U
    |eg                    @   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 kr td|f |S )Nzunsupported dtype for %s())_blas_kindsget	TypeError)dtype	func_namekind r"   L/var/www/website-v5/atlas_env/lib/python3.8/site-packages/numba/np/linalg.pyget_blas_kind0   s    
r$   c                  C   s.   zdd l } W n tk
r(   tdY nX d S Nr   z*scipy 0.16+ is required for linear algebra)Zscipy.linalg.cython_blasImportErrorscipyr"   r"   r#   ensure_blas7   s    r)   c                  C   s.   zdd l } W n tk
r(   tdY nX d S r%   )scipy.linalg.cython_lapackr&   r'   r"   r"   r#   ensure_lapack>   s    r+   c                 C   s   |  |||}t||S N)get_constant_genericr   alloca_once_value)contextbuildertyvalconstr"   r"   r#   make_constant_slotE   s    r4   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   s
   t   d S r,   )r)   selfr"   r"   r#   __init__P   s    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   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   rE   r"   r"   r#   rF   ^   s"    z_BLAS.numba_xxgemmN)__name__
__module____qualname____doc__r8   classmethodr:   rF   r"   r"   r"   r#   r5   J   s   

r5   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   s
   t   d S r,   )r+   r6   r"   r"   r#   r8   y   s    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   rH   r"   r"   r#   rO   |   s    z_LAPACK.numba_xxgetrfc              	   C   s0   t t jt jt |t jt t}t d|S )Nnumba_ez_xxgetrirP   rH   r"   r"   r#   rR      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_rgeevrG   rH   r"   r"   r#   rS      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_cgeevrG   rH   r"   r"   r#   rT      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wtyperE   r"   r"   r#   rU      s    z_LAPACK.numba_ez_xxxevdc                 C   s,   t t jt jt jt |t j}t d|S )Nnumba_xxpotrfrG   rH   r"   r"   r#   rV      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   styperE   r"   r"   r#   rW      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_geqrfrG   rH   r"   r"   r#   rY      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_xxgqrrG   rH   r"   r"   r#   rZ      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#   r[      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_xgesvrP   rH   r"   r"   r#   r]     s    
z_LAPACK.numba_xgesvN)rI   rJ   rK   rL   r8   rM   rO   rR   rS   rT   rU   rV   rW   rY   rZ   r[   r]   r"   r"   r"   r#   rN   s   s0   


	



	



rN   c                 c   s   g }g }g }t |j|D ]r\}}t|tjr6|jdkrB|| }	}
n4|jdd}	t|	|}t| |||f}
|	|	|
f |	|	 |	|
 qt|j
f| t|fV  |D ]\}}| j||| qd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   Arrayra   copyr   r   appendreturn_typetuplenrtdecref)r/   r0   rE   rc   ZnewtysnewargsZcopiesr1   r2   newtynewvalZcopysigr"   r"   r#   make_contiguous  s    

ro   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$array size too large to fit in C int)OverflowError)nZ_maxintr"   r#   impl5  s    zcheck_c_int.<locals>.implN)compile_internalr   r   noner?   )r/   r0   rq   rs   r"   rr   r#   check_c_int/  s     rv   c              	   C   sB   |j t||dd" | |}|  |d W 5 Q R X dS )z[
    Check the integer error return from one of the BLAS wrappers in
    _helperlib.c.
    Flikelyz#BLAS wrapper returned with an errorNif_thenr   is_not_nullget_python_api
gil_ensurefatal_errorr/   r0   respyapir"   r"   r#   check_blas_return=  s    
r   c              	   C   sB   |j t||dd" | |}|  |d W 5 Q R X dS )z]
    Check the integer error return from one of the LAPACK wrappers in
    _helperlib.c.
    Frw   z%LAPACK wrapper returned with an errorNry   r   r"   r"   r#   check_lapack_returnI  s    
r   c                 C   s   t t dttttttg}t|j|d}	t	|}
t 
tt|
}t 
tt|}||	|||||t||t||tf}t| || dS )zQ
    Call the BLAS vector * vector product function for the given arguments.
    r   Znumba_xxdotN)r   FunctionTypeIntTypell_charintp_t	ll_void_pr   get_or_insert_functionmoduler$   Constantordintcallbitcastr   )r/   r0   	conjugater   rq   a_datab_dataout_datafntyfnr!   kind_valr   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rt|\}}|d }n|\}}|d }t|
}t tt|}t t|rt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   trq   N)r   r   r   r   r   r   r   r   r   r   r4   ra   r$   r   r   r   r   r   )r/   r0   do_transZm_typem_shapesm_datav_datar   r   r   r   alphabetamrq   ldar!   r   transr   r"   r"   r#   call_xxgemvk  sB         



