pyoculus.utils.cyl_cart_transform.mat_cart2cyl

pyoculus.utils.cyl_cart_transform.mat_cart2cyl(mat: array, r: float, phi: float, z: float) → array

Transforms a matrix \(A\) from cartesian coordinates to cylindrical coordinates at \((r, \phi, z)\).

\[\begin{split}\begin{bmatrix} A^r_r & A^r_\phi & A^r_z \\ A^\phi_r & A^\phi_\phi & A^\phi_z \\ A^z_r & A^z_\phi & A^z_z \\ \end{bmatrix} = \begin{bmatrix} \partial_x r & \partial_y r & \partial_z r \\ \partial_x \phi & \partial_y \phi & \partial_z \phi \\ \partial_x z & \partial_y z & \partial_z z \\ \end{bmatrix} \begin{bmatrix} A^x_x & A^x_y & A^x_z \\ A^y_x & A^y_y & A^y_z \\ A^z_x & A^z_y & A^z_z \\ \end{bmatrix} \begin{bmatrix} \partial_r x & \partial_\phi x & \partial_z x \\ \partial_r y & \partial_\phi y & \partial_z y \\ \partial_r z & \partial_\phi z & \partial_z z \\ \end{bmatrix}.\end{split}\]

Parameters:

• mat (array) – The matrix \(A\) in cartesian coordinates.

• r (float) – The radial coordinate.

• phi (float) – The azimuthal coordinate.

• z (float) – The vertical coordinate.

Returns:

The matrix \(A\) in cylindrical coordinates.

Return type:

array