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.

Galleries and Tutorials using simpeg.objective_function.L2ObjectiveFunction#

Maps: ComboMaps

Maps: ComboMaps

PF: Gravity: Tiled Inversion Linear

PF: Gravity: Tiled Inversion Linear

Magnetic inversion on a TreeMesh with remanence

Magnetic inversion on a TreeMesh with remanence

Magnetic inversion on a TreeMesh

Magnetic inversion on a TreeMesh

Magnetic Amplitude inversion on a TreeMesh

Magnetic Amplitude inversion on a TreeMesh

3D DC inversion of Dipole Dipole array

3D DC inversion of Dipole Dipole array

Parametric DC inversion with Dipole Dipole array

Parametric DC inversion with Dipole Dipole array

2D inversion of Loop-Loop EM Data

2D inversion of Loop-Loop EM Data

EM: TDEM: 1D: Inversion

EM: TDEM: 1D: Inversion

EM: TDEM: 1D: Inversion with VTEM waveform

EM: TDEM: 1D: Inversion with VTEM waveform

Method of Equivalent Sources for Removing VRM Responses

Method of Equivalent Sources for Removing VRM Responses

FLOW: Richards: 1D: Inversion

FLOW: Richards: 1D: Inversion

Petrophysically guided inversion (PGI): Linear example

Petrophysically guided inversion (PGI): Linear example

Petrophysically guided inversion: Joint linear example with nonlinear relationships

Petrophysically guided inversion: Joint linear example with nonlinear relationships

Heagy et al., 2017 1D RESOLVE and SkyTEM Bookpurnong Inversions

Heagy et al., 2017 1D RESOLVE and SkyTEM Bookpurnong Inversions

Heagy et al., 2017 1D RESOLVE Bookpurnong Inversion

Heagy et al., 2017 1D RESOLVE Bookpurnong Inversion

Heagy et al., 2017 1D FDEM and TDEM inversions

Heagy et al., 2017 1D FDEM and TDEM inversions

PF: Gravity: Laguna del Maule Bouguer Gravity

PF: Gravity: Laguna del Maule Bouguer Gravity

Straight Ray with Volume Data Misfit Term

Straight Ray with Volume Data Misfit Term

1D Inversion of Time-Domain Data for a Single Sounding

1D Inversion of Time-Domain Data for a Single Sounding

2.5D DC Resistivity and IP Least-Squares Inversion

2.5D DC Resistivity and IP Least-Squares Inversion

3D Least-Squares Inversion of DC and IP Data

3D Least-Squares Inversion of DC and IP Data

1D Inversion of for a Single Sounding

1D Inversion of for a Single Sounding

Least-Squares Inversion of Gravity Anomaly Data

Least-Squares Inversion of Gravity Anomaly Data

Sparse Norm Inversion of Gravity Anomaly Data

Sparse Norm Inversion of Gravity Anomaly Data

Compare weighting strategy with Inversion of surface Gravity Anomaly Data

Compare weighting strategy with Inversion of surface Gravity Anomaly Data

Least-Squares 1D Inversion of Sounding Data

Least-Squares 1D Inversion of Sounding Data

Sparse 1D Inversion of Sounding Data

Sparse 1D Inversion of Sounding Data

Parametric 1D Inversion of Sounding Data

Parametric 1D Inversion of Sounding Data

2.5D DC Resistivity Least-Squares Inversion

2.5D DC Resistivity Least-Squares Inversion

2.5D DC Resistivity Inversion with Sparse Norms

2.5D DC Resistivity Inversion with Sparse Norms

3D Least-Squares Inversion of DC Resistivity Data

3D Least-Squares Inversion of DC Resistivity Data

Sparse Norm Inversion for Total Magnetic Intensity Data on a Tensor Mesh

Sparse Norm Inversion for Total Magnetic Intensity Data on a Tensor Mesh

Linear Least-Squares Inversion

Linear Least-Squares Inversion

Sparse Inversion with Iteratively Re-Weighted Least-Squares

Sparse Inversion with Iteratively Re-Weighted Least-Squares

Sparse Norm Inversion of 2D Seismic Tomography Data

Sparse Norm Inversion of 2D Seismic Tomography Data

Joint PGI of Gravity + Magnetic on an Octree mesh using full petrophysical information

Joint PGI of Gravity + Magnetic on an Octree mesh using full petrophysical information

Joint PGI of Gravity + Magnetic on an Octree mesh without petrophysical information

Joint PGI of Gravity + Magnetic on an Octree mesh without petrophysical information

Cross-gradient Joint Inversion of Gravity and Magnetic Anomaly Data

Cross-gradient Joint Inversion of Gravity and Magnetic Anomaly Data