test_KarcherMeanFactor.py

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"""
GTSAM Copyright 2010-2019, Georgia Tech Research Corporation,
Atlanta, Georgia 30332-0415
All Rights Reserved
 
See LICENSE for the license information
 
KarcherMeanFactor unit tests.
Author: Frank Dellaert
"""
 
# pylint: disable=invalid-name, no-name-in-module, no-member
 
import unittest
 
import numpy as np
from gtsam.utils.test_case import GtsamTestCase
 
import gtsam
from gtsam import Rot3
 
KEY = 0
MODEL = gtsam.noiseModel.Unit.Create(3)
 
# Rot3 version
R = Rot3.Expmap(np.array([0.1, 0, 0]))
 
 
class TestKarcherMean(GtsamTestCase):
 
    def test_find(self):
        """
        Check that optimizing for Karcher mean (which minimizes Between distance)
        gets correct result.
        """
        rotations = [R, R.inverse()]
        expected = Rot3()
        actual = gtsam.FindKarcherMeanRot3(rotations)
        self.gtsamAssertEquals(expected, actual)
 
    def test_find_karcher_mean_identity(self):
        """Averaging 3 identity rotations should yield the identity."""
        a1Rb1 = Rot3()
        a2Rb2 = Rot3()
        a3Rb3 = Rot3()
 
        aRb_list = [a1Rb1, a2Rb2, a3Rb3]
        aRb_expected = Rot3()
 
        aRb = gtsam.FindKarcherMeanRot3(aRb_list)
        self.gtsamAssertEquals(aRb, aRb_expected)
 
    def test_factor(self):
        """Check that the InnerConstraint factor leaves the mean unchanged."""
        # Make a graph with two variables, one between, and one InnerConstraint
        # The optimal result should satisfy the between, while moving the other
        # variable to make the mean the same as before.
        # Mean of R and R' is identity. Let's make a BetweenFactor making R21 =
        # R*R*R, i.e. geodesic length is 3 rather than 2.
        graph = gtsam.NonlinearFactorGraph()
        R12 = R.compose(R.compose(R))
        graph.add(gtsam.BetweenFactorRot3(1, 2, R12, MODEL))
        keys = [1, 2]
        graph.add(gtsam.KarcherMeanFactorRot3(keys))
 
        initial = gtsam.Values()
        initial.insert(1, R.inverse())
        initial.insert(2, R)
        expected = Rot3()
 
        result = gtsam.GaussNewtonOptimizer(graph, initial).optimize()
        actual = gtsam.FindKarcherMeanRot3([result.atRot3(1), result.atRot3(2)])
        self.gtsamAssertEquals(expected, actual)
        self.gtsamAssertEquals(R12, result.atRot3(1).between(result.atRot3(2)))
 
 
if __name__ == "__main__":
    unittest.main()