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:
- nP
int
Number of model parameters.
- mapping
simpeg.mapping.BaseMap
A SimPEG mapping object that maps from the model space to the quantity evaluated in the objective function.
- W
None
orscipy.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.- counter
None
orsimpeg.utils.Counter
Assign a SimPEG
Counter
object to store iterations and run-times.- debugbool
Print debugging information.
- nP
Attributes
Weighting matrix applied in the objective function.
Mapping from the model to the quantity evaluated in the object function.
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
#
PF: Gravity: Tiled Inversion Linear
Magnetic inversion on a TreeMesh with remanence
Magnetic inversion on a TreeMesh
Magnetic Amplitude inversion on a TreeMesh
3D DC inversion of Dipole Dipole array
Parametric DC inversion with Dipole Dipole array
2D inversion of Loop-Loop EM Data
EM: TDEM: 1D: Inversion with VTEM waveform
Method of Equivalent Sources for Removing VRM Responses
Petrophysically guided inversion (PGI): Linear example
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 Bookpurnong Inversion
Heagy et al., 2017 1D FDEM and TDEM inversions
PF: Gravity: Laguna del Maule Bouguer Gravity
Straight Ray with Volume Data Misfit Term
1D Inversion of Time-Domain Data for a Single Sounding
2.5D DC Resistivity and IP Least-Squares Inversion
3D Least-Squares Inversion of DC and IP Data
1D Inversion of for a Single Sounding
Least-Squares Inversion of Gravity Anomaly Data
Sparse Norm Inversion of Gravity Anomaly Data
Compare weighting strategy with Inversion of surface Gravity Anomaly Data
Least-Squares 1D Inversion of Sounding Data
Sparse 1D Inversion of Sounding Data
Parametric 1D Inversion of Sounding Data
2.5D DC Resistivity Least-Squares Inversion
2.5D DC Resistivity Inversion with Sparse Norms
3D Least-Squares Inversion of DC Resistivity Data
Sparse Norm Inversion for Total Magnetic Intensity Data on a Tensor Mesh
Linear Least-Squares Inversion
Sparse Inversion with Iteratively Re-Weighted Least-Squares
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 without petrophysical information
Cross-gradient Joint Inversion of Gravity and Magnetic Anomaly Data