cosapp.core.numerics.root

Module provides dispatch to different non-linear algorithms.

Functions

get_kwargs()	Returns kwargs as a dictionary, using inspect.currentframe
root(fun, x0[, args, method, options])

Classes

BaseNumericalSolver([options])
CustomSolver([tol, factor, max_iter, …])	Custom Newton-Raphson solver.
NumpySolver(method[, options])	Encapsulation of scipy.optimize.root

class cosapp.core.numerics.root.BaseNumericalSolver(options={})

Bases: abc.ABC

classmethod from_options(options: Dict[str, Any]) → ConcreteSolver

property options

abstract solve(fun: Callable[[Sequence[float], Any], numpy.ndarray], x0: Sequence[float], args: Tuple[Any] = (), *other_args, **kwargs) → Union[cosapp.core.numerics.basics.SolverResults, scipy.optimize._optimize.OptimizeResult]

transfer_options(options: Dict[str, Any]) → None

class cosapp.core.numerics.root.CustomSolver(tol='auto', factor=1.0, max_iter=100, verbose=False, eps=1.1920928955078125e-07, jac_update_tol=0.01, history=False, partial_jac=True, partial_jac_tries=5, tol_update_period=4, tol_to_noise_ratio=16)

Bases: cosapp.core.numerics.root.BaseNumericalSolver

Custom Newton-Raphson solver.

static lu_factor(matrix: numpy.ndarray)

solve(fresidues: Callable[[Sequence[float], Any], numpy.ndarray], x0: Sequence[float], args: Tuple[Union[float, str]] = (), jac=None, recorder=None, **options) → cosapp.core.numerics.basics.SolverResults

Customized Newton-Raphson algorithm to solve fresidues starting with x0.

Parameters

• fresidues (Callable[[Sequence[float], Any], numpy.ndarray[float]]) – Callable residues function

• x0 (Sequence[float]) – Initial solution guess

• args (Tuple[Any, ..]) – Additional arguments for fun

• options (dict, optional) – A dictionary of problem-dependent solver options.

• Options –

• ------- –

• jac_lup ((ndarray[float], ndarray[int]), optional) – LU decomposition of Jacobian given as tuple (LU, perm) to reuse as initial direction

• jac (ndarray, optional) – Jacobian to reuse for partial update

• compute_jacobian (bool) – Force to update the Jacobian matrix even if the provided one is useful

• lower_bound (numpy.ndarray) – Min values for parameters iterated by solver.

• upper_bound (numpy.ndarray) – Max values for parameters iterated by solver.

• abs_step (numpy.ndarray) – Max absolute step for parameters iterated by solver.

• rel_step (numpy.ndarray) – Max relative step for parameters iterated by solver.

Returns

The solution represented as a SolverResults object. See cosapp.core.numerics.basics.SolverResults for details.

Return type

SolverResults

class cosapp.core.numerics.root.NumpySolver(method: str, options={})

Bases: cosapp.core.numerics.root.BaseNumericalSolver

Encapsulation of scipy.optimize.root

solve(fun: Callable[[Sequence[float], Any], numpy.ndarray], x0: Sequence[float], args: Tuple[Union[float, str]] = (), jac=None, callback=None) → scipy.optimize._optimize.OptimizeResult

Cancel residues produced by fun starting with x0 as initial guess.

Parameters

• fun (Callable[[Sequence[float], Any], numpy.ndarray[float]]) – Callable residues function

• x0 (Sequence[float]) – Initial solution guess

• args (Tuple[Any, ..]) – Additional arguments passed to fun

• jac (bool or callable, optional) – If jac is a Boolean and is True, fun is assumed to return the value of Jacobian along with the objective function. If False, the Jacobian will be estimated numerically. jac can also be a callable returning the Jacobian of fun. In this case, it must accept the same arguments as fun. (default: None)

• callback (Callable, optional) – Optional callback function. It is called on every iteration as callback(x, r), where x is the current solution and r the corresponding residual.

Returns

The solution represented as a OptimizeResult object. Important attributes are: x the solution array, success a Boolean flag indicating if the algorithm exited successfully and message which describes the cause of the termination. See cosapp.core.numerics.basics.SolverResults for a description of other attributes.

Return type

scipy.optimize.OptimizeResult

cosapp.core.numerics.root.get_kwargs()

Returns kwargs as a dictionary, using inspect.currentframe

cosapp.core.numerics.root.root(fun: Callable[[Sequence[float], Any], numpy.ndarray], x0: Sequence[float], args: Tuple[Any] = (), method: cosapp.core.numerics.enum.NonLinearMethods = <NonLinearMethods.POWELL: 'hybr'>, options: Dict[str, Any] = {}) → Union[cosapp.core.numerics.basics.SolverResults, scipy.optimize._optimize.OptimizeResult]