Module coordinates 

Coordinate and vector-component transformations in orthonormal local frames.

Upstream: treams.special.car2cyl, car2sph, cyl2car, cyl2sph, sph2car, sph2cyl, car2pol, pol2car (point) and their v-prefixed vector twins such as vcar2sph (vector), from _coord.pyx. Spherical coordinates are (r, theta, phi) with the polar angle theta, cylindrical ones (rho, phi, z), as in treams.

Enums

Transform

Coordinate conversion; vector positions are expressed in the input system.

Functions

apply 🔒

The product of a real 3 x 3 matrix and a complex vector.

cartesian_from_cylindrical 🔒

Cartesian (x, y, z) of cylindrical (rho, phi, z).

cylindrical_from_cartesian 🔒

Cylindrical (rho, phi, z) of Cartesian (x, y, z).

cylindrical_from_spherical 🔒

Cylindrical (rho, phi, z) of spherical (r, theta, phi).

frame 🔒

Rotation of vector components into the output frame of transform, and its derivatives with respect to the (at most two) angles it depends on. Inverse transforms use the transposed matrices. Polar vectors use the first two rows/columns; no radial metric factors occur.

point

Transform a point. Polar conversions ignore and return zero in the third slot.

point_pullback

The gradient with respect to the input coordinates of point, given the gradient cotangent with respect to its output.

point_pushforward

The directional derivative of point along the input tangent.

radius 🔒

sqrt(a^2 + b^2): a fused multiply-add where the squares stay normal, hypot elsewhere.

spherical_from_cylindrical 🔒

Spherical (r, theta, phi) of cylindrical (rho, phi, z).

transpose 🔒

The transpose of a 3 x 3 matrix.

validate 🔒

Checks that every component is finite.

vector

Transform vector components at a point in the source coordinate system.

vector_pullback

The gradients with respect to the vector components and the position of vector, given the gradient cotangent with respect to its output components.

vector_pushforward

The directional derivative of vector along its components and position.