 


r   c           !         s8  t t dttttttttttttttg}t j|d}|\}}|\}}|j	}t
|  |d}t
|  |d}t ttdt ttd fdd}||||\}}}||||\}}}||	|
\}}}t|}t tt|} ||||||| |t|||| |t||f} t|  |  d	S )
zQ
    Call the BLAS matrix * matrix product function for the given arguments.
    r   rF   r   r   r   rq   c                    s8   | j j krn| j dkr$|d n|d  |tfS )Nr_   r   r   )ra   r   r   )r1   shapesdatar0   Znotransout_typer   r"   r#   get_array_param  s    
z$call_xxgemm.<locals>.get_array_paramN)r   r   r   r   r   r   r   r   r   r   r4   r   r   r$   r   r   r   )!r/   r0   Zx_typex_shapesx_datay_typey_shapesy_datar   
out_shapesr   r   r   r   k_krq   r   r   r   r   Ztransar   data_aZtransbldbdata_b_ZldcZdata_cr!   r   r   r"   r   r#   call_xxgemm  sT            

    
 r   c                 C   s(   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   rq   outr"   r"   r#   dot_impl  s    

zdot_2_mm.<locals>.dot_implrt   r   rh   r/   r0   rE   rc   r   r   r"   r"   r#   dot_2_mm  s    r   c                 C   s(   dd }|  ||||}t| ||j|S )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   _mrq   r   r"   r"   r#   r     s    
zdot_2_vm.<locals>.dot_implr   r   r"   r"   r#   dot_2_vm  s    r   c                 C   s(   dd }|  ||||}t| ||j|S )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   rq   _nr   r"   r"   r#   r     s    
zdot_2_mv.<locals>.dot_implr   r   r"   r"   r#   dot_2_mv  s    r   Fc              	   C   s   |j \}}|j}t|| ||d }t|| ||d }	t||j\}
dd }| ||ttj	f|j  | 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   rq   r"   r"   r#   
check_args  s    zdot_2_vv.<locals>.check_args)rc   rh   r   r   unpack_tupler   rt   r   r   ru   rv   alloca_onceget_value_typer   r   load)r/   r0   rE   rc   r   atybtyr   r   r   rq   r   r   r"   r"   r#   dot_2_vv  s    
 r   c                 C   s   t d| |S )z
    np.dot(a, b)
    znp.dot()
dot_2_implleftrightr"   r"   r#   dot_2  s    r   c                 C   s   t d| |S )z
    a @ b
    z'@'r   r   r"   r"   r#   matmul_2  s    r   c                    sd   t |tjr`t |tjr`tfdd |jdks<|jdkrTtd||ff t  fddS d S )Nc                    s   |j |j f  fdd}|j|jkr0td  dkrJt|jdd}n> dksZ dkrlt|jd	d}n d
kr||j}ntd t||||fS )Nc              
      s   t   t| |||\}} dkr<t| |||W  5 Q R  S  dkr^t| |||W  5 Q R  S  dkrt| |||W  5 Q R  S  dkrt| |||W  5 Q R  S tdW 5 Q R X d S )N   r   r   r   r   r   r   r   unreachable)r)   ro   r   r   r   r   AssertionErrorr/   r0   rE   rc   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   re   r   )typingcontextr   r   r   rh   )namer   r#   _impl  s     zdot_2_impl.<locals>._implr^   z/%s is faster on contiguous arrays, called on %sc                    s
    | |S r,   r"   r   r   r"   r#   <lambda>F      zdot_2_impl.<locals>.<lambda>rd   r   re   r   ra   warningswarnr   )r   r   r   r"   )r   r   r#   r     s    ! r   c                    s^   t | tjrZt |tjrZtdd  | jdks8|jdkrNtd| |ff t  fd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r8tdt|j|||fS )Nc              
   S   sB   t   t| |||$\}}t| |||ddW  5 Q R  S Q R X d S )NT)r   )r)   ro   r   r   r"   r"   r#   codegenQ  s    z$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                    s
    | |S 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r6t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   rq   r"   r"   r#   dot_3_vm_check_argsh  s    
r   c                 C   s:   | j \}}|j \}||kr"td|j |fkr6t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   rq   r"   r"   r#   dot_3_mv_check_argss  s    
r   c                 C   s  |j \}}}||jkst|j}t|| ||d }t|| ||d }	t|| ||d }
t||j}t||	j}t||
j}|j|jk r|}|}|d }|d }|j	dk}|	j
|j
 }}t}n4|}|}|d }|d }|j	dk}|j
|	j
 }}t}| ||ttjf|j  | |D ]}t| || q| tjd}|d||}|d||}|||}|j|dd`\}}|$ t||
j
||
j|
jd W 5 Q R X | t| |||||||
j
 W 5 Q R X W 5 Q R X t| ||j|
 S )	zE
    np.dot(vector, matrix, out)
    np.dot(matrix, vector, out)
    r   r   r   r   r_   ==Frw   )rc   rh   r   r   r   r   r   r   r   ra   r   r   r   rt   r   r   ru   rv   get_constantr?   icmp_signedor_if_elsememsetmulitemsizenitemsr   r   	_getvalue)r/   r0   rE   rc   xtyytyouttyr   xyr   r   r   r   Zmtyr   Zv_shaper   r   r   r   r   r2   zero
both_emptyZmatrix_emptyis_emptyr   nonemptyr"   r"   r#   dot_3_vm~  s`    

