archimedes.optimize.LMResult

class archimedes.optimize.LMResult

Result of Levenberg-Marquardt optimization.

This class provides detailed information about the optimization process and results, following SciPy conventions while adding specialized fields for system identification applications.

Variables:

• x (ndarray or Tree) – Solution parameters with the same structure as the initial guess. For system identification, this preserves the nested parameter organization (e.g., {"mass": 1.0, "damping": {"c1": 0.1}}).

• success (bool) – Whether optimization terminated successfully. True for status codes 1-4 (converged), False for status code 5 (max iterations reached).

• status (LMStatus) – Detailed termination status code indicating the specific convergence criterion that was satisfied or reason for termination.

• message (str) – Human-readable description of the termination reason corresponding to the status code.

• fun (float) – Final objective function value. For least-squares problems, this is 0.5 times the sum of squared residuals.

• jac (ndarray) – Final gradient vector of shape (n,). For constrained problems, this is the full gradient (not projected).

• hess (ndarray) – Final Hessian matrix or approximation of shape (n, n). This can be used for uncertainty quantification and further analysis.

• nfev (int) – Number of objective function evaluations performed during optimization. Each evaluation computes the objective value, gradient, and Hessian.

• njev (int) – Number of Jacobian evaluations. For this implementation, this equals nfev since gradient and Hessian are computed simultaneously.

• nit (int) – Number of algorithm iterations. Each iteration may involve multiple function evaluations due to the trust region approach.

• history (List[Dict[str, Any]]) –

  Detailed iteration history containing convergence diagnostics:

  • iter : Iteration number

  • cost : Objective function value

  • grad_norm : Gradient norm (or projected gradient for constrained)

  • lambda : Levenberg-Marquardt damping parameter

  • x : Parameter values at this iteration

  • step_norm : Step size (when step is accepted)

  • actred : Actual reduction in objective

  • prered : Predicted reduction from quadratic model

  • ratio : Ratio of actual to predicted reduction

See also

lm_solve

Function that returns this result type

LMStatus

Detailed description of status codes

Methods

clear()
copy()
fromkeys(iterable[, value])	Create a new dictionary with keys from iterable and values set to value.
get(key[, default])	Return the value for key if key is in the dictionary, else default.
items()
keys()
pop(k[,d])	If the key is not found, return the default if given; otherwise, raise a KeyError.
popitem()	Remove and return a (key, value) pair as a 2-tuple.
setdefault(key[, default])	Insert key with a value of default if key is not in the dictionary.
update([E, ]**F)	If E is present and has a .keys() method, then does: for k in E: D[k] = E[k] If E is present and lacks a .keys() method, then does: for k, v in E: D[k] = v In either case, this is followed by: for k in F: D[k] = F[k]
values()

__init__(*args, **kwargs)

clear() → None.  Remove all items from D.

copy() → a shallow copy of D

classmethod fromkeys(iterable, value=None, /)

Create a new dictionary with keys from iterable and values set to value.

get(key, default=None, /)

Return the value for key if key is in the dictionary, else default.

items() → a set-like object providing a view on D's items

keys() → a set-like object providing a view on D's keys

pop(k[, d]) → v, remove specified key and return the corresponding value.

If the key is not found, return the default if given; otherwise, raise a KeyError.

popitem()

Remove and return a (key, value) pair as a 2-tuple.

Pairs are returned in LIFO (last-in, first-out) order. Raises KeyError if the dict is empty.

setdefault(key, default=None, /)

Insert key with a value of default if key is not in the dictionary.

Return the value for key if key is in the dictionary, else default.

update([E, ]**F) → None.  Update D from dict/iterable E and F.

If E is present and has a .keys() method, then does: for k in E: D[k] = E[k] If E is present and lacks a .keys() method, then does: for k, v in E: D[k] = v In either case, this is followed by: for k in F: D[k] = F[k]

values() → an object providing a view on D's values