a j:@sddlZddlmZddlmZmZddlmZm Z ddl m Z m Z gdZ edZdd d Zdd d ZdddZdddZdddddZdS)N)warn)rfftirfft)loggammapoch)array_namespacecopy)fhtifht fhtoffsetc Cst|}|jd}|dkrR|dd}|j||jd}||| |||}|t|||||d} t|| |d} |dkr| || ||||9} | S)NrrrZdtype)offsetbiasxpr shapeZarangeZfloat64expZasarrayfhtcoeff_fhtq) adlnmurrrnj_cjuAr"?E:\soccer\ml_env\Lib\site-packages\scipy/fft/_fftlog_backend.pyr s   r c Cst|}|jd}|dkrT|dd}|j||jd}|||||||}|t|||||dd} t|| d|d} |dkr| || |||} | S) NrrrrrT)rrinverse)r$rr) r!rrrrrrrrr rr"r"r#r )s  r Fc Cs||}}|d|d}|d|d} tdtj|d|||dd} tj|ddtd} tj|ddtd} | | jdd<| | jdd<t| | d|| jdd<t| | d| dt|9} | j| j8_| jt|7_| j| j7_| j| 7_tj | | dd| jd<t | dsRd|t | || | d<t | dr|st dd d t| } d| d<n2| ddkr|rt d d d t| } tj| d<| S) z:Compute the coefficient array for a fast Hankel transform.rrrrN)outrz.singular transform; consider changing the bias) stacklevelz6singular inverse transform; consider changing the bias)npZlinspacepiemptycompleximagrealrLN_2risfiniterisinfrr inf) rrrrrr$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)rr.r,round) rrinitialrr2r3rr4r5ZzpZzmargr"r"r#r vs. r rcCs^|dur t}|jd}t|dd}|s0||9}n|||}t||dd}|j|dd}|S)zUCompute the biased fast Hankel transform. This is the basic FFTLog routine. Nr)Zaxis)r(rrZconjrflip)rr r$rrr!r"r"r#rs   r)rr)rr)rrF)rr)F)numpyr(warningsrZ_basicrrZspecialrrZscipy._lib._array_apir r __all__logr.r r rr rr"r"r"r#s     2 9