ftjddlZddlmZddlmZmZddlmZm Z ddl m Z m Z gdZ ejdZdd Zdd Zdd Ze dddZddddZdS)N)warn)rfftirfft)loggammapoch)array_namespacexp_capabilities)fhtifht fhtoffsetc t|}||}|jd}|dkrF|dz dz }|||j}||| ||z z|zz}|t |||||} t|| |} |dkr%| || ||z |z|zzz} | S)Nrrrdtype)offsetbiasxpr asarrayshapearangefloat64expfhtcoeff_fhtq) adlnmurrrnj_cjuAs W/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/scipy/fft/_fftlog_backend.pyr r s   B 1 A  A qyysAg IIarzI * * ua#gs*++ + 8AsBvDAAABBA arA qyy RVVTEAGS=612 3 33 Hc t|}||}|jd}|dkrH|dz dz }|||j}|||||z |z|zzz}|t |||||d} t|| d|} |dkr"| || ||z z|zz} | S) NrrrrrT)rrinverse)r+rr) r'r!r"rrrr#r$r%r&r s r(r r *s   B 1 A  A qyysAg IIarzI * * ta#gs]V3455 5 8AsBvD$OOOPPA aDR(((A qyy RVVTE1s7OC' ( (( Hr)FcB||}}|dz|zdz }|dz|z dz } tjdtj|dzz||zz |dzdz} tj|dzdzt} tj|dzdzt} | | jdd<| | jdd<t| | || jdd<t| | | dt|z zz} | xj| jzc_| xjt|zz c_| xj| jz c_| xj| z c_tj | | |dzdkr d| jd<tj | dsd|zt| || z z| d<tj | dr-|s+tdd tj| } d| d<nB| ddkr6|r4td d tj| } tj| d<| S) 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(rrFs4d!D Q$q&!B Q$q&!B Aruad|QsU+QT!V44A Aaw'''A Aaw'''AAF111IAF111I QAAF111I QAD4KAFFafFFFFd1fFFFFafFFFFaKFFF1! 1uzzr  ;qt  &!td2r"uoo%!  x!~~ g  =!LLLL GAJJ! 1w ERSTTTT GAJJv! Hr)T) out_of_scopec<||}}|dz|zdz }|dz|z dz }tjd|zz }t|d|zz} t|d|zz} t|z |z | j| jztjz z} || tj| z |zzS)aReturn 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?)r0r2rr7r5round) r!r"initialrr<r=rr>r?zpzmargs r(rrys^t!D Q$q&!B Q$q&!B qu A "r!t)  B "r!t)  B $; rw0"%7 7C 3#&+ ++r)rc|t}|jd}t|d}|s||z}n|||z}t ||d}||d}|S)zUCompute the biased fast Hankel transform. This is the basic FFTLog routine. Nr)axis)r0rrconjrflip)r r&r+rr#r's r(rrs  z   A QRA  Q RWWQZZ aA A Hr))rr)rrF)F)numpyr0warningsr_basicrrspecialrr scipy._lib._array_apir r __all__logr7r r rrrr)r(rTs$$$$$$$$BBBBBBBB & & &rvayy    8    80 0 0 0 fd###6,6,6,$#6,r T       r)