
    Bj3F                        d dl Z d dlmZmZ d dlmZmZ d dlZd dlm	Z
 d dlmZ d dlmZ d dlmZmZmZ d dlmZmZ g dZded         z  Zh d	Zej        j        j        Zd
ededededef
dZdej        dedej         dej        fdZ!	 dGdededefdZ"d
ede#edf         de#edf         defdZ$de%dededz  dedededefdZ&de%dededz  dededed edefd!Z'de%dededz  dedededefd"Z( eej)                   e            	 	 	 dHdededz  dededef
d$                        Z* eej+                   e            	 	 	 dHdededz  dededef
d%                        Z, eej-                   e            	 	 	 dHdededz  dededef
d&                        Z. eej/                   e            	 	 	 dHdededz  dededef
d'                        Z0 eej1                   e            	 	 	 dHdededz  dededef
d(                        Z2 eej3                   e            	 	 	 dHdededz  dededef
d)                        Z4 G d* d+e          Z5ded,edz  dedz  de5fd-Z6d.ee         defd/Z7d0e%ded,e#edf         de#edf         dededefd1Z8 eej9                   e            	 	 	 dIded2edz  dedz  dedef
d3                        Z: eej;                   e            	 	 	 dIded2edz  dedz  dedef
d4                        Z< eej=                   e            	 	 	 dIded2edz  dedz  dedef
d5                        Z> eej?                   e            	 	 	 dIded2edz  dedz  dedef
d6                        Z@ G d7 d8e          ZAd9e%ded2edz  dedz  deAf
d:ZB eejC                   e            	 	 	 dIded2edz  dedz  dedef
d;                        ZD eejE                   e            	 	 	 dIded2edz  dedz  dedef
d<                        ZF eejG                   e            	 	 	 dJded2edz  dedz  dedef
d>                        ZH eejI                   e            	 	 	 dJded2edz  dedz  dedef
d?                        ZJ eejK                   e            	 	 	 dJded2edz  dedz  dedef
d@                        ZL eejM                   e            	 	 	 dJded2edz  dedz  dedef
dA                        ZN eejO                   e            	 	 	 dJded2edz  dedz  dedef
dB                        ZP eejQ                   e            	 	 	 dJded2edz  dedz  dedef
dC                        ZRdedz  d
edeSe         fdDZT eejU                  dKdededz  defdE            ZV eejW                  dKdededz  defdF            ZXdS )L    N)IterableSequence)Literal
NamedTuple)register_decomposition)DimsType	ShapeTypeTensorLikeType)_maybe_convert_to_dtypeout_wrapper)fftfft2fftnhffthfft2hfftnrfftrfft2rfftnifftifft2ifftnihfftihfft2ihfftnirfftirfft2irfftnfftshift	ifftshift)forwardbackwardortho>   Nr#   r!   r"   xnormsignal_numelr!   returnc                     t          j        t          v fd           dk    r| dt          j        |          z  z  S | r
du pdk    p|odk    }|r| d|z  z  n| S )z3Apply normalization to the un-normalized FFT resultc                      d  S )NzInvalid normalization mode:  )r%   s   R/var/www/html/Carbon-Document/venv/lib/python3.11/site-packages/torch/_refs/fft.py<lambda>z_apply_norm.<locals>.<lambda>/   s    /Td/T/T     r#      Nr"   r!   )torch_check_NORM_VALUESmathsqrt)r$   r%   r&   r!   	normalizes    `   r+   _apply_normr5   +   s     
L%'T'T'T'TUUUwA	,///00E$$,"D$*2D %DI%  &/51L !!A5r-   dtyperequire_complexdevicec                 2     j         r S  j        st          j                     t          j        t          j        g}|j        dv }|r|                    t          j                   t          j	         |v  fd           |rt          j                     S )z@Helper to promote a dtype to one supported by the FFT primitives)cudametaxpuc                      d  S )NzUnsupported dtype r*   r6   s   r+   r,   z#_promote_type_fft.<locals>.<lambda>J   s    1Me1M1M r-   )
is_complexis_floating_pointr/   get_default_dtypefloat32float64typeappendfloat16r0   utilscorresponding_complex_dtype)r6   r7   r8   allowed_typesmaybe_support_halfs   `    r+   _promote_type_fftrK   :   s       " *'))]EM2M(?? ,U]+++	L-')M)M)M)MNNN 91%88Lr-   Ftc                 \    | j         }t          ||| j                  }t          | |          S )zEHelper to promote a tensor to a dtype supported by the FFT primitives)r6   rK   r8   r   )rL   r7   cur_typenew_types       r+   _maybe_promote_tensor_fftrP   R   s.     wH ?AHEEH"1h///r-   dims.sizesc                    t          |          t          |          k    r/t          dt          |           dt          |                     d}| j        }dgt          |          z  dz  }t          t          |                    D ]}||         dk    r|||                  ||         k     r:d}t          |          d||         z  z
  dz
  }||         |||                  z
  ||<   |||                  ||         k    r#|                     ||         d||                   } |rt          j        | |          n| S )	z
    Fixes the shape of x such that x.size(dims[i]) == sizes[i],
    either by zero-padding, or by slicing x starting from 0.
    z.dims and sizes must have the same length, got z and Fr      Tr.   )lenAssertionErrorshaperangenarrowr/   constant_pad_nd)r$   rQ   rR   	must_copyx_sizes
pad_amountipad_idxs           r+   _resize_fft_inputra   [   sH    4yyCJJYSYYYYSQVZZYY
 
