_-Ph dZddlZdZdZdS)z.Compute coefficients for polynomial smoothers.Nc6||ks|dkrtd|d|dtjtjtj|dzz|z }d||z zd|zz|z}tj|}|tj|dz}|S)aChebyshev polynomial coefficients for the interval [a,b]. Parameters ---------- a,b : float The left and right endpoints of the interval. degree : int Degree of desired Chebyshev polynomial Returns ------- Coefficients of the Chebyshev polynomial C(t) with minimum magnitude on the interval [a,b] such that C(0) = 1.0. The coefficients are returned in descending order. Notes ----- a,b typically represent the interval of the spectrum for some matrix that you wish to damp with a Chebyshev smoother. Examples -------- >>> from pyamg.relaxation.chebyshev import chebyshev_polynomial_coefficients >>> print(chebyshev_polynomial_coefficients(1.0,2.0, 3)) [-0.32323232 1.45454545 -2.12121212 1. ] rzinvalid interval [,]g?) ValueErrornpcospiarangepolypolyval)abdegree std_roots scaled_roots scaled_polys Z/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/pyamg/relaxation/chebyshev.py!chebyshev_polynomial_coefficientsrs8 Avva6a66!666777ru & 1 1C 786ABBI!A#;!i-014L',''K2:k1---K c |dz dtjdtjztj|ddzzd|zdzz z z}d|z }tj|ddd}|d|zdzdzz }tj||}tjd |z |zdgf}tj||}|dd }||fS) aDetermine the coefficients for a MLS polynomial smoother. Parameters ---------- rho : float Spectral radius of the matrix in question degree : int Degree of polynomial coefficients to generate Returns ------- Tuple of arrays (coeffs,roots) containing the coefficients for the (symmetric) polynomial smoother and the roots of polynomial prolongation smoother. The coefficients of the polynomial are in descending order References ---------- .. [1] Parallel multigrid smoothing: polynomial versus Gauss--Seidel M. F. Adams, M. Brezina, J. J. Hu, and R. S. Tuminaro J. Comp. Phys., 188 (2003), pp. 593--610 Examples -------- >>> from pyamg.relaxation.chebyshev import mls_polynomial_coefficients >>> mls = mls_polynomial_coefficients(2.0, 2) >>> print(mls[0]) # coefficients [ 6.4 -48. 144. -220. 180. -75.8 14.5] >>> print(mls[1]) # roots [1.4472136 0.5527864] g@g?float64)dtyperNg)rr r r r polymulhstack)rhorrootsSSSA_maxS_hatcoeffss rmls_polynomial_coefficientsr$4sJ G rvagryyAAAAEFF SVWXX X ZE IE tttACJsNQ&'G Jq!  E IW e+aS1 2 2EZq ! !FSbSk\F E?r)__doc__numpyrrr$rrr(s@44+++\66666r