diff options
author | 2011-11-07 17:14:06 +0000 | |
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committer | 2011-11-07 17:14:06 +0000 | |
commit | 45a6bb34c3e67c865b489518767eadf747d391d7 (patch) | |
tree | 2a27bfd03741e4e261fe6244740ffc7034fd37a1 | |
parent | f422668d39c51a7281e55404cfed4a262747eb51 (diff) |
Add simple example on how to compute Cholesky decomposition.
-rw-r--r-- | Eigen/src/Cholesky/LDLT.h | 2 | ||||
-rw-r--r-- | Eigen/src/Cholesky/LLT.h | 9 | ||||
-rw-r--r-- | doc/C06_TutorialLinearAlgebra.dox | 3 | ||||
-rw-r--r-- | doc/snippets/LLT_example.cpp | 12 |
4 files changed, 23 insertions, 3 deletions
diff --git a/Eigen/src/Cholesky/LDLT.h b/Eigen/src/Cholesky/LDLT.h index f47b2ea56..25d4a732c 100644 --- a/Eigen/src/Cholesky/LDLT.h +++ b/Eigen/src/Cholesky/LDLT.h @@ -31,7 +31,7 @@ namespace internal { template<typename MatrixType, int UpLo> struct LDLT_Traits; } -/** \ingroup cholesky_Module +/** \ingroup Cholesky_Module * * \class LDLT * diff --git a/Eigen/src/Cholesky/LLT.h b/Eigen/src/Cholesky/LLT.h index c284e53c8..f061cbf42 100644 --- a/Eigen/src/Cholesky/LLT.h +++ b/Eigen/src/Cholesky/LLT.h @@ -29,7 +29,7 @@ namespace internal{ template<typename MatrixType, int UpLo> struct LLT_Traits; } -/** \ingroup cholesky_Module +/** \ingroup Cholesky_Module * * \class LLT * @@ -49,6 +49,9 @@ template<typename MatrixType, int UpLo> struct LLT_Traits; * use LDLT instead for the semidefinite case. Also, do not use a Cholesky decomposition to determine whether a system of equations * has a solution. * + * Example: \include LLT_example.cpp + * Output: \verbinclude LLT_example.out + * * \sa MatrixBase::llt(), class LDLT */ /* HEY THIS DOX IS DISABLED BECAUSE THERE's A BUG EITHER HERE OR IN LDLT ABOUT THAT (OR BOTH) @@ -334,8 +337,10 @@ template<typename MatrixType> struct LLT_Traits<MatrixType,Upper> /** Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of \a matrix * - * * \returns a reference to *this + * + * Example: \include TutorialLinAlgComputeTwice.cpp + * Output: \verbinclude TutorialLinAlgComputeTwice.out */ template<typename MatrixType, int _UpLo> LLT<MatrixType,_UpLo>& LLT<MatrixType,_UpLo>::compute(const MatrixType& a) diff --git a/doc/C06_TutorialLinearAlgebra.dox b/doc/C06_TutorialLinearAlgebra.dox index 77f13f4a0..e8b3b7953 100644 --- a/doc/C06_TutorialLinearAlgebra.dox +++ b/doc/C06_TutorialLinearAlgebra.dox @@ -144,6 +144,9 @@ You need an eigendecomposition here, see available such decompositions on \ref T Make sure to check if your matrix is self-adjoint, as is often the case in these problems. Here's an example using SelfAdjointEigenSolver, it could easily be adapted to general matrices using EigenSolver or ComplexEigenSolver. +The computation of eigenvalues and eigenvectors does not necessarily converge, but such failure to converge is +very rare. The call to info() is to check for this possibility. + <table class="example"> <tr><th>Example:</th><th>Output:</th></tr> <tr> diff --git a/doc/snippets/LLT_example.cpp b/doc/snippets/LLT_example.cpp new file mode 100644 index 000000000..46fb40704 --- /dev/null +++ b/doc/snippets/LLT_example.cpp @@ -0,0 +1,12 @@ +MatrixXd A(3,3); +A << 4,-1,2, -1,6,0, 2,0,5; +cout << "The matrix A is" << endl << A << endl; + +LLT<MatrixXd> lltOfA(A); // compute the Cholesky decomposition of A +MatrixXd L = lltOfA.matrixL(); // retrieve factor L in the decomposition +// The previous two lines can also be written as "L = A.llt().matrixL()" + +cout << "The Cholesky factor L is" << endl << L << endl; +cout << "To check this, let us compute L * L.transpose()" << endl; +cout << L * L.transpose() << endl; +cout << "This should equal the matrix A" << endl; |