 	
 IgGs7||#a'J3t99 / /8r>>47eAh&&I*ooDG3a7G"'(WT!W-="=Jw47eAh&&a!U1X..A3<C5 J///!Cr-   	func_nameinputndimc                 |   t          |d          }t          j        |j        |d          f}||nd|j        |         dz
  z  t          j        dk    fd           |t          ||dz  dz   f	          }|rt          j        |          }t          j
        ||
          }t          |||          S )zBCommon code for performing any complex to real FFT (irfft or hfft)Tr7   Fwrap_scalarNrT   r.   c                      d  dS NzInvalid number of data points (z) specifiedr*   last_dim_sizes   r+   r,   z_fft_c2r.<locals>.<lambda>       L-LLL r-   )rQ   rR   re   rm   r%   r&   r!   )rP   rG   canonicalize_dimndimrX   r/   r0   ra   conjprimsfft_c2rr5   )	rb   rc   rd   re   r%   r!   rQ   outputrm   s	           @r+   _fft_c2rrw   y   s     &eTBBBE"5:sFFFHDAAAS1AA1E,FM	LLLLL  
 	}!%d=A;MPQ;Q:STTT "
5!!]5d-HHHFvD}gVVVVr-   onesidedc                    	 t          j        j        j          fd           t	                    t          j        j        |d          f}||nj        |         	t          j        	dk    	fd           |t          ||f          t          j        ||          }t          ||	|          }|r|nt          j        |          S )zBCommon code for performing any real to complex FFT (rfft or ihfft)c                        dj          S )Nz0 expects a floating point input tensor, but got r>   rb   rc   s   r+   r,   z_fft_r2c.<locals>.<lambda>   s    9[[ek[[ r-   Frh   Nr.   c                      d  dS rk   r*   dim_sizes   r+   r,   z_fft_r2c.<locals>.<lambda>       VVVV r-   re   rx   )r/   r0   r6   r?   rP   rG   rq   rr   rX   ra   rt   fft_r2cr5   rs   )
rb   rc   rd   re   r%   r!   rx   rQ   retr~   s
   ``       @r+   _fft_r2cr      s     
LK""[[[[[   &e,,E"5:sFFFHDMqqu{3'7H	LAVVVV   	}!%t44
-4(
;
;
;C
c47
3
3C.33uz#.r-   c                 \    t          j        j        j         fd           t	          j        j        |d          f}||nj        |         t          j        dk    fd           |t          ||f          t          j
        ||          }t          |||          S )zCCommon code for performing any complex to complex FFT (fft or ifft)c                        dj          S Nz) expects a complex input tensor, but got r>   r{   s   r+   r,   z_fft_c2c.<locals>.<lambda>   s    9TTu{TT r-   Frh   Nr.   c                      d  dS rk   r*   r}   s   r+   r,   z_fft_c2c.<locals>.<lambda>   r   r-   re   r!   )r/   r0   r6   r?   rG   rq   rr   rX   ra   rt   fft_c2cr5   )	rb   rc   rd   re   r%   r!   rQ   r   r~   s	   ``      @r+   _fft_c2cr      s     
LTTTTT   "5:sFFFHDMqqu{3'7H	LAVVVV   	}!%t44
-4
9
9
9CsD(G444r-   rU   c           	      p    | j         j        rt          d| |||d          S t          d| |||dd          S )Nr   Tr!   Fr!   rx   r6   r?   r   r   rc   rd   re   r%   s       r+   r   r      sJ     { RuadDAAAAuadD5QQQQr-   c           	      p    | j         j        rt          d| |||d          S t          d| |||dd          S )Nr   Fr   r   r   r   s       r+   r   r      sJ     { Tq#tUCCCCq#tUUSSSSr-   c           	      .    t          d| |||dd          S )Nr   Tr   r   r   s       r+   r   r      s!     FE1c4MMMMr-   c                 ,    t          d| |||d          S )Nr   Fr   rw   r   s       r+   r   r      s     GUAsD%@@@@r-   c                 ,    t          d| |||d          S )Nr   Tr   r   r   s       r+   r   r      s     FE1c4>>>>r-   c           	      .    t          d| |||dd          S )Nr   FTr   r   r   s       r+   r   r     s!     GUAsD%$OOOOr-   c                   D    e Zd ZU eedf         ed<   eedf         ed<   dS )_ShapeAndDims.rX   rQ   N__name__
__module____qualname__tupleint__annotations__r*   r-   r+   r   r     s:         c?
S/r-   r   rX   c                    | j         | j        |pt          |t                    s|f}t	          j        |d          }t          j        t          t          |                    t          |          k    d            |t          |t                    s|f}t          j        |du pt          |          t          |          k    d            t          |          t          j        k    fd           | t          t          z
                      }t          fdt          ||          D                       }nI|,t          t                              }t                    }nt          fd|D                       }|D ]t          j        d	k    fd
           t          ||          S )zTConvert the shape and dim arguments into a canonical form where neither are optionalNFrh   c                      dS )NzFFT dims must be uniquer*   r*   r-   r+   r,   z6_canonicalize_fft_shape_and_dim_args.<locals>.<lambda>&  s    9R r-   c                      dS )Nz=When given, dim and shape arguments must have the same lengthr*   r*   r-   r+   r,   z6_canonicalize_fft_shape_and_dim_args.<locals>.<lambda>0  s    S r-   c                      d d  dS )NzGot shape with z" values but input tensor only has z dimensions.r*   )	input_dimtransform_ndims   r+   r,   z6_canonicalize_fft_shape_and_dim_args.<locals>.<lambda>6  s(     0n 0 0!0 0 0 r-   c              3   >   K   | ]\  }}|d k    r|n|         V  dS )rU   Nr*   ).0sdinput_sizess      r+   	<genexpr>z7_canonicalize_fft_shape_and_dim_args.<locals>.<genexpr>?  sK       
 
