o
    ig                    @   sX  d Z ddlZddlZddlmZ ddlZddlZddlm	Z	m
Z
mZmZ ddlmZ ddlmZmZmZ ddlmZmZ ddlmZmZmZ d	d
lmZmZmZ ddlmZ  e!dZ"e"# Z$e$Z%e!dZ&e&# Z'ej(Z(e(# Z)ej*Z+ej*Z,ej-dej.dej/dej0diZ1dddZ2dd Z3dd Z4dd Z5G dd dZ6G dd dZ7ej8dd  Z9d!d" Z:d#d$ Z;d%d& Z<d'd( Z=d)d* Z>d+d, Z?d-d. Z@d/d0 ZAd1d2 ZBdd4d5ZCeejDd6d7 ZEeejFd8d9 ZGd:d; ZHeejId<d= ZId>d? ZJd@dA ZKdBdC ZLdDdE ZMeejDdFdG ZNeOdHeP ZQedIdJ ZRddLdMZSdNdO ZTdPdQ ZUeeUdRdS ZVedTdU ZWedVdW ZXeejYjZdXdY Z[edZd[ Z\dd\d]Z]eejYj^d^d_ Z_eejYj`d`da ZaeejYjbdbdc ZceejYjdddde ZeeejYjfdfdg ZgeejYjhddhdiZieejYjjdjdk Zkdldm Zleeldndo Zmdpdq Zneendrds Zodtdu Zpeepdvdw Zqdxdy Zreerdzd{ Zsd|d} Zteetd~d Zudd Zveevdd ZweejYjxdddZydd Zzeezdd Z{eejYj|dd Z}eejYj~dddZdd ZeejYjdd ZeejYjdd Zdd Zeedd Zdd Zeedd Zdd ZeejYjdddZeejYjdddZedd ZeejYjdddZeejYjdd ZeejdddZdddZedd Zedd Zdd ZeejdddZdd Zdd Zeejdd ZdS )z.
Implementation of linear algebra operations.
    N)ir)lower_builtinimpl_ret_borrowedimpl_ret_new_refimpl_ret_untracked)	signature)	intrinsicoverloadregister_jitable)typescgutils)TypingErrorNumbaTypeErrorNumbaPerformanceWarning   )
make_array_empty_nd_impl
array_copy)numpy_support       sdcz<BLAS function>c                 C   s$   t | }|d u rtd|f |S )Nzunsupported dtype for %s())_blas_kindsget	TypeError)dtype	func_namekind r"   ^/var/www/html/eduruby.in/lip-sync/lip-sync-env/lib/python3.10/site-packages/numba/np/linalg.pyget_blas_kind0   s   
r$   c                  C   &   zdd l } W d S  ty   tdw Nr   z*scipy 0.16+ is required for linear algebra)Zscipy.linalg.cython_blasImportErrorZscipyr"   r"   r#   ensure_blas7   
   r)   c                  C   r%   r&   )Zscipy.linalg.cython_lapackr'   r(   r"   r"   r#   ensure_lapack>   r*   r+   c                 C   s   |  |||}t||S N)Zget_constant_genericr   Zalloca_once_value)contextbuildertyvalconstr"   r"   r#   make_constant_slotE   s   r2   c                   @   s0   e Zd ZdZdd Zedd Zedd ZdS )	_BLASzM
    Functions to return type signatures for wrapped
    BLAS functions.
    c                 C   
   t   d S r,   )r)   selfr"   r"   r#   __init__P      
z_BLAS.__init__c              	   C   s<   t |d|}ttjtjt|tjt|}td|S )Nunderlying_floatnumba_xxnrm2getattrr   intccharintpCPointerExternalFunctionclsr   Zrtypesigr"   r"   r#   r:   S   s   z_BLAS.numba_xxnrm2c                 C   s`   t t jt jt jt jt jt jt |t |t jt |t jt |t |t j}t d|S )Nnumba_xxgemmr   r=   r>   r?   r@   rA   rC   r   rD   r"   r"   r#   rE   ^   s"   z_BLAS.numba_xxgemmN)__name__
__module____qualname____doc__r7   classmethodr:   rE   r"   r"   r"   r#   r3   J   s    

r3   c                   @   s   e Zd ZdZdd Zedd Zedd Zedd	 Zed
d Z	edd Z
edd Zedd Zedd Zedd Zedd Zedd ZdS )_LAPACKzO
    Functions to return type signatures for wrapped
    LAPACK functions.
    c                 C   r4   r,   )r+   r5   r"   r"   r#   r7   y   r8   z_LAPACK.__init__c              
   C   s4   t t jt jt jt |t jt t}t d|S )Nnumba_xxgetrfr   r=   r>   r?   r@   F_INT_nbtyperA   rG   r"   r"   r#   rN   |   s   z_LAPACK.numba_xxgetrfc              	   C   s0   t t jt jt |t jt t}t d|S )Nnumba_ez_xxgetrirO   rG   r"   r"   r#   rQ      s   z_LAPACK.numba_ez_xxgetric                 C   sX   t t jt jt jt jt |t jt |t |t |t jt |t j}t d|S )Nnumba_ez_rgeevrF   rG   r"   r"   r#   rR      s   z_LAPACK.numba_ez_rgeevc                 C   sP   t t jt jt jt jt |t jt |t |t jt |t j}t d|S )Nnumba_ez_cgeevrF   rG   r"   r"   r#   rS      s   z_LAPACK.numba_ez_cgeevc                 C   sD   t |d|}ttjtjtjtjt|tjt|}td|S )Nr9   numba_ez_xxxevdr;   )rC   r   ZwtyperD   r"   r"   r#   rT      s   z_LAPACK.numba_ez_xxxevdc                 C   s,   t t jt jt jt |t j}t d|S )Nnumba_xxpotrfrF   rG   r"   r"   r#   rU      s   z_LAPACK.numba_xxpotrfc                 C   s\   t |d|}ttjtjtjtjt|tjt|t|tjt|tj}td|S )Nr9   numba_ez_gesddr;   )rC   r   styperD   r"   r"   r#   rV      s   z_LAPACK.numba_ez_gesddc              
   C   s4   t t jt jt jt |t jt |}t d|S )Nnumba_ez_geqrfrF   rG   r"   r"   r#   rX      s   z_LAPACK.numba_ez_geqrfc                 C   s8   t t jt jt jt jt |t jt |}t d|S )Nnumba_ez_xxgqrrF   rG   r"   r"   r#   rY      s   	z_LAPACK.numba_ez_xxgqrc                 C   s^   t |d|}ttjtjtjtjt|tjt|tjt|tjttj}td|S )Nr9   numba_ez_gelsd)r<   r   r=   r>   r?   r@   float64rA   rB   r"   r"   r#   rZ      s   
z_LAPACK.numba_ez_gelsdc                 C   s@   t t jt jt jt |t jt tt |t j}t d|S )Nnumba_xgesvrO   rG   r"   r"   r#   r\     s   
z_LAPACK.numba_xgesvN)rH   rI   rJ   rK   r7   rL   rN   rQ   rR   rS   rT   rU   rV   rX   rY   rZ   r\   r"   r"   r"   r#   rM   s   s2    


