o
    8ήc9[                    @   sp  d 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 ddl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 ddlmZ e dZ!e!" Z#e#Z$e dZ%e%" Z&ej'Z'e'" Z(ej)Z*ej)Z+ej,dej-dej.dej/diZ0dddZ1dd Z2dd Z3dd Z4G dd dZ5G dd dZ6ej7d d! Z8d"d# Z9d$d% Z:d&d' Z;d(d) Z<d*d+ Z=d,d- Z>d.d/ Z?d0d1 Z@d2d3 ZAdd5d6ZBeejCejDejDd7d8 ZEeejFejDejDeE eejGejDejDd9d: ZGd;d< ZHd=d> ZId?d@ ZJdAdB ZKeejCejDejDejDdCdD ZLeM ZNeOdEeNZPedFdG ZQddIdJZRdKdL ZSdMdN ZTeeTdOdP ZUedQdR ZVedSdT ZWeejXjYdUdV ZZedWdX Z[ddYdZZ\eejXj]d[d\ Z^eejXj_d]d^ Z`eejXjad_d` ZbeejXjcdadb ZdeejXjedcdd ZfeejXjgddedfZheejXjidgdh Zjdidj Zkeekdkdl Zldmdn Zmeemdodp Zndqdr Zoeeodsdt Zpdudv Zqeeqdwdx Zrdydz Zseesd{d| Ztd}d~ Zueeudd ZveejXjwdddZxdd Zyeeydd ZzeejXj{dd Z|eejXj}dddZ~dd ZeejXjdd ZeejXjdd Zdd Zeedd Zdd Zeedd Zdd ZeejXjdddZeejXjdddZedd ZeejXjdddZeejXj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)overloadregister_jitable)typescgutils)TypingErrorNumbaTypeError   )
make_array_empty_nd_impl
array_copy)numpy_support)glue_lowering       sdcz<BLAS function>c                 C   s$   t | }|d u rtd|f |S )Nzunsupported dtype for %s())_blas_kindsget	TypeError)dtype	func_namekind r!   6/tmp/pip-target-vg8gfxp4/lib/python/numba/np/linalg.pyget_blas_kind/   s   
r#   c                  C   &   zdd l } W d S  ty   tdw Nr   z*scipy 0.16+ is required for linear algebra)scipy.linalg.cython_blasImportErrorscipyr!   r!   r"   ensure_blas6   
   r*   c                  C   r$   r%   )scipy.linalg.cython_lapackr'   r(   r!   r!   r"   ensure_lapack=   r+   r-   c                 C   s   |  |||}t||S N)get_constant_genericr   alloca_once_value)contextbuildertyvalconstr!   r!   r"   make_constant_slotD   s   r6   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__O      
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>   R   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
   rA   rB   rC   rD   rE   rG   r   rI   r!   r!   r"   rJ   ]   s"   z_BLAS.numba_xxgemmN)__name__
__module____qualname____doc__r;   classmethodr>   rJ   r!   r!   r!   r"   r7   I   s    

r7   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   r8   r.   )r-   r9   r!   r!   r"   r;   x   r<   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
   rA   rB   rC   rD   F_INT_nbtyperE   rL   r!   r!   r"   rS   {   s   z_LAPACK.numba_xxgetrfc              	   C   s0   t t jt jt |t jt t}t d|S )Nnumba_ez_xxgetrirT   rL   r!   r!   r"   rV      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_rgeevrK   rL   r!   r!   r"   rW      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_cgeevrK   rL   r!   r!   r"   rX      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 )Nr=   numba_ez_xxxevdr?   )rG   r   wtyperI   r!   r!   r"   rY      s   z_LAPACK.numba_ez_xxxevdc                 C   s,   t t jt jt jt |t j}t d|S )Nnumba_xxpotrfrK   rL   r!   r!   r"   r[      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 )Nr=   numba_ez_gesddr?   )rG   r   styperI   r!   r!   r"   r\      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_geqrfrK   rL   r!   r!   r"   r^      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_xxgqrrK   rL   r!   r!   r"   r_      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 )Nr=   numba_ez_gelsd)r@   r
   rA   rB   rC   rD   float64rE   rF   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_xgesvrT   rL   r!   r!   r"   rb     s   
z_LAPACK.numba_xgesvN)rM   rN   rO   rP   r;   rQ   rS   rV   rW   rX   rY   r[   r\   r^   r_   r`   rb   r!   r!   r!   r"   rR   r   s2    