 
  
r  c           '      C   s  |j \}}}||jkst|j}t|| ||d }t|| ||d }	t|| ||d }
t||j}t||	j}t||
j}|\}}|\}}|jdkstdd }| 	||t
tjf|j  | t| || t| || t| || |j}|	j}|
j}| tjd}|d||}|d||}|d||}|||||}|j|dd	\}}|$ t||
j||
j|
jd W 5 Q R X |V | tjd}|d||}|d||}||\} }!| x ||b\}"}#|" t| |d||||| W 5 Q R X |#( |j|jk}$t| ||$||||| W 5 Q R X W 5 Q R X W 5 Q R X |!~ ||h\}%}&|%( |j|jk}$t| ||$||||| W 5 Q R X |&" t| |||||||||| W 5 Q R X W 5 Q R X W 5 Q R X W 5 Q R X W 5 Q R X W 5 Q R X t| ||j|
 S )
z%
    np.dot(matrix, matrix, out)
    r   r   r   r_   c                 S   s>   | j \}}|j \}}||kr$td|j ||fkr:tdd S )Nz;incompatible array sizes for np.dot(a, b) (matrix * matrix)zFincompatible output array size for np.dot(a, b, out) (matrix * matrix)r   )r   r   r   r   r   r   rq   r"   r"   r#   r     s    

zdot_3_mm.<locals>.check_argsr   Frw   )rc   rh   r   r   r   r   r   r   ra   rt   r   r   ru   rv   r   r   r?   r   r   r   r   r   r   r   r   r   r   r   r   )'r/   r0   rE   rc   r   r   r  r   r  r  r   r   r   r   r   r   r   rq   r   r   r   r   r  r  Zx_emptyZy_emptyr  r   r  oneZis_left_vecZis_right_vecZr_vecZr_matZv_vZm_vr   Zv_mZm_mr"   r"   r#   dot_3_mm  s    
 
 
       "          @
r
  c                    st   t | tjrpt |tjrpt |tjrptdd  | jdksN|jdksN|jdkrdtd| |ff t  fddS dS )z
    np.dot(a, b, out)
    c                 S   s:   dd }|j |j ks |j |j kr(tdt|||||fS )Nc              
   S   s   t   t| |||x\}}tdd |jd d D }|dhkrZt| |||W  5 Q R  S |ddhkrt| |||W  5 Q R  S tdW 5 Q R X d S )Nc                 s   s   | ]}|j V  qd S r,   r   ).0r  r"   r"   r#   	<genexpr>  s     z8dot_3.<locals>._impl.<locals>.codegen.<locals>.<genexpr>r   r   r   )r)   ro   setrc   r
  r  r   )r/   r0   rE   rc   r   r"   r"   r#   r     s    
z%dot_3.<locals>._impl.<locals>.codegenz/np.dot() arguments must all have the same dtype)r   r   r   )r   r   r   r   r   r"   r"   r#   r     s    zdot_3.<locals>._implr^   r   c                    s    | ||S r,   r"   r   r   r   r   r"   r#   r   1  r   zdot_3.<locals>.<lambda>Nr   r  r"   r   r#   dot_3  s    

r  Znumba_fatal_errorc                 C   s.   t | D ]}t | s
t jdq
d S )Nz$Array must not contain infs or NaNs.)r   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sFd| }t|dd| jdksdd| }t|ddt | jtjtj	fsd| }t|ddd S )	N	np.linalgr   z&%s.%s() only supported for array typesFhighlightingr   z%%s.%s() only supported on 2-D arrays.3%s.%s() only supported on float and complex arrays.)
rd   r   Optionaltypere   r   r   r   FloatComplex)r   r    	la_prefixprefixinterpmsgr"   r"   r#   _check_linalg_matrix?  s    
r$  c                 G   s>   |d j }|dd  D ]"}|j |krd|  }t|ddqd S )Nr   r   zAnp.linalg.%s() only supports inputs that have homogeneous dtypes.Fr  )r   r   )r    r   t0r   r#  r"   r"   r#   _check_homogeneous_typesT  s
    

r&  c                   C   s   d S r,   r"   r"   r"   r"   r#   _copy_to_fortran_order\  s    r'  c                    s&   | j dk| j dk  fdd}|S )Nr   Ac                    sJ   rt | }n6 r<| jj}|r0t | jj}qFt | }n
t | }|S r,   )r   rf   flagsf_contiguousTasfortranarray)r   acpyZflag_fZA_layoutZF_layoutr"   r#   rs   f  s    
z&ol_copy_to_fortran_order.<locals>.implr`   )r   rs   r"   r.  r#   ol_copy_to_fortran_order`  s    

