make_cheb_matrix_only_x

rubin_sim.moving_objects.make_cheb_matrix_only_x(n_points, n_poly)

Compute C1^(-1)C2 using Newhall89 approach without dx/dt

Compute xMultiplier using only the equality constraint of the x-values at the endpoints. To be used when first derivatives are not available. If chebyshev approximations are strung together piecewise only the x-values and not the first derivatives will be continuous at the boundaries. Multiplying this matrix by the x-values to be fit produces the chebyshev coefficients. This function need only be called once for a given polynomial degree and number of points. See Newhall, X. X. 1989, Celestial Mechanics, 45, p. 305-310.

Parameters:

n_pointsint

Number of point to be fits. Must be greater than 2.

n_polyint

Number of polynomial terms. Polynomial degree + 1

Returns:

c1c2: np.ndarray

xMultiplier, Even rows of C1^(-1)C2 w/ shape (n_points+1)x(n_poly) to be multiplied by x values