doiSSKrSSKJr SSKJrJr SSKJrJ r SSK J r J r /SQr \R"S5rSS jrSS jrSS jr\ "S S 9SSj5rSSS.Sjjrg)N)warn)rfftirfft)loggammapoch)array_namespacexp_capabilities)fhtifht fhtoffsetc v[U5nURU5nURSnUS:wa=US- S- nURXeRS9nXR U*X- -U-5-nUR[ XaX#US95n [X US9n US:wa XR U*WW- U-U--5-n U $)Nrrrdtype)offsetbiasxpr asarrayshapearangefloat64expfhtcoeff_fhtq) adlnmurrrnj_cjuAs U/var/www/html/land-ocr/venv/lib/python3.13/site-packages/scipy/fft/_fftlog_backend.pyr r s  B 1 A  A qysAg IIazzI * uags*+ + 8ABDABA arA qy VVTEAGS=612 33 Hc x[U5nURU5nURSnUS:wa?US- S- nURXeRS9nXR XHU- U-U--5-nUR[ XaX#USS95n [X SUS9n US:waXR U*WW- -U-5-n U $) NrrrrrT)rrinverse)r*rr) r&r r!rrrr"r#r$r%rs r'r r *s  B 1 A  A qysAg IIazzI * t#gs]V345 5 8ABD$OPA aDR(A qy VVTE1s7OC' (( Hr(ctX4pvUS-U-S- nUS-U- S- n [R"S[RUS--X-- US-S-5n [R"US-S-[S9n [R"US-S-[S9n XR SS&XR SS&[XS9 XR SS&[XS9 U S[U- --n U =R U R -slU =R [U-- slU =R U R - slU =R U - sl[R"XS9 US-S:XaSU R S'[R"U S5(dSU-[XU - 5-U S'[R"U S5(a.U(d'[SS S 9 [R"U 5n SU S'U $U SS:Xa:U(a3[S S S 9 [R"U 5n [RU S'U $) z:Compute the coefficient array for a fast Hankel transform.rrrrN)outrz.singular transform; consider changing the bias) stacklevelz6singular inverse transform; consider changing the bias)nplinspacepiemptycompleximagrealrLN_2risfiniter isinfrcopyinf) r"r r!rrr*lnkrqrxmyr%vs r'rrFs! Q$q&!B Q$q&!B Aruuad|QU+QT!V4A Aaw'A Aaw'AFF1IFF1I QFF1I QD4KAFFaffFFFd1fFFFaffFFFaKFFF1 1uzr  ;;qt  !td2"uo%!  xx!~~g =!L GGAJ! H 1w ERST GGAJvv! Hr(T) out_of_scopecLX#pTUS-U-S- nUS-U- S- n[RSU-- n[USU--5n [USU--5n [U- U- U RU R-[R- -n XK[R "U 5- U--$)a^Return optimal offset for a fast Hankel transform. Returns an offset close to `initial` that fulfils the low-ringing condition of [1]_ for the fast Hankel transform `fht` with logarithmic spacing `dln`, order `mu` and bias `bias`. Parameters ---------- dln : float Uniform logarithmic spacing of the transform. mu : float Order of the Hankel transform, any positive or negative real number. initial : float, optional Initial value for the offset. Returns the closest value that fulfils the low-ringing condition. bias : float, optional Exponent of power law bias, any positive or negative real number. Returns ------- offset : float Optimal offset of the uniform logarithmic spacing of the transform that fulfils a low-ringing condition. Examples -------- >>> from scipy.fft import fhtoffset >>> dln = 0.1 >>> mu = 2.0 >>> initial = 0.5 >>> bias = 0.0 >>> offset = fhtoffset(dln, mu, initial, bias) >>> offset 0.5454581477676637 See Also -------- fht : Definition of the fast Hankel transform. References ---------- .. [1] Hamilton A. J. S., 2000, MNRAS, 312, 257 (astro-ph/9905191) rry?)r/r1rr6r4round) r r!initialrr;r<rr=r>zpzmargs r'rrys^! Q$q&!B Q$q&!B qu A "r!t) B "r!t) B $; rww0"%%7 7C #&+ ++r(rcUc[nURSn[USS9nU(dXQ-nOXSRU5-n[ XTSS9nUR USS9nU$)zMCompute the biased fast Hankel transform. This is the basic FFTLog routine. r)axis)r/rrconjrflip)rr%r*rr"r&s r'rrsi  z   A QRA   WWQZ aA A Hr()rK)rKrKF)F)numpyr/warningsr_basicrrspecialrr scipy._lib._array_apir r __all__logr6r r rrrr(r'rTs^$B & vvay 8 80 fd#6,$6,r T r(