r/  c                 C   s6   | dkr2| dk rt   dst| dkr2tjdd S )Nr   z(Matrix is singular to machine precision.)fatal_error_funcr   r   r  r  rr"   r"   r#   _inv_err_handler|  s    r3  c                 C   s   | d S )zFpass a list of variables to be preserved through dead code eliminationr   r"   r   r"   r"   r#   _dummy_liveness_func  s    r5  c                    sP   t   t| d t | jt | jtt| jd  fdd}|S )Ninvc                    s   | j d }| j d |kr(d}tj|t|  t| }|dkrD|S tj|td} |||j||j}t	|  ||j||j}t	| t
|j|jg |S )N.Last 2 dimensions of the array must be square.r   r   )r   r   r  r  r  r'  r   F_INT_nptypectypesr3  r5  size)r   rq   r#  r-  ipivr2  r!   rO   Znumba_xxgetrir"   r#   inv_impl  s    
zinv_impl.<locals>.inv_impl)r+   r$  rN   rO   r   rR   r   r$   )r   r@  r"   r?  r#   r@    s    
r@  c                 C   s2   | dkr.| dk rt   dst| dkr.tdd S )Nr   z&Internal algorithm failed to converge.)r0  r   r   r1  r"   r"   r#   %_handle_err_maybe_convergence_problem  s    rA  c                 C   sf   |rdnd}||f}t | tjs,td| | jdksBtd| t | jtjtjfsbtd| d S )Nr  r   z'%s.%s() only supported for array types r   +%s.%s() only supported on 1 and 2-D arrays r  )rd   r   re   r   r   r   r  r  r   r    r   r!  r"  r"   r"   r#   _check_linalg_1_or_2d_matrix  s    
rD  c                    sR   t   t| d t | jtt| jdtd td} fdd}|S )NcholeskyULc                    s   | j d }| j d |kr(d}tj||  }|dkr<|S  ||j|}|dkr|dk rlt  dslt|dkrtjdt|D ]}d|d ||f< q|S )Nr7  r8  r9  r   z Matrix is not positive definite.)	r   r   r  r  rf   r<  r0  r   range)r   rq   r#  r   r2  colZUPr!   rV   r"   r#   cho_impl  s&    
zcho_impl.<locals>.cho_impl)r+   r$  rN   rV   r   r   r$   )r   ZLOrK  r"   rJ  r#   rK    s    
rK  c                    s   t   t| d t | jt | jtt| jdtd td fdd} fdd}t| jt	j
jr|S |S d S )NeigNVc                    s  | j d }| j d |kr(d}tj|t|  t| }d}|}tj|| jd}tj|| jd}tj||f| jd}tj||f| jd}	|dkr||	jfS  ||j	||j	|j	|j	||	j	|}
t
|
 t|rtdt|j|j|	j|j|jg ||	jfS )z7
        eig() implementation for real arrays.
        r7  r8  r9  r   r:  r   z.eig() argument must not cause a domain change.)r   r   r  r  r  r'  r   r   r+  r<  rA  anyr   r5  r=  r   rq   r#  r-  ldvlldvrwrwivlvrr2  JOBVLJOBVRr!   rS   r"   r#   real_eig_impl
  sD    


zeig_impl.<locals>.real_eig_implc           
         s   | j d }| j d |kr(d}tj|t|  t| }d}|}tj|| jd}tj||f| jd}tj||f| jd}|dkr||jfS  ||j	||j	|j	||j	|}	t
|	 t|j|j|j|jg ||jfS )z:
        eig() implementation for complex arrays.
        r7  r8  r9  r   r:  r   )r   r   r  r  r  r'  r   r   r+  r<  rA  r5  r=  
r   rq   r#  r-  rQ  rR  wrU  rV  r2  rX  rY  r!   rT   r"   r#   cmplx_eig_implB  s8    

z eig_impl.<locals>.cmplx_eig_implr+   r$  rN   rS   r   rT   r   r$   rd   r   scalarsr  )r   rZ  r^  r"   rX  rY  r!   rT   rS   r#   eig_impl  s    
8(rb  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r|S |S d S )NeigvalsrM  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
|rtdt|j|j|	j|j|jg |S )z;
        eigvals() implementation for real arrays.
        r7  r8  r9  r   r:  r   z2eigvals() argument must not cause a domain change.)r   r   r  r  r  r'  r   r   r<  rA  rO  r   r5  r=  rP  rW  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.
        r7  r8  r9  r   r:  r   )r   r   r  r  r  r'  r   r   r<  rA  r5  r=  r[  r]  r"   r#   cmplx_eigvals_impl  s8    
z(eigvals_impl.<locals>.cmplx_eigvals_implr_  )r   rd  re  r"   ra  r#   eigvals_implo  s    
;)rf  c                    sp   t   t| d t| jd| j}t|t | jtt	| jdtd td fdd}|S )Neighr9   rN  rG  c                    s   | j d }| j d |kr(d}tj|t|  t| }tj|d}|dkrV||fS  ||j||j}t| t	|j
|j
g ||fS Nr7  r8  r9  r:  r   r   r   r  r  r  r'  r   r<  rA  r5  r=  r   rq   r#  r-  r\  r2  JOBZUPLOr!   rU   Zw_dtyper"   r#   	eigh_impl  s(    
zeigh_impl.<locals>.eigh_impl
r+   r$  r<   r   
np_supportas_dtyperN   rU   r   r$   )r   w_typern  r"   rk  r#   rn    s    

rn  c                    sp   t   t| d t| jd| j}t|t | jtt	| jdtd td fdd}|S )Neigvalshr9   rM  rG  c                    s   | j d }| j d |kr(d}tj|t|  t| }tj|d}|dkrR|S  ||j||j}t| t	|j
|j
g |S rh  ri  rj  rk  r"   r#   eigvalsh_impl(  s(    
z$eigvalsh_impl.<locals>.eigvalsh_implro  )r   rr  rt  r"   rk  r#   rt    s    

