meepmeep.numba2d.pos_cd

meepmeep.numba2d.pos_cd(time: float | ndarray[tuple[Any, ...], dtype[_ScalarT]], c: ndarray[tuple[Any, ...], dtype[_ScalarT]], dc: ndarray[tuple[Any, ...], dtype[_ScalarT]])

Evaluate the (x, y) 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-plane position with respect to each of the seven orbital parameters. Both the position polynomial and the seven 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:

timefloat or ndarray

Time(s) relative to the Taylor series expansion point.

cNDArray

A (2, 5) coefficient matrix produced by solve2d. Rows index the spatial dimensions (x, y) and columns the Taylor order from position through snap (pre-scaled by the factorial of the order).

dcNDArray

A (7, 2, 5) tensor of parameter-derivative coefficients produced by solve2d_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:

pxfloat or ndarray

Sky-plane x position in units of stellar radii. Shape (N,) for an array time.

pyfloat or ndarray

Sky-plane y position in units of stellar radii. Shape (N,) for an array time.

dpxNDArray

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.

dpyNDArray

Partial derivatives of py with respect to the same seven parameters. Shape (7,) for a scalar time, (N, 7) for an array time.