simpeg.maps.ParametricCircleMap.deriv#

ParametricCircleMap.deriv(m, v=None)[source]#

Derivative of the mapping with respect to the input parameters.

Let m=[σ0,σ1,x0,y0,R] be the set of model parameters the defines a circle within a wholespace. The mapping :math:`mathbf{u}(mathbf{m})`from the parameterized model to all cells within a 2D mesh is given by:

u(m)=σ0+(σ1σ0)[12+π1arctan(a[(xcx0)2+(ycy0)2R])]

The derivative of the mapping with respect to the model parameters is a numpy.ndarray of shape (mesh.nC, 5) given by:

um=[uσ0[uσ1[ux0[uy0[uR]
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.