def implicit_solve(self, next_x, func, method="hybr", **kwargs):
"""A solver for implicit equations.
Finds the implicitly defined :math:`x_{i+1}` for the given right hand side function :math:`f(x_{i+1})`, such
that :math:`x_{i+1}=f(x_{i+1})`.
Parameters
----------
next_x : :py:class:`numpy.ndarray`
A starting guess for the implicitly defined value.
rhs_call : :py:class:`callable`
The right hand side function depending on the implicitly defined new value.
method : :py:class:`str`
*(optional, default=``hybr``)*
Method fo the root finding algorithm. See `scipy.optimize.root
<http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.root.html#scipy.optimize.root>` for
details.
Returns
-------
next_x : :py:class:`numpy.ndarray`
The calculated new value.
Raises
------
ValueError :
* if ``next_x`` is not a :py:class:`numpy.ndarray` of shape :py:attr:`.IProblem.dim`
* if ``fun`` is not :py:class:`callable`
* if computed solution is not a `:py:class:`numpy.ndarray`
UserWarning :
If the implicit solver did not converged, i.e. the solution object's ``success`` is not :py:class:`True`.
"""
assert_is_instance(next_x, np.ndarray, descriptor="Initial Guess", checking_obj=self)
assert_is_callable(func, descriptor="Function of RHS for Implicit Solver", checking_obj=self)
sol = find_root(fun=func, x0=next_x.reshape(-1), method=method)
if not sol.success:
warnings.warn("Implicit solver did not converged.")
LOG.debug("sol.x: %s" % sol.x)
LOG.error("Implicit solver failed: %s" % sol.message)
else:
assert_is_instance(sol.x, np.ndarray, descriptor="Solution", checking_obj=self)
return sol.x.reshape(self.dim_for_time_solver)
def testSimpleRoot(self):
_func = lambda x: np.array([-1.0 + 1.0j, -1.0], dtype=np.complex) + x
_in_x = np.array([0.0, 0.0], dtype=np.complex)
_sol = find_root(_func, _in_x)
self.assertTrue(_sol.success)
self.assertNumpyArrayAlmostEqual(_sol.x, np.array([1.0 - 1.0j, 1.0], dtype=np.complex))