A bAAk!n
 
 
 
 
 
r-   c              3   (   K   | ]}|         V  d S Nr*   )r   r   r   s     r+   r   z7_canonicalize_fft_shape_and_dim_args.<locals>.<genexpr>I  s'      ;;Q+a.;;;;;;r-   r   c                      d  dS rk   r*   )rd   s   r+   r,   z6_canonicalize_fft_shape_and_dim_args.<locals>.<lambda>L  s    $Ta$T$T$T r-   )rX   rQ   )rr   rX   
isinstancer   rG   canonicalize_dimsr/   r0   rV   setr   rY   zipr   )	rc   rX   re   ret_dims	ret_shaper   r   rd   r   s	        @@@@r+   $_canonicalize_fft_shape_and_dim_argsr     s    
I+K
#x(( 	&C*9cuMMM 	H#h--/1R1R	
 	
 	
 %** 	HE 	4K13s88s5zz1SS	
 	
 	
 Ui'0 0 0 0 0	
 	
 	
 ;U9~#=yIIJJH  
 
 
 
eX..
 
 
 
 
		 
y))**+&&		 ;;;;(;;;;;	 V VQUTTTTUUUUyx8888r-   xsc                     d}| D ]}||z  }|S )zCompute product of a listr.   r*   )r   prodr$   s      r+   _prodr   Q  s&    D  	Kr-   function_namec                      t          j        j        j         fd           t	          ||          }t          j        |||          }t          ||t          |          |          S )zECommon code for n-dimensional complex to complex FFTs (fftn or ifftn)c                        dj          S r   r>   )r   rc   s   r+   r,   z_fftn_c2c.<locals>.<lambda>d  s     = ! !;! ! r-   r   rp   )	r/   r0   r6   r?   ra   rt   r   r5   r   )r   rc   rX   re   r%   r!   r$   rv   s   ``      r+   	_fftn_c2cr   Y  s     
L	! 	! 	! 	! 	!  
 	%e,,A]1#w777FvDuU||WUUUUr-   r   c                 v    t          | ||          \  }}t          | d          }t          d||||d          S )NTrg   r   r   r   rP   r   rc   r   re   r%   rX   r$   s         r+   r   r   l  sF     8q#FFLUC!%>>>AVQsD$????r-   c                 v    t          | ||          \  }}t          | d          }t          d||||d          S )NTrg   r   Fr   r   r   s         r+   r   r   y  sF     8q#FFLUC!%>>>AWaT5AAAAr-   c                 $    t          j         j        j          fd           t	           ||          \  }}t           d           t           ||           t          j         |d          }t          ||t          |          d          S )Nc                      d j          S )Nz2rfftn expects a real-valued input tensor, but got r>   rc   s   r+   r,   zrfftn.<locals>.<lambda>  s    RU[RR r-   Frg   Tr   rp   )r/   r0   r6   r?   r   rP   ra   rt   r   r5   r   )rc   r   re   r%   rX   outs   `     r+   r   r     s     
LK""RRRR   6eQDDJE3%eUCCCEeS%00E
-3
6
6
6CsE%LL$OOOOr-   c                 h    t          j         j        j          fd           t	           ||          \  }}t          j        t          |          dk    d            t           d           t           ||           t          j	         |dd          d          }t          |          d	k    r-t          |||d         d
          }t          j        |          S t          j        |          }t          j        ||d d         d          }t          ||t          |          d
