updated tutorial

doc/tutorial.cpp

@@ -1,36 +1,62 @@
-#include <Eigen/Core>
+#include <Eigen/Array>
 
-USING_PART_OF_NAMESPACE_EIGEN
-
-using namespace std;
-
-int main(int, char **)
+int main(int argc, char *argv[])
 {
-  Matrix<double,2,2> m; // 2x2 fixed-size matrix with uninitialized entries
-  m(0,0) = 1;
-  m(0,1) = 2;
-  m(1,0) = 3;
-  m(1,1) = 4;
+  std::cout.precision(2);
 
-  cout << "Here is a 2x2 matrix m:" << endl << m << endl;
-  cout << "Let us now build a 4x4 matrix m2 by assembling together four 2x2 blocks." << endl;
-  MatrixXd m2(4,4); // dynamic matrix with initial size 4x4 and uninitialized entries
-  // notice how we are mixing fixed-size and dynamic-size types.
+  // 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();
   
-  cout << "In the top-left block, we put the matrix m shown above." << endl;
-  m2.block<2,2>(0,0) = m;
-  cout << "In the bottom-left block, we put the matrix m*m, which is:" << endl << m*m << endl;
-  m2.block<2,2>(2,0) = m * m;
-  cout << "In the top-right block, we put the matrix m+m, which is:" << endl << m+m << endl;
-  m2.block<2,2>(0,2) = m + m;
-  cout << "In the bottom-right block, we put the matrix m-m, which is:" << endl << m-m << endl;
-  m2.block<2,2>(2,2) = m - m;
-  cout << "Now the 4x4 matrix m2 is:" << endl << m2 << endl;
-  
-  cout << "Row 0 of m2 is:" << endl << m2.row(0) << endl;
-  cout << "The third element in that row is " << m2.row(0)[2] << endl;
-  cout << "Column 1 of m2 is:" << endl << m2.col(1) << endl;
-  cout << "The transpose of m2 is:" << endl << m2.transpose() << endl;
-  cout << "The matrix m2 with row 0 and column 1 removed is:" << endl << m2.minor(0,1) << endl;
-  return 0;
-}
+  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 transpose() 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;
+}