rt  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$|dkr0tjdt|  t| }|}t||}|r` }|}|}	n}|}|}	tj||f| jd}
tj|d}tj||	f| jd}||||j	||j	|
j	||j	|	}t
| t|j|j|
j|jg |
j||jfS )Nr7  r8  r   Arrays cannot be emptyr:  )r   r   r  r  r  r'  minr   r   r<  rA  r5  r=  r+  )r   full_matricesrq   r   r-  lduminmnrl  ucolldvtur   vtr2  ZJOBZ_AZJOBZ_Sr!   rW   s_dtyper"   r#   svd_implY  sD    


zsvd_impl.<locals>.svd_impl)r   )
r+   r$  r<   r   rp  rq  rN   rW   r   r$   )r   ry  s_typer  r"   r  r#   r  H  s    

.r  c                    sP   t   t| d t | jt | jtt| jd  fdd}|S )Nqrc                    sN  | j d }| j d }|dks$|dkr0tjdt|  t| }|}t||}tj|| jd} |||j	||j	}|dk rt
  dsttj||f| jdj}t|D ]*}	t|	d D ]}
||
|	f ||
|	f< qqt||D ]&}	t|D ]}
||
|	f ||
|	f< qqވ ||||j	||j	}t| t|j|jg |d d d |f |fS )Nr7  r8  r   rw  r:  r   )r   r   r  r  r  r'  rx  r   r   r<  r0  r   r   r+  rH  rA  r5  r=  )r   rq   r   qr   r{  tauretr2  ijr!   rY   rZ   r"   r#   qr_impl  sN    


	zqr_impl.<locals>.qr_impl)r+   r$  rN   rY   r   rZ   r   r$   )r   r  r"   r  r#   r    s    
9r  c                 C   s   t dS )z;
    Correctly copy 'b' into the 'bcpy' scratch space.
    NNotImplementedErrorbcpyr   nrhsr"   r"   r#   _system_copy_in_b  s    r  c                 C   s&   |j dkrdd }|S dd }|S d S )Nr   c                 S   s   || d |j d df< d S )Nr7  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 )Nr8  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  s
    
r  c                 C   s   t dS )zK
    Compute the number of right hand sides in the system of equations
    Nr  r   r"   r"   r#   _system_compute_nrhs  s    r  c                 C   s&   | j dkrdd }|S dd }|S d S )Nr   c                 S   s   dS Nr   r"   r  r"   r"   r#   r    s    z,_system_compute_nrhs_impl.<locals>.oneD_implc                 S   s
   | j d S )Nr7  r  r  r"   r"   r#   r    s    z,_system_compute_nrhs_impl.<locals>.twoD_implr  )r   r  r  r"   r"   r#   _system_compute_nrhs_impl  s
    
r  c                 C   s   t dS )zD
    Check that AX=B style system input is dimensionally valid.
    Nr  r   r   r"   r"   r#   !_system_check_dimensionally_valid  s    r  c                 C   s*   |j }|dkrdd }|S dd }|S d S )Nr   c                 S   s,   | j d }|j d }||kr(tjdd S )Nr8  r7  <Incompatible array sizes, system is not dimensionally valid.r   r   r  r  r   r   ambmr"   r"   r#   r    s    

z9_system_check_dimensionally_valid_impl.<locals>.oneD_implc                 S   s,   | j d }|j d }||kr(tjdd S )Nr8  r  r  r  r"   r"   r#   r    s    

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   s   t dS )z:
    Check that AX=B style system input is not empty.
    Nr  r  r"   r"   r#   _system_check_non_empty  s    r  c                 C   s*   |j }|dkrdd }|S dd }|S d S )Nr   c                 S   sF   | j d }| j d }|j d }|dks6|dks6|dkrBtjdd S Nr8  r7  r   rw  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sH|dksH|dksH|dkrTt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$  s    r  c                 C   s   t dS )z:
    Compute the residual from the 'b' scratch space.
    Nr  )r   rq   r  r"   r"   r#   _lstsq_residual:  s    r  c                    s   | j }| j}tt|d| |dkrTt|tjrB fdd}|S  fdd}|S n8|dks`tt|tjr| fdd}|S  fd	d}|S d S )
Nr9   r   c                    s6   t jd d}t t | |d df d |d< |S Nr   r:  r   r   )r   r   sumabsr   rq   r  r   
real_dtyper"   r#   
cmplx_implI  s    $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   rH  r  r  r   rq   r  r   r   r  r"   r#   r  W  s    &c                    s>   t j| d}t|D ]"}t | |d |f d ||< q|S r  )r   r   rH  r  r  r  r"   r#   r  ^  s     )	r   r   rp  rq  r<   rd   r   r  r   )r   rq   r  r   r   r  r  r"   r  r#   _lstsq_residual_implA  s    r  c                 C   s   t dS )z
    Extract 'x' (the lstsq solution) from the 'bcpy' scratch space.
    Note 'b' is only used to check the system input dimension...
    Nr  r   r  rq   r"   r"   r#   _lstsq_solutionf  s    r  c                 C   s&   | j dkrdd }|S dd }|S 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,   rf   r  r"   r"   r#   r  u  s    z'_lstsq_solution_impl.<locals>.twoD_implr  )r   r  rq   r  r  r"   r"   r#   _lstsq_solution_impln  s
    
