# Extracting submatrices in Eigen (C++).

23 Jun 2021Whenever I needed to copy a submatrix in Eigen (the matrix library in C++), I would just walk through it with two `for`

loops like it was 1998. BUT recent experience with the docs and other languages led me to believe there was a submatrix function in Eigen somewhere, I just wasn’t using the right search terms or looking in the right place.

And, this time I found it! The function is a `Matrix**`

class member `block()`

from
Faisal Khan’s post on Eigen, scroll down to ‘Block Operations’ has the information about the block operator, but a lot of good information about Eigen too.

Here’s the Eigen Docs: Block operations where I noticed this:

As usual with Eigen expressions, this abstraction has zero runtime cost provided that you let your compiler optimize.

Here’s a snippet that shows the block operator with a sequence of steps I do frequently: have a 4 x 4 projection matrix and want to extract the rotation matrix and translation vector.

```
Matrix4d ProjectionMat;
Matrix3d RotationMat;
MatrixXd translationVec;
...
RotationMat = ProjectionMat.block<3, 3>(0, 0);
translationVec = ProjectionMat.block<3, 1>(0, 3);
```

What about vectors? **YES WHAT ABOUT THEM?** The Eigen Docs: Block operations includes these, but down the page.

Interestingly, there are some special `head`

, `tail`

, `segment`

functions that I will be using … a lot.

Example: create a vector (`planeNormal`

) that is the first three elements of the 4-element `planeEq`

vector. What I frequently do is normalize the `planeEq`

vector such that its normal vector is a unit vector, so that I can compute the distance of points to the plane using a fast dot product. (More info, equation 9 from Mathworld, Point-Plane distance.)

```
Vector4d planeEq = svd.matrixV().col(3);
Vector3d planeNormal = planeEq.head<3>();
planeEq = planeEq/planeNormal.norm();
```