Sherman Morrison Method for Implicit Solvers

[psv4]

Closes #267 and Closes #214 .

Replaces the costly Jacobian inverse calculation for implicit solvers with the good Sherman-Morrison method.

Additionally, reorders the tableau for GL4 to be closer to its definition and switches the implicit trapezoid method to use the DIRK solver.

[psv4]

Tests

python tests/run_all.py ........\torchdiffeq\torchdiffeq\torchdiffeq\_impl\rk_common.py:554: UserWarning: Functional iteration did not converge. Solution may be incorrect. warnings.warn('Functional iteration did not converge. Solution may be incorrect.') \torchdiffeq\torchdiffeq\torchdiffeq\_impl\rk_common.py:464: UserWarning: Functional iteration did not converge. Solution may be incorrect. warnings.warn('Functional iteration did not converge. Solution may be incorrect.') ...........\scipy\integrate\_ivp\ivp.py:621: UserWarning: The following arguments have no effect for a chosen solver: `min_step`. solver = method(fun, t0, y0, tf, vectorized=vectorized, **options) \scipy\integrate\_ivp\rk.py:505: UserWarning: The following arguments have no effect for a chosen solver: `min_step`. super().__init__(fun, t0, y0, t_bound, max_step, rtol, atol, ... ---------------------------------------------------------------------- Ran 22 tests in 343.978s OK 

[psv4]

@rtqichen this was a bigger update. For my work, the Jacobian inverse would take too much memory if it were dense. Following this paper, I switched it to sparse and it can actually run faster now. Additionally, cleaned up the __init__ with the super().