simpeg.data_misfit.L2DataMisfit#

class simpeg.data_misfit.L2DataMisfit(data, simulation, debug=False, counter=None, **kwargs)[source]#

Bases: BaseDataMisfit

Least-squares data misfit.

Define the data misfit as the L2-norm of the weighted residual between observed data and predicted data for a given model. I.e.:

\[\phi_d (\mathbf{m}) = \big \| \mathbf{W_d} \big ( \mathbf{d}_\text{pred} - \mathbf{d}_\text{obs} \big ) \big \|_2^2\]

where \(\mathbf{d}_\text{obs}\) is the observed data vector, \(\mathbf{d}_\text{pred}\) is the predicted data vector for a model vector \(\mathbf{m}\), and \(\mathbf{W_d}\) is the data weighting matrix. The diagonal elements of \(\mathbf{W_d}\) are the reciprocals of the data uncertainties \(\boldsymbol{\varepsilon}\). Thus:

\[\mathbf{W_d} = \text{diag} \left ( \boldsymbol{\varepsilon}^{-1} \right )\]

Parameters:

datasimpeg.data.Data: A SimPEG data object that has observed data and uncertainties.
simulationsimpeg.simulation.BaseSimulation: A SimPEG simulation object.
debugbool: Print debugging information.
counterNone or simpeg.utils.Counter: Assign a SimPEG Counter object to store iterations and run-times.

Attributes

`W`	The data weighting matrix.
`counter`	SimPEG `Counter` object to store iterations and run-times.
`data`	A SimPEG data object.
`debug`	Print debugging information.
`mapping`	Mapping from the model to the quantity evaluated in the object function.
`nD`	Number of data.
`nP`	Number of model parameters.
`shape`	Shape of the Jacobian.
`simulation`	A SimPEG simulation object.

Methods

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