perf(linear): compute JacobianFactor::gradient() directly, skip HessianFactor conversion

[jashshah999]

Problem

JacobianFactor::gradient(Key, VectorValues) converts the entire factor to a HessianFactor to compute a single gradient entry (flagged by an existing TODO at line 881):

Vector JacobianFactor::gradient(Key key, const VectorValues& x) const {
  // TODO: optimize it for JacobianFactor without converting to a HessianFactor
  HessianFactor hessian(*this);
  return hessian.gradient(key, x);
}

The HessianFactor constructor computes A'A which is O(n*m^2) for an n-row, m-column Jacobian. This is unnecessary when only one key's gradient is needed.

Fix

Compute the gradient directly:

1. Evaluate unwhitened residual e = A*x - b by iterating over Jacobian blocks — O(n*m)
2. Apply noise model: e = Sigma^{-1} * e (double whiten)
3. Return A_k' * e for the requested key — O(n*d_k)

Total cost: O(nm) vs O(nm^2) for the old path. No heap allocation for the HessianFactor.

Tests

Two new tests in testJacobianFactor.cpp:

• gradient: isotropic noise model, verifies numerical equivalence with the HessianFactor path
• gradient_no_noise: no noise model (unit covariance), same verification

[Copilot]

Pull request overview

Note

Copilot was unable to run its full agentic suite in this review.

This PR optimizes JacobianFactor::gradient(Key, VectorValues) by computing a single-key gradient directly from Jacobian blocks, avoiding conversion to HessianFactor and its AᵀA construction cost.

Changes:

• Reimplemented JacobianFactor::gradient() to compute the residual and project onto a requested key’s Jacobian block.
• Added unit tests comparing the new path to the existing HessianFactor-based gradient for isotropic and no-noise cases.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 4 comments.

File	Description
gtsam/linear/JacobianFactor.cpp	Replaces HessianFactor conversion with direct residual/gradient computation.
gtsam/linear/tests/testJacobianFactor.cpp	Adds tests validating gradient equivalence against HessianFactor.

[jashshah999]

Pushed a fix for the noise model handling. The previous version applied whitenInPlace twice, computing R*R*e instead of R^T*R*e. These differ when R is non-symmetric (any non-diagonal covariance). Now whitens both A_k and e once: (R*A_k)^T * (R*e) = A_k^T * R^T*R * e.

Also added a bounds check for missing keys and a test with non-diagonal (Gaussian) covariance that would have caught this.

[dellaert]

@jashshah999 please "resolve" copilot comments you addressed and/or are irrelevant.
The CI failed on some platforms. Please check. If these are CI hiccups, please merge in develop to re-trigger CI.

[jashshah999]

Resolved all Copilot threads (replied to each). Also merged develop to re-trigger CI.

[dellaert]

Very nice. We'll merge when CI passes.