From 61158b1922e2aeeb132fbf6ceea551f61c400cde Mon Sep 17 00:00:00 2001
From: Benoit Jacob <jacob.benoit.1@gmail.com>
Date: Fri, 7 Sep 2007 08:18:21 +0000
Subject: add operator *= between matrices, with automatic aliasing. add
 tutorial in doc/ subdirectory.

---
 doc/tutorial.cpp | 60 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 60 insertions(+)
 create mode 100644 doc/tutorial.cpp

(limited to 'doc/tutorial.cpp')

diff --git a/doc/tutorial.cpp b/doc/tutorial.cpp
new file mode 100644
index 000000000..51847460f
--- /dev/null
+++ b/doc/tutorial.cpp
@@ -0,0 +1,60 @@
+#include"../src/All.h"
+
+using namespace std;
+using namespace Eigen;
+
+int main(int, char **)
+{
+  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;
+  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;
+  MatrixX<double> m2(4, 4); // dynamic matrix with initial size 4x4 and uninitialized entries
+  // notice how we are mixing fixed-size and dynamic-size types.
+  
+  cout << "In the top-left block, we put the matrix m shown above." << endl;
+  // here we need to use .xpr() to allow write access to the block.
+  m2.xpr().block(0,1,0,1) = m;
+  cout << "In the bottom-left block, we put the matrix m*m, which is:" << endl << m*m << endl;
+  m2.xpr().block(2,3,0,1) = m * m;
+  cout << "In the top-right block, we put the matrix m+m, which is:" << endl << m+m << endl;
+  m2.xpr().block(0,1,2,3) = m + m;
+  cout << "In the bottom-right block, we put the matrix m-m, which is:" << endl << m-m << endl;
+  m2.xpr().block(2,3,2,3) = m - m;
+  cout << "Now the 4x4 matrix m2 is:" << endl << m2 << endl;
+  
+  // here we don't need to use .xpr() because we only need read access.
+  cout << "The central 2x2 block of m2 is:" << endl << m2.block(1,2,1,2) << endl;
+  cout << "Row 0 of m2, written as a column vector, is:" << endl << m2.row(0) << endl;
+  cout << "Column 1 of m2 is:" << endl << m2.col(1) << endl;
+  cout << "The matrix m2 with row 0 and column 1 removed is:" << endl << m2.minor(0,1) << endl;
+
+  cout << endl << "Now let us study a tricky issue." << endl;
+  cout << "Recall that the matrix product m*m is:" << endl << m*m << endl;
+  cout << "We want to store that into m, i.e. do \"m = m * m;\"" << endl;
+  cout << "Here we must be very careful. For if we do \"m = m * m;\"," << endl
+       << "the matrix m becomes" << endl;
+  Matrix<double,2,2> m_save = m;
+  m = m * m; // the bogus operation
+  cout << m << "," << endl;
+  cout << "which is not what was wanted!" << endl
+       << "Explanation: because of the way expression templates work, the matrix m gets" << endl
+       << "overwritten _while_ the matrix product m * m is being computed." << endl
+       << "This is the counterpart of eliminating temporary objects!" << endl
+       << "Anyway, if you want to store m * m into m, you can do this:" << endl
+       << "            m.alias() = m * m;" << endl;
+  m = m_save;
+  m.alias() = m * m;
+  cout << "And m is now:" << endl << m << endl << "as was expected." << endl;
+  cout << "To make your life easier, operator*= between matrices automatically" << endl
+       << "creates an alias. So a *= b is equivalent to a.alias() *= b," << endl
+       << "when a and b are matrices. So, coming back to the original matrix m," << endl
+       << "if we do m *= m, the matrix m becomes:" << endl;
+  m = m_save;
+  m *= m;
+  cout << m << endl << "as expected." << endl;
+  return 0;
+}
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