chebfit¶
- rubin_sim.moving_objects.chebfit(t, x, dxdt=None, x_multiplier=None, dx_multiplier=None, n_poly=7)¶
Fit Chebyshev polynomial constrained at endpoints using Newhall89 approach.
Return Chebyshev coefficients and statistics from fit to array of positions (x) and optional velocities (dx/dt). If both the function and its derivative are specified, then the value and derivative of the interpolating polynomial at the endpoints will be exactly equal to the input endpoint values. Many approximations may be piecewise strung together and the function value and its first derivative will be continuous across boundaries. If derivatives are not provided, only the function value will be continuous across boundaries.
If x_multiplier and dx_multiplier are not provided or are an inappropriate shape for t and x, they will be recomputed. See Newhall, X. X. 1989, Celestial Mechanics, 45, p. 305-310 for details.
- Parameters:
- t
np.ndarray Array of regularly sampled independent variable (e.g. time)
- x
np.ndarray Array of regularly sampled dependent variable (e.g. declination)
- dxdt`np.ndarray’, optional
Optionally, array of first derivatives of x with respect to t, at the same grid points. (e.g. sky velocity ddecl/dt)
- x_multiplier
np.ndarray, optional Optional 2D Matrix with rows of C1^(-1)C2 corresponding to x. Use make_cheb_matrix to compute
- dx_multiplier
np.ndarray, optional Optional 2D Matrix with rows of C1^(-1)C2 corresponding to dx/dt. Use make_cheb_matrix to compute
- n_poly
int, optional Number of polynomial terms. Degree + 1. Must be >=2 and <=2*n_points, when derivative information is specified, or <=n_points, when no derivative information is specified. Default = 7.
- t
- Returns: