# SimPEG.maps.Projection#

class SimPEG.maps.Projection(nP, index, **kwargs)[source]#

Projection mapping.

Projection mapping can be used to project and/or rearange model parameters. For a set of model parameter $$\mathbf{m}$$, the mapping $$\mathbf{u}(\mathbf{m})$$ can be defined by a linear projection matrix $$\mathbf{P}$$ acting on the model, i.e.:

$\mathbf{u}(\mathbf{m}) = \mathbf{Pm}$

The number of model parameters the mapping acts on is defined by nP. Projection and/or rearrangement of the parameters is defined by index. Thus the dimensions of the mapping is (nInd, nP).

Parameters
nPint

Number of model parameters the mapping acts on

indexnumpy.ndarray of int

Indexes defining the projection from the model space

Examples

Here we define a mapping that rearranges and projects 2 model parameters to a vector space spanning 4 parameters.

>>> from SimPEG.maps import Projection
>>> import numpy as np

>>> nP = 2
>>> index = np.array([1, 0, 1, 0], dtype=int)
>>> mapping = Projection(nP, index)

>>> m = np.array([6, 8])
>>> mapping * m
array([8, 6, 8, 6])


Attributes

 shape Dimensions of the mapping.

Methods

 deriv(m[, v]) Derivative of the mapping with respect to the input parameters.

## Galleries and Tutorials using SimPEG.maps.Projection#

Magnetic inversion on a TreeMesh

Magnetic inversion on a TreeMesh

Petrophysically guided inversion: Joint linear example with nonlinear relationships

Petrophysically guided inversion: Joint linear example with nonlinear relationships

Heagy et al., 2017 Casing Example

Heagy et al., 2017 Casing Example

Tensor Meshes

Tensor Meshes

Cylindrical Meshes

Cylindrical Meshes

Tree Meshes

Tree Meshes

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

Parametric 1D Inversion of Sounding Data

Parametric 1D Inversion of Sounding Data

Cross-gradient Joint Inversion of Gravity and Magnetic Anomaly Data

Cross-gradient Joint Inversion of Gravity and Magnetic Anomaly Data