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 s||krtj	dd}nt|	||}t||	|}t|j|	j|
j|jg ||||
d | fS )Nr7  r8  r:  r   r   )r   r  r  r  r  rx  maxr'  r   r   r+  r  int32r<  rA  r  r  r5  r=  )r   r   rcondrq   r   r  r{  Zmaxmnr-  r  r   Zrank_ptrr2  rankr   r  r!   np_dtr[   r  r"   r#   
lstsq_impl  sF    





zlstsq_impl.<locals>.lstsq_impl)r  )r+   r$  rD  r&  rp  rq  r   r<   rN   r[   r   r$   )r   r   r  nb_dtZr_typer  r"   r  r#   r  z  s    


?r  c                 C   s   t dS )z
    Extract 'x' (the solution) from the 'bcpy' scratch space.
    Note 'b' is only used to check the system input dimension...
    Nr  r   r  r"   r"   r#   _solve_compute_return  s    r  c                 C   s&   | j dkrdd }|S dd }|S d S )Nr   c                 S   s
   |j  S r,   r  r  r"   r"   r#   r    s    z-_solve_compute_return_impl.<locals>.oneD_implc                 S   s   |S r,   r"   r  r"   r"   r#   r    s    z-_solve_compute_return_impl.<locals>.twoD_implr  )r   r  r  r  r"   r"   r#   _solve_compute_return_impl  s
    
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rZt||S t	||| tj|t
d} |||j||j|j|}t| t|j|j|jg t||S )Nr7  r:  r   )r   r  r  r  r'  r   r   r+  r  r  r;  r<  r3  r5  r=  )r   r   rq   r  r-  r  r>  r2  r!   r  r]   r"   r#   
solve_impl  s0    



zsolve_impl.<locals>.solve_impl)r+   r$  rD  r&  rp  rq  r   rN   r]   r   r$   )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   rv  r_   r   r:  r   r  c                    s  | j d }| j d }t|  t| }|dks4|dkrH|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 ]$}|| |
krd||  ||< |}q|d7 }||krBt|D ]2}t|D ]"}|||f ||  |||f< qqn@t|D ]6}|| }t|D ]}|||f | |||f< q^qJ|||j
|j
||j
|j
|j
|}	t|j|j|j|jjjg |j | j jS )Nr7  r8  r   r:  r   r   )r   r  r'  r+  r  reshaperx  r   r   r   r<  rA  rH  r5  r=  )r   r  rq   r   r-  r{  r~  r   r  r2  Zcut_atZcut_idxr   r  r  Zs_local	ZJOBZTRANSAZTRANSBr!   rW   rF   r	  r  r  r"   r#   	pinv_implD  sv    '



& 	zpinv_impl.<locals>.pinv_impl)r  )r+   r$  r<   r   rp  rq  rN   rW   r5   rF   r   r$   r   array)r   r  r  dtr  r"   r  r#   r  *  s     

 r  c                 C   s2   t | jtjrtdd }|S tdd }|S dS )z
    Walks the diag of a LUP decomposed matrix
    uses that det(A) = prod(diag(lup(A)))
    and also that log(a)+log(b) = log(a*b)
    The return sign is adjusted based on the values found
    such that the log(value) stays in the real domain.
    c                 S   sV   |d }d}t | D ]8}t|||f }||||f |  }|t| }q||fS )Ny                r   )rH  r   r  log)rq   r   sgnZcsgnaccr   Zabselr"   r"   r#   cmplx_diag_walker  s    z3_get_slogdet_diag_walker.<locals>.cmplx_diag_walkerc                 S   sL   d}t | D ]2}|||f }|dk r0| }| }|t| }q|d |fS )Nr   )rH  r   r  )rq   r   r  r  r   r  r"   r"   r#   real_diag_walker  s    z2_get_slogdet_diag_walker.<locals>.real_diag_walkerN)rd   r   r   r  r
   )r   r  r  r"   r"   r#   _get_slogdet_diag_walker  s    
	
r  c                    sl   t   t| d t | jtt| jdt| | d t| jd| jd fdd}|S )Nslogdetr   r9   r   c                    s   | j d }| j d |kr(d}tj||dkr8 fS t|  t| }tj|td}|||j||j}|dkrdtj	 fS t
| d}t|D ]}||| |d k }q|d@ }|dkrd}t|jg |||S )Nr7  r8  r9  r   r:  r   r   )r   r   r  r  r  r'  r   r;  r<  infr3  rH  r5  r=  )r   rq   r#  r-  r>  r2  r  r   ONEZEROZdiag_walkerr!   rO   r"   r#   slogdet_impl  s*    
	z"slogdet_impl.<locals>.slogdet_impl)	r+   r$  rN   rO   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   s   t dS )z)
    Compute singular values of *a*.
    Nr  r4  r"   r"   r#   _compute_singular_values;  s    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`
    ru  rM  r9   r   r:  c           
         s   | j d }| j d }|dks$|dkr0tjdt|  |}t||}d}d}t| }tj|d} |||j||jj|j|}	t	|	 t
|jjj|jg |S )z+
        Computes singular values.
        r7  r8  r   rw  r   r:  )r   r   r  r  r  rx  r'  r   r<  rA  r5  r=  )
r   rq   r   rz  r{  r|  r}  r-  r   r2  ZJOBZ_Nr!   np_ret_typerW   r~  r  r"   r#   sv_functionW  s6    


