
    (ph                        S SK r S SKrS SKrS SKrS SKJrJrJr  S SK	J
r
  S SKJr  S SKJrJrJr  \\R"                  R%                  S5      /r\R"                  R(                  rS r\R"                  R-                  SS	S
/5      \R"                  R-                  S/ SQ5      \R"                  R-                  S/ SQ5      \R"                  R-                  SSS/5      S 5       5       5       5       r\R"                  R0                  S 5       r\R"                  R-                  SSS/5      S 5       r\" S	SS9\R"                  R-                  S\\/5      S 5       5       r\R"                  R-                  SSS/5      S 5       rg)    N)fhtifht	fhtoffset)poch)array_api_compatible)xp_assert_closexp_assert_lessarray_namespaceskip_xp_backendsc                    S n[         R                  " SSS5      n[         R                  " US   US   -  5      nSnSnSnU R                  U" X$5      5      n[	        XsXEUS	9n/ S
Qn	U R                  XR
                  S9n	[        X5        [        X4US9n[	        XsXEUS	9n/ SQn	U R                  XR
                  S9n	[        X5        Sn[        X4US9n[	        XsXEUS	9n/ SQn	U R                  XR
                  S9n	[        X5        Sn[        X4US9n[	        XsXEUS	9n/ SQn	U R                  XR
                  S9n	[        X5        g )Nc                 L    XS-   -  [         R                  " U S-  * S-  5      -  $ N      )npexp)rmus     N/var/www/html/venv/lib/python3.13/site-packages/scipy/fft/tests/test_fftlog.pyf&test_fht_agrees_with_fftlog.<locals>.f   s%    a4yAa((          r   r   g333333?        offsetbias)g=lSgl1Z?gpR_g~]
o?g0d@?g?g02u?g7c4Uo?gU/5?gޠ3JgQiIg!m9?g 1g?Jb7?g tj3Bg 	'K?dtyper   )g Dy?g TIg 94?gB M?gQ89w?gĥ?gZT3%?gz;_x?g9%P?gv@݆gAAY]?gayig;gGI<!?g F\mgH ?g @(LGg?)gU_g0E>y7?g4⬞	F?gR^ء*9g-g?g!a?gR޴ ?gmMUU?g .?g'?eHgZ7ZP?gmܷ`%gCGT?g2Tg҅u>g/&g)gG3>g`4]<]?g[8+?g,8GdP?g
u?g,ח$5?g~}?gra,4?gV?gh`>EgDgyٖ?gP2ZSg͆˝?gܺJ?g[U+@g"%@)r   logspacelogasarrayr   float64r   r   )
xpr   r   dlnr   r   r   aourstheirss
             r   test_fht_agrees_with_fftlogr,      s\   ) 	B2A
&&1ad
C	BFD


1Q8A qrt4D@F ZZjjZ1FD! sT*Fqrt4D@F ZZjjZ1FD! DsT*Fqrt4D@F ZZjjZ1FD! DsT*Fqrt4D@F ZZjjZ1FD!r   optimalTFr   )r         ?g      r   )r   g?gn@   ?   c                 ,   [         R                  R                  S5      nUR                  UR	                  U 5      5      nUR                  SS5      nUR                  SS5      nU(       a
  [        XxX!S9n[        XgXUS9n	[        XXUS9n
[        XSS	9  g )
N   E3  r   r   initialr   r   gv!>)rtol)
r   randomRandomStater%   standard_normaluniformr   r   r   r   )r/   r   r   r-   r'   rngr)   r(   r   Aa_s              r   test_fht_identityr@   ]   s    
 ))



