Add efficient finite-difference Jacobians of mj_step.

- Add `qH` and `qHDiagInv` to `mjData` to save factorized modified inertia.
- Add `mj_EulerSkip`, `mj_implicitSkip`, to `engine_forward.c`.
- Using the above functions, implement `mj_stepSkip` in `engine_derivative.c`.
- Add `mjd_stepFD` and `mjd_transitionFD` to `engine_derivative.c` to compute `mj_step` Jacobians.
  - Exploit "Skip" functionality for speed.
  - Correctly handle quaternion derivatives.
  - Handle warmstarts and control limits.

PiperOrigin-RevId: 456584811
Change-Id: Iee8541f11e7b66feb8f431cb102d9bbe65461f79

introspect/functions.py

@@ -6873,4 +6873,44 @@ FUNCTIONS: Mapping[str, FunctionDecl] = dict([
          ),
          doc='Sigmoid function over 0<=x<=1 constructed from half-quadratics.',
      )),
+    ('mjd_transitionFD',
+     FunctionDecl(
+         name='mjd_transitionFD',
+         return_type=ValueType(name='void'),
+         parameters=(
+             FunctionParameterDecl(
+                 name='m',
+                 type=PointerType(
+                     inner_type=ValueType(name='mjModel', is_const=True),
+                 ),
+             ),
+             FunctionParameterDecl(
+                 name='d',
+                 type=PointerType(
+                     inner_type=ValueType(name='mjData'),
+                 ),
+             ),
+             FunctionParameterDecl(
+                 name='eps',
+                 type=ValueType(name='mjtNum'),
+             ),
+             FunctionParameterDecl(
+                 name='centered',
+                 type=ValueType(name='mjtByte'),
+             ),
+             FunctionParameterDecl(
+                 name='A',
+                 type=PointerType(
+                     inner_type=ValueType(name='mjtNum'),
+                 ),
+             ),
+             FunctionParameterDecl(
+                 name='B',
+                 type=PointerType(
+                     inner_type=ValueType(name='mjtNum'),
+                 ),
+             ),
+         ),
+         doc='finite differenced state-transition and control-transition matrices dy = A*dx + B*du',  # pylint: disable=line-too-long
+     )),
 ])