simpeg.maps.ParametricBlock.deriv#

ParametricBlock.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:

$$\frac{\partial \mathbf{u}}{\partial \mathbf{m}}=[\frac{\partial \mathbf{u}}{\partial {\sigma }_0}\frac{\partial \mathbf{u}}{\partial {\sigma }_1}\frac{\partial \mathbf{u}}{\partial x_b}\frac{\partial \mathbf{u}}{\partial dx}\frac{\partial \mathbf{u}}{\partial y_b}\frac{\partial \mathbf{u}}{\partial dy}\frac{\partial \mathbf{u}}{\partial z_b}\frac{\partial \mathbf{u}}{\partial dz})]$$

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.