+C


3&&q)*A
++b!
C	R	B3F>ABD1A	abd	3BB'r   c                    [         R                  R                  S5      nU R                  UR	                  S5      5      nUR                  SS5      nSu  pE[        R                  " SS9 n[        X#XES9  U(       a   S	5       e S S S 5        S
u  pE[        R                  " SS9 n[        X#XES9  U(       a   S	5       e S S S 5        Su  pE[        R                  " [        5       n[        X#XES9  U(       d   S5       e S S S 5        S
u  pE[        R                  " [        5       n[        X#XES9  U(       d   S5       e S S S 5        g ! , (       d  f       N= f! , (       d  f       N= f! , (       d  f       Nq= f! , (       d  f       g = f)Nr3   r0   r4   r   )g      r.   T)recordr"   z)fht warned about a well-defined transform)g            ?)g      rC   z+fht did not warn about a singular transformz,ifht did not warn about a singular transform)r   r9   r:   r%   r;   r<   warningscatch_warningsr   pytestwarnsWarningr   )r'   r=   r)   r(   r   r   rB   s          r   test_fht_special_casesrI   s   s>   
))



+C


3&&r*+A
++b!
C
 HB		 	 	-AB"FFFz6 
.
 HB		 	 	-AB"FFFz6 
. HB	g	&AB"DDDv 
 HB	g	&QR#EEEv 
	) 
.	- 
.	- 
	 
	s0   *E$E$E)$E:
E
E&)
E7:
Fc                    [         R                  R                  S5      nUR                  SS5      nUR                  SU-
  S5      n[         R                  " SSU 5      nUR                  XT-  5      n[         R                  " US   US   -  5      n[        XsS	US
9n[        XgX8US9n	[         R                  " U5      US S S2   -  n
UR                  SU
-  U-  [        US-   U-
  S-  U5      -  5      n[        X5        g )Nr3   r      r4   rC   r5   r   r   r   r6   r   )r   r9   r:   r<   r#   r%   r$   r   r   r   r   r   )r/   r'   r=   r   gammar   r)   r(   r   r>   kAts               r   test_fht_exactrO      s    
))



+C
 
Q	B KK2s#E
B1A


18A
&&1ad
Cs%8FABE2A
vq2wA 
QqS5L4AeQ#>>	?BAr   z,array-likes only supported for NumPy backend)np_onlyreasonopc                     SS/SS//SS/SS//SS/SS///n[        U" USS5      U" U R                  U5      SS5      5        g )Nr.   g       @)r   r%   )r'   rR   xs      r   test_array_likerU      s`     *sCj	!*sCj	!*sCj	!	#A Bq#sOR

1sC%@Ar         c                 :  ^  T R                  S5      n[        U5      nSn[        R                  " SSU5      n[        R
                  " US   US   -  5      n[        US[        R
                  " S5      -  US9nT R                  XRR                  S	9n[        R                  " U5      UR                  US
S9-  nU 4S jn	U	" XT5      n
[        XXGS9nU	" X5      nT R                  T R                  X-
  U-  5      5      n[        UT R                  S5      S   5        g )Nr.   r   ir   r   i
   )r7   r   r    r4   )axisc                 D   > XS-   -  TR                  U S-  * S-  5      -  $ r   )r   )rT   r   r'   s     r   r   test_gh_21661.<locals>.f   s&    6{2661a4%'?**r   )r   r   g `m3*pC )r%   r
   r   r#   mathr$   r   r!   r   flipr   maxabsr	   )r'   r/   onexp_testr   r   r(   r   rM   r   a_rfht_vala_krel_errs   `             r   test_gh_21661rh      s    
**S/Cc"G	B
B1A
((1Q4!A$;
CsBO;F


1II
&A7<<<33A+ A(C#r1G
A(CffRVVW]c123G7BJJx045r   )rD   r^   numpyr   rF   scipy.fft._fftlogr   r   r   scipy.specialr   scipy.conftestr   scipy._lib._array_apir   r	   r
   markusefixtures
pytestmarkr   r,   parametrizer@   thread_unsaferI   rO   rU   rh   r]   r   r   <module>rs      s       2 2  / R R"FKK$;$;<N$OQ
;;// I"X T5M2#340r2h'( ( 1 5 3($  F  FF r2h' (6 $GIT{+B ,IB sCj)6 *6r   