Add some more examples for the API documentation.

The only missing examples now are for homogeneous() and hnormalized();
I don't know what they're used for ...

doc/examples/MatrixBase_cwise_const.cpp

@@ -0,0 +1,18 @@
+#define EIGEN2_SUPPORT
+#include <Eigen/Core>
+#include <iostream>
+
+using namespace Eigen;
+using namespace std;
+
+int main()
+{
+  Matrix3i m = Matrix3i::Random();
+  cout << "Here is the matrix m:" << endl << m << endl;
+  Matrix3i n = Matrix3i::Random();
+  cout << "And here is the matrix n:" << endl << n << endl;
+  cout << "The coefficient-wise product of m and n is:" << endl;
+  cout << m.cwise() * n << endl;
+  cout << "Taking the cube of the coefficients of m yields:" << endl;
+  cout << m.cwise().pow(3) << endl;
+}

doc/snippets/ColPivHouseholderQR_solve.cpp

@@ -0,0 +1,8 @@
+Matrix3f m = Matrix3f::Random();
+Matrix3f y = Matrix3f::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the matrix y:" << endl << y << endl;
+Matrix3f x;
+x = m.colPivHouseholderQr().solve(y);
+assert(y.isApprox(m*x));
+cout << "Here is a solution x to the equation mx=y:" << endl << x << endl;

doc/snippets/DirectionWise_replicate.cpp

@@ -0,0 +1,4 @@
+MatrixXi m = MatrixXi::Random(2,3);
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "m.colwise().replicate<3>() = ..." << endl;
+cout << m.colwise().replicate<3>() << endl;

doc/snippets/DirectionWise_replicate_int.cpp

@@ -0,0 +1,4 @@
+Vector3i v = Vector3i::Random();
+cout << "Here is the vector v:" << endl << v << endl;
+cout << "v.rowwise().replicate(5) = ..." << endl;
+cout << v.rowwise().replicate(5) << endl;

doc/snippets/FullPivHouseholderQR_solve.cpp

@@ -0,0 +1,8 @@
+Matrix3f m = Matrix3f::Random();
+Matrix3f y = Matrix3f::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the matrix y:" << endl << y << endl;
+Matrix3f x;
+x = m.fullPivHouseholderQr().solve(y);
+assert(y.isApprox(m*x));
+cout << "Here is a solution x to the equation mx=y:" << endl << x << endl;

doc/snippets/MatrixBase_replicate.cpp

@@ -0,0 +1,4 @@
+MatrixXi m = MatrixXi::Random(2,3);
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "m.replicate<3,2>() = ..." << endl;
+cout << m.replicate<3,2>() << endl;

doc/snippets/MatrixBase_replicate_int_int.cpp

@@ -0,0 +1,4 @@
+Vector3i v = Vector3i::Random();
+cout << "Here is the vector v:" << endl << v << endl;
+cout << "v.replicate(2,5) = ..." << endl;
+cout << v.replicate(2,5) << endl;