# SimPEG.maps.SphericalSystem.inverse#

SphericalSystem.inverse(u)[source]#

Maps vectors in Cartesian coordinates to spherical coordinates.

Let $$\mathbf{v_x}$$, $$\mathbf{v_y}$$ and $$\mathbf{v_z}$$ store the x, y and z components of a set of vectors in Cartesian coordinates such that:

$\begin{split}\mathbf{u} = \begin{bmatrix} \mathbf{x} \\ \mathbf{y} \\ \mathbf{z} \end{bmatrix}\end{split}$

The inverse mapping recovers the vectors in spherical coordinates, i.e.:

$\begin{split}\mathbf{m}(\mathbf{u}) = \begin{bmatrix} \mathbf{a} \\ \mathbf{t} \\ \mathbf{p} \end{bmatrix}\end{split}$

where $$\mathbf{a}$$ are the amplitudes, $$\mathbf{t}$$ are the azimuthal angles and $$\mathbf{p}$$ are the radial angles.

Parameters
unumpy.ndarray

The x, y and z components of a set of vectors in Cartesian coordinates. If the mapping is defined for a mesh, the numpy.ndarray has length 3*mesh.nC .

Returns
numpy.ndarray

The amplitudes ($$\mathbf{a}$$), azimuthal angles ($$\mathbf{t}$$) and radial angles ($$\mathbf{p}$$) for the set of vectors in spherical coordinates. If the mapping is defined for a mesh, the numpy.ndarray has length 3*mesh.nC .