z2_compute_singular_values_impl.<locals>.sv_function)
rN   rW   r   r   r$   r<   rp  rq  r   r   )r   nb_ret_typenp_dtyper  r"   r  r#   _compute_singular_values_implB  s    
/r  c                 C   s   t dS )z.
    Compute the L2-norm of 1D-array *a*.
    Nr  r4  r"   r"   r#   _oneD_norm_2  s    r  c                    sL   t | jd| j}t|t | jtt| jd  fdd}|S )Nr9   normc                    sl   t | }tjdd}t| jd | j } || j||j}|dk rTt  dsTtt	|j
| j
g |d S )Nr  r:  r   )lenr   r   r   stridesr   r<  r0  r   r5  r=  )r   rq   r  jmpr2  r!   r  xxnrm2r"   r#   rs     s    z_oneD_norm_2_impl.<locals>.impl)r<   r   rp  rq  r5   r:   r   r$   )r   r  rs   r"   r  r#   _oneD_norm_2_impl  s    
r  c           	         s
  t | jd| j}t|}t| j}t | j}tt| jd}| jdkrv|d t	j
fkrhddd}n
ddd}|S | jdk r|d t	j
fkr| jdkrtd	d
  n$| jdkrtdd
  ntdd
  d fdd	}nt|jjdfdd	}|S dstd S )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   sD  t | }|dkrdS |dkr$t| S |tjkrft| d }td|D ]}t| | }||krD|}qD|S |tj krt| d }td|D ]}t| | }||k r|}q|S |dkrd}t|D ]}| | dkr|d7 }q|S |dkrd}t|D ]}|t| | 7 }q|S d}t|D ]}|t| | | 7 }q|d|  S d S )Nr   r   r   r   r   )r  r  r   r  r  rH  )r   r   rq   r  r   r2   r"   r"   r#   r    sD    


r   r_   c                 S   s   | S r,   r"   r4  r"   r"   r#   array_prepare	  s    z%_get_norm_impl.<locals>.array_preparer   c                 S   s   | j S r,   )r+  r4  r"   r"   r#   r  	  s    c                 S   s   |   S r,   r  r4  r"   r"   r#   r   	  s    c                    s(   | j }|dkrdS  | }t||S )Nr   r   )r=  r  r  )r   r   rq   Za_c)r  r"   r#   r  &	  s
    z!_get_norm_impl.<locals>.twoD_implc           	         s  | j d }| j d }| jdkr"dS |tjkrtd}t|D ]6}d}t|D ]}|t| ||f 7 }qH||kr8|}q8|S |tj krȈ }t|D ]6}d}t|D ]}|t| ||f 7 }q||k r|}q|S |dkrd}t|D ]6}d}t|D ]}|t| ||f 7 }q||kr|}q|S |dkrr }t|D ]<}d}t|D ]}|t| ||f 7 }q@||k r0|}q0|S |dkrt| d S |dkrt| d S tdd S )Nr7  r8  r   r   r   r   z Invalid norm order for matrices.)r   r=  r   r  rH  r  r  r   )	r   r   rq   r   Z
global_maxiitmpjjZ
global_min)max_valr"   r#   r  1	  sZ    








r   )N)N)N)N)r<   r   rp  rq  r5   r:   r   r$   r   r   ru   ra   r
   r   finfor  r  r   )	r   Zord_flagr  r  r  r  r!   r  r  r"   )r  r  r#   _get_norm_impl  s2    


9


	Er  c                 C   s   t   t| d t| |S )Nr  )r+   rD  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 kr\t | }|dks0|d krFt|d |d }qt|d |d }n,tj| |}tjtj| |}|| }t|rtjS |S d S )Nr   r8  r   r7  )r  r   divider  r  r6  isnanr  )r   pr   r2  Znorm_aZ
norm_inv_ar"   r"   r#   rs   	  s    
zcond_impl.<locals>.impl)Nr  )r   r  rs   r"   r"   r#   	cond_impl	  s    