	



	



rR   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
   Arrayrf   copyr   r   appendreturn_typetuplenrtdecref)r1   r2   rI   rh   newtysnewargscopiesr3   r4   newtynewvalcopysigr!   r!   r"   make_contiguous  s"   

rw   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_maxintr!   r"   impl4  s   zcheck_c_int.<locals>.implN)compile_internalr   r
   nonerC   )r1   r2   ry   r|   r!   rz   r"   check_c_int.  s
   r   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likelyz#BLAS wrapper returned with an errorNif_thenr   is_not_nullget_python_api
gil_ensurefatal_errorr1   r2   respyapir!   r!   r"   check_blas_return<  
   
"r   c                 C   r   )z]
    Check the integer error return from one of the LAPACK wrappers in
    _helperlib.c.
    Fr   z%LAPACK wrapper returned with an errorNr   r   r!   r!   r"   check_lapack_returnH  r   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   numba_xxdotN)r   FunctionTypeIntTypell_charintp_t	ll_void_pr   get_or_insert_functionmoduler#   Constantordintcallbitcastr   )r1   r2   	conjugater   ry   a_datab_dataout_datafntyfnr    kind_valr   r!   r!   r"   
call_xxdotT  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   numba_xxgemv      ?        Fr   r   try   N)r   r   r   r   r   r   r   r   r   r   r6   rf   r#   r   r   r   r   r   )r1   r2   do_transm_typem_shapesm_datav_datar   r   r   r   alphabetamry   ldar    r   transr   r!   r!   r"   call_xxgemvj  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   rJ   r   r   r   ry   c                    s8   | j j krn| j dkr|d n|d  |tfS )Nrd   r   r   )rf   r   r   )r3   shapesdatar2   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   r6   r   r   r#   r   r   r   )!r1   r2   x_typex_shapesx_datay_typey_shapesy_datar   
out_shapesr   r   r   r   k_kry   r   r   r   r   transar   data_atransbldbdata_b_ldcdata_cr    r   r   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   ry   outr!   r!   r"   dot_impl  s   

zdot_2_mm.<locals>.dot_implr}   r   rm   r1   r2   rI   rh   r   r   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   _mry   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   ry   _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$   | j \}|j \}||krtdd S )Nz;incompatible array sizes for np.dot(a, b) (vector * vector)r   
ValueError)r   r   r   ry   r!   r!   r"   
check_args  s
   zdot_2_vv.<locals>.check_args)rh   rm   r   r   unpack_tupler   r}   r   r
   r~   r   alloca_onceget_value_typer   r   load)r1   r2   rI   rh   r   atybtyr   r   r   ry   r   r   r!   r!   r"   dot_2_vv  s   

