Add cholesky's members to MatrixBase

Various documentation improvements including new snippets (AngleAxis and Cholesky)

doc/snippets/AngleAxis_mimic_euler.cpp

@@ -0,0 +1,4 @@
+Matrix3f m = AngleAxisf(0.25*M_PI, Vector3f::UnitX())
+           * AngleAxisf(0.5*M_PI,  Vector3f::UnitY())
+           * AngleAxisf(0.33*M_PI, Vector3f::UnitZ());
+cout << m << endl;

doc/snippets/CMakeLists.txt

@@ -20,4 +20,6 @@ ADD_CUSTOM_COMMAND(
   ARGS >${CMAKE_CURRENT_BINARY_DIR}/${snippet}.out
 )
 ADD_DEPENDENCIES(all_snippets ${compile_snippet_target})
+set_source_files_properties(${CMAKE_CURRENT_BINARY_DIR}/${compile_snippet_src}
+                            PROPERTIES OBJECT_DEPENDS ${snippet_src})
 ENDFOREACH(snippet_src)

doc/snippets/Cholesky_solve.cpp

@@ -0,0 +1,6 @@
+typedef Matrix<float,Dynamic,2> DataMatrix;
+// let's generate some samples on the 3D plane of equation z = 2x+3y (with some noise)
+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 = elevations in least square sense:
+cout << (samples.adjoint() * samples).cholesky().solve((samples.adjoint()*elevations).eval()) << endl;

doc/snippets/compile_snippet.cpp.in

@@ -1,8 +1,11 @@
 #include <Eigen/Core>
 #include <Eigen/Array>
 #include <Eigen/LU>
+#include <Eigen/Cholesky>
+#include <Eigen/Geometry>
 
 USING_PART_OF_NAMESPACE_EIGEN
+using namespace Eigen;
 using namespace std;
 
 int main(int, char**)