a
    kh9R                     @   s  d dl mZ d dlmZ d dlmZ ddlmZmZm	Z	m
Z
mZmZ ddlmZ d Zdd	 e D Zeefi d
dddddddddddddZddddddZdd e D Zd d e D ZG d!d" d"eeZeD ]Zeed#e e
 qeD ]Zeed#e e	 qd$d%d&d'd(d)d*d+d,d-d.d/d0d1d2d3d4d5d6d7d8d9d:d;d<d=Zd>dd?Zd@d e D ZdAd e D ZG dBdC dCeZ eD ]Zee d#e e
 qeD ]Zee d#e e	 qdDd e D Z!dEd e D Z"G dFdG dGeZ#e!D ]Zee#d#e e
 qe"D ]Zee#d#e e	 qdHd e D Z$dId e D Z%G dJdK dKeZ&e$D ]Zee&d#e e
 qne%D ]Zee&d#e e	 qdLS )M    )S)Lambda)Pow   )PythonCodePrinter_known_functions_math_print_known_const_print_known_func_unpack_integral_limitsArrayPrinter)CodePrinterz!erf erfc factorial gamma loggammac                 C   s    g | ]\}}|t vr||fqS  )_not_in_numpy.0kvr   r   B/var/www/auris/lib/python3.9/site-packages/sympy/printing/numpy.py
<listcomp>	       r   ZarccosZarccoshZarcsinZarcsinhZarctanZarctan2Zarctanhexp2sign	logaddexp
logaddexp2isinfisnan)acosacoshasinasinhatanatan2atanhr   r   r   r   r   r   epiZeuler_gammananinf)ZExp1PiZ
EulerGammaNaNInfinityc                 C   s   i | ]\}}|d | qS znumpy.r   r   r   r   r   
<dictcomp>"   r   r+   c                 C   s   i | ]\}}|d | qS r*   r   r   r   r   r   r+   #   r   c                       s  e Zd ZdZdZeZeZdY fdd	Z	dd Z
dd	 Zd
d Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zd d! Zd"d# Zd$d% Zd&d' Z fd(d)Zd*d+ Zd,d- Zd.d/ ZdZd1d2Ze d3d4d5Z!d6d7 Z"d8d9 Z#d:d; Z$d<d= Z%d>d? Z&d@dA Z'dBdC Z(dDdE Z)dFdG Z*dHdI Z+dJdK Z,dLdM Z-dNdO Z.dPdQ Z/dRdS Z0dTZ1dUZ2dVZ3dWZ4dXZ5e6j7Z8e6j7Z9e6j7Z:e6j7Z;  Z<S )[NumPyPrinterza
    Numpy printer which handles vectorized piecewise functions,
    logical operators, etc.
    numpyNc                    s@   d | j| _d | j| _i tj| j| _t j|d dS )z
        `settings` is passed to CodePrinter.__init__()
        `module` specifies the array module to use, currently 'NumPy', 'CuPy'
        or 'JAX'.