          S )Nc                      d j          S )Nz3ihfftn expects a real-valued input tensor, but got r>   r   s   r+   r,   zihfftn.<locals>.<lambda>  s    SekSS r-   r   c                      dS )Nz'ihfftn must transform at least one axisr*   r*   r-   r+   r,   zihfftn.<locals>.<lambda>  s    )R r-   Frg   rU   Tr   r.   rp   r   )r/   r0   r6   r?   r   rV   rP   ra   rt   r   r5   rs   conj_physicalr   r   )rc   r   re   r%   rX   tmps   `     r+   r   r     s*    
LK""SSSS   6eQDDJE3	LUa!R!RSSS%eUCCCEeS%00E
-3rss8d
;
;
;C
3xx1}}#DuQxOOOz#

c
"
"C
-SbS5
9
9
9CsE%LL%PPPPr-   c                   N    e Zd ZU eedf         ed<   eedf         ed<   eed<   dS )_CanonicalizeC2rReturn.rX   re   rm   Nr   r*   r-   r+   r   r     sF         c?	sCxr-   r   fnamec                     t          |||          \  }}t          j        t          |          dk     fd           ||d         dk    rd|j        |d                  dz
  z  n|d         t          j        dk    fd           t          |          }dz  dz   |d<   t          t          |          |          S )	zCanonicalize shape and dim arguments for n-dimensional c2r transforms,
    as well as calculating the last_dim_size which is shape[dim[-1]] for the outputr   c                        dS )Nz! must transform at least one axisr*   )r   s   r+   r,   z:_canonicalize_fft_c2r_shape_and_dim_args.<locals>.<lambda>  s    E)T)T)T r-   NrU   rT   r.   c                      d  dS rk   r*   rl   s   r+   r,   z:_canonicalize_fft_c2r_shape_and_dim_args.<locals>.<lambda>  rn   r-   )rX   re   rm   )r   r/   r0   rV   rX   listr   r   )r   rc   r   re   rX   
shape_listrm   s   `     @r+   (_canonicalize_fft_c2r_shape_and_dim_argsr     s     8q#FFLUC	LUa!T!T!T!TUUUyAbERKKU[R1A56b		LLLLL  
 eJ"a'!+JrN!JS   r-   c                     t          d| ||          \  }}}t          | d          } t          | ||          } t          j        | ||          t          |t          fd|D                       d          S )Nr   Trg   ro   c              3   2   K   | ]}j         |         V  d S r   rX   )r   r   r   s     r+   r   zirfftn.<locals>.<genexpr>  s)      'B'B	!'B'B'B'B'B'Br-   Fr   )r   rP   ra   rt   ru   r5   r   )rc   r   re   r%   rX   rm   r   s         @r+   r   r     s     !I%C! !E3 &eTBBBEeS%00E
-3m
D
D
DCsD%'B'B'B'Bc'B'B'B"B"BERRRRr-   c           	         t          d| ||          \  }}}t          | d          } t          | ||          } t          |          dk    rt	          j        | |d d         d          n| }t          ||t          |d d                   d          }t	          j        |          }t	          j	        ||dd          |          }t          |||d          S )	Nr   Trg   r.   rU   r   r   ro   )
r   rP   ra   rV   rt   r   r5   r   r   ru   )rc   r   re   r%   rX   rm   r   r   s           r+   r   r     s     !I3! !E3 &eTBBBEeS%00E>A#hhll%-3ss8T
:
:
:
:PUC
c4uSbSz!2!2D
A
A
AC

