simpeg.maps.SphericalSystem.inverse#

SphericalSystem.inverse(u)[source]#

Maps vectors in Cartesian coordinates to spherical coordinates.

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

$$\begin{array}{r}\mathbf{u}=\left[\begin{array}{c}\mathbf{x}\\ \mathbf{y}\\ \mathbf{z}\end{array}\right]\end{array}$$

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

$$\begin{array}{r}\mathbf{m}(\mathbf{u})=\left[\begin{array}{c}\mathbf{a}\\ \mathbf{t}\\ \mathbf{p}\end{array}\right]\end{array}$$

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 .