	



	



rM   c                 c   s    g }g }g }t |j|D ]9\}}t|tjr|jdv r"||}	}
n|jdd}	t|	|}t| |||f}
|	|	|
f |	|	 |	|
 qt|j
g|R  t|fV  |D ]\}}| j||| qWdS )z
    Ensure that all array arguments are contiguous, if necessary by
    copying them.
    A new (sig, args) tuple is yielded.
    CFClayoutN)zipargs
isinstancer   Arrayr`   copyr   r   appendreturn_typetupleZnrtZdecref)r-   r.   rD   rb   ZnewtysZnewargsZcopiesr/   r0   ZnewtyZnewvalZcopysigr"   r"   r#   make_contiguous  s"   

ri   c                    s0   d  fdd}|  ||ttjtj|f dS )z.
    Check whether *n* fits in a C `int`.
    ic                    s   |  krt dd S )Nz$array size too large to fit in C int)OverflowError)nZ_maxintr"   r#   impl5  s   zcheck_c_int.<locals>.implN)compile_internalr   r   noner?   )r-   r.   rk   rm   r"   rl   r#   check_c_int/  s
   rp   c                 C   X   |j t||dd | |}|  |d W d   dS 1 s%w   Y  dS )z[
    Check the integer error return from one of the BLAS wrappers in
    _helperlib.c.
    FZlikelyz#BLAS wrapper returned with an errorNZif_thenr   Zis_not_nullZget_python_apiZ
gil_ensureZfatal_errorr-   r.   resZpyapir"   r"   r#   check_blas_return=  
   
"rv   c                 C   rq   )z]
    Check the integer error return from one of the LAPACK wrappers in
    _helperlib.c.
    Frr   z%LAPACK wrapper returned with an errorNrs   rt   r"   r"   r#   check_lapack_returnI  rw   rx   c                 C   s   t t dttttttg}t|j|d}	t	|}
t 
tt|
}t 
tt|}||	|||||t||t||tf}t| || dS )zQ
    Call the BLAS vector * vector product function for the given arguments.
    r   Znumba_xxdotN)r   FunctionTypeIntTypell_charintp_t	ll_void_pr   get_or_insert_functionmoduler$   Constantordintcallbitcastrv   )r-   r.   	conjugater   rk   Za_dataZb_dataout_datafntyfnr!   kind_valru   r"   r"   r#   
call_xxdotU  s   


r   c                 C   s  t t dttttttttttg
}t|j|d}	|j	}
t
| ||
d}t
| ||
d}|jdkr:|\}}|d }n|\}}|d }t|
}t tt|}t t|rWtdntd	}||	||||||t||t|||t||t||tf
}t| || d
S )zQ
    Call the BLAS matrix * vector product function for the given arguments.
    r   Znumba_xxgemv      ?        Fr   r   trk   N)r   ry   rz   r{   r|   r}   r   r~   r   r   r2   r`   r$   r   r   r   r   rv   )r-   r.   do_transZm_typem_shapesm_datav_datar   r   r   r   alphabetamrk   ldar!   r   transru   r"   r"   r#   call_xxgemvk  s6   





r   c           !         s8  t t dttttttttttttttg}t j|d}|\}}|\}}|j	}t
|  |d}t
|  |d}t ttdt ttd fdd}||||\}}}||||\}}}||	|
\}}}t|}t tt|} ||||||| |t|||| |t||f} t|  |  d	S )
zQ
    Call the BLAS matrix * matrix product function for the given arguments.
    r   rE   r   r   r   rk   c                    s8   | j j krn| j dkr|d n|d  |tfS )Nr^   r   r   )r`   r   r}   )r/   Zshapesdatar.   Znotransout_typer   r"   r#   get_array_param  s   
z$call_xxgemm.<locals>.get_array_paramN)r   ry   rz   r{   r|   r}   r   r~   r   r   r2   r   r   r$   r   r   rv   )!r-   r.   Zx_typex_shapesx_dataZy_typey_shapesy_datar   
out_shapesr   r   r   r   k_krk   r   r   r   r   Ztransar   Zdata_aZtransbZldbZdata_b_ZldcZdata_cr!   r   ru   r"   r   r#   call_xxgemm  s:   
r   c                 C   (   dd }|  ||||}t| ||j|S )z 
    np.dot(matrix, matrix)
    c                 S   sN   | j \}}|j \}}|dkrt||f| jS t||f| j}t| ||S Nr   shapenpzerosr   emptydot)abr   r   r   rk   outr"   r"   r#   dot_impl  s   

zdot_2_mm.<locals>.dot_implrn   r   rg   r-   r.   rD   rb   r   ru   r"   r"   r#   dot_2_mm     r   c                 C   r   )z 
    np.dot(vector, matrix)
    c                 S   sH   | j \}|j \}}|dkrt|f| jS t|f| j}t| ||S r   r   )r   r   r   _mrk   r   r"   r"   r#   r     s   
zdot_2_vm.<locals>.dot_implr   r   r"   r"   r#   dot_2_vm  r   r   c                 C   r   )z 
    np.dot(matrix, vector)
    c                 S   sH   | j \}}|j \}|dkrt|f| jS t|f| j}t| ||S r   r   )r   r   r   rk   _nr   r"   r"   r#   r     s   
zdot_2_mv.<locals>.dot_implr   r   r"   r"   r#   dot_2_mv  r   r   Fc              	   C   s   |j \}}|j}t|| ||d }t|| ||d }	t||j\}
dd }| ||ttj	g|j R  | t
| ||
 t|| |}t| ||||
|j|	j| ||S )z<
    np.dot(vector, vector)
    np.vdot(vector, vector)
    r   r   c                 S   s$   | j \}|j \}||krtdd S )Nz;incompatible array sizes for np.dot(a, b) (vector * vector)r   
ValueError)r   r   r   rk   r"   r"   r#   
check_args  s
   zdot_2_vv.<locals>.check_args)rb   rg   r   r   unpack_tupler   rn   r   r   ro   rp   Zalloca_onceZget_value_typer   r   load)r-   r.   rD   rb   r   ZatyZbtyr   r   r   rk   r   r   r"   r"   r#   dot_2_vv  s   