        zPython with {}z_{}codesettingsN)format_modulelanguageprintmethodr   _kfsuper__init__selfr/   	__class__r   r   r6   /   s    zNumPyPrinter.__init__c                    s"   d}d | fdd|D S )z+General sequence printer: converts to tuple, z({},)c                 3   s   | ]}  |V  qd S N_print)r   itemr8   r   r   	<genexpr>B   r   z*NumPyPrinter._print_seq.<locals>.<genexpr>)r0   join)r8   seq	delimiterr   r@   r   
_print_seq=   s    zNumPyPrinter._print_seqc                 C   s   d|  tj S )N-)r>   r   r)   r8   exprr   r   r   _print_NegativeInfinityD   s    z$NumPyPrinter._print_NegativeInfinityc                    sj   |  d tjurJ|  d |  d g }dd fdd|D S dd fdd|jD S )zMatrix multiplication printerr   r   ({})z).dot(c                 3   s   | ]}  |V  qd S r<   r=   r   ir@   r   r   rA   K   r   z-NumPyPrinter._print_MatMul.<locals>.<genexpr>c                 3   s   | ]}  |V  qd S r<   r=   rK   r@   r   r   rA   L   r   )Zas_coeff_matricesr   ZOner0   rB   args)r8   rH   Z	expr_listr   r@   r   _print_MatMulG   s    zNumPyPrinter._print_MatMulc                 C   s2   d | | jd | |jd | |jd S )zMatrix power printerz
{}({}, {})z.linalg.matrix_powerr   r   r0   _module_formatr1   r>   rM   rG   r   r   r   _print_MatPowN   s    zNumPyPrinter._print_MatPowc                 C   s$   d | | jd | |jd S )zMatrix inverse printer{}({})z.linalg.invr   rO   rG   r   r   r   _print_InverseS   s    zNumPyPrinter._print_Inversec                 C   sX   |j \}}|jd dkr|j}|jd dkr2|j}d| | jd | || |f S )Nr   r   
%s(%s, %s)z.dot)rM   shapeTrP   r1   r>   )r8   rH   Zarg1Zarg2r   r   r   _print_DotProductX   s    
zNumPyPrinter._print_DotProductc                 C   s*   d|  | jd | |j| |jf S )NrT   z.linalg.solve)rP   r1   r>   ZmatrixZvectorrG   r   r   r   _print_MatrixSolvee   s    

zNumPyPrinter._print_MatrixSolvec                 C   s    d | | jd | |jS )NrR   z.zerosr0   rP   r1   r>   rU   rG   r   r   r   _print_ZeroMatrixj   s    
zNumPyPrinter._print_ZeroMatrixc                 C   s    d | | jd | |jS )NrR   z.onesrY   rG   r   r   r   _print_OneMatrixn   s    
zNumPyPrinter._print_OneMatrixc                    s~   ddl m}m} |j}t|ts4t||f|||}d  jd d	 fdd|j
d D  |j
d  |jS )	Nr   )rL   jz{}(lambda {}: {}, {})z.fromfunctionr;   c                 3   s   | ]}  |V  qd S r<   r=   r   argr@   r   r   rA   x   r   z5NumPyPrinter._print_FunctionMatrix.<locals>.<genexpr>r   )Z	sympy.abcrL   r\   lamda
isinstancer   r0   rP   r1   rB   rM   r>   rU   )r8   rH   rL   r\   r_   r   r@   r   _print_FunctionMatrixr   s    
z"NumPyPrinter._print_FunctionMatrixc                    sZ    jd  d fdd|jd d D d|jd dt|jd   S )	N	.multiply c                 3   s    | ]}d   |V  qdS z{}({}, Nr0   r>   r]   funcr8   r   r   rA   }   s   z6NumPyPrinter._print_HadamardProduct.<locals>.<genexpr>{}{})r   rP   r1   rB   rM   r0   r>   lenrG   r   rf   r   _print_HadamardProduct{   s    z#NumPyPrinter._print_HadamardProductc                    sZ    jd  d fdd|jd d D d|jd dt|jd   S )	Nz.kronrc   c                 3   s    | ]}d   |V  qdS rd   re   r]   rf   r   r   rA      s   z7NumPyPrinter._print_KroneckerProduct.<locals>.<genexpr>rh   ri   rj   r   rk   rG   r   rf   r   _print_KroneckerProduct   s    z$NumPyPrinter._print_KroneckerProductc                 C   s2   d | | jd | | jd | |jd S )Nz
