Eigen
3.2.1

This page lists the most important API changes between Eigen2 and Eigen3, and gives tips to help porting your application from Eigen2 to Eigen3.
In order to ease the switch from Eigen2 to Eigen3, Eigen3 features Eigen2 support modes.
The quick way to enable this is to define the EIGEN2_SUPPORT
preprocessor token before including any Eigen header (typically it should be set in your project options).
A more powerful, staged migration path is also provided, which may be useful to migrate larger projects from Eigen2 to Eigen3. This is explained in the Eigen 2 support modes page.
The USING_PART_OF_NAMESPACE_EIGEN macro has been removed. In Eigen 3, just do:
This is the single trickiest change between Eigen 2 and Eigen 3. It only affects code using std::complex
numbers as scalar type.
Eigen 2's dot product was linear in the first variable. Eigen 3's dot product is linear in the second variable. In other words, the Eigen 2 code
is equivalent to the Eigen 3 code
In yet other words, dot products are complexconjugated in Eigen 3 compared to Eigen 2. The switch to the new convention was commanded by common usage, especially with the notation for dot products of columnvectors.
Eigen 2  Eigen 3 

vector.start(length)
vector.start<length>()
vector.end(length)
vector.end<length>()
 vector.head(length)
vector.head<length>()
vector.tail(length)
vector.tail<length>()

Eigen 2  Eigen 3 

matrix.corner(TopLeft,r,c)
matrix.corner(TopRight,r,c)
matrix.corner(BottomLeft,r,c)
matrix.corner(BottomRight,r,c)
matrix.corner<r,c>(TopLeft)
matrix.corner<r,c>(TopRight)
matrix.corner<r,c>(BottomLeft)
matrix.corner<r,c>(BottomRight)
 matrix.topLeftCorner(r,c)
matrix.topRightCorner(r,c)
matrix.bottomLeftCorner(r,c)
matrix.bottomRightCorner(r,c)
matrix.topLeftCorner<r,c>()
matrix.topRightCorner<r,c>()
matrix.bottomLeftCorner<r,c>()
matrix.bottomRightCorner<r,c>()

Notice that Eigen3 also provides these new convenience methods: topRows(), bottomRows(), leftCols(), rightCols(). See in class DenseBase.
In Eigen2, coefficient wise operations which have no proper mathematical definition (as a coefficient wise product) were achieved using the .cwise() prefix, e.g.:
In Eigen3 this .cwise() prefix has been superseded by a new kind of matrix type called Array for which all operations are performed coefficient wise. You can easily view a matrix as an array and vice versa using the MatrixBase::array() and ArrayBase::matrix() functions respectively. Here is an example:
Note that the .array() function is not at all a synonym of the deprecated .cwise() prefix. While the .cwise() prefix changed the behavior of the following operator, the array() function performs a permanent conversion to the array world. Therefore, for binary operations such as the coefficient wise product, both sides must be converted to an array as in the above example. On the other hand, when you concatenate multiple coefficient wise operations you only have to do the conversion once, e.g.:
With Eigen2 you would have written:
In Eigen 2 you had to play with the part, extract, and marked functions to deal with triangular and selfadjoint matrices. In Eigen 3, all these functions have been removed in favor of the concept of views:
Eigen 2  Eigen 3 

A.part<UpperTriangular>();
A.part<StrictlyLowerTriangular>();
 A.triangularView<Upper>()
A.triangularView<StrictlyLower>()

A.extract<UpperTriangular>();
A.extract<StrictlyLowerTriangular>();
 A.triangularView<Upper>()
A.triangularView<StrictlyLower>()

A.marked<UpperTriangular>();
A.marked<StrictlyLowerTriangular>();
 A.triangularView<Upper>()
A.triangularView<StrictlyLower>()

A.part<SelfAdfjointUpperTriangular>();
A.extract<SelfAdfjointLowerTriangular>();
 
UpperTriangular
LowerTriangular
UnitUpperTriangular
UnitLowerTriangular
StrictlyUpperTriangular
StrictlyLowerTriangular

Eigen 2  Eigen 3 

A.triangularSolveInPlace<XxxTriangular>(Y);
 A.triangularView<Xxx>().solveInPlace(Y);