r   c                 C   s   t   t| |||a\}}dd |jdd D }|ddgkr-t| |||W  d   S |ddgkrAt| |||W  d   S |ddgkrUt| |||W  d   S |ddgkrit| |||W  d   S J 1 snw   Y  dS )z 
    np.dot(a, b)
    a @ b
    c                 S   s   g | ]}|j qS r!   ndim.0xr!   r!   r"   
<listcomp>  s    zdot_2.<locals>.<listcomp>N   r   )r*   rw   rh   r   r   r   r   r1   r2   rI   rh   ndimsr!   r!   r"   dot_2  s"   r   c                 C   sN   t   t| |||\}}t| |||ddW  d   S 1 s w   Y  dS )z
    np.vdot(a, b)
    T)r   N)r*   rw   r   )r1   r2   rI   rh   r!   r!   r"   vdot$  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   ry   r!   r!   r"   dot_3_vm_check_args/  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   ry   r!   r!   r"   dot_3_mv_check_args:  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   rd   ==Fr   N)rh   rm   r   r   r   r   r   r   rf   r   r   r   r}   r   r
   r~   r   get_constantrC   icmp_signedor_if_elsememsetmulitemsizenitemsr   r   	_getvalue)r1   r2   rI   rh   xtyytyouttyr   r   yr   r   r   r   mtyr   v_shaper   r   r   r   r   r4   zero
both_emptymatrix_emptyis_emptyr   nonemptyr!   r!   r"   dot_3_vmE  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| ||$||||| W d
   n	1 sw   Y  |& t| |||||||||| W d
   n	1 sw   Y  W d
   n	1 sw   Y  W d
   n	1 sw   Y  W d
   n	1 sw   Y  W d
   n	1 sw   Y  W d
   n	1 sw   Y  t| ||j|
 S )z%
    np.dot(matrix, matrix, out)
    r   r   r   rd   c                 S   s>   | j \}}|j \}}||krtd|j ||fkrtdd S )Nz;incompatible array sizes for np.dot(a, b) (matrix * matrix)zFincompatible output array size for np.dot(a, b, out) (matrix * matrix)r   )r   r   r   r   r   r   ry   r!   r!   r"   r     s   

zdot_3_mm.<locals>.check_argsr   Fr   N)rh   rm   r   r   r   r   r   rf   r}   r   r
   r~   r   r   r   rC   r   r   r   r   r   r   r   r   r   r   r   r   )'r1   r2   rI   rh   r  r  r  r   r   r  r   r   r   r   r   r   r   ry   r   r   r   r   r  r  x_emptyy_emptyr
  r   r  oneis_left_vecis_right_vecr_vecr_matv_vm_vr   v_mm_mr!   r!   r"   dot_3_mm~  s   





&r  c                 C   s   t   t| |||>\}}tdd |jdd D }|tdgkr0t| |||W  d   S |tddgkrFt| |||W  d   S J 1 sKw   Y  dS )z
    np.dot(a, b, out)
    c                 s   s    | ]}|j V  qd S r.   r   r   r!   r!   r"   	<genexpr>  s    zdot_3.<locals>.<genexpr>Nr   r   )r*   rw   setrh   r  r  r   r!   r!   r"   dot_3  s   r  numba_fatal_errorc                 C   s.   t | D ]}t | st jdqd S )Nz$Array must not contain infs or NaNs.)r   nditerisfiniteitemlinalgLinAlgError)r   vr!   r!   r"   _check_finite_matrix  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highlightingr   z%%s.%s() only supported on 2-D arrays.3%s.%s() only supported on float and complex arrays.)
ri   r
   Optionaltyperj   r   r   r   FloatComplex)r   r   	la_prefixprefixinterpmsgr!   r!   r"   _check_linalg_matrix  s    
r0  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_types  s   

r2  c                   C   s   d S r.   r!   r!   r!   r!   r"   _copy_to_fortran_order     r3  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   rk   flagsf_contiguousTasfortranarray)r   acpyflag_fA_layoutF_layoutr!   r"   r|     s   