{}({}({}))z
.conjugatez
.transposer   rO   rG   r   r   r   _print_Adjoint   s
    zNumPyPrinter._print_Adjointc                 C   s8   d | | jd | |j}d | | jd |S )NrR   z.diagz{}({}, (-1, 1))z.reshape)r0   rP   r1   r>   r^   )r8   rH   Zvectr   r   r   _print_DiagonalOf   s    
zNumPyPrinter._print_DiagonalOfc                 C   s$   d | | jd | |jd S )NrR   z	.diagflatr   rO   rG   r   r   r   _print_DiagMatrix   s    zNumPyPrinter._print_DiagMatrixc              
   C   sJ   d | | jd | |j| | jd | |jd | |jd S )Nz{}({}, {}({}, {}))rb   .eyer   r   )r0   rP   r1   r>   r^   rU   rG   r   r   r   _print_DiagonalMatrix   s    z"NumPyPrinter._print_DiagonalMatrixc                    s   ddl m m  fddddfdd|jD }ddfd	d|jD }d
jd ||t	j
S )zPiecewise function printerr   )ITEsimplify_logicc                    s&   |   r| S | S dS )z$ Problem having an ITE in the cond. N)Zhasr>   Zcond)rt   r8   ru   r   r   
print_cond   s    
z1NumPyPrinter._print_Piecewise.<locals>.print_condz[{}],c                 3   s   | ]}  |jV  qd S r<   )r>   rH   r]   r@   r   r   rA      r   z0NumPyPrinter._print_Piecewise.<locals>.<genexpr>c                 3   s   | ]} |j V  qd S r<   rv   r]   )rw   r   r   rA      r   z{}({}, {}, default={})z.select)Zsympy.logic.boolalgrt   ru   r0   rB   rM   rP   r1   r>   r   r(   )r8   rH   exprsZcondsr   )rt   rw   r8   ru   r   _print_Piecewise   s      
zNumPyPrinter._print_Piecewisec                    sf   ddddddd}|j |v rZ| |j}| |j}dj| | jd	 ||j   ||d
S t |S )z.Relational printer for Equality and Unequalityequal	not_equalZlessZ
less_equalZgreaterZgreater_equal)z==z!=<z<=>z>=z{op}({lhs}, {rhs}).)oplhsrhs)	Zrel_opr>   r   r   r0   rP   r1   r5   _print_Relational)r8   rH   r   r   r   r9   r   r   r      s    
zNumPyPrinter._print_Relationalc                    s.   d   jd d fdd|jD S )Logical And printer{}.reduce(({}))z.logical_andrx   c                 3   s   | ]}  |V  qd S r<   r=   rK   r@   r   r   rA      r   z*NumPyPrinter._print_And.<locals>.<genexpr>r0   rP   r1   rB   rM   rG   r   r@   r   
_print_And   s    zNumPyPrinter._print_Andc                    s.   d   jd d fdd|jD S )Logical Or printerr   z.logical_orrx   c                 3   s   | ]}  |V  qd S r<   r=   rK   r@   r   r   rA      r   z)NumPyPrinter._print_Or.<locals>.<genexpr>r   rG   r   r@   r   	_print_Or   s    zNumPyPrinter._print_Orc                    s.   d   jd d fdd|jD S )zLogical Not printerrR   z.logical_notrx   c                 3   s   | ]}  |V  qd S r<   r=   rK   r@   r   r   rA      r   z*NumPyPrinter._print_Not.<locals>.<genexpr>r   rG   r   r@   r   
_print_Not   s    zNumPyPrinter._print_NotFc                 C   s<   |j jr&|j jr&t|j|j  dd}| j||| jd dS )NF)evaluatez.sqrt)rationalsqrt)exp
is_integerZis_negativer   baseZevalfZ_hprint_Powr1   )r8   rH   r   r   r   r   
_print_Pow   s    zNumPyPrinter._print_Pow)r   c                    sn   t |dkrtd| nt |dkr6 |d S  d} fdd|D }| d| dd	| d
S )Nr   zNeed at least one argument for r   zfunctools.reducec                    s   g | ]}  |qS r   r=   r]   r@   r   r   r      r   z8NumPyPrinter._helper_minimum_maximum.<locals>.<listcomp>(z, [r;   z]))rl   NotImplementedErrorr>   rP   rB   )r8   r   rM   Z_reduces_argsr   r@   r   _helper_minimum_maximum   s    
z$NumPyPrinter._helper_minimum_maximumc                 C   s
