inversion_ideas.minimize.GaussNewtonConjugateGradient

class inversion_ideas.minimize.GaussNewtonConjugateGradient(*, maxiter=100, rtol=1e-05, stopping_criterion=None, cg_rtol=1e-05, cg_atol=0.0, cg_kwargs=None, line_search_maxiter=10, line_search_kwargs=None)

Minimize non-linear objective functions using a Gauss-Newton Conjugate Gradient.

Apply Gauss-Newton iterations using a Conjugate Gradient to find search directions, and use a backtracking line search to update the model after each iteration. The conjugate gradient algorithm is applied through the scipy.sparse.linalg.cg() function, and the backtracking line search through backtracking_line_search().

Parameters:

maxiterint, optional

Maximum number of Gauss-Newton iterations.

rtolfloat, optional

Relative tolerance for the objective function. If the relative difference between the current and previous value of the objective function is below rtol, then the minimization is considered as converged.

stopping_criterionbase.Condition, callable() or None, optional

Additional stopping condition that will make the Gauss-Newton iterations to finish. When a condition is passed, the Gauss-Newton iterations will finish if the condition is met, the Gauss-Newton converges (relative difference below rtol), or if maximum number of iterations are reached. If None, Gauss-Newton iterations will finish if convergence or maximum number of iterations are reached.

cg_rtolfloat, optional

Relative tolerance for the conjugate gradient algorithm. This value will be passed to the scipy.sparse.linalg.cg() through the rtol argument.

cg_atolfloat, optional

Absolute tolerance for the conjugate gradient algorithm. This value will be passed to the scipy.sparse.linalg.cg() through the atol argument.

cg_kwargsdict or None, optional

Dictionary with extra arguments passed to the scipy.sparse.linalg.cg() function.

Hint

Don’t include "rtol" or "atol" in this dictionary. Pass them directly through the cg_rtol and cg_atol arguments.

line_search_maxiterint, optional

Maximum number of line search iterations.

line_search_kwargsdict or None, optional

Dictionary with extra arguments passed to the backtracking_line_search() function.

Hint

Don’t include "maxiter" in this dictionary. Pass it directly through the line_search_maxiter arguments.

Methods

__call__(objective, initial_model, *[, ...])	Create iterator over Gauss-Newton minimization.
run(objective, initial_model, *args, **kwargs)	Run all iterations of the minimizer at once.

Methods

Methods documentation

GaussNewtonConjugateGradient.__call__(objective, initial_model, *, preconditioner=None, callback=None)

Create iterator over Gauss-Newton minimization.

Parameters:

objectivebase.Objective

Objective function to be minimized.

initial_model(n_params,) array

Initial model used to start the minimization.

preconditioner(n_params, n_params) array, sparse array or LinearOperator, optional

Matrix used as preconditioner in the conjugate gradient algorithm. If None, no preconditioner will be used. If the preconditioner implements an update method, the preconditioner will be updated before every conjugate gradient minimization.

callbackcallable(), optional

Callable that gets called after each iteration.

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GaussNewtonConjugateGradient.run(objective, initial_model, *args, **kwargs)

Run all iterations of the minimizer at once.

Parameters:

objectivebase.Objective

Objective function to be minimized.

initial_model(n_params,) array

Initial model used to start the minimization.

*args

Any extra positional argument will be passed to the __call__ method.

*kwargs

Any extra keyword argument will be passed to the __call__ method.

Returns:

inverted_model(n_params,) array

Final inverted model.

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