simpeg.objective_function.L2ObjectiveFunction#

class simpeg.objective_function.L2ObjectiveFunction(nP=None, mapping=None, W=None, has_fields=False, counter=None, debug=False)[source]#

Bases: BaseObjectiveFunction

Weighted least-squares objective function class.

Weighting least-squares objective functions in SimPEG are defined as follows:

\[\phi = \big \| \mathbf{W} f(\mathbf{m}) \big \|_2^2\]

where \(\mathbf{m}\) are the model parameters, \(f\) is a mapping operator, and \(\mathbf{W}\) is the weighting matrix.

Parameters:

nPint: Number of model parameters.
mappingsimpeg.mapping.BaseMap: A SimPEG mapping object that maps from the model space to the quantity evaluated in the objective function.
WNone or scipy.sparse.csr_matrix: The weighting matrix applied in the objective function. By default, this is set to the identity matrix.
has_fieldsbool: If True, predicted fields for a simulation and a given model can be used to evaluate the objective function quickly.
counterNone or simpeg.utils.Counter: Assign a SimPEG Counter object to store iterations and run-times.
debugbool: Print debugging information.

Attributes

`W`	Weighting matrix applied in the objective function.
`mapping`	Mapping from the model to the quantity evaluated in the object function.
`nP`	Number of model parameters.

Methods

`__call__`(m)	Evaluate the objective function for a given model.
`deriv`(m)	Gradient of the objective function evaluated for the model provided.
`deriv2`(m[, v])	Hessian of the objective function evaluated for the model provided.
`map_class`	alias of `IdentityMap`
`test`([x, num, random_seed])	Run a convergence test on both the first and second derivatives.