   |  |S r<   )_print_minimumrG   r   r   r   
_print_Min   s    zNumPyPrinter._print_Minc                 C   s*   d | | jd | |j| |jS )N{}({}, axis={})z.aminr0   rP   r1   r>   arrayZaxisrG   r   r   r   _print_amin   s    zNumPyPrinter._print_aminc                 C   s$   |  | jd }| j|g|jR  S )Nz.minimumrP   r1   r   rM   r8   rH   r   r   r   r   r      s    zNumPyPrinter._print_minimumc                 C   s
   |  |S r<   )_print_maximumrG   r   r   r   
_print_Max   s    zNumPyPrinter._print_Maxc                 C   s*   d | | jd | |j| |jS )Nr   z.amaxr   rG   r   r   r   _print_amax   s    zNumPyPrinter._print_amaxc                 C   s$   |  | jd }| j|g|jR  S )Nz.maximumr   r   r   r   r   r      s    zNumPyPrinter._print_maximumc                 C   s$   d|  | jd | |jd f S )N%s(%s)z.angler   rP   r1   r>   rM   rG   r   r   r   
_print_arg   s    zNumPyPrinter._print_argc                 C   s$   d|  | jd | |jd f S )Nr   z.imagr   r   rG   r   r   r   	_print_im   s    zNumPyPrinter._print_imc                    s.   d   jd d fdd|jD f S )Nr   z.modr;   c                 3   s   | ]}  |V  qd S r<   r=   r]   r@   r   r   rA     r   z*NumPyPrinter._print_Mod.<locals>.<genexpr>)rP   r1   rB   rM   rG   r   r@   r   
_print_Mod   s    zNumPyPrinter._print_Modc                 C   s$   d|  | jd | |jd f S )Nr   z.realr   r   rG   r   r   r   	_print_re  s    zNumPyPrinter._print_rec                 C   s*   d|  | jd | |jd tj f S )Nr   z.sincr   )rP   r1   r>   rM   r   r'   rG   r   r   r   _print_sinc  s    zNumPyPrinter._print_sincc                 C   s|   d|j v r:| | j d| j }| d| |j  dS | j|jjd }|d u rf| | j d}d|| |	 f S )Nr   r   r   rj   .arrayr   )
rU   rP   r1   _zerosr>   Zknown_functionsgetr:   __name__tolistr8   rH   rg   r   r   r   _print_MatrixBase	  s    
zNumPyPrinter._print_MatrixBasec                 C   sH   |j }tdd |D r<d| | jd | |j d f S tdd S )Nc                 s   s   | ]}|j V  qd S r<   )Z
is_Integer)r   Zdimr   r   r   rA     r   z/NumPyPrinter._print_Identity.<locals>.<genexpr>r   rr   r   zFSymbolic matrix dimensions are not yet supported for identity matrices)rU   allrP   r1   r>   r   )r8   rH   rU   r   r   r   _print_Identity  s    $zNumPyPrinter._print_Identityc                 C   s(   d | | jd | |jd  S )NrR   z.blockr   )r0   rP   r1   r>   rM   r   rG   r   r   r   _print_BlockMatrix  s    zNumPyPrinter._print_BlockMatrixc                 C   s   |  dkr8| | j d}| d| |d  dS d|jv rr| | j d| j }| d| |j dS | | j d}| d| |  dS )Nr   r   r   r   rj   r   )ZrankrP   r1   r>   rU   r   r   r   r   r   r   _print_NDimArray  s    
zNumPyPrinter._print_NDimArrayaddZeinsumZ	transposeZoneszeros)N)F)=r   
__module____qualname____doc__r1   _numpy_known_functionsr4   _numpy_known_constants_kcr6   rE   rI   rN   rQ   rS   rW   rX   rZ   r[   ra   rm   rn   ro   rp   rq   rs   rz   r   r   r   r   r   strr   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   Z_addZ_einsumZ
_transposeZ_onesr   r   Z_print_not_supported_print_lowergamma_print_uppergamma_print_fresnelc_print_fresnels__classcell__r   r   r9   r   r,   %   sh   	
		
r,   Z_print_ZexpierferfcZjvZyvZivkvcosm1powm1	factorialgammaZgammalnpsi	polygammaZpochZeval_jacobiZeval_gegenbauerZeval_chebytZeval_chebyuZeval_legendreZeval_hermiteZeval_laguerreZeval_genlaguerrebetaZlambertw)ZEir   r   ZbesseljZbesselyZbesseliZbesselkr   r   r   r   ZloggammaZdigammar   ZRisingFactorialZjacobiZ
