# MeepMeep: fast orbit calculations for exoplanet modelling
# Copyright (C) 2022-2026 Hannu Parviainen
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
"""Single-expansion-point 3D position evaluators with orbital-parameter derivatives."""
from numba import njit, prange, types
from numba.extending import overload
from numpy import floor, zeros, ndarray
from numpy.typing import NDArray
from ._common import _is_1d_array
@njit(fastmath=True, inline='always')
def _pos_cd_w(time, c, dc, dpx, dpy, dpz):
"""Write-into kernel shared by the scalar and vector evaluators.
Writes the seven-parameter gradients into the caller-provided ``(7,)``
buffers ``dpx``, ``dpy``, and ``dpz`` and returns the position values.
The hot vector loops (here and in ``orbit3dd``) pass preallocated
output rows or reusable scratch buffers here instead of allocating per
sample.
"""
px = c[0, 0] + time * (c[0, 1] + time * (c[0, 2] + time * (c[0, 3] + time * c[0, 4])))
py = c[1, 0] + time * (c[1, 1] + time * (c[1, 2] + time * (c[1, 3] + time * c[1, 4])))
pz = c[2, 0] + time * (c[2, 1] + time * (c[2, 2] + time * (c[2, 3] + time * c[2, 4])))
for k in range(7):
dpx[k] = dc[k, 0, 0] + time * (dc[k, 0, 1] + time * (dc[k, 0, 2] + time * (dc[k, 0, 3] + time * dc[k, 0, 4])))
dpy[k] = dc[k, 1, 0] + time * (dc[k, 1, 1] + time * (dc[k, 1, 2] + time * (dc[k, 1, 3] + time * dc[k, 1, 4])))
dpz[k] = dc[k, 2, 0] + time * (dc[k, 2, 1] + time * (dc[k, 2, 2] + time * (dc[k, 2, 3] + time * dc[k, 2, 4])))
return px, py, pz
@njit(fastmath=True)
def _pos_cd_s(time, c, dc):
"""Scalar kernel for :func:`pos_cd`. See that function for documentation."""
dpx = zeros(7)
dpy = zeros(7)
dpz = zeros(7)
px, py, pz = _pos_cd_w(time, c, dc, dpx, dpy, dpz)
return px, py, pz, dpx, dpy, dpz
def _pos_cd_v_body(time, c, dc):
"""Vector-kernel body for :func:`pos_cd`; see that function for documentation.
Compiled twice: ``pos_cd_v`` is the serial kernel (``prange`` compiles
as a plain ``range`` without ``parallel=True``) and ``pos_cd_vp`` the
parallel twin. The loop writes only into per-sample output elements,
so no per-thread scratch is needed.
"""
n = time.size
px = zeros(n)
py = zeros(n)
pz = zeros(n)
dpx = zeros((n, 7))
dpy = zeros((n, 7))
dpz = zeros((n, 7))
for j in prange(n):
px[j], py[j], pz[j] = _pos_cd_w(time[j], c, dc, dpx[j], dpy[j], dpz[j])
return px, py, pz, dpx, dpy, dpz
pos_cd_v = njit(fastmath=True)(_pos_cd_v_body)
pos_cd_vp = njit(fastmath=True, parallel=True)(_pos_cd_v_body)
[docs]
def pos_cd(time: float | NDArray, c: NDArray, dc: NDArray):
"""
Evaluate the (x, y, z) position and its orbital-parameter derivatives at an expansion-point-centered time.
Centered companion to `position.pos_c` that additionally returns
the partial derivatives of the sky-frame position with respect to
each of the seven orbital parameters. Both the position polynomials
and the eighteen derivative polynomials are evaluated using Horner's
scheme on the same centered time `time`.
Accepts a scalar time or a 1-D array of times and dispatches to the
appropriate kernel at compile time (inside ``@njit``) or at call time
(pure Python), mirroring the value-only `position.pos_c`.
Parameters
----------
time : float or ndarray
Time(s) relative to the Taylor series expansion point.
c : NDArray
A (3, 5) coefficient matrix produced by `solve3d`. Rows index
the spatial dimensions (x, y, z) and columns the Taylor order
from position through snap (pre-scaled by the factorial of the
order).
dc : NDArray
A (7, 3, 5) tensor of parameter-derivative coefficients produced
by `solve3d_d`. The leading axis enumerates the seven Keplerian
parameters in the canonical order `(tc, p, a, i, e, w, lan)`; the
remaining axes mirror the layout of `c`.
Returns
-------
px : float or ndarray
Sky-plane x position in units of stellar radii. Shape (N,) for an
array `time`.
py : float or ndarray
Sky-plane y position in units of stellar radii. Shape (N,) for an
array `time`.
pz : float or ndarray
Line-of-sight z position in units of stellar radii. Positive
values point toward the observer. Shape (N,) for an array `time`.
dpx : NDArray
Partial derivatives of `px` with respect to `(tc, p, a, i, e, w, lan)`.
