pytransform3d.uncertainty.to_ellipsoid

pytransform3d.uncertainty.to_ellipsoid(mean, cov)

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.