many small fixes and documentation improvements,

this should be alpha5.

doc/snippets/MatrixBase_extract.cpp

@@ -0,0 +1,8 @@
+Matrix3i m = Matrix3i::random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the upper-triangular matrix extracted from m:" << endl
+     << m.extract<Eigen::Upper>() << endl;
+cout << "Here is the strictly-upper-triangular matrix extracted from m:" << endl
+     << m.extract<Eigen::StrictlyUpper>() << endl;
+cout << "Here is the unit-lower-triangular matrix extracted from m:" << endl
+     << m.extract<Eigen::UnitLower>() << endl;

doc/snippets/MatrixBase_inverse.cpp

@@ -0,0 +1,7 @@
+Matrix2d m = Matrix2d::random();
+cout << "Here is the matrix m:" << endl << m << endl;
+Matrix2d::InverseType m_inv = m.inverse();
+if(m_inv.exists())
+  cout << "m is invertible, and its inverse is:" << endl << m_inv << endl;
+else
+  cout << "m is not invertible." << endl;

doc/snippets/MatrixBase_lazy.cpp

@@ -0,0 +1,10 @@
+Matrix2d m; m << 1,2,3,4;
+Matrix2d n;
+n = (m*m).lazy(); // if we did "n = m*m;" then m*m would first be evaluated into
+ // a temporary, because the Product expression has the EvalBeforeAssigningBit.
+ // This temporary would then be copied into n. Introducing this temporary is
+ // useless here and wastes time. Doing "n = (m*m).lazy();" evaluates m*m directly
+ // into n, which is faster. But, beware! This is only correct because m and n
+ // are two distinct matrices. Doing "m = (m*m).lazy();" would not produce the
+ // expected result.
+cout << n << endl;

doc/snippets/MatrixBase_marked.cpp

@@ -0,0 +1,9 @@
+Matrix3d m = Matrix3d::zero();
+m.part<Eigen::Upper>().setOnes();
+cout << "Here is the matrix m:" << endl << m << endl;
+Matrix3d n = Matrix3d::ones();
+n.part<Eigen::Lower>() *= 2;
+cout << "Here is the matrix n:" << endl << n << endl;
+cout << "And now here is m.inverse()*n, taking advantage of the fact that"
+        " m is upper-triangular:" << endl
+     << m.marked<Eigen::Upper>().inverseProduct(n);

doc/snippets/MatrixBase_part.cpp

@@ -0,0 +1,8 @@
+Matrix3d m = Matrix3i::zero();
+m.part<Eigen::StrictlyUpper>().setOnes();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "And let us now compute m*m.adjoint() in a very optimized way" << endl
+     << "taking advantage of the symmetry." << endl;
+Matrix3d n;
+n.part<Eigen::SelfAdjoint>() = (m*m.adjoint()).lazy();
+cout << "The result is:" << endl << n << endl;

doc/snippets/MatrixBase_quickInverse.cpp

@@ -0,0 +1,5 @@
+Matrix4d m = Matrix4d::zero();
+m.part<Eigen::Upper>().setOnes();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "We know for sure that it is invertible." << endl;
+cout << "Here is its inverse:" << m.quickInverse() << endl;

doc/snippets/MatrixBase_template_int_end.cpp

@@ -0,0 +1,5 @@
+RowVector4i v = RowVector4i::random();
+cout << "Here is the vector v:" << endl << v << endl;
+cout << "Here is v.end(2):" << endl << v.end<2>() << endl;
+v.end<2>().setZero();
+cout << "Now the vector v is:" << endl << v << endl;

doc/snippets/MatrixBase_template_int_int_corner_enum.cpp

@@ -0,0 +1,6 @@
+Matrix4i m = Matrix4i::random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the bottom-right 2x3 corner in m:" << endl
+     << m.corner<2,3>(Eigen::BottomRight) << endl;
+m.corner<2,3>(Eigen::BottomRight).setZero();
+cout << "Now the matrix m is:" << endl << m << endl;

doc/snippets/MatrixBase_template_int_start.cpp

@@ -0,0 +1,5 @@
+RowVector4i v = RowVector4i::random();
+cout << "Here is the vector v:" << endl << v << endl;
+cout << "Here is v.start(2):" << endl << v.start<2>() << endl;
+v.start<2>().setZero();
+cout << "Now the vector v is:" << endl << v << endl;

doc/snippets/compile_snippet.cpp.in

@@ -1,4 +1,5 @@
 #include <Eigen/Core>
+#include <Eigen/LU>
 USING_PART_OF_NAMESPACE_EIGEN
 using namespace std;
 int main(int, char**)