o ¢Äi¸ã@sŽddlZddlmZddlmZmZddlmZm Z ddl m Z gd¢Z e  d¡Zdd d „Zdd d „Zddd„Zddd„Zdddœdd„ZdS)éN)Úwarné)ÚrfftÚirffté)ÚloggammaÚpoch)Úarray_namespace)ÚfhtÚifhtÚ fhtoffsetçc Cs®t|ƒ}| |¡}|jd}|dkr.|dd}|j||jd}|| | |||¡}| t|||||d¡} t|| |d} |dkrU| | | ||||¡9} | S)Néÿÿÿÿrrr©Zdtype)ÚoffsetÚbias©Úxp©r ZasarrayÚshapeZarangeZfloat64ÚexpÚfhtcoeffÚ_fhtq) ÚaÚdlnÚmurrrÚnÚj_cÚjÚuÚA©r!úS/home/kim/smarthome/.venv/lib/python3.10/site-packages/scipy/fft/_fftlog_backend.pyr s    r c Cs°t|ƒ}| |¡}|jd}|dkr/|dd}|j||jd}|| |||||¡}| t|||||dd¡} t|| d|d} |dkrV| | | |||¡} | S) NrrrrrT)rrÚinverse)r#rr) r rrrrrrrrrrr!r!r"r *s   r Fc CsÄ||}}|d|d}|d|d} t dtj|d|||dd¡} tj|ddtd} tj|ddtd} | | jdd…<| | jdd…<t| | d|| jdd…<t| | d| dt|9} | j| j8_| jt|7_| j| j7_| j| 7_tj | | d|ddkršd| jd<t  | d¡s®d|t | || ƒ| d<t  | d¡rÈ|sÈt dd d t | ¡} d| d<| S| ddkrà|ràt d d d t | ¡} tj| d<| S) z:Compute the coefficient array for a fast Hankel transform.rrrrN)Úoutrz.singular transform; consider changing the biasé)Ú stacklevelz6singular inverse transform; consider changing the bias)ÚnpZlinspaceÚpiÚemptyÚcomplexÚimagÚrealrÚLN_2rÚisfiniterÚisinfrÚcopyÚinf) rrrrrr#ÚlnkrÚqrÚxmÚyrÚvr!r!r"rFs> (      ú   rc CsŒ||}}|d|d}|d|d}tjd|}t|d|ƒ} t|d|ƒ} t||| j| jtj} || t | ¡|S)aîReturn 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) rryð?)r'r(rr-r+Úround) rrÚinitialrr2r3rr4r5ZzpZzmÚargr!r!r"r ys .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)Zaxis)r'rrZconjrÚflip)rrr#rrr r!r!r"r²s   r)r r )r r F)F)Únumpyr'ÚwarningsrZ_basicrrZspecialrrZscipy._lib._array_apir Ú__all__Úlogr-r r rr rr!r!r!r"Ús       39