Vehicle-cpp/zjw/工控机安装资料/eigen-3.4.0/doc/Pitfalls.dox

namespace Eigen {

/** \page TopicPitfalls Common pitfalls


\section TopicPitfalls_template_keyword Compilation error with template methods

See this \link TopicTemplateKeyword page \endlink.


\section TopicPitfalls_aliasing Aliasing

Don't miss this \link TopicAliasing page \endlink on aliasing,
especially if you got wrong results in statements where the destination appears on the right hand side of the expression.


\section TopicPitfalls_alignment_issue Alignment Issues (runtime assertion)

%Eigen does explicit vectorization, and while that is appreciated by many users, that also leads to some issues in special situations where data alignment is compromised.
Indeed, prior to C++17,  C++ does not have quite good enough support for explicit data alignment.
In that case your program hits an assertion failure (that is, a "controlled crash") with a message that tells you to consult this page:
\code
http://eigen.tuxfamily.org/dox/group__TopicUnalignedArrayAssert.html
\endcode
Have a look at \link TopicUnalignedArrayAssert it \endlink and see for yourself if that's something that you can cope with.
It contains detailed information about how to deal with each known cause for that issue.

Now what if you don't care about vectorization and so don't want to be annoyed with these alignment issues? Then read \link getrid how to get rid of them \endlink.


\section TopicPitfalls_auto_keyword C++11 and the auto keyword

In short: do not use the auto keywords with %Eigen's expressions, unless you are 100% sure about what you are doing. In particular, do not use the auto keyword as a replacement for a \c Matrix<> type. Here is an example:

\code
MatrixXd A, B;
auto C = A*B;
for(...) { ... w = C * v;  ...}
\endcode

In this example, the type of C is not a \c MatrixXd but an abstract expression representing a matrix product and storing references to \c A and \c B.
Therefore, the product of \c A*B will be carried out multiple times, once per iteration of the for loop.
Moreover, if the coefficients of `A` or `B` change during the iteration, then `C` will evaluate to different values as in the following example:

\code
MatrixXd A = ..., B = ...;
auto C = A*B;
MatrixXd R1 = C;
A = ...;
MatrixXd R2 = C;
\endcode
for which we end up with `R1` &ne; `R2`.


Here is another example leading to a segfault:
\code
auto C = ((A+B).eval()).transpose();
// do something with C
\endcode
The problem is that \c eval() returns a temporary object (in this case a \c MatrixXd) which is then referenced by the \c Transpose<> expression.
However, this temporary is deleted right after the first line, and then the \c C expression references a dead object.
One possible fix consists in applying \c eval() on the whole expression:
\code
auto C = (A+B).transpose().eval();
\endcode

The same issue might occur when sub expressions are automatically evaluated by %Eigen as in the following example:
\code
VectorXd u, v;
auto C = u + (A*v).normalized();
// do something with C
\endcode
Here the \c normalized() method has to evaluate the expensive product \c A*v to avoid evaluating it twice.
Again, one possible fix is to call \c .eval() on the whole expression:
\code
auto C = (u + (A*v).normalized()).eval();
\endcode
In this case, \c C will be a regular \c VectorXd object.
Note that DenseBase::eval() is smart enough to avoid copies when the underlying expression is already a plain \c Matrix<>.


\section TopicPitfalls_header_issues Header Issues (failure to compile)

With all libraries, one must check the documentation for which header to include.
The same is true with %Eigen, but slightly worse: with %Eigen, a method in a class may require an additional \c \#include over what the class itself requires!
For example, if you want to use the \c cross() method on a vector (it computes a cross-product) then you need to:
\code
#include<Eigen/Geometry>
\endcode
We try to always document this, but do tell us if we forgot an occurrence.


\section TopicPitfalls_ternary_operator Ternary operator

In short: avoid the use of the ternary operator <code>(COND ? THEN : ELSE)</code> with %Eigen's expressions for the \c THEN and \c ELSE statements.
To see why, let's consider the following example:
\code
Vector3f A;
A << 1, 2, 3;
Vector3f B = ((1 < 0) ? (A.reverse()) : A);
\endcode
This example will return <code>B = 3, 2, 1</code>. Do you see why?
The reason is that in c++ the type of the \c ELSE statement is inferred from the type of the \c THEN expression such that both match.
Since \c THEN is a <code>Reverse<Vector3f></code>, the \c ELSE statement A is converted to a <code>Reverse<Vector3f></code>, and the compiler thus generates:
\code
Vector3f B = ((1 < 0) ? (A.reverse()) : Reverse<Vector3f>(A));
\endcode
In this very particular case, a workaround would be to call A.reverse().eval() for the \c THEN statement, but the safest and fastest is really to avoid this ternary operator with %Eigen's expressions and use a if/else construct.


\section TopicPitfalls_pass_by_value Pass-by-value

If you don't know why passing-by-value is wrong with %Eigen, read this \link TopicPassingByValue page \endlink first.

While you may be extremely careful and use care to make sure that all of your code that explicitly uses %Eigen types is pass-by-reference you have to watch out for templates which define the argument types at compile time.

If a template has a function that takes arguments pass-by-value, and the relevant template parameter ends up being an %Eigen type, then you will of course have the same alignment problems that you would in an explicitly defined function passing %Eigen types by reference.

Using %Eigen types with other third party libraries or even the STL can present the same problem.
<code>boost::bind</code> for example uses pass-by-value to store arguments in the returned functor.
This will of course be a problem.

There are at least two ways around this:
  - If the value you are passing is guaranteed to be around for the life of the functor, you can use boost::ref() to wrap the value as you pass it to boost::bind. Generally this is not a solution for values on the stack as if the functor ever gets passed to a lower or independent scope, the object may be gone by the time it's attempted to be used.
  - The other option is to make your functions take a reference counted pointer like boost::shared_ptr as the argument. This avoids needing to worry about managing the lifetime of the object being passed.


\section TopicPitfalls_matrix_bool Matrices with boolean coefficients

The current behaviour of using \c Matrix with boolean coefficients is inconsistent and likely to change in future versions of Eigen, so please use it carefully!

A simple example for such an inconsistency is 

\code
template<int Size>
void foo() {
  Eigen::Matrix<bool, Size, Size> A, B, C;
  A.setOnes();
  B.setOnes();

  C = A * B - A * B;
  std::cout << C << "\n";
}
\endcode

since calling \c foo<3>() prints the zero matrix while calling \c foo<10>() prints the identity matrix.

*/
}