z&ol_copy_to_fortran_order.<locals>.implre   )r   r|   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_handler0  s   rC  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   rE  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#  r3  r   F_INT_nptypectypesrC  rE  size)r   ry   r/  r:  ipivrB  r    rS   numba_xxgetrir!   r"   inv_implL  s   
zinv_impl.<locals>.inv_impl)r-   r0  rR   rS   r   rV   r   r#   )r   rR  r!   rP  r"   rR  @  s   
rR  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   rA  r!   r!   r"   %_handle_err_maybe_convergence_problemh  s   rS  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'  )ri   r
   rj   r   r   r   r*  r+  r   r   r,  r-  r.  r!   r!   r"   _check_linalg_1_or_2d_matrixr  s   
rV  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 )NrH  rI  rJ  r   z Matrix is not positive definite.)r   r   r   r!  rk   rM  r@  range)r   ry   r/  r   rB  colUPr    r[   r!   r"   cho_impl  s&   
zcho_impl.<locals>.cho_impl)r-   r0  rR   r[   r   r   r#   )r   LOr^  r!   r\  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.
        rH  rI  rJ  r   rK  r   z.eig() argument must not cause a domain change.)r   r   r   r!  r#  r3  r   r   r8  rM  rS  anyr   rE  rN  r   ry   r/  r:  ldvlldvrwrwivlvrrB  JOBVLJOBVRr    rW   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.
        rH  rI  rJ  r   rK  r   )r   r   r   r!  r#  r3  r   r   r8  rM  rS  rE  rN  
r   ry   r/  r:  re  rf  wri  rj  rB  rl  rm  r    rX   r!   r"   cmplx_eig_impl  s8   


z eig_impl.<locals>.cmplx_eig_implr-   r0  rR   rW   r   rX   r   r#   ri   r
   scalarsr+  )r   rn  rr  r!   rl  rm  r    rX   rW   r"   eig_impl  s   
8(rv  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eigvalsra  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.
        rH  rI  rJ  r   rK  r   z2eigvals() argument must not cause a domain change.)r   r   r   r!  r#  r3  r   r   rM  rS  rc  r   rE  rN  rd  rk  r!   r"   real_eigvals_impl1  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.
        rH  rI  rJ  r   rK  r   )r   r   r   r!  r#  r3  r   r   rM  rS  rE  rN  ro  rq  r!   r"   cmplx_eigvals_impll  s8   
z(eigvals_impl.<locals>.cmplx_eigvals_implrs  )r   rx  ry  r!   ru  r"   eigvals_impl#  s   
;)rz  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eighr=   rb  rY  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 NrH  rI  rJ  rK  r   r   r   r   r!  r#  r3  r   rM  rS  rE  rN  r   ry   r/  r:  rp  rB  JOBZUPLOr    rY   w_dtyper!   r"   	eigh_impl  s(   
zeigh_impl.<locals>.eigh_impl
r-   r0  r@   r   
np_supportas_dtyperR   rY   r   r#   )r   w_typer  r!   r  r"   r       

r  c                    r{  )Neigvalshr=   ra  rY  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 r}  r~  r  r  r!   r"   eigvalsh_impl  s(   
z$eigvalsh_impl.<locals>.eigvalsh_implr  )r   r  r  r!   r  r"   r    r  r  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svdr=   r5  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 )NrH  rI  r   Arrays cannot be emptyrK  )r   r   r   r!  r#  r3  minr   r   rM  rS  rE  rN  r8  )r   full_matricesry   r   r:  lduminmnr  ucolldvtur   vtrB  JOBZ_AJOBZ_Sr    r\   s_dtyper!   r"   svd_impl  sD   


zsvd_impl.<locals>.svd_implr   )
r-   r0  r@   r   r  r  rR   r\   r   r#   )r   r  s_typer  r!   r  r"   r    s   

.r  c                    rF  )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 )NrH  rI  r   r  rK  r   )r   r   r   r!  r#  r3  r  r   r   rM  r@  r   r8  rZ  rS  rE  rN  )r   ry   r   qr   r  tauretrB  ijr    r^   r_   r!   r"   qr_implO  sR   


	zqr_impl.<locals>.qr_impl)r-   r0  rR   r^   r   r_   r   r#   )r   r  r!   r  r"   r  >  s   
9r  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 )NrH  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 )NrI  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    r4  z,_system_compute_nrhs_impl.<locals>.oneD_implc                 S   s
   | j d S )NrH  r  r  r!   r!   r"   r    r<   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 )NrI  rH  <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 )NrI  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 NrI  rH  r   r  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$|dkr*tjdd S r  r  )r   r   r  r  r  bnr!   r!   r"   r    s   



