o 5Biu@sddlZddlmZddlmZmZddlmZm Z ddl m Z m Z gdZ edZdd d Zdd d ZdddZdddZdddddZdS)N)warn)rfftirfft)loggammapoch)array_namespacecopy)fhtifht fhtoffsetc Cst|}|jd}|dkr)|dd}|j||jd}||| |||}|t|||||d} t|| |d} |dkrP| || ||||9} | S)Nrrrdtype)offsetbiasxpr shapearangefloat64expasarrayfhtcoeff_fhtq) adlnmurrrnj_cjuAr&Y/var/www/html/Trade-python/venv/lib/python3.10/site-packages/scipy/fft/_fftlog_backend.pyr s   r c Cst|}|jd}|dkr*|dd}|j||jd}|||||||}|t|||||dd} t|| d|d} |dkrQ| || |||} | S) NrrrrrT)rrinverse)r(rr) r%rr rrrr!r"r#r$rr&r&r'r )s  r Fc Cs||}}|d|d}|d|d} tdtj|d|||dd} tj|ddtd} tj|ddtd} | | jdd<| | jdd<t| | d|| jdd<t| | d| dt|9} | j| j8_| jt|7_| j| j7_| j| 7_tj | | dd| jd<t | dsd|t | || | d<t | dr|st dd d t| } d| d<| S| ddkr|rt d d d t| } tj| d<| S) z:Compute the coefficient array for a fast Hankel transform.rrrrN)outrz.singular transform; consider changing the bias) stacklevelz6singular inverse transform; consider changing the bias)nplinspacepiemptycompleximagrealrLN_2risfiniterisinfrr inf) r!rr rrr(lnkrqrxmyr$vr&r&r'rDs< (      rc Cs||}}|d|d}|d|d}tjd|}t|d|} t|d|} t||| j| jtj} || t| |S)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?)r,r.rr3r1round) rr initialrr7r8rr9r:zpzmargr&r&r'r vs .r rcCs^|durt}|jd}t|dd}|s||9}n|||}t||dd}|j|dd}|S)zUCompute the biased fast Hankel transform. This is the basic FFTLog routine. Nr)axis)r,rrconjrflip)rr$r(rr!r%r&r&r'rs   r)rr)rrF)F)numpyr,warningsr_basicrrspecialrrscipy._lib._array_apir r __all__logr3r r rr rr&r&r&r's      29