r   c                 C      t d| |S )z
    np.dot(a, b)
    znp.dot()
dot_2_implleftrightr"   r"   r#   dot_2     r   c                 C   r   )z
    a @ b
    z'@'r   r   r"   r"   r#   matmul_2  r   r   c                    sh   t |tjr0t |tjr2tfdd |jdvs|jdvr*td||ff t  fddS d S d S )Nc                    s   |j |j f  fdd}|j|jkrtd  dkr%t|jdd}n dks- dkr6t|jd	d}n d
kr>|j}ntd t||||fS )Nc                    s   t   t| |||O\}} dkrt| |||W  d    S  dkr1t| |||W  d    S  dkrCt| |||W  d    S  dkrUt| |||W  d    S td1 s\w   Y  d S )N   r   r   r   r   r   r   r   unreachable)r)   ri   r   r   r   r   AssertionErrorr-   r.   rD   rb   ndimsr"   r#   _dot2_codegen#  s    
z0dot_2_impl.<locals>._impl.<locals>._dot2_codegenz)%s arguments must all have the same dtyper   r   r^   r   r   r   r   z*%s: inputs must have compatible dimensions)ndimr   r   r   rd   r   )typingcontextr   r   r   rg   )namer   r#   _impl  s    zdot_2_impl.<locals>._implr]   z/%s is faster on contiguous arrays, called on %sc                    
    | |S r,   r"   r   r   r"   r#   <lambda>F     
 zdot_2_impl.<locals>.<lambda>rc   r   rd   r   r`   warningswarnr   )r   r   r   r"   )r   r   r#   r     s   !r   c                    sb   t | tjr-t |tjr/tdd  | jdvs|jdvr'td| |ff t  fddS dS dS )z
    np.vdot(a, b)
    c                 S   sJ   dd }|j dks|j dkrtd|j|jkrtdt|j|||fS )Nc                 S   sN   t   t| |||\}}t| |||ddW  d    S 1 s w   Y  d S )NT)r   )r)   ri   r   r   r"   r"   r#   codegenQ  s
   $z$vdot.<locals>._impl.<locals>.codegenr   z&np.vdot() only supported on 1-D arraysz0np.vdot() arguments must all have the same dtype)r   r   r   r   )r   r   r   r   r"   r"   r#   r   O  s   zvdot.<locals>._implr]   6np.vdot() is faster on contiguous arrays, called on %sc                    r   r,   r"   r   r   r"   r#   r   e  r   zvdot.<locals>.<lambda>Nr   r   r"   r   r#   vdotI  s   
r   c                 C   s:   | j \}|j \}}||krtd|j |fkrtdd S )Nz;incompatible array sizes for np.dot(a, b) (vector * matrix)zFincompatible output array size for np.dot(a, b, out) (vector * matrix)r   )r   r   r   r   r   rk   r"   r"   r#   dot_3_vm_check_argsh  s   
r   c                 C   s:   | j \}}|j \}||krtd|j |fkrtdd S )Nz;incompatible array sizes for np.dot(a, b) (matrix * vector)zFincompatible output array size for np.dot(a, b, out) (matrix * vector)r   )r   r   r   r   r   rk   r"   r"   r#   dot_3_mv_check_argss  s   
r   c                 C   s.  |j \}}}||jksJ |j}t|| ||d }t|| ||d }	t|| ||d }
t||j}t||	j}t||
j}|j|jk rd|}|}|d }|d }|jdk}|	j	|j	}}t
}n|}|}|d }|d }|jdk}|j	|	j	}}t}| ||ttjg|j R  | |D ]}t| || q| tjd}|d||}|d||}|||}|j|ddI\}}| t||
j	||
j|
jd W d	   n1 sw   Y  | t| |||||||
j	 W d	   n1 sw   Y  W d	   n	1 sw   Y  t| ||j|
 S )
zE
    np.dot(vector, matrix, out)
    np.dot(matrix, vector, out)
    r   r   r   r   r^   ==Frr   N)rb   rg   r   r   r   r   r   r   r`   r   r   r   rn   r   r   ro   rp   get_constantr?   icmp_signedor_if_elsememsetmulitemsizenitemsr   r   	_getvalue)r-   r.   rD   rb   xtyytyouttyr   xyr   r   r   r   Zmtyr   Zv_shaper   r   r   r   r   r0   zero
both_emptyZmatrix_emptyis_emptyr   nonemptyr"   r"   r#   dot_3_vm~  sb   



r   c           '      C   s  |j \}}}||jksJ |j}t|| ||d }t|| ||d }	t|| ||d }
t||j}t||	j}t||
j}|\}}|\}}|jdksRJ dd }| ||t	t
jg|j R  | t| || t| || t| || |j}|	j}|
j}| t
jd}|d||}|d||}|d||}|||||}|j|dd	I\}}| t||
j||
j|
jd W d
   n1 sw   Y  | | t
jd}|d||}|d||}||\} }!| b ||L\}"}#|" t| |d||||| W d
   n	1 sw   Y  |# |j|jk}$t| ||$||||| W d
   n	1 s<w   Y  W d
   n	1 sLw   Y  W d
   n	1 s\w   Y  |!e ||O\}%}&|% |j|jk}$t| ||$||||| W d
   n	1 sw   Y  |& t| |||||||||| W d
   n	1 sw   Y  W d
   n	1 sw   Y  W d
   n	1 sw   Y  W d
   n	1 sw   Y  W d
   n	1 sw   Y  W d
   n	1 sw   Y  t| ||j|
 S )z%
    np.dot(matrix, matrix, out)
    r   r   r   r^   c                 S   s>   | j \}}|j \}}||krtd|j ||fkrtdd S )Nz;incompatible array sizes for np.dot(a, b) (matrix * matrix)zFincompatible output array size for np.dot(a, b, out) (matrix * matrix)r   )r   r   r   r   r   r   rk   r"   r"   r#   r     s   

zdot_3_mm.<locals>.check_argsr   Frr   N)rb   rg   r   r   r   r   r   r`   rn   r   r   ro   rp   r   r   r?   r   r   r   r   r   r   r   r   r   r   r   r   )'r-   r.   rD   rb   r   r   r   r   r   r   r   r   r   r   r   r   r   rk   r   r   r   r   r   r   Zx_emptyZy_emptyr   r   r   oneZis_left_vecZis_right_vecZr_vecZr_matZv_vZm_vr   Zv_mZm_mr"   r"   r#   dot_3_mm  s   





