Function cart_to_sph_velocity

examples/pde/bhrt.cpp:211–237

* @brief Transform the velocity vectors from cartesian to spherical coordinates * * @param vel * @param pos * @return af::array */

 * @return af::array
 */
af::array cart_to_sph_velocity(const af::array& vel, const af::array& pos) {
    if (vel.dims() != pos.dims())
        throw make_error("Arrays must have the same dimensions");
    else if (pos.dims()[0] != 3)
        throw make_error("Arrays must have 3 principal coordintes");

    af::array x = pos(0, af::span);
    af::array y = pos(1, af::span);
    af::array z = pos(2, af::span);

    af::array r = af::sqrt(x * x + y * y + z * z);
    af::array o = af::acos(z / r);
    af::array p = af::atan2(y, x);

    af::array ux = vel(0, af::span);
    af::array uy = vel(1, af::span);
    af::array uz = vel(2, af::span);

    af::array ur = (ux * x + uy * y + uz * z) / r;
    af::array up = (uy * af::cos(p) - ux * af::sin(p)) / (r * af::sin(o));
    af::array uo =
        (af::cos(o) * (ux * af::cos(p) + uy * af::sin(p)) - uz * af::sin(o)) /
        r;
    af::array transformed_vel = af::join(0, ur, uo, up);

    return transformed_vel;
}

/**
 * @brief Transform the velocity vectors from cartesian to spherical coordinates