 z/_system_check_non_empty_impl.<locals>.twoD_implr   r  r!   r!   r"   _system_check_non_empty_impl  s   r  c                 C   r  )z:
    Compute the residual from the 'b' scratch space.
    r  )r   ry   r  r!   r!   r"   _lstsq_residual  r  r  c                    s   | j }| j}tt|d| |dkr)t|tjr! fdd}|S  fdd}|S |dks/J t|tjr= fdd}|S  fd	d}|S )
Nr=   r   c                    s6   t jd d}t t | |d df d |d< |S Nr  rK  r   r   )r   r   sumabsr   ry   r  r   
real_dtyper!   r"   
cmplx_impl  s   $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_impl  s   z'_lstsq_residual_impl.<locals>.real_implr   c                    sD   t j| d}t|D ]}t t | |d |f d ||< q|S NrK  r   )r   r   rZ  r  r  r   ry   r  r   r   r  r!   r"   r    s   &c                    s>   t j| d}t|D ]}t | |d |f d ||< q|S r  )r   r   rZ  r  r  r  r!   r"   r    s    )r   r   r  r  r@   ri   r
   r+  )r   ry   r  r   r   r  r  r!   r  r"   _lstsq_residual_impl  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  ry   r!   r!   r"   _lstsq_solution     r  c                 C   s"   | j dkrdd }|S dd }|S )Nr   c                 S   s   |j  d | S r.   r8  ravelr  r!   r!   r"   r  %  s   z'_lstsq_solution_impl.<locals>.oneD_implc                 S   s   |d |d d f   S r.   rk   r  r!   r!   r"   r  )  s   z'_lstsq_solution_impl.<locals>.twoD_implr   )r   r  ry   r  r  r!   r!   r"   _lstsq_solution_impl"  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lstsqr=   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 )NrH  rI  rK  r   r   )r   r  r#  r  r  r  maxr3  r   r   r8  r  int32rM  rS  r  r  rE  rN  )r   r   rcondry   r   r  r  maxmnr:  r  r   rank_ptrrB  rankr   r   r    np_dtr`   r  r!   r"   
lstsq_implK  sF   





zlstsq_impl.<locals>.lstsq_implr  )r-   r0  rV  r2  r  r  r   r@   rR   r`   r   r#   )r   r   r  nb_dtr_typer  r!   r  r"   r  .  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    r<   z-_solve_compute_return_impl.<locals>.oneD_implc                 S   s   |S r.   r!   r  r!   r!   r"   r    r4  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 )NrH  rK  r   )r   r  r#  r  r3  r   r   r8  r  r  rL  rM  rC  rE  rN  )r   r   ry   r  r:  r  rO  rB  r    r  rb   r!   r"   
solve_impl  s0   




zsolve_impl.<locals>.solve_impl)r-   r0  rV  r2  r  r  r   rR   rb   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pinvr=   r  rd   r   rK  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 )NrH  rI  r   rK  r   r   )r   r#  r3  r8  r  reshaper  r   r   r   rM  rS  rZ  rE  rN  )r   r  ry   r   r:  r  r  r   r  rB  cut_atcut_idxr   r  r  s_local	JOBTRANSATRANSBr    r\   rJ   r  r  r  r!   r"   	pinv_impl  s~   
'


