Jacobian (H) computation inside Unary factor

[tsugiar]

Hello ,

I have a doubt about how H should be derived within Unary factor. According to the link below, the H
derivation should fit following formula h(q.exp(epsilon)) = h(q) + H.epsilon,
https://gtsam.org/tutorials/intro.html

On gps location measurement, the H value is:
H = [ c(theta), -s(theta), 0
s(theta), c(theta), 0]

For comparison, PriorFactor structure looks very similar with Unary to me. Both of them are derived from
NoiseModeFactor base class. So, I take a look into how evaluateError function is implemented within file "PriorFactor.h".
Specifically, how H is matrix populated within the function. Within the function,
H matrix is an identity, see code snippet below:

Vector evaluateError(const T& x, boost::optional<Matrix&> H = boost::none) const override {
if (H) (*H) = Matrix::Identity(traits::GetDimension(x),traits::GetDimension(x));
...
}

So, my question is how to distinguish reasoning between these two cases ?

Thank you,
Tanto