"""Pyccel kernels for the mapping and Jacobian matrix of :class:`struphy.geometry.domains.ShafranovShiftCylinder`."""
from numpy import cos, pi, sin
from pyccel.decorators import pure
[docs]
@pure
def shafranov_shift(
eta1: float,
eta2: float,
eta3: float,
rx: float,
ry: float,
lz: float,
de: float,
f_out: "float[:]",
):
r"""
Point-wise evaluation of
.. math::
F_x &= r_x\,\eta_1\cos(2\pi\,\eta_2)+(1-\eta_1^2)r_x\Delta\,,
F_y &= r_y\,\eta_1\sin(2\pi\,\eta_2)\,,
F_z &= L_z\,\eta_3\,.
Parameters
----------
eta1, eta2, eta3 : float
Logical coordinate in [0, 1].
rx, ry : float
Axes lengths.
lz : float
Length in third direction.
de : float
Shift factor, should be in [0, 0.1].
f_out : array[float]
Output: (x, y, z) = F(eta1, eta2, eta3).
"""
f_out[0] = (eta1 * rx) * cos(2 * pi * eta2) + (1 - eta1**2) * rx * de
f_out[1] = (eta1 * ry) * sin(2 * pi * eta2)
f_out[2] = eta3 * lz
[docs]
@pure
def shafranov_shift_df(
eta1: float,
eta2: float,
eta3: float,
rx: float,
ry: float,
lz: float,
de: float,
df_out: "float[:,:]",
):
"""Jacobian matrix for :meth:`struphy.geometry.domains.shafranov_shift_cylinder.shafranov_shift_cylinder_kernels.shafranov_shift`."""
df_out[0, 0] = rx * cos(2 * pi * eta2) - 2 * eta1 * rx * de
df_out[0, 1] = -2 * pi * (eta1 * rx) * sin(2 * pi * eta2)
df_out[0, 2] = 0.0
df_out[1, 0] = ry * sin(2 * pi * eta2)
df_out[1, 1] = 2 * pi * (eta1 * ry) * cos(2 * pi * eta2)
df_out[1, 2] = 0.0
df_out[2, 0] = 0.0
df_out[2, 1] = 0.0
df_out[2, 2] = lz
