Add cholesky's members to MatrixBase

Various documentation improvements including new snippets (AngleAxis and Cholesky)

Eigen/src/Cholesky/Cholesky.h

@@ -66,7 +66,7 @@ template<typename MatrixType> class Cholesky
     bool isPositiveDefinite(void) const { return m_isPositiveDefinite; }
 
     template<typename Derived>
-    typename Derived::Eval solve(MatrixBase<Derived> &b);
+    typename Derived::Eval solve(const MatrixBase<Derived> &b) const;
 
     void compute(const MatrixType& matrix);
 
@@ -110,10 +110,14 @@ void Cholesky<MatrixType>::compute(const MatrixType& a)
 /** \returns the solution of A x = \a b using the current decomposition of A.
   * In other words, it returns \code A^-1 b \endcode computing
   * \code L^-*  L^1 b \endcode from right to left.
+  *
+  * Example: \include Cholesky_solve.cpp
+  * Output: \verbinclude Cholesky_solve.out
+  *
   */
 template<typename MatrixType>
 template<typename Derived>
-typename Derived::Eval Cholesky<MatrixType>::solve(MatrixBase<Derived> &b)
+typename Derived::Eval Cholesky<MatrixType>::solve(const MatrixBase<Derived> &b) const
 {
   const int size = m_matrix.rows();
   ei_assert(size==b.size());
@@ -121,5 +125,14 @@ typename Derived::Eval Cholesky<MatrixType>::solve(MatrixBase<Derived> &b)
   return m_matrix.adjoint().template extract<Upper>().inverseProduct(matrixL().inverseProduct(b));
 }
 
+/** \cholesky_module
+  * \returns the Cholesky decomposition of \c *this
+  */
+template<typename Derived>
+inline const Cholesky<typename ei_eval<Derived>::type>
+MatrixBase<Derived>::cholesky() const
+{
+  return Cholesky<typename ei_eval<Derived>::type>(derived());
+}
 
 #endif // EIGEN_CHOLESKY_H

Eigen/src/Cholesky/CholeskyWithoutSquareRoot.h

@@ -77,7 +77,7 @@ template<typename MatrixType> class CholeskyWithoutSquareRoot
     }
 
     template<typename Derived>
-    typename Derived::Eval solve(MatrixBase<Derived> &b);
+    typename Derived::Eval solve(const MatrixBase<Derived> &b) const;
 
     void compute(const MatrixType& matrix);
 
@@ -127,7 +127,7 @@ void CholeskyWithoutSquareRoot<MatrixType>::compute(const MatrixType& a)
   */
 template<typename MatrixType>
 template<typename Derived>
-typename Derived::Eval CholeskyWithoutSquareRoot<MatrixType>::solve(MatrixBase<Derived> &vecB)
+typename Derived::Eval CholeskyWithoutSquareRoot<MatrixType>::solve(const MatrixBase<Derived> &vecB) const
 {
   const int size = m_matrix.rows();
   ei_assert(size==vecB.size());
@@ -140,5 +140,14 @@ typename Derived::Eval CholeskyWithoutSquareRoot<MatrixType>::solve(MatrixBase<D
       );
 }
 
+/** \cholesky_module
+  * \returns the Cholesky decomposition without square root of \c *this
+  */
+template<typename Derived>
+inline const CholeskyWithoutSquareRoot<typename ei_eval<Derived>::type>
+MatrixBase<Derived>::choleskyNoSqrt() const
+{
+  return derived();
+}
 
 #endif // EIGEN_CHOLESKY_WITHOUT_SQUARE_ROOT_H

Eigen/src/Core/MatrixBase.h

@@ -532,6 +532,10 @@ template<typename Derived> class MatrixBase
     void computeInverse(typename ei_eval<Derived>::type *result) const;
     Scalar determinant() const;
 
+/////////// Cholesky module ///////////
+
+    const Cholesky<typename ei_eval<Derived>::type> cholesky() const;
+    const CholeskyWithoutSquareRoot<typename ei_eval<Derived>::type> choleskyNoSqrt() const;
 
 /////////// QR module ///////////
 

Eigen/src/Core/util/ForwardDeclarations.h

@@ -96,6 +96,8 @@ void ei_cache_friendly_product(
 
 template<typename ExpressionType, bool CheckExistence = true> class Inverse;
 template<typename MatrixType> class QR;
+template<typename MatrixType> class Cholesky;
+template<typename MatrixType> class CholeskyWithoutSquareRoot;
 
 // Geometry module:
 template<typename Lhs, typename Rhs> class Cross;

Eigen/src/Geometry/AngleAxis.h

@@ -29,7 +29,7 @@
   *
   * \class AngleAxis
   *
-  * \brief Represents a 3D rotation as a rotation angle around an arbitray 3D axis
+  * \brief Represents a 3D rotation as a rotation angle around an arbitrary 3D axis
   *
   * \param _Scalar the scalar type, i.e., the type of the coefficients.
   *
@@ -37,7 +37,14 @@
   * \li \c AngleAxisf for \c float
   * \li \c AngleAxisd for \c double
   *
-  * \sa class Quaternion, class Transform
+  * \addexample AngleAxisForEuler \label How to define a rotation from Euler-angles
+  *
+  * Combined with MatrixBase::Unit{X,Y,Z}, AngleAxis can be used to easily
+  * mimic Euler-angles. Here is an example:
+  * \include AngleAxis_mimic_euler.cpp
+  * Output: \verbinclude AngleAxis_mimic_euler.out
+  *
+  * \sa class Quaternion, class Transform, MatrixBase::UnitX()
   */
 template<typename _Scalar>
 class AngleAxis