&r   c                    s|   t | tjr8t |tjr:t |tjr<tdd  | jdvs'|jdvs'|jdvr2td| |ff t  fddS dS dS dS )z
    np.dot(a, b, out)
    c                 S   s:   dd }|j |j ks|j |j krtdt|||||fS )Nc                 S   s   t   t| |||<\}}tdd |jd d D }|dhkr.t| |||W  d    S |ddhkrBt| |||W  d    S td1 sIw   Y  d S )Nc                 s   s    | ]}|j V  qd S r,   r   ).0r   r"   r"   r#   	<genexpr>  s    z8dot_3.<locals>._impl.<locals>.codegen.<locals>.<genexpr>r   r   r   )r)   ri   setrb   r   r   r   )r-   r.   rD   rb   r   r"   r"   r#   r     s   
z%dot_3.<locals>._impl.<locals>.codegenz/np.dot() arguments must all have the same dtype)r   r   r   )r   r   r   r   r   r"   r"   r#   r     s   zdot_3.<locals>._implr]   r   c                        | ||S r,   r"   r   r   r   r   r"   r#   r   1  s    zdot_3.<locals>.<lambda>Nr   r   r"   r   r#   dot_3  s    

r   Znumba_fatal_errorc                 C   s.   t | D ]}t | st jdqd S )Nz$Array must not contain infs or NaNs.)r   ZnditerisfiniteitemlinalgLinAlgError)r   vr"   r"   r#   _check_finite_matrix7  s   r  Tc                 C   s   |rdnd}||f}t | tjr| j} t | tjs#d| }t|dd| jdks2d| }t|ddt | jtjtj	fsFd| }t|ddd S )	N	np.linalgr   z&%s.%s() only supported for array typesFZhighlightingr   z%%s.%s() only supported on 2-D arrays.3%s.%s() only supported on float and complex arrays.)
rc   r   Optionaltyperd   r   r   r   FloatComplex)r   r    	la_prefixprefixinterpmsgr"   r"   r#   _check_linalg_matrix?  s    
r  c                 G   s>   |d j }|dd  D ]}|j |krd|  }t|ddqd S )Nr   r   zAnp.linalg.%s() only supports inputs that have homogeneous dtypes.Fr  )r   r   )r    r   t0r   r  r"   r"   r#   _check_homogeneous_typesT  s   

r  c                   C   s   d S r,   r"   r"   r"   r"   r#   _copy_to_fortran_order\     r  c                    s&   | j dk| j dk  fdd}|S )Nr   Ac                    sP   r	t | }|S  r!| jj}|rt | jj}|S t | }|S t | }|S r,   )r   re   flagsf_contiguousTZasfortranarray)r   acpyZflag_fZA_layoutZF_layoutr"   r#   rm   f  s   


z&ol_copy_to_fortran_order.<locals>.implr_   )r   rm   r"   r  r#   ol_copy_to_fortran_order`  s   

r  c                 C   s6   | dkr| dk rt   J | dkrtjdd S d S )Nr   z(Matrix is singular to machine precision.)fatal_error_funcr   r  r  rr"   r"   r#   _inv_err_handler|  s   r!  c                 C   s   | d S )zFpass a list of variables to be preserved through dead code eliminationr   r"   r   r"   r"   r#   _dummy_liveness_func  s   r#  c                    P   t   t| d t | jt | jtt| jd  fdd}|S )Ninvc                    s   | j d }| j d |krd}tj|t|  t| }|dkr"|S tj|td} |||j||j}t	|  ||j||j}t	| t
|j|jg |S )N.Last 2 dimensions of the array must be square.r   r   )r   r   r  r  r  r  r   F_INT_nptypectypesr!  r#  size)r   rk   r  r  ipivr   r!   rN   Znumba_xxgetrir"   r#   inv_impl  s   
zinv_impl.<locals>.inv_impl)r+   r  rM   rN   r   rQ   r   r$   )r   r/  r"   r.  r#   r/    s   
r/  c                 C   s2   | dkr| dk rt   J | dkrtdd S d S )Nr   z&Internal algorithm failed to converge.)r  r   r  r"   r"   r#   %_handle_err_maybe_convergence_problem  s   r0  c                 C   sf   |rdnd}||f}t | tjstd| | jdks!td| t | jtjtjfs1td| d S )Nr  r   z'%s.%s() only supported for array types r   +%s.%s() only supported on 1 and 2-D arrays r	  )rc   r   rd   r   r   r   r  r  r   r    r  r  r  r"   r"   r#   _check_linalg_1_or_2d_matrix  s   
r3  c                    sR   t   t| d t | jtt| jdtd td} fdd}|S )NcholeskyULc                    s   | j d }| j d |krd}tj||  }|dkr|S  ||j|}|dkr>|dk r4t  J |dkr>tjdt|D ]
}d|d ||f< qB|S )Nr&  r'  r(  r   z Matrix is not positive definite.)r   r   r  r  re   r+  r  range)r   rk   r  r   r   colZUPr!   rU   r"   r#   cho_impl  s&   
zcho_impl.<locals>.cho_impl)r+   r  rM   rU   r   r   r$   )r   ZLOr:  r"   r9  r#   r:    s   
r:  c                    s   t   t| d t | jt | jtt| jdtd td fdd} fdd}t| jt	j
jrB|S |S )NeigNVc                    s  | j d }| j d |krd}tj|t|  t| }d}|}tj|| jd}tj|| jd}tj||f| jd}tj||f| jd}	|dkrM||	jfS  ||j	||j	|j	|j	||	j	|}
t
|
 t|rntdt|j|j|	j|j|jg ||	jfS )z7
        eig() implementation for real arrays.
        r&  r'  r(  r   r)  r   z.eig() argument must not cause a domain change.)r   r   r  r  r  r  r   r   r  r+  r0  anyr   r#  r,  r   rk   r  r  ldvlldvrwrZwivlvrr   JOBVLJOBVRr!   rR   r"   r#   real_eig_impl
  sD   



zeig_impl.<locals>.real_eig_implc           
         s   | j d }| j d |krd}tj|t|  t| }d}|}tj|| jd}tj||f| jd}tj||f| jd}|dkrE||jfS  ||j	||j	|j	||j	|}	t
|	 t|j|j|j|jg ||jfS )z:
        eig() implementation for complex arrays.
        r&  r'  r(  r   r)  r   )r   r   r  r  r  r  r   r   r  r+  r0  r#  r,  
r   rk   r  r  r@  rA  wrC  rD  r   rF  rG  r!   rS   r"   r#   cmplx_eig_implB  s8   


z eig_impl.<locals>.cmplx_eig_implr+   r  rM   rR   r   rS   r   r$   rc   r   Zscalarsr  )r   rH  rL  r"   rF  rG  r!   rS   rR   r#   eig_impl  s   
8(rO  c                    s   t   t| d t | jt | jtt| jdtd td fdd} fdd}t| jt	j
jrB|S |S )Neigvalsr<  c                    s   | j d }| j d |krd}tj|t|  t| }d}d}tj|| jd}|dkr.|S tj|| jd}tjd| jd}tjd| jd}	 ||j||j|j|j||	j|}
t	|
 t
|rgtdt|j|j|	j|j|jg |S )z;
        eigvals() implementation for real arrays.
        r&  r'  r(  r   r)  r   z2eigvals() argument must not cause a domain change.)r   r   r  r  r  r  r   r   r+  r0  r>  r   r#  r,  r?  rE  r"   r#   real_eigvals_impl}  sD   

