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.

x

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}}).

Type:

ndarray or PyTree

success

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

Type:

bool

status

Detailed termination status code indicating the specific convergence criterion that was satisfied or reason for termination.

Type:

LMStatus

message

Human-readable description of the termination reason corresponding to the status code.

Type:

str

fun

Final objective function value. For least-squares problems, this is 0.5 times the sum of squared residuals.

Type:

float

jac

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

Type:

ndarray

hess

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

Type:

ndarray

nfev

Number of objective function evaluations performed during optimization. Each evaluation computes the objective value, gradient, and Hessian.

Type:

int

njev

Number of Jacobian evaluations. For this implementation, this equals nfev since gradient and Hessian are computed simultaneously.

Type:

int

nit

Number of algorithm iterations. Each iteration may involve multiple function evaluations due to the trust region approach.

Type:

int

history

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

Type:

List[Dict[str, Any]]

See also

lm_solve

Function that returns this result type

LMStatus

Detailed description of status codes

__init__(*args, **kwargs)

Methods

__init__(*args, **kwargs)
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()