# 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 2D planet sky-plane (x, y) position evaluators."""
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_c_s(time, c):
"""Scalar kernel for :func:`pos_c`. See that function for documentation."""
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])))
return px, py
def _pos_c_v_body(time, c):
"""Vector-kernel body for :func:`pos_c`; see that function for documentation.
Compiled twice: ``pos_c_v`` is the serial kernel (``prange`` compiles
as a plain ``range`` without ``parallel=True``) and ``pos_c_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)
for j in prange(n):
px[j], py[j] = _pos_c_s(time[j], c)
return px, py
pos_c_v = njit(fastmath=True)(_pos_c_v_body)
pos_c_vp = njit(fastmath=True, parallel=True)(_pos_c_v_body)
[docs]
def pos_c(time: float | NDArray, c: NDArray) -> tuple[float | NDArray, float | NDArray]:
"""
Evaluate the planet's sky-plane (x, y) position at an expansion-point-centered time.
This is the "centered" variant of `pos`: it assumes the caller has
already subtracted the expansion time `te` (and any epoch offset) so
that `time` is a small displacement around the expansion point. The polynomial is
evaluated using Horner's scheme.
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). The array path is an explicit loop over the scalar
kernel, which avoids the full-array temporaries that NumPy
broadcasting would allocate for every Horner step.
Parameters
----------
time : float or NDArray
Time relative to the Taylor series expansion point, i.e.
`t = tc - (te + epoch*p)`. Must lie within the expansion point's region of
validity for the truncation error to remain small.
c : NDArray
A (2, 5) coefficient matrix produced by `solve2d`. See `pos` for
the column ordering convention.
Returns
-------
px : float or NDArray
Sky-plane x position in units of stellar radii.
py : float or NDArray
Sky-plane y position in units of stellar radii.
Notes
-----
This is the fastest 2D position evaluator in the module since it skips
the epoch-folding arithmetic. Prefer it whenever the expansion-point index and
centered time are already known (e.g. inside multi-expansion-point dispatch loops).
"""
if isinstance(time, ndarray):
return pos_c_v(time, c)
return _pos_c_s(time, c)
@overload(pos_c, jit_options={'fastmath': True}, inline='always')
def _pos_c_overload(time, c):
if _is_1d_array(time):
def impl(time, c):
return pos_c_v(time, c)
return impl
if isinstance(time, types.Float):
def impl(time, c):
return _pos_c_s(time, c)
return impl
return None
@njit(fastmath=True, inline='always')
def _pos_s(time, tc, p, c, te):
"""Scalar kernel for :func:`pos`. See that function for documentation."""
epoch = floor((time - tc - te + 0.5 * p) / p)
return _pos_c_s(time - (tc + te + epoch * p), c)
def _pos_v_body(time, tc, p, c, te):
"""Vector-kernel body for :func:`pos`; see that function for documentation.
Compiled twice: ``pos_v`` is the serial kernel (``prange`` compiles
as a plain ``range`` without ``parallel=True``) and ``pos_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)
for j in prange(n):
epoch = floor((time[j] - tc - te + 0.5 * p) / p)
px[j], py[j] = _pos_c_s(time[j] - (tc + te + epoch * p), c)
return px, py
pos_v = njit(fastmath=True)(_pos_v_body)
pos_vp = njit(fastmath=True, parallel=True)(_pos_v_body)
[docs]
def pos(time: float | NDArray, tc: float, p: float, c: NDArray, te: float = 0.0):
"""
Evaluate the planet's sky-plane (x, y) position at an absolute time using a 2D Taylor expansion.
This is the "direct" variant of the 2D position evaluator: it accepts an
absolute observation time, folds it back into a single orbital epoch
around the expansion point `te`, and then evaluates the 5th-order Taylor
polynomial stored in `c` using Horner's scheme.
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).
Parameters
----------
time : float or NDArray
Absolute observation time(s) in the same units as `tc` and `p`
(typically days). Scalar or array inputs are both accepted; the
return type matches.
tc : float
Transit-centre time (time of inferior conjunction), on the same
time axis as `time`.
p : float
Orbital period, used to fold `time` into a single epoch around
the expansion point.
c : NDArray
A (2, 5) coefficient matrix produced by `solve2d`. Row 0 holds the
x-direction coefficients and row 1 the y-direction coefficients,
ordered as [position, velocity, acceleration/2, jerk/6, snap/24]
(i.e. already pre-scaled by the factorial of the Taylor order).
te : float, optional
Expansion-point offset from the transit centre [days] - the same value that
was passed to `solve2d`. Defaults to 0.0, the expansion point at the
transit centre.
Returns
-------
px : float or NDArray
Sky-plane x position(s) in units of stellar radii.
py : float or NDArray
Sky-plane y position(s) in units of stellar radii.
Notes
-----
Epoch folding uses `epoch = floor((time - tc - te + p/2) / p)`, which
centers the residual `t = time - (tc + te + epoch*p)` on the expansion point. This
keeps the polynomial argument small and preserves the accuracy of the
truncated Taylor series.
"""
if isinstance(time, ndarray):
return pos_v(time, tc, p, c, te)
return _pos_s(time, tc, p, c, te)
@overload(pos, jit_options={'fastmath': True}, inline='always')
def _pos_overload(time, tc, p, c, te=0.0):
if _is_1d_array(time):
def impl(time, tc, p, c, te=0.0):
return pos_v(time, tc, p, c, te)
return impl
if isinstance(time, types.Float):
def impl(time, tc, p, c, te=0.0):
return _pos_s(time, tc, p, c, te)
return impl
return None