zpinv_impl.<locals>.pinv_implr  )r-   r0  r@   r   r  r  rR   r\   r7   rJ   r   r#   r   array)r   r  r  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   )rZ  r   r  log)ry   r   sgncsgnaccr   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   )rZ  r   r  )ry   r   r  r  r   r"  r!   r!   r"   real_diag_walker  s   z2_get_slogdet_diag_walker.<locals>.real_diag_walker)ri   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   r=   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 )NrH  rI  rJ  r   rK  r   r   )r   r   r   r!  r#  r3  r   rL  rM  infrC  rZ  rE  rN  )r   ry   r/  r:  rO  rB  r  r   ONEZEROdiag_walkerr    rS   r!   r"   slogdet_impl  s*   
	z"slogdet_impl.<locals>.slogdet_impl)	r-   r0  rR   rS   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_impl  s   zdet_impl.<locals>.det_implr-   r0  )r   r  r!   r!   r"   r    s   
r  c                 C   r  )z)
    Compute singular values of *a*.
    r  rD  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`
    r  ra  r=   r   r   rK  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.
        rH  rI  r   r  r   rK  )r   r   r   r!  r#  r  r3  r   rM  rS  rE  rN  )
r   ry   r   r  r  r  r  r:  r   rB  JOBZ_Nr    np_ret_typer\   r  r  r!   r"   sv_function  s6   


z2_compute_singular_values_impl.<locals>.sv_function)
rR   r\   r   r   r#   r@   r  r  r   r   )r   nb_ret_typenp_dtyper  r!   r  r"   _compute_singular_values_impl  s   
/r  c                 C   r  )z.
    Compute the L2-norm of 1D-array *a*.
    r  rD  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 )Nr=   normc                    sh   t | }tjdd}t| jd | j } || j||j}|dk r(t  J t|j	| j	g |d S )Nr  rK  r   )
lenr   r   r   stridesr   rM  r@  rE  rN  )r   ry   r  jmprB  r    r  xxnrm2r!   r"   r|   M  s   z_oneD_norm_2_impl.<locals>.impl)r@   r   r  r  r7   r>   r   r#   )r   r  r|   r!   r  r"   _oneD_norm_2_implD  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 )Nr=   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  rZ  )r   r   ry   r  r   r4   r!   r!   r"   r    sJ   
r   rd   c                 S   s   | S r.   r!   rD  r!   r!   r"   array_prepare     z%_get_norm_impl.<locals>.array_preparer   c                 S   s   | j S r.   )r8  rD  r!   r!   r"   r!    s   c                 S   s   |   S r.   r  rD  r!   r!   r"   r!       c                    s(   | j }|dkr	dS  | }t||S )Nr   r   )rN  r  r  )r   r   ry   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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)NrH  rI  r   r   r   r   z Invalid norm order for matrices.)r   rN  r   r  rZ  r  r  r   )	r   r   ry   r   
global_maxiitmpjj
global_min)max_valr!   r"   r    sb   



r   r.   )r@   r   r  r  r7   r>   r   r#   r   r
   r~   rf   r	   r   finfor)  r  )	r   ord_flagr  r  r  r  r    r  r  r!   )r!  r*  r"   _get_norm_implh  s6   


<
9



PEr-  c                 C   s   t   t| d t| |S )Nr  )r-   rV  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   rI  r   rH  )r  r   divider   r  rG  isnanr  )r   pr   rB  norm_a
norm_inv_ar!   r!   r"   r|   >	  s   
zcond_impl.<locals>.implr.   r  )r   r2  r|   r!   r!   r"   	cond_impl8	  s   

$r5  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   rZ  r  )svr   r  r   r!   r!   r"   _get_rank_from_singular_valuese	  s   
r8  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 )Nr=   c                    s@   t | }| jd }| jd }t||}|d |   }t||S )Nr   r   )r  r   r  r8  )r   tolr   rB  r   lr   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  r8  )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
   r~   r@   r   r  r  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                    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   r6  )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   rD  rC  r!   r"   _get_matrix_rank_impl	  s   

z/matrix_rank_impl.<locals>._get_matrix_rank_impl)r-   rV  )r   r:  rF  r!   rE  r"   matrix_rank_impls	  s
   


