* fix in IO.h, a useless copy was made because of assignment from

  Derived to MatrixBase.
* the optimization of eval() for Matrix now consists in a partial
  specialization of ei_eval, which returns a reference type for Matrix.
  No overriding of eval() in Matrix anymore. Consequence: careful,
  ei_eval is no longer guaranteed to give a plain matrix type!
  For that, use ei_plain_matrix_type, or the PlainMatrixType typedef.
* so lots of changes to adapt to that everywhere. Hope this doesn't
  break (too much) MSVC compilation.
* add code examples for the new image() stuff.
* lower a bit the precision for floats in the unit tests as
  we were already doing some workarounds in inverse.cpp and we got some
  failed tests.

2 files changed, 22 insertions, 0 deletions

diff --git a/doc/snippets/LU_computeImage.cpp b/doc/snippets/LU_computeImage.cpp
new file mode 100644
index 000000000..5c812cc4c
--- /dev/null
+++ b/doc/snippets/LU_computeImage.cpp
@@ -0,0 +1,13 @@
+MatrixXd m(3,3);
+m << 1,1,0,
+     1,3,2,
+     0,1,1;
+cout << "Here is the matrix m:" << endl << m << endl;
+LU<Matrix3d> lu(m);
+// allocate the matrix img with the correct size to avoid reallocation
+MatrixXd img(m.rows(), lu.rank());
+lu.computeImage(&img);
+cout << "Notice that the middle column is the sum of the two others, so the "
+     << "columns are linearly dependent." << endl;
+cout << "Here is a matrix whose columns have the same span but are linearly independent:"
+     << endl << img << endl;
diff --git a/doc/snippets/LU_image.cpp b/doc/snippets/LU_image.cpp
new file mode 100644
index 000000000..0d1088a2f
--- /dev/null
+++ b/doc/snippets/LU_image.cpp
@@ -0,0 +1,9 @@
+Matrix3d m;
+m << 1,1,0,
+     1,3,2,
+     0,1,1;
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Notice that the middle column is the sum of the two others, so the "
+     << "columns are linearly dependent." << endl;
+cout << "Here is a matrix whose columns have the same span but are linearly independent:"
+     << endl << m.lu().image() << endl;