Move eigen to third party (#282)

* remove useless statement

* Add eigen to third_party dir

* remove reducdant lines

third_party/eigen/doc/tutorial.cpp

@@ -0,0 +1,73 @@
+#include <Eigen/Array>
+
+int main(int argc, char *argv[]) {
+  std::cout.precision(2);
+
+  // demo static functions
+  Eigen::Matrix3f m3 = Eigen::Matrix3f::Random();
+  Eigen::Matrix4f m4 = Eigen::Matrix4f::Identity();
+
+  std::cout << "*** Step 1 ***\nm3:\n" << m3 << "\nm4:\n" << m4 << std::endl;
+
+  // demo non-static set... functions
+  m4.setZero();
+  m3.diagonal().setOnes();
+
+  std::cout << "*** Step 2 ***\nm3:\n" << m3 << "\nm4:\n" << m4 << std::endl;
+
+  // demo fixed-size block() expression as lvalue and as rvalue
+  m4.block<3, 3>(0, 1) = m3;
+  m3.row(2) = m4.block<1, 3>(2, 0);
+
+  std::cout << "*** Step 3 ***\nm3:\n" << m3 << "\nm4:\n" << m4 << std::endl;
+
+  // demo dynamic-size block()
+  {
+    int rows = 3, cols = 3;
+    m4.block(0, 1, 3, 3).setIdentity();
+    std::cout << "*** Step 4 ***\nm4:\n" << m4 << std::endl;
+  }
+
+  // demo vector blocks
+  m4.diagonal().block(1, 2).setOnes();
+  std::cout << "*** Step 5 ***\nm4.diagonal():\n" << m4.diagonal() << std::endl;
+  std::cout << "m4.diagonal().start(3)\n"
+            << m4.diagonal().start(3) << std::endl;
+
+  // demo coeff-wise operations
+  m4 = m4.cwise() * m4;
+  m3 = m3.cwise().cos();
+  std::cout << "*** Step 6 ***\nm3:\n" << m3 << "\nm4:\n" << m4 << std::endl;
+
+  // sums of coefficients
+  std::cout << "*** Step 7 ***\n m4.sum(): " << m4.sum() << std::endl;
+  std::cout << "m4.col(2).sum(): " << m4.col(2).sum() << std::endl;
+  std::cout << "m4.colwise().sum():\n" << m4.colwise().sum() << std::endl;
+  std::cout << "m4.rowwise().sum():\n" << m4.rowwise().sum() << std::endl;
+
+  // demo intelligent auto-evaluation
+  m4 =
+      m4 *
+      m4;  // auto-evaluates so no aliasing problem (performance penalty is low)
+  Eigen::Matrix4f other = (m4 * m4).lazy();  // forces lazy evaluation
+  m4 =
+      m4 + m4;  // here Eigen goes for lazy evaluation, as with most expressions
+  m4 = -m4 + m4 +
+       5 * m4;  // same here, Eigen chooses lazy evaluation for all that.
+  m4 = m4 *
+       (m4 +
+        m4);  // here Eigen chooses to first evaluate m4 + m4 into a temporary.
+  // indeed, here it is an optimization to cache this intermediate result.
+  m3 =
+      m3 *
+      m4.block<3, 3>(
+          1, 1);  // here Eigen chooses NOT to evaluate block() into a temporary
+  // because accessing coefficients of that block expression is not more costly
+  // than accessing
+  // coefficients of a plain matrix.
+  m4 = m4 * m4.transpose();  // same here, lazy evaluation of the transpose.
+  m4 = m4 *
+       m4.transpose().eval();  // forces immediate evaluation of the transpose
+
+  std::cout << "*** Step 8 ***\nm3:\n" << m3 << "\nm4:\n" << m4 << std::endl;
+}