z'eigvals_impl.<locals>.real_eigvals_implc           
         s   | j d }| j d |krd}tj|t|  t| }d}d}tj|| jd}|dkr.|S tjd| jd}tjd| jd} ||j||j|j||j|}	t	|	 t
|j|j|j|jg |S )z>
        eigvals() implementation for complex arrays.
        r&  r'  r(  r   r)  r   )r   r   r  r  r  r  r   r   r+  r0  r#  r,  rI  rK  r"   r#   cmplx_eigvals_impl  s8   
z(eigvals_impl.<locals>.cmplx_eigvals_implrM  )r   rQ  rR  r"   rN  r#   eigvals_implo  s   
;)rS  c                    p   t   t| d t| jd| j}t|t | jtt	| jdtd td fdd}|S )Neighr9   r=  r6  c                    s   | j d }| j d |krd}tj|t|  t| }tj|d}|dkr+||fS  ||j||j}t| t	|j
|j
g ||fS Nr&  r'  r(  r)  r   r   r   r  r  r  r  r   r+  r0  r#  r,  r   rk   r  r  rJ  r   JOBZZUPLOr!   rT   Zw_dtyper"   r#   	eigh_impl  s(   
zeigh_impl.<locals>.eigh_impl
r+   r  r<   r   
np_supportas_dtyperM   rT   r   r$   )r   w_typer[  r"   rY  r#   r[       

r[  c                    rT  )Neigvalshr9   r<  r6  c                    s   | j d }| j d |krd}tj|t|  t| }tj|d}|dkr)|S  ||j||j}t| t	|j
|j
g |S rV  rW  rX  rY  r"   r#   eigvalsh_impl(  s(   
z$eigvalsh_impl.<locals>.eigvalsh_implr\  )r   r_  rb  r"   rY  r#   rb    r`  rb  c                    sr   t   t| d t| jd| j}t|t | jtt	| jdtd tdd fdd	}|S )	Nsvdr9   r  Sr   c                    s   | j d }| j d }|dks|dkrtjdt|  t| }|}t||}|r0 }|}|}	n}|}|}	tj||f| jd}
tj|d}tj||	f| jd}||||j	||j	|
j	||j	|	}t
| t|j|j|
j|jg |
j||jfS )Nr&  r'  r   Arrays cannot be emptyr)  )r   r   r  r  r  r  minr   r   r+  r0  r#  r,  r  )r   full_matricesrk   r   r  lduminmnrZ  ucolldvtur   vtr   ZJOBZ_AZJOBZ_Sr!   rV   s_dtyper"   r#   svd_implY  sD   


zsvd_impl.<locals>.svd_implr   )
r+   r  r<   r   r]  r^  rM   rV   r   r$   )r   rg  s_typerp  r"   rn  r#   rp  H  s   

.rp  c                    r$  )Nqrc                    sJ  | j d }| j d }|dks|dkrtjdt|  t| }|}t||}tj|| jd} |||j	||j	}|dk rCt
  J tj||f| jdj}t|D ]}	t|	d D ]}
||
|	f ||
|	f< qZqRt||D ]}	t|D ]}
||
|	f ||
|	f< qsqm ||||j	||j	}t| t|j|jg |d d d |f |fS )Nr&  r'  r   re  r)  r   )r   r   r  r  r  r  rf  r   r   r+  r  r   r  r7  r0  r#  r,  )r   rk   r   qr   ri  tauretr   ijr!   rX   rY   r"   r#   qr_impl  sR   


	zqr_impl.<locals>.qr_impl)r+   r  rM   rX   r   rY   r   r$   )r   rz  r"   ry  r#   rz    s   
9rz  c                 C      t )z;
    Correctly copy 'b' into the 'bcpy' scratch space.
    NotImplementedErrorbcpyr   nrhsr"   r"   r#   _system_copy_in_b     r  c                 C   s"   |j dkrdd }|S dd }|S )Nr   c                 S   s   || d |j d df< d S )Nr&  r   r   r~  r"   r"   r#   	oneD_impl  s   z)_system_copy_in_b_impl.<locals>.oneD_implc                 S   s   || d |j d d |f< d S )Nr'  r  r~  r"   r"   r#   	twoD_impl  s   z)_system_copy_in_b_impl.<locals>.twoD_implr   )r  r   r  r  r  r"   r"   r#   _system_copy_in_b_impl  
   
r  c                 C   r{  )zK
    Compute the number of right hand sides in the system of equations
    r|  r   r"   r"   r#   _system_compute_nrhs  r  r  c                 C   s"   | j dkrdd }|S dd }|S )Nr   c                 S   s   dS Nr   r"   r  r"   r"   r#   r    r  z,_system_compute_nrhs_impl.<locals>.oneD_implc                 S   s
   | j d S )Nr&  r  r  r"   r"   r#   r    r8   z,_system_compute_nrhs_impl.<locals>.twoD_implr   )r   r  r  r"   r"   r#   _system_compute_nrhs_impl  r  r  c                 C   r{  )zD
    Check that AX=B style system input is dimensionally valid.
    r|  r   r   r"   r"   r#   !_system_check_dimensionally_valid  r  r  c                 C   &   |j }|dkrdd }|S dd }|S )Nr   c                 S   s,   | j d }|j d }||krtjdd S )Nr'  r&  <Incompatible array sizes, system is not dimensionally valid.r   r   r  r  r   r   ambmr"   r"   r#   r       

z9_system_check_dimensionally_valid_impl.<locals>.oneD_implc                 S   s,   | j d }|j d }||krtjdd S )Nr'  r  r  r  r"   r"   r#   r    r  z9_system_check_dimensionally_valid_impl.<locals>.twoD_implr   r   r   r   r  r  r"   r"   r#   &_system_check_dimensionally_valid_impl  s   r  c                 C   r{  )z:
    Check that AX=B style system input is not empty.
    r|  r  r"   r"   r#   _system_check_non_empty  r  r  c                 C   r  )Nr   c                 S   sF   | j d }| j d }|j d }|dks|dks|dkr!tjdd S Nr'  r&  r   re  r  )r   r   r  anr  r"   r"   r#   r  (  s   


z/_system_check_non_empty_impl.<locals>.oneD_implc                 S   sX   | j d }| j d }|j d }|j d }|dks$|dks$|dks$|dkr*tjdd S r  r  )r   r   r  r  r  bnr"   r"   r#   r  0  s   



