pytransform3d.uncertainty.to_ellipsoid¶
- pytransform3d.uncertainty.to_ellipsoid(mean, cov)[source]¶
Compute error ellipsoid.
An error ellipsoid indicates the equiprobable surface. The resulting ellipsoid includes one standard deviation of the data along each main axis, which covers approximately 68.27% of the data. Multiplying the radii with factors > 1 will increase the coverage. The usual factors for Gaussian distributions apply:
1 - 68.27%
1.65 - 90%
1.96 - 95%
2 - 95.45%
2.58 - 99%
3 - 99.73%
- Parameters:
- meanarray-like, shape (3,)
Mean of distribution.
- covarray-like, shape (3, 3)
Covariance of distribution.
- Returns:
- ellipsoid2originarray, shape (4, 4)
Ellipsoid frame in world frame. Note that there are multiple solutions possible for the orientation because an ellipsoid is symmetric. A body-fixed rotation around a main axis by 180 degree results in the same ellipsoid.
- radiiarray, shape (3,)
Radii of ellipsoid, coinciding with standard deviations along the three axes of the ellipsoid. These are sorted in ascending order.
