def scale_errors(error_component, tol_scale):
abs_square_error = rk_util.abs_square(error_component)
abs_square_tol_scale = rk_util.abs_square(tol_scale)
return tf.divide(abs_square_error, abs_square_tol_scale)
def test_abs_square(self, dtype): test_values = np.array([1 + 2j, 0.3 - 1j, 3.5 - 3.7j]) input_values = tf.cast(test_values, dtype) actual_abs_square = rk_util.abs_square(input_values) expected_abs_square = tf.math.square(tf.abs(input_values)) self.assertAllClose(actual_abs_square, expected_abs_square)
def _step(
self,
solver_state,
diagnostics,
max_ode_fn_evals,
ode_fn,
atol,
rtol,
safety,
ifactor,
dfactor
):
"""Take an adaptive Runge-Kutta step.
Args:
solver_state: `_DopriSolverInternalState` - solver internal state.
diagnostics: `_DopriDiagnostics` - info on the current `_solve` call.
max_ode_fn_evals: Integer `Tensor` specifying the maximum number of ode_fn
evaluations.
ode_fn: Callable(t, y) -> dy_dt.
atol: Absolute tolerance allowed, see `_solve` method for details.
rtol: Relative tolerance allowed, see `_solve` method for details.
safety: Safety factor, see `_solve` method for details.
ifactor: Maximum factor by which the step size can increase, see `_solve`
method for details.
dfactor: Minimum factor by which the step size can decrease, see `_solve`
method for details.
Returns:
solver_state: `_RungeKuttaSolverInternalState` holding new solver state.
Note that the step might not advance the time if the error tolerance
criterias were not met. In this case step_size is decreased.
diagnostics: `_DopriDiagnostics` holding diagnostic values after RK step.
"""
y0, f0, _, t0, dt, interp_coeff = solver_state
assertion_ops = []
# TODO(dkochkov) Profile performance impact of `control_dependencies` here.
with tf.name_scope('assertions'):
if self._max_num_steps is not None:
check_max_num_steps = tf.debugging.assert_less(
diagnostics.num_ode_fn_evaluations, max_ode_fn_evals,
'max_num_steps exceeded')
assertion_ops.append(check_max_num_steps)
if self._validate_args:
check_underflow = tf.debugging.assert_greater(
t0 + dt, t0, 'underflow in dt')
check_numerics = tf.debugging.assert_all_finite(
y0, 'non-finite values in solution')
assertion_ops.append(check_underflow)
assertion_ops.append(check_numerics)
with tf.control_dependencies(assertion_ops):
y1, f1, y1_error, k = rk_util.runge_kutta_step(
ode_fn, y0, f0, t0, dt, _TABLEAU)
with tf.name_scope('error_ratio'):
# We use the same criteria for accepting step as in scipy.
abs_y0 = tf.nest.map_structure(tf.abs, y0)
abs_y1 = tf.nest.map_structure(tf.abs, y1)
max_y_vals = tf.nest.map_structure(tf.math.maximum, abs_y0, abs_y1)
ones_nest = rk_util.nest_constant(abs_y0)
error_tol = rk_util.weighted_sum([atol, rtol], [ones_nest, max_y_vals])
scaled_errors = tf.nest.map_structure(tf.divide,
rk_util.abs_square(y1_error),
rk_util.abs_square(error_tol))
error_ratio = rk_util.nest_rms_norm(scaled_errors)
accept_step = error_ratio <= 1
with tf.name_scope('update/state'):
y_next = tf.where(accept_step, y1, y0)
f_next = tf.where(accept_step, f1, f0)
t_next = tf.where(accept_step, t0 + dt, t0)
new_coefficients = rk_util.rk_fourth_order_interpolation_coefficients(
y0, y1, k, dt, _TABLEAU)
new_and_old_coefficients = zip(new_coefficients, interp_coeff)
interp_coeff = [tf.where(accept_step, new_c, old_c)
for new_c, old_c in new_and_old_coefficients]
dt_next = util.next_step_size(
dt, self.ORDER, error_ratio, safety, dfactor, ifactor)
solver_state = _RungeKuttaSolverInternalState(
y_next, f_next, t0, t_next, dt_next, interp_coeff)
diagnostics = diagnostics._replace(
num_ode_fn_evaluations=diagnostics.num_ode_fn_evaluations +
self.ODE_FN_EVALS_PER_STEP)
return solver_state, diagnostics