Shape (7,) for a scalar `time`, (N, 7) for an array `time`.
dpy : NDArray
Partial derivatives of `py` with respect to the same seven parameters.
Shape (7,) for a scalar `time`, (N, 7) for an array `time`.
dpz : NDArray
Partial derivatives of `pz` with respect to the same seven parameters.
Shape (7,) for a scalar `time`, (N, 7) for an array `time`.
"""
if isinstance(time, ndarray):
return pos_cd_v(time, c, dc)
return _pos_cd_s(time, c, dc)
@overload(pos_cd, jit_options={'fastmath': True})
def _pos_cd_overload(time, c, dc):
if _is_1d_array(time):
def impl(time, c, dc):
return pos_cd_v(time, c, dc)
return impl
if isinstance(time, types.Float):
def impl(time, c, dc):
return _pos_cd_s(time, c, dc)
return impl
return None
@njit(fastmath=True)
def _pos_d_s(time, tc, p, c, dc, te):
"""Scalar kernel for :func:`pos_d`. See that function for documentation."""
epoch = floor((time - tc - te + 0.5 * p) / p)
return _pos_cd_s(time - (tc + te + epoch * p), c, dc)
def _pos_d_v_body(time, tc, p, c, dc, te):
"""Vector-kernel body for :func:`pos_d`; see that function for documentation.
Compiled twice: ``pos_d_v`` is the serial kernel (``prange`` compiles
as a plain ``range`` without ``parallel=True``) and ``pos_d_vp`` the
parallel twin. The loop writes only into per-sample output elements,
so no per-thread scratch is needed.
"""
n = time.size
px = zeros(n)
py = zeros(n)
pz = zeros(n)
dpx = zeros((n, 7))
dpy = zeros((n, 7))
dpz = zeros((n, 7))
for j in prange(n):
epoch = floor((time[j] - tc - te + 0.5 * p) / p)
px[j], py[j], pz[j] = _pos_cd_w(time[j] - (tc + te + epoch * p), c, dc, dpx[j], dpy[j], dpz[j])
return px, py, pz, dpx, dpy, dpz
pos_d_v = njit(fastmath=True)(_pos_d_v_body)
pos_d_vp = njit(fastmath=True, parallel=True)(_pos_d_v_body)
[docs]
def pos_d(time: float | NDArray, tc: float, p: float, c: NDArray, dc: NDArray, te: float = 0.0):
"""
Evaluate the (x, y, z) position and its orbital-parameter derivatives at an absolute time.
Direct counterpart of `pos_cd`: accepts an absolute observation time
`time`, folds it back into a single orbital epoch around the
expansion point, and delegates the polynomial evaluation to
`pos_cd`.
Accepts a scalar time or a 1-D array of times and dispatches to the
appropriate kernel at compile time (inside ``@njit``) or at call time
(pure Python), mirroring the value-only `position.pos`.
Parameters
----------
time : float or ndarray
Absolute observation time(s) in the same units as `tc` and `p`.
tc : float
Transit-centre time (time of inferior conjunction), on the same
time axis as `time`.
p : float
Orbital period, used for epoch folding.
c : NDArray
A (3, 5) Taylor coefficient matrix produced by `solve3d`.
dc : NDArray
A (7, 3, 5) parameter-derivative tensor produced by `solve3d_d`,
with the leading axis ordered as `(tc, p, a, i, e, w, lan)`.
te : float, optional
Expansion-point offset from the transit centre [days] - the same value that
was passed to `solve3d_d`. Defaults to 0.0, the expansion point at the
transit centre.
Returns
-------
px : float or ndarray
Sky-plane x position in units of stellar radii. Shape (N,) for an
array `time`.
py : float or ndarray
Sky-plane y position in units of stellar radii. Shape (N,) for an
array `time`.
pz : float or ndarray
Line-of-sight z position in units of stellar radii. Positive
values point toward the observer. Shape (N,) for an array `time`.
dpx : NDArray
Partial derivatives of `px` w.r.t. `(tc, p, a, i, e, w, lan)`.
Shape (7,) for a scalar `time`, (N, 7) for an array `time`.
dpy : NDArray
Partial derivatives of `py` w.r.t. `(tc, p, a, i, e, w, lan)`.
Shape (7,) for a scalar `time`, (N, 7) for an array `time`.
dpz : NDArray
Partial derivatives of `pz` w.r.t. `(tc, p, a, i, e, w, lan)`.
Shape (7,) for a scalar `time`, (N, 7) for an array `time`.
"""
if isinstance(time, ndarray):
return pos_d_v(time, tc, p, c, dc, te)
return _pos_d_s(time, tc, p, c, dc, te)
@overload(pos_d, jit_options={'fastmath': True})
def _pos_d_overload(time, tc, p, c, dc, te=0.0):
if _is_1d_array(time):
def impl(time, tc, p, c, dc, te=0.0):
return pos_d_v(time, tc, p, c, dc, te)
return impl
if isinstance(time, types.Float):
def impl(time, tc, p, c, dc, te=0.0):
return _pos_d_s(time, tc, p, c, dc, te)
return impl
return None