_IS_APPROX(symm, chollo.matrixL().toDense() * chollo.matrixL().adjoint().toDense());
|
||||
chollo.solve(vecB, &vecX);
|
||||
vecX = chollo.solve(vecB);
|
||||
VERIFY_IS_APPROX(symm * vecX, vecB);
|
||||
chollo.solve(matB, &matX);
|
||||
matX = chollo.solve(matB);
|
||||
VERIFY_IS_APPROX(symm * matX, matB);
|
||||
|
||||
// test the upper mode
|
||||
LLT<SquareMatrixType,UpperTriangular> cholup(symmUp);
|
||||
VERIFY_IS_APPROX(symm, cholup.matrixL().toDense() * cholup.matrixL().adjoint().toDense());
|
||||
cholup.solve(vecB, &vecX);
|
||||
vecX = cholup.solve(vecB);
|
||||
VERIFY_IS_APPROX(symm * vecX, vecB);
|
||||
cholup.solve(matB, &matX);
|
||||
matX = cholup.solve(matB);
|
||||
VERIFY_IS_APPROX(symm * matX, matB);
|
||||
}
|
||||
|
||||
@ -118,9 +118,9 @@ template<typename MatrixType> void cholesky(const MatrixType& m)
|
||||
LDLT<SquareMatrixType> ldlt(symm);
|
||||
// TODO(keir): This doesn't make sense now that LDLT pivots.
|
||||
//VERIFY_IS_APPROX(symm, ldlt.matrixL() * ldlt.vectorD().asDiagonal() * ldlt.matrixL().adjoint());
|
||||
ldlt.solve(vecB, &vecX);
|
||||
vecX = ldlt.solve(vecB);
|
||||
VERIFY_IS_APPROX(symm * vecX, vecB);
|
||||
ldlt.solve(matB, &matX);
|
||||
matX = ldlt.solve(matB);
|
||||
VERIFY_IS_APPROX(symm * matX, matB);
|
||||
}
|
||||
|
||||
@ -132,7 +132,7 @@ template<typename MatrixType> void cholesky_verify_assert()
|
||||
|
||||
LLT<MatrixType> llt;
|
||||
VERIFY_RAISES_ASSERT(llt.matrixL())
|
||||
VERIFY_RAISES_ASSERT(llt.solve(tmp,&tmp))
|
||||
VERIFY_RAISES_ASSERT(llt.solve(tmp))
|
||||
VERIFY_RAISES_ASSERT(llt.solveInPlace(&tmp))
|
||||
|
||||
LDLT<MatrixType> ldlt;
|
||||
@ -141,7 +141,7 @@ template<typename MatrixType> void cholesky_verify_assert()
|
||||
VERIFY_RAISES_ASSERT(ldlt.vectorD())
|
||||
VERIFY_RAISES_ASSERT(ldlt.isPositive())
|
||||
VERIFY_RAISES_ASSERT(ldlt.isNegative())
|
||||
VERIFY_RAISES_ASSERT(ldlt.solve(tmp,&tmp))
|
||||
VERIFY_RAISES_ASSERT(ldlt.solve(tmp))
|
||||
VERIFY_RAISES_ASSERT(ldlt.solveInPlace(&tmp))
|
||||
}
|
||||
|
||||
|
||||
@ -49,8 +49,8 @@ template<typename MatrixType> void lu_non_invertible()
|
||||
cols2 = cols = MatrixType::ColsAtCompileTime;
|
||||
}
|
||||
|
||||
typedef typename ei_lu_kernel_impl<MatrixType>::ReturnMatrixType KernelMatrixType;
|
||||
typedef typename ei_lu_image_impl <MatrixType>::ReturnMatrixType ImageMatrixType;
|
||||
typedef typename ei_fullpivlu_kernel_impl<MatrixType>::ReturnMatrixType KernelMatrixType;
|
||||
typedef typename ei_fullpivlu_image_impl <MatrixType>::ReturnMatrixType ImageMatrixType;
|
||||
typedef Matrix<typename MatrixType::Scalar, Dynamic, Dynamic> DynamicMatrixType;
|
||||
typedef Matrix<typename MatrixType::Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime>
|
||||
CMatrixType;
|
||||
|
||||
Loading…
Reference in New Issue
Block a user