$r  c                 C   s4   d}t t| D ]}| | |kr*|d }q q0q|S )zJ
    Gets rank from singular values with cut-off at a given tolerance
    r   r   rH  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                    sX   |d t jfkrFt| jd| j}t|}t|j d fdd	}|S ddd}|S d S )Nr9   c                    s@   t | }| jd }| jd }t||}|d |   }t||S )Nr   r   )r  r   r  r  )r   tolr   r2  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_impl)N)N)	r   ru   r<   r   rp  rq  r   r  eps)r   r  nb_typenp_typer  r  r"   r  r#   _2d_matrix_rank_impl	  s    

z.matrix_rank_impl.<locals>._2d_matrix_rank_implc                    s:   | j }|dkrddd}|S |dkr. | |S ds6td S )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   )N)r   r   )r   r  r   r  r  r"   r#   _get_matrix_rank_impl	  s    

z/matrix_rank_impl.<locals>._get_matrix_rank_impl)r+   rD  )r   r  r  r"   r  r#   matrix_rank_impl	  s
    

r  c                    sF   t | d t| j t|d|}t|tjs6t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           
         sJ  |dkr<t j| j d}t| jd D ]}d|||f< q&|S | jd | jd  }}||krbtd|dkrr|  S |dk rt j|  }|dkr|S | }n|dkr|  S | }|dk r|d	krt ||S |d
krt t |||S nZ|}|}|}d}	|dkrB|d@ r,|	r |}d}	nt ||}t ||}|d? }q|S d S )Nr   r:  r   r7  r8  zinput must be a square arrayr      r      TF)	r   r   r   rH  r   rf   r  r6  r   )
r   rq   r(  r   r  r  r  r  r  flagr  r"   r#   matrix_power_impl
  sH    


z,matrix_power_impl.<locals>.matrix_power_impl)	r$  rp  rq  r   r<   rd   r   Integerr   )r   rq   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rnt|D ]}|| ||| f 7 }qRn"t|D ]}|| || |f 7 }qv|S r   )r   r  rx  rH  )r   offsetrowscolsr   rq   r  r  r"   r"   r#   matrix_trace_impl]
  s    
z,matrix_trace_impl.<locals>.matrix_trace_impl)r   )r$  rd   r   r   r  r   )r   r  r  r"   r"   r#   r  R
  s
    
r  c                 C   s>   |rdnd}||f}t | tjr:| jdks:td| ddd S )Nr  r   r   rB  Fr  )rd   r   re   r   r   rC  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   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krtS tS d S r,   )r   ru   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                    s    | ||S r,   r"   r'  rs   r"   r#   
outer_impl
  s    zouter_impl.<locals>.outer_impl)N)r  r(  )r   r   r   r+  r"   r*  r#   r+  
  s
    r+  c                 C   sh   t | tjrT| jdkr(td| jqd| jdkrBtdd }|S tdd }|S ntdd }|S 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 )Nr7  r8  r   r  )r  xnxmr"   r"   r#   	nrm_shape
  s    

z(_kron_normaliser_impl.<locals>.nrm_shapec                 S   s   | j d }| d|S )Nr7  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    )rd   r   re   ra   r   formatr   r
   )r  r/  r"   r"   r#   _kron_normaliser_impl
  s    




r1  c                 C   s   t | tj}t |tj}|rV|rV| jdks4|jdkrDtdd }|S tdd }|S n8|rjtdd }|S |r~tdd }|S tdd }|S d S )Nr   c                 S   s   |S r,   r"   r   r   r   r"   r"   r#   r  
  s    z_kron_return.<locals>.retc                 S   s   | |jS r,   )r  r=  r2  r"   r"   r#   r  
  s    c                 S   s   | | jS r,   r  r   r2  r"   r"   r#   r  
  s    c                 S   s   | |jS r,   r3  r2  r"   r"   r#   r  
  s    c                 S   s   |d S r   r"   r2  r"   r"   r#   r  
  s    )rd   r   re   r   r
   )r   r   Za_is_arrZb_is_arrr  r"   r"   r#   _kron_return
  s*    




r4  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 ]h}|| }t|D ]R}|| }||d d f }t|D ],}|| }|||f | |
|||| f< qqvqb| ||
S )Nr8  r7  r:  )r   r   r   rH  )r   r   r#  r$  r  r  r  r  cmcnr_   r  Zrjmpr   Zirjmpslcr  Zcjmpr  fix_afix_bZret_cr"   r#   	kron_impl
  s$    



&zkron_impl.<locals>.kron_impl)r  r1  r4  r<   )r   r   r<  r"   r9  r#   r<  
  s    
(r<  )r   )F)T)T)r   )r  )r  )N)N)N)r   )T)N)rL   
contextlibr   llvmliter   numpyr   operatornumba.core.imputilsr   r   r   r   numba.core.typingr   numba.core.extendingr   r	   r
   
numba.corer   r   numba.core.errorsr   r   r   arrayobjr   r   r   numba.npr   rp  r   r   
as_pointerZ	ll_char_pr   ll_intcZ	ll_intc_pr   Z	ll_intp_pr  r;  rQ   float32r\   	complex64
complex128r   r$   r)   r+   r4   r5   rN   contextmanagerro   rv   r   r   r   r   r   r   r   r   r   r   r   matmulr   r   r   r   r   r  r
  r  rA   r=   r0  r  r$  r&  r'  r/  r3  r5  r  r6  r@  rA  rD  rE  rK  rL  rb  rc  rf  rg  rn  rs  rt  ru  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r%  r&  r(  r)  r+  r1  r4  r5  r<  r"   r"   r"   r#   <module>   s<  

    
) $
%2


,
9Y
#



	


'
	


+

r

v

0

0
A

P




$

^


<
 $$

:


F
# H

,

A

P

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