 z/_system_check_non_empty_impl.<locals>.twoD_implr   r  r"   r"   r#   _system_check_non_empty_impl$  s   r  c                 C   r{  )z:
    Compute the residual from the 'b' scratch space.
    r|  )r   rk   r  r"   r"   r#   _lstsq_residual:  r  r  c                    s   | j }| j}tt|d| |dkr)t|tjr! fdd}|S  fdd}|S |dks/J t|tjr= fdd}|S  fd	d}|S )
Nr9   r   c                    s6   t jd d}t t | |d df d |d< |S Nrq  r)  r   r   )r   r   sumabsr   rk   r  ru   
real_dtyper"   r#   
cmplx_implI  s   $z(_lstsq_residual_impl.<locals>.cmplx_implc                    s0   t jd d}t | |d df d |d< |S r  )r   r   r  r  r  r"   r#   	real_implO  s   z'_lstsq_residual_impl.<locals>.real_implr   c                    sD   t j| d}t|D ]}t t | |d |f d ||< q|S Nr)  r   )r   r   r7  r  r  r   rk   r  ru   r   r  r"   r#   r  W  s   &c                    s>   t j| d}t|D ]}t | |d |f d ||< q|S r  )r   r   r7  r  r  r  r"   r#   r  ^  s    )r   r   r]  r^  r<   rc   r   r  )r   rk   r  r   r   r  r  r"   r  r#   _lstsq_residual_implA  s   r  c                 C   r{  )z
    Extract 'x' (the lstsq solution) from the 'bcpy' scratch space.
    Note 'b' is only used to check the system input dimension...
    r|  r   r  rk   r"   r"   r#   _lstsq_solutionf     r  c                 C   s"   | j dkrdd }|S dd }|S )Nr   c                 S   s   |j  d | S r,   r  ravelr  r"   r"   r#   r  q  s   z'_lstsq_solution_impl.<locals>.oneD_implc                 S   s   |d |d d f   S r,   re   r  r"   r"   r#   r  u  s   z'_lstsq_solution_impl.<locals>.twoD_implr   )r   r  rk   r  r  r"   r"   r#   _lstsq_solution_impln  r  r        c                    s   t   t| d t|d td| | t| j| j}t|d|}t|t 	| jt
t|d d fdd	}|S )Nlstsqr9   r  c                    s2  | j d }| j d }t|}t|  t| t| | t| | t||}t||}t| }tj	||fdj
}	t|	|| tj	|d}
tj	dtjd} ||||j||	j||
j||j}t| |d }||k so||krwtj	dd}nt|	||}t||	|}t|j|	j|
j|jg ||||
d | fS )Nr&  r'  r)  r   r   )r   r  r  r  r  rf  maxr  r   r   r  r  int32r+  r0  r  r  r#  r,  )r   r   rcondrk   r   r  ri  Zmaxmnr  r  r   Zrank_ptrr   rankru   r   r!   np_dtrZ   r  r"   r#   
lstsq_impl  sF   





zlstsq_impl.<locals>.lstsq_implr  )r+   r  r3  r  r]  r^  r   r<   rM   rZ   r   r$   )r   r   r  nb_dtZr_typer  r"   r  r#   r  z  s   


?r  c                 C   r{  )z
    Extract 'x' (the solution) from the 'bcpy' scratch space.
    Note 'b' is only used to check the system input dimension...
    r|  r   r  r"   r"   r#   _solve_compute_return  r  r  c                 C   s"   | j dkrdd }|S dd }|S )Nr   c                 S   s
   |j  S r,   r  r  r"   r"   r#   r    r8   z-_solve_compute_return_impl.<locals>.oneD_implc                 S   s   |S r,   r"   r  r"   r"   r#   r    r  z-_solve_compute_return_impl.<locals>.twoD_implr   )r   r  r  r  r"   r"   r#   _solve_compute_return_impl  r  r  c                    sh   t   t| d t|d td| | t| j| j}t | jt	t
|d  fdd}|S )Nsolvec              	      s   | j d }t|}t|  t| t| | t| }tj||fdj}|dkr-t||S t	||| tj|t
d} |||j||j|j|}t| t|j|j|jg t||S )Nr&  r)  r   )r   r  r  r  r  r   r   r  r  r  r*  r+  r!  r#  r,  )r   r   rk   r  r  r  r-  r   r!   r  r\   r"   r#   
solve_impl  s0   




zsolve_impl.<locals>.solve_impl)r+   r  r3  r  r]  r^  r   rM   r\   r   r$   )r   r   r  r  r"   r  r#   r    s   

)r  V瞯<c              
      s   t   t| d t| jd| j}t|t | jt 	| jt
t| jdt
d t
dt
dt| j}tjdg|dtjdg|dd f	d	d
	}|S )Npinvr9   rd  r^   r   r)  r   r  c                    s  | j d }| j d }t|  t| }|dks|dkr$|j | j jS t||}tj||f| j	d}tj|d}tj||f| j	d} |||j
||j
|j
||j
|}	t|	 |d | }
d}t|D ]}|| |
krxd||  ||< |}qf|d7 }||krt|D ]}t|D ]}|||f ||  |||f< qqnt|D ]}|| }t|D ]}|||f | |||f< qq|||j
|j
||j
|j
|j
|}	t|j|j|j|jjjg |j | j jS )Nr&  r'  r   r)  r   r   )r   r  r  r  r  reshaperf  r   r   r   r+  r0  r7  r#  r,  )r   r  rk   r   r  ri  rl  r   rm  r   Zcut_atZcut_idxr   rw  rx  Zs_local	ZJOBZTRANSAZTRANSBr!   rV   rE   r   ro  r   r"   r#   	pinv_implD  s~   
'


zpinv_impl.<locals>.pinv_implr  )r+   r  r<   r   r]  r^  rM   rV   r3   rE   r   r$   r   array)r   r  rr  dtr  r"   r  r#   r  *  s    

 r  c                 C   s.   t | jtjrtdd }|S tdd }|S )z
    Walks the diag of a LUP decomposed matrix
    uses that det(A) = prod(diag(lup(A)))
    and also that log(a)+log(b) = log(a*b)
    The return sign is adjusted based on the values found
    such that the log(value) stays in the real domain.
    c                 S   sV   |d }d}t | D ]}t|||f }||||f |  }|t| }q
||fS )Ny                r   )r7  r   r  log)rk   r   sgnZcsgnaccr   Zabselr"   r"   r#   cmplx_diag_walker  s   z3_get_slogdet_diag_walker.<locals>.cmplx_diag_walkerc                 S   sL   d}t | D ]}|||f }|dk r| }| }|t| }q|d |fS )Nr   )r7  r   r  )rk   r   r  r  r   r  r"   r"   r#   real_diag_walker  s   z2_get_slogdet_diag_walker.<locals>.real_diag_walker)rc   r   r   r  r
   )r   r  r  r"   r"   r#   _get_slogdet_diag_walker  s   
	
r  c                    sl   t   t| d t | jtt| jdt| | d t| jd| jd fdd}|S )Nslogdetr   r9   r   c                    s   | j d }| j d |krd}tj||dkr fS t|  t| }tj|td}|||j||j}|dkr@dtj	 fS t
| d}t|D ]}||| |d k }qJ|d@ }|dkrad}t|jg |||S )Nr&  r'  r(  r   r)  r   r   )r   r   r  r  r  r  r   r*  r+  infr!  r7  r#  r,  )r   rk   r  r  r-  r   r  r   ZONEZZEROZdiag_walkerr!   rN   r"   r#   slogdet_impl  s*   
	z"slogdet_impl.<locals>.slogdet_impl)	r+   r  rM   rN   r   r   r$   r  r<   )r   r  r"   r  r#   r    s   