rG  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   rK  r   rH  rI  zinput must be a square arrayr      r      TF)	r   r   r   rZ  r   rk   r   rG  r   )
r   ry   r5  r   r  r  r  r  r  flagr  r!   r"   matrix_power_impl	  sL   
z,matrix_power_impl.<locals>.matrix_power_impl)	r0  r  r  r   r@   ri   r
   Integerr   )r   ry   ntrM  r!   rL  r"   rM  	  s   
?rM  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  r  rZ  )r   offsetrowscolsr   ry   r  r  r!   r!   r"   matrix_trace_impl
  s   
z,matrix_trace_impl.<locals>.matrix_trace_implNr   )r0  ri   r   r
   rN  r   )r   rR  rU  r!   r!   r"   rU  
  s
   
rU  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   rT  Fr%  )ri   r
   rj   r   r   rU  r!   r!   r"   _check_scalar_or_lt_2d_mat%
  s   
rW  c                 C   s@   t | }t |}t | |jdf| d|jfS r  r   asarraymultiplyr  r  rN  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  rX  r[  r!   r!   r"   outer_impl_arr7
  s   

r_  c                 C   s   |d t jfv r	tS tS r.   )r
   r~   r^  r_  r   r   r   r!   r!   r"   _get_outer_implA
  s   ra  c                    s:   t | ddd t |ddd t| || d fdd	}|S )NouterFrQ  c                    s    | ||S r.   r!   r`  r|   r!   r"   
outer_implP
  s   zouter_impl.<locals>.outer_implr.   )rW  ra  )r   r   r   rd  r!   rc  r"   rd  H
  s
   rd  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)rd   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 )NrH  rI  r   r  )r   xnxmr!   r!   r"   	nrm_shape^
  s   

z(_kron_normaliser_impl.<locals>.nrm_shapec                 S   s   | j d }| d|S )NrH  r   re  )r   rf  r!   r!   r"   rh  e
  s   
c                 S   s   t dt| }| |d< |S )Nr  r   )r   r   r)  )r   r   r!   r!   r"   rh  k
  s   )ri   r
   rj   rf   r   formatr   r	   )r   rh  r!   r!   r"   _kron_normaliser_implV
  s   




rj  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"   r  z
  r"  z_kron_return.<locals>.retc                 S   s   | |jS r.   )r  rN  rk  r!   r!   r"   r  
     c                 S   s   | | jS r.   r  r   rk  r!   r!   r"   r  
  rl  c                 S   s   | |jS r.   rm  rk  r!   r!   r"   r  
  rl  c                 S   s   |d S r   r!   rk  r!   r!   r"   r  
  r#  )ri   r
   rj   r   r	   )r   r   a_is_arrb_is_arrr  r!   r!   r"   _kron_returns
  s*   




rp  c                    sX   t | ddd t |ddd t| t|t| |t| d|   fdd}|S )NkronFrQ  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 )NrI  rH  rK  )r   r   r   rZ  )r   r   r\  r]  r  r  r  r  cmcnrd   r  rjmpr   irjmpslcr  cjmpr  fix_afix_bret_cr!   r"   	kron_impl
  s(   



"zkron_impl.<locals>.kron_impl)rW  rj  rp  r@   )r   r   r|  r!   rx  r"   r|  
  s   
(r|  )r   )F)Tr  r  r  r.   rV  )rP   
contextlibllvmliter   numpyr   operatornumba.core.imputilsr   r   r   r   numba.core.typingr   numba.core.extendingr   r	   
numba.corer
   r   numba.core.errorsr   r   arrayobjr   r   r   numba.npr   r  numba.core.overload_gluer   r   r   
as_pointer	ll_char_pr   ll_intc	ll_intc_pr   	ll_intp_pr  rL  rU   float32ra   	complex64
complex128r   r#   r*   r-   r6   r7   rR   contextmanagerrw   r   r   r   r   r   r   r   r   r   r   r   rj   r   matmulr   r   r   r  r  r  rA   fatal_error_sigrE   r@  r#  r0  r2  r3  r?  rC  rE  r   rG  rR  rS  rV  rW  r^  r`  rv  rw  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/  r5  r8  r9  rG  rH  rM  rP  rU  rW  r^  r_  ra  rb  rd  rj  rp  rq  r|  r!   r!   r!   r"   <module>   s4   


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