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:
\[\mathbf{m} = \mathbf{u}^{-1}(\mathbf{x}) = \mathbf{P^{-1} m} \;\;\;\;\; \textrm{where} \;\;\;\;\; \mathbf{P} = diag(\mathbf{w})\]- Parameters:
- D
numpy.ndarray A set of input values
- D
- Returns:
numpy.ndarrayA
numpy.ndarraycontaining result of applying the inverse mapping to the elements in D; which in this case is simply dividing each element by its corresponding weight.