)r  c                 C   s   t   t| d dd }|S )Ndetc                 S   s   t j| \}}|t | S r,   )r   r  r  exp)r   r  r  r"   r"   r#   det_impl4  s   zdet_impl.<locals>.det_implr+   r  )r   r  r"   r"   r#   r  -  s   
r  c                 C   r{  )z)
    Compute singular values of *a*.
    r|  r"  r"   r"   r#   _compute_singular_values;  r  r  c                    s   t  | jtt| jdtd t| jd| j}t|t| j}tj	d|dtj	d|d fdd}|S )z>
    Returns a function to compute singular values of `a`
    rc  r<  r9   r   r)  c           
         s   | j d }| j d }|dks|dkrtjdt|  |}t||}d}d}t| }tj|d} |||j||jj|j|}	t	|	 t
|jjj|jg |S )z+
        Computes singular values.
        r&  r'  r   re  r   r)  )r   r   r  r  r  rf  r  r   r+  r0  r#  r,  )
r   rk   r   rh  ri  rj  rk  r  r   r   ZJOBZ_Nr!   np_ret_typerV   rl  rm  r"   r#   sv_functionW  s6   


z2_compute_singular_values_impl.<locals>.sv_function)
rM   rV   r   r   r$   r<   r]  r^  r   r   )r   nb_ret_typenp_dtyper  r"   r  r#   _compute_singular_values_implB  s   
/r  c                 C   r{  )z.
    Compute the L2-norm of 1D-array *a*.
    r|  r"  r"   r"   r#   _oneD_norm_2  r  r  c                    sL   t | jd| j}t|t | jtt| jd  fdd}|S )Nr9   normc                    sh   t | }tjdd}t| jd | j } || j||j}|dk r(t  J t|j	| j	g |d S )Nrq  r)  r   )
lenr   r   r   stridesr   r+  r  r#  r,  )r   rk   rv  Zjmpr   r!   r  xxnrm2r"   r#   rm     s   z_oneD_norm_2_impl.<locals>.impl)r<   r   r]  r^  r3   r:   r   r$   )r   r  rm   r"   r  r#   _oneD_norm_2_impl  s   
r  c           	         s  t | jd| j}t|}t| j}t | j}tt| jd}| jdkr<|d t	j
fv r5ddd}|S ddd}|S | jdkr|d t	j
fv ro| jdkrTtd	d
  n| jdkr`tdd
  ntdd
  d fdd	}|S t|jjdfdd	}|S J )Nr9   r  r   c                 S   s   t | S r,   )r  r   r   r"   r"   r#   r    s   z!_get_norm_impl.<locals>.oneD_implc                 S   s<  t | }|dkr
dS |dkrt| S |tjkr3t| d }td|D ]}t| | }||kr0|}q"|S |tj krUt| d }td|D ]}t| | }||k rR|}qD|S |dkrnd}t|D ]}| | dkrk|d7 }q_|S |dkrd}t|D ]
}|t| | 7 }qx|S d}t|D ]}|t| | | 7 }q|d|  S )Nr   r   r   r   r   )r  r  r   r  r  r7  )r   r   rk   rv  r   r0   r"   r"   r#   r    sJ   
r   r^   c                 S   s   | S r,   r"   r   r"   r"   r#   array_prepare	     z%_get_norm_impl.<locals>.array_preparer   c                 S   s   | j S r,   )r  r  r"   r"   r#   r  	  s   c                 S   s   |   S r,   r  r  r"   r"   r#   r   	     c                    s(   | j }|dkr	dS  | }t||S )Nr   r   )r,  r  r  )r   r   rk   Zx_c)r  r"   r#   r  &	  s
   z!_get_norm_impl.<locals>.twoD_implc           	         s  | j d }| j d }| jdkrdS |tjkr:d}t|D ]}d}t|D ]}|t| ||f 7 }q$||kr7|}q|S |tj krd }t|D ]}d}t|D ]}|t| ||f 7 }qN||k ra|}qF|S |dkrd}t|D ]}d}t|D ]}|t| ||f 7 }qv||kr|}qn|S |dkr }t|D ]}d}t|D ]}|t| ||f 7 }q||k r|}q|S |dkrt| d S |dkrt| d S td)Nr&  r'  r   r   r   r   z Invalid norm order for matrices.)r   r,  r   r  r7  r  r  r   )	r   r   rk   r   Z
global_maxiitmpZjjZ
global_min)max_valr"   r#   r  1	  sb   



r   r,   )r<   r   r]  r^  r3   r:   r   r$   r   r   ro   r`   r
   r   finfor  r  )	r   Zord_flagr  r  r  r  r!   r  r  r"   )r  r  r#   _get_norm_impl  s6   


<
9



PEr  c                 C   s   t   t| d t| |S )Nr  )r+   r3  r  r  r"   r"   r#   	norm_impl{	  s   

r  c                 C   s   t   t| d ddd}|S )Ncondc                 S   s   |dks|dks|d u r.t | }|dks|d u r#t|d |d }n!t|d |d }ntj| |}tjtj| |}|| }t|rLtjS |S )Nr   r'  r   r&  )r  r   divider  r  r%  isnanr  )r   pr   r   Znorm_xZ
norm_inv_xr"   r"   r#   rm   	  s   
zcond_impl.<locals>.implr,   r  )r   r  rm   r"   r"   r#   	cond_impl	  s   

$r  c                 C   s4   d}t t| D ]}| | |kr|d }q |S |S )zJ
    Gets rank from singular values with cut-off at a given tolerance
    r   r   r7  r  )svr   r  r   r"   r"   r#   _get_rank_from_singular_values	  s   
r  c                    s.   t   t| d dd   fdd}|| |S )ah  
    Computes rank for matrices and vectors.
    The only issue that may arise is that because numpy uses double
    precision lapack calls whereas numba uses type specific lapack
    calls, some singular values may differ and therefore counting the
    number of them above a tolerance may lead to different counts,
    and therefore rank, in some cases.
    matrix_rankc                    sT   |d t jfv r#t| jd| j}t|}t|j d fdd	}|S ddd}|S )Nr9   c                    s@   t | }| jd }| jd }t||}|d |   }t||S )Nr   r   )r  r   r  r  )r  tolr   r   r   lr   Zeps_valr"   r#   _2d_tol_none_impl	  s   



zImatrix_rank_impl.<locals>._2d_matrix_rank_impl.<locals>._2d_tol_none_implc                 S   s   t | }t||S r,   )r  r  )r  r  r   r"   r"   r#   _2d_tol_not_none_impl	  s   
zMmatrix_rank_impl.<locals>._2d_matrix_rank_impl.<locals>._2d_tol_not_none_implr,   )	r   ro   r<   r   r]  r^  r   r  Zeps)r  r  Znb_typeZnp_typer  r  r"   r  r#   _2d_matrix_rank_impl	  s   