gegenbauerZ
chebyshevtZ
chebyshevuZlegendreZhermiteZlaguerreZassoc_laguerrer   ZLambertWZgolden_ratio)ZGoldenRatior'   c                 C   s   i | ]\}}|d | qS )zscipy.special.r   r   r   r   r   r+   Y  r   c                 C   s   i | ]\}}|d | qS )zscipy.constants.r   r   r   r   r   r+   Z  r   c                       s   e Zd Zi ejeZi ejeZd& fdd	Zdd Z	e	Z
dd Zdd	 Zd
d Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zd d! Zd"d# Zd$d% Z  ZS )'SciPyPrinterNc                    s   t  j|d d| _d S )Nr.   zPython with SciPy and NumPy)r5   r6   r2   r7   r9   r   r   r6   a  s    zSciPyPrinter.__init__c                 C   sd   g g g   }}}|   D ]*\\}}}|| || || qdj| d||||jdS )Nz+{name}(({data}, ({i}, {j})), shape={shape})zscipy.sparse.coo_matrix)namedatarL   r\   rU   )Ztodokitemsappendr0   rP   rU   )r8   rH   rL   r\   r   rcr   r   r   r   _print_SparseRepMatrixe  s    


z#SciPyPrinter._print_SparseRepMatrixc              	   C   s:   d | d| |jd | |jd | |jd S )Nz{0}({2}, {1}, {3})zscipy.special.lpmvr   r      r0   rP   r>   rM   rG   r   r   r   _print_assoc_legendret  s    z"SciPyPrinter._print_assoc_legendrec              	   C   s4   d | d| d| |jd | |jd S )N{0}({2})*{1}({2}, {3})scipy.special.gammazscipy.special.gammaincr   r   r   rG   r   r   r   r   {  s    zSciPyPrinter._print_lowergammac              	   C   s4   d | d| d| |jd | |jd S )Nr   r   zscipy.special.gammainccr   r   r   rG   r   r   r   r     s    zSciPyPrinter._print_uppergammac                    s     d}  d} fdd|jD }d| d|d  d|d  d|d	  d
| d|d  d|d  d|d  d| d|d  d|d  dS )Nscipy.special.betainczscipy.special.betac                    s   g | ]}  |qS r   r=   r]   r@   r   r   r     r   z/SciPyPrinter._print_betainc.<locals>.<listcomp>r   r   r;   r      z) - r   z))             * rj   )rP   rM   )r8   rH   Zbetaincr   rM   r   r@   r   _print_betainc  s    

JzSciPyPrinter._print_betaincc              
   C   sH   d | d| |jd | |jd | |jd | |jd S )Nz'{0}({1}, {2}, {4}) - {0}({1}, {2}, {3})r   r   r   r   r   r   rG   r   r   r   _print_betainc_regularized  s    z'SciPyPrinter._print_betainc_regularizedc                 C   s   d | d| |jd S )N	{}({})[0]scipy.special.fresnelr   r   rG   r   r   r   r     s    zSciPyPrinter._print_fresnelsc                 C   s   d | d| |jd S )N	{}({})[1]r   r   r   rG   r   r   r   r     s    zSciPyPrinter._print_fresnelcc                 C   s   d | d| |jd S )Nr   scipy.special.airyr   r   rG   r   r   r   _print_airyai  s    zSciPyPrinter._print_airyaic                 C   s   d | d| |jd S )Nr   r   r   r   rG   r   r   r   _print_airyaiprime  s    zSciPyPrinter._print_airyaiprimec                 C   s   d | d| |jd S )Nz	{}({})[2]r   r   r   rG   r   r   r   _print_airybi  s    zSciPyPrinter._print_airybic                 C   s   d | d| |jd S )Nz	{}({})[3]r   r   r   rG   r   r   r   _print_airybiprime  s    zSciPyPrinter._print_airybiprimec                 C   s   |  |j|j S r<   r>   Z_eval_rewrite_as_zetarM   rG   r   r   r   _print_bernoulli  s    zSciPyPrinter._print_bernoullic                 C   s   |  |j|j S r<   r   rG   r   r   r   _print_harmonic  s    zSciPyPrinter._print_harmonicc                    