simpeg.maps.Weighting.inverse#

Weighting.inverse(D)[source]#

Apply the inverse of the weighting mapping to an array.

For the weighting mapping $\mathbf{u}(\mathbf{m})$, the inverse mapping on a variable $\mathbf{x}$ is performed by multplying each element by the reciprocal of its corresponding weighting value, i.e.:

$$\mathbf{m}={\mathbf{u}}^{-1}(\mathbf{x})={\mathbf{w}}^{-1}\odot \mathbf{x}$$

where $\odot$ is the Hadamard product. The inverse mapping may also be defined using a linear operator as follows:

$$\mathbf{m}={\mathbf{u}}^{-1}(\mathbf{x})={\mathbf{P}}^{\mathbf{-}\mathbf{1}}\mathbf{m}\text{where}\mathbf{P}=diag(\mathbf{w})$$

Parameters:

Dnumpy.ndarray

A set of input values

Returns:

numpy.ndarray

A numpy.ndarray containing result of applying the inverse mapping to the elements in D; which in this case is simply dividing each element by its corresponding weight.