z.matrix_rank_impl.<locals>._2d_matrix_rank_implc                    s2   | j }|dkrddd}|S |dkr | |S J )Nr   c                 S   s(   t t| D ]}| | dkr dS qdS )Nr   r   r   r  )r  r  r   r"   r"   r#   _1d_matrix_rank_impl	  s
   zMmatrix_rank_impl.<locals>._get_matrix_rank_impl.<locals>._1d_matrix_rank_implr   r   r,   r   )r  r  r   r  r  r"   r#   _get_matrix_rank_impl	  s   

z/matrix_rank_impl.<locals>._get_matrix_rank_impl)r+   r3  )r  r  r   r"   r  r#   matrix_rank_impl	  s
   


r  c                    sF   t | d t| j t|d|}t|tjstd fdd}|S )zL
    Computes matrix power. Only integer powers are supported in numpy.
    matrix_powerr   zExponent must be an integer.c           
         sH  |dkrt j| j d}t| jd D ]}d|||f< q|S | jd | jd }}||kr1td|dkr9|  S |dk rOt j|  }|dkrK|S | }n
|dkrW|  S | }|dk rw|d	krgt ||S |d
krut t |||S d S |}|}|}d}	|dkr|d@ r|	r|}d}	nt ||}t ||}|d? }|dks|S )Nr   r)  r   r&  r'  zinput must be a square arrayr      r      TF)	r   r   r   r7  r   re   r  r%  r   )
r   rk   r  r   r  r  r  r  rv  flagr  r"   r#   matrix_power_impl
  sL   
z,matrix_power_impl.<locals>.matrix_power_impl)	r  r]  r^  r   r<   rc   r   Integerr   )r   rk   ntr  r"   r  r#   r  
  s   
?r  c                 C   s8   t | ddd t|ttjfstd| d	dd}|S )
z)
    Computes the trace of an array.
    traceFr  z!integer argument expected, got %sr   c                 S   s   | j \}}|}|dk r|| }|dkr|| }tt||d}d}|dkr8t|D ]}|| ||| f 7 }q)|S t|D ]}|| || |f 7 }q<|S r   )r   r  rf  r7  )r   offsetrowscolsr   rk   rv  rw  r"   r"   r#   matrix_trace_impl]
  s   
z,matrix_trace_impl.<locals>.matrix_trace_implNr   )r  rc   r   r   r  r   )r   r  r  r"   r"   r#   r  R
  s
   
r  c                 C   sB   |rdnd}||f}t | tjr| jdkstd| ddd S d S )Nr  r   r   r1  Fr  )rc   r   rd   r   r   r2  r"   r"   r#   _check_scalar_or_lt_2d_matq
  s   
r  c                 C   s@   t | }t |}t | |jdf| d|jfS r  r   Zasarraymultiplyr  r  r,  r   r   r   aabbr"   r"   r#   outer_impl_none{
  s
   

r  c                 C   sF   t | }t |}t | |jdf| d|jf| |S r  r  r  r"   r"   r#   outer_impl_arr
  s   

r  c                 C   s   |d t jfv r	tS tS r,   )r   ro   r  r  r   r   r   r"   r"   r#   _get_outer_impl
  s   r  c                    s:   t | ddd t |ddd t| || d fdd	}|S )NouterFr  c                    r   r,   r"   r  rm   r"   r#   
outer_impl
  s   zouter_impl.<locals>.outer_implr,   )r  r  )r   r   r   r  r"   r  r#   r  
  s
   r  c                 C   s`   t | tjr(| jdvrtd| j| jdkr tdd }|S tdd }|S tdd }|S )N)r^   r   z^np.linalg.kron only supports 'C' or 'F' layout input arrays. Received an input of layout '{}'.r   c                 S   s    | j d }| j d }| ||S )Nr&  r'  r   r  )r   xnZxmr"   r"   r#   	nrm_shape
  s   

z(_kron_normaliser_impl.<locals>.nrm_shapec                 S   s   | j d }| d|S )Nr&  r   r  )r   r  r"   r"   r#   r   
  s   
c                 S   s   t dt| }| |d< |S )Nr   r   )r   r   r  )r   r   r"   r"   r#   r   
  s   )rc   r   rd   r`   r   formatr   r
   )r   r   r"   r"   r#   _kron_normaliser_impl
  s   




r"  c                 C   s   t | tj}t |tj}|r*|r*| jdks|jdkr"tdd }|S tdd }|S |r4tdd }|S |r>tdd }|S tdd }|S )Nr   c                 S   s   |S r,   r"   r   r   r   r"   r"   r#   rv  
  r  z_kron_return.<locals>.retc                 S   s   | |jS r,   )r  r,  r#  r"   r"   r#   rv  
     c                 S   s   | | jS r,   r  r   r#  r"   r"   r#   rv  
  r$  c                 S   s   | |jS r,   r%  r#  r"   r"   r#   rv  
  r$  c                 S   s   |d S r   r"   r#  r"   r"   r#   rv  
  r  )rc   r   rd   r   r
   )r   r   Za_is_arrZb_is_arrrv  r"   r"   r#   _kron_return
  s*   




r&  c                    sX   t | ddd t |ddd t| t|t| |t| d|   fdd}|S )NkronFr  r   c              	      s   | }|}|j d }|j d }|j d }|j d }|| }|| }	tj||	f d}
t|D ]4}|| }t|D ])}|| }||d d f }t|D ]}|| }|||f | |
|||| f< qMq;q1| ||
S )Nr'  r&  r)  )r   r   r   r7  )r   r   r  r  r  r  r  r  cmZcnr^   rw  Zrjmpr   ZirjmpZslcrx  Zcjmpr  Zfix_aZfix_bZret_cr"   r#   	kron_impl
  s(   



"zkron_impl.<locals>.kron_impl)r  r"  r&  r<   )r   r   r*  r"   r)  r#   r*  
  s   
(r*  )r   )F)Trq  r  r  r,   r  )rK   
contextlibr   Zllvmliter   numpyr   operatorZnumba.core.imputilsr   r   r   r   Znumba.core.typingr   Znumba.core.extendingr   r	   r
   Z
numba.corer   r   Znumba.core.errorsr   r   r   Zarrayobjr   r   r   Znumba.npr   r]  rz   r{   Z
as_pointerZ	ll_char_pr}   Zll_intcZ	ll_intc_pr|   Z	ll_intp_pr  r*  rP   Zfloat32r[   Z	complex64Z
complex128r   r$   r)   r+   r2   r3   rM   contextmanagerri   rp   rv   rx   r   r   r   r   r   r   r   r   r   matmulr   r   r   r   r   r   r   r   rA   r=   r  r  r  r  r  r  r!  r#  r  r%  r/  r0  r3  r4  r:  r;  rO  rP  rS  rU  r[  ra  rb  rc  rp  rs  rz  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r
  r  r  r  r  r  r  r  r"  r&  r'  r*  r"   r"   r"   r#   <module>   s6   


) $
%2


,
9Y
#



	


'

	


+

r

v

0

0
A
P




$

^



< $
$

:

F
# 
H
,


A
P



	"