JacobianFactorQ - GTSAM Docs

A JacobianFactorQ is one of the specialized Jacobian factor classes used internally by smart factors. It represents the orthogonal null-space projection produced when a smart projection factor eliminates its landmark.

Authors: Frank Dellaert, et al. (see THANKS for the full author list)

See LICENSE for the license information

try:
    import google.colab
    %pip install --quiet gtsam-develop
except ImportError:
    pass

import gtsam
import numpy as np

from gtsam.symbol_shorthand import X

Obtain one from a smart factor¶

A JacobianFactorQ is normally returned by smart-factor linearization rather than constructed directly. We create two calibrated cameras, add their measurements of one landmark to a smart projection factor, and call createJacobianQFactor() to eliminate the landmark. Because each camera has an 11-dimensional tangent vector, this example returns JacobianFactorQ112.

calibration = gtsam.Cal3_S2(500.0, 500.0, 0.0, 320.0, 240.0)
cameras = [
    gtsam.PinholeCameraCal3_S2(gtsam.Pose3(), calibration),
    gtsam.PinholeCameraCal3_S2(
        gtsam.Pose3(gtsam.Rot3(), np.array([1.0, 0.0, 0.0])),
        calibration,
    ),
]
landmark = np.array([0.0, 0.0, 5.0])
factor = gtsam.SmartProjectionFactorPinholeCameraCal3_S2(
    gtsam.noiseModel.Isotropic.Sigma(2, 1.0)
)
values = gtsam.Values()
for index, camera in enumerate(cameras):
    factor.add(camera.project(landmark), X(index))
    values.insert(X(index), camera)

jacobian = factor.createJacobianQFactor(values, 0.0)
assert isinstance(jacobian, gtsam.JacobianFactorQ112)
print("type:", type(jacobian).__name__)
print("keys:", jacobian.keys())
print("A shape:", jacobian.getA().shape)
print("b shape:", jacobian.getb().shape)

type: JacobianFactorQ112
keys: [8646911284551352320, 8646911284551352321]
A shape: (4, 22)
b shape: (4,)

Inspect the projected linear system¶

The returned object behaves like any other JacobianFactor. keys() identifies the camera variables, while getA() and getb() expose the whitened linear system. The dimension checks below show how the two camera blocks appear in the matrix.

assert jacobian.rows() == jacobian.getA().shape[0]
assert jacobian.getA().shape[1] == 11 * len(cameras)
assert jacobian.getb().shape == (jacobian.rows(),)

When to use it¶

JacobianFactorQ is an internal linear factor for smart factors. Most applications select the Jacobian-Q mode through SmartFactorParams and pass the returned factor to a Gaussian solver rather than manipulating it directly. SmartProjectionFactor shows the higher-level nonlinear factor.

Source¶

JacobianFactorQ.h

AI assistance caveat¶

AI was used to help draft this documentation, and inaccuracies could be present.