[eigen] precision loss after conversion from rotation matrix to quaternion and back

[Tobias Langner <tobias.langner@xxxxxxxxxxxx>]

Hello all,

So here is my problem:

I have this rotation matrix (Scalar type double):

 0.124564 -0.800873  0.584451
-0.971925 0.0176983  0.231399
 -0.19596 -0.597765 -0.777352

Then I convert it to a Quaternion (Scalar type double) using the 
constructor. The quaternion coefficients  (x,y,z,w) are:
0.686334 -0.645749 0.14151 -0.302026

Finally I convert the Quaternion back to a rotation matrix using the 
function toRotationMatrix(), which yields a slightly different matrix:

 0.125967  -0.80092  0.584312
-0.971878 0.0178409  0.231823
-0.195821 -0.597341 -0.776092
0.686334 -0.645749 0.14151 -0.302026

As you can see some numbers differ on the third significant digit, which 
cannot be explained by floating point rounding errors. So where does it 
come from? If I repeat the procedure the rotation matrix will not differ 
again. It changes only on the first forth-and-back conversion.
I'd appreciate any help.

Best regards,

Tobias