Some of Eigen 2's matrix decompositions have been renamed in Eigen 3, while some others have been removed and are replaced by other decompositions in Eigen 3.
Eigen 2  Eigen 3  Notes 

LU  FullPivLU  See also the new PartialPivLU, it's much faster 
QR  HouseholderQR  See also the new ColPivHouseholderQR, it's more reliable 
SVD  JacobiSVD  We currently don't have a bidiagonalizing SVD; of course this is planned. 
EigenSolver and friends  #include<Eigen/Eigenvalues>
 Moved to separate module 
Eigen 2  Eigen 3  Notes 

A.lu();
 A.fullPivLu();
 Now A.lu() returns a PartialPivLU 
A.lu().solve(B,&X);
 X = A.lu().solve(B);
X = A.fullPivLu().solve(B);
 The returned by value is fully optimized 
A.llt().solve(B,&X);
 The returned by value is fully optimized and the selfadjointView API allows you to select the triangular part to work on (default is lower part)  
A.llt().solveInPlace(B);
 In place solving  
A.ldlt().solve(B,&X);
 The returned by value is fully optimized and the selfadjointView API allows you to select the triangular part to work on 
The Geometry module is the one that changed the most. If you rely heavily on it, it's probably a good idea to use the Eigen 2 support modes to perform your migration.
In Eigen 2, the Transform class didn't really know whether it was a projective or affine transformation. In Eigen 3, it takes a new Mode template parameter, which indicates whether it's Projective or Affine transform. There is no default value.
The Transform3f (etc) typedefs are no more. In Eigen 3, the Transform typedefs explicitly refer to the Projective and Affine modes:
Eigen 2  Eigen 3  Notes 

Transform3f  Affine3f or Projective3f  Of course 3f is just an example here 
In Eigen all operations are performed in a lazy fashion except the matrix products which are always evaluated into a temporary by default. In Eigen2, lazy evaluation could be enforced by tagging a product using the .lazy() function. However, in complex expressions it was not easy to determine where to put the lazy() function. In Eigen3, the lazy() feature has been superseded by the MatrixBase::noalias() function which can be used on the left hand side of an assignment when no aliasing can occur. Here is an example:
However, the noalias mechanism does not cover all the features of the old .lazy(). Indeed, in some extremely rare cases, it might be useful to explicit request for a lay product, i.e., for a product which will be evaluated one coefficient at once, on request, just like any other expressions. To this end you can use the MatrixBase::lazyProduct() function, however we strongly discourage you to use it unless you are sure of what you are doing, i.e., you have rigourosly measured a speed improvement.
The EIGEN_ALIGN_128 macro has been renamed to EIGEN_ALIGN16. Don't be surprised, it's just that we switched to counting in bytes ;)
The EIGEN_DONT_ALIGN option still exists in Eigen 3, but it has a new cousin: EIGEN_DONT_ALIGN_STATICALLY. It allows to get rid of all static alignment issues while keeping alignment of dynamicsize heapallocated arrays, thus keeping vectorization for dynamicsize objects.
A common issue with Eigen 2 was that when mapping an array with Map, there was no way to tell Eigen that your array was aligned. There was a ForceAligned option but it didn't mean that; it was just confusing and has been removed.
New in Eigen3 is the Aligned option. See the documentation of class Map. Use it like this:
There also are related convenience static methods, which actually are the preferred way as they take care of such things as constness:
In Eigen2, #include<Eigen/StdVector>
tweaked std::vector to automatically align elements. The problem was that that was quite invasive. In Eigen3, we only override standard behavior if you use Eigen::aligned_allocator<T> as your allocator type. So for example, if you use std::vector<Matrix4f>, you need to do the following change (note that aligned_allocator is under namespace Eigen):
Eigen 2  Eigen 3 

std::vector<Matrix4f>
 std::vector<Matrix4f, aligned_allocator<Matrix4f> >

In Eigen2, global internal functions and structures were prefixed by ei_
. In Eigen3, they all have been moved into the more explicit internal
namespace. So, e.g., ei_sqrt(x)
now becomes internal::sqrt(x)
. Of course it is not recommended to rely on Eigen's internal features.