Squashed 'third_party/eigen/' content from commit 61d72f6

Change-Id: Iccc90fa0b55ab44037f018046d2fcffd90d9d025
git-subtree-dir: third_party/eigen
git-subtree-split: 61d72f6383cfa842868c53e30e087b0258177257
diff --git a/doc/examples/Tutorial_PartialLU_solve.cpp b/doc/examples/Tutorial_PartialLU_solve.cpp
new file mode 100644
index 0000000..a560879
--- /dev/null
+++ b/doc/examples/Tutorial_PartialLU_solve.cpp
@@ -0,0 +1,18 @@
+#include <Eigen/Core>
+#include <Eigen/LU>
+#include <iostream>
+
+using namespace std;
+using namespace Eigen;
+
+int main()
+{
+   Matrix3f A;
+   Vector3f b;
+   A << 1,2,3,  4,5,6,  7,8,10;
+   b << 3, 3, 4;
+   cout << "Here is the matrix A:" << endl << A << endl;
+   cout << "Here is the vector b:" << endl << b << endl;
+   Vector3f x = A.lu().solve(b);
+   cout << "The solution is:" << endl << x << endl;
+}