SimPEG.maps.ParametricEllipsoid.deriv#

ParametricEllipsoid.deriv(m)[source]#

Derivative of the mapping with respect to the input parameters.

Let \(\mathbf{m} = [\sigma_0, \;\sigma_1,\; x_b, \; dx, (\; y_b, \; dy, \; z_b , dz)]\) be the set of model parameters the defines a block/ellipsoid within a wholespace. The mapping \(\mathbf{u}(\mathbf{m})\) from the parameterized model to all active cells is given by:

The derivative of the mapping \(\mathbf{u}(\mathbf{m})\) with respect to the model parameters is a numpy.ndarray of shape (nAct, nP) given by:

\[\frac{\partial \mathbf{u}}{\partial \mathbf{m}} = \Bigg [ \frac{\partial \mathbf{u}}{\partial \sigma_0} \;\; \frac{\partial \mathbf{u}}{\partial \sigma_1} \;\; \frac{\partial \mathbf{u}}{\partial x_b} \;\; \frac{\partial \mathbf{u}}{\partial dx} \;\; \frac{\partial \mathbf{u}}{\partial y_b} \;\; \frac{\partial \mathbf{u}}{\partial dy} \;\; \frac{\partial \mathbf{u}}{\partial z_b} \;\; \frac{\partial \mathbf{u}}{\partial dz} \Bigg ) \Bigg ]\]

Parameters:

m(nP) numpy.ndarray: A vector representing a set of model parameters
v(nP) numpy.ndarray: If not None, the method returns the derivative times the vector v

Returns:

scipy.sparse.csr_matrix: Derivative of the mapping with respect to the model parameters. If the input argument v is not None, the method returns the derivative times the vector v.