c
"
"C
-RSS
G
G
GCsD->>>>r-   rU   c                 H    t           j                            | |||          S N)r   re   r%   )r/   r   r   rc   r   re   r%   s       r+   r   r     s      9>>%1#D>999r-   c                 H    t           j                            | |||          S r   )r/   r   r   r   s       r+   r   r           9??5A3T?:::r-   c                 H    t           j                            | |||          S r   )r/   r   r   r   s       r+   r   r     r   r-   c                 H    t           j                            | |||          S r   )r/   r   r   r   s       r+   r   r     #     9EQCd;;;r-   c                 H    t           j                            | |||          S r   )r/   r   r   r   s       r+   r   r   )  r   r-   c                 H    t           j                            | |||          S r   )r/   r   r   r   s       r+   r   r   4  r   r-   c                     | !t          t          |j                            S t          | t                    s| gS t          |           S )zIConvert Optional[DimsType] to a simple list, defaulting to all dimensions)r   rY   rr   r   r   )re   r$   s     r+   _default_alldimsr   ?  sB    
{E!&MM"""X&& uCyyr-   c                 l     t          |           } fd|D             }t          j         ||          S )Nc                 0    g | ]}j         |         d z  S )rT   r   r   r   rc   s     r+   
<listcomp>zfftshift.<locals>.<listcomp>L  s$    ///QU[^q ///r-   r   r/   rollrc   re   rQ   shifts   `   r+   r   r   I  s?    C''D////$///E:eUD)))r-   c                 l     t          |           } fd|D             }t          j         ||          S )Nc                 6    g | ]}j         |         d z   dz  S )r.   rT   r   r   s     r+   r   zifftshift.<locals>.<listcomp>S  s)    5551ek!nq Q&555r-   r   r   s   `   r+   r    r    P  s?    C''D5555555E:eUD)))r-   )F)NrU   N)NNN)Nr   Nr   )Yr2   collections.abcr   r   typingr   r   r/   torch._prims_primsrt   torch._prims_common_prims_commonrG   torch._decompr   r   r	   r
   torch._prims_common.wrappersr   r   __all__NormTyper1   _opsopsatenr   boolr5   r6   r8   rK   rP   r   ra   strrw   r   r   fft_fftr   fft_ifftr   fft_rfftr   	fft_irfftr   fft_hfftr   	fft_ihfftr   r   r   r   r   fft_fftnr   	fft_ifftnr   	fft_rfftnr   
fft_ihfftnr   r   r   
fft_irfftnr   	fft_hfftnr   fft_fft2r   	fft_ifft2r   	fft_rfft2r   
fft_irfft2r   	fft_hfft2r   
fft_ihfft2r   r   r   fft_fftshiftr   fft_ifftshiftr    r*   r-   r+   <module>r     s    . . . . . . . . & & & & & & & &        # # # # # # 0 0 0 0 0 0 C C C C C C C C C C M M M M M M M M  2 '899555z~66%6586CG66 6 6 6;)-7<|
[   2 050 00(,00 0 0 0DD"38_D5:38_DD D D D<WWW TzW 
	W
 W W W W W W6/// Tz/ 
	/
 / / / / / / /:555 Tz5 
	5
 5 5 5 5 5 54 %% 		R 	R	R
Tz	R 
	R 		R
 	R 	R 	R  &%	R && 		T 	T	T
Tz	T 
	T 		T
 	T 	T 	T  '&	T && 	N NN
TzN 
N 	N
 N N N  '&N '' 	A AA
TzA 
A 	A
 A A A  ('A && 	? ??
Tz? 
? 	?
 ? ? ?  '&? '' 	P PP
TzP 
P 	P
 P P P  ('P    J   
6969"+d"2699AD6969 69 69 69rhsm     VVV c?V 
sCx	V
 V V V V V V& && 	@ @@4@ 
D@ 	@
 @ @ @  '&@ '' 	B BB4B 
DB 	B
 B B B  ('B '' 	P PP4P 
DP 	P
 P P P  ('P" (( 	Q QQ4Q 
DQ 	Q
 Q Q Q  )(Q4    Z    4 
D	
    8 (( 	S SS4S 
DS 	S
 S S S  )(S '' 	? ??4? 
D? 	?
 ? ? ?  ('?& && #	: ::4: 
D: 	:
 : : :  '&: '' #	; ;;4; 
D; 	;
 ; ; ;  ('; '' #	; ;;4; 
D; 	;
 ; ; ;  ('; (( #	< <<4< 
D< 	<
 < < <  )(< '' #	; ;;4; 
D; 	;
 ; ; ;  ('; (( #	< <<4< 
D< 	<
 < < <  )(<(T/ n c     )*** *N *D *N * * * +** *++* *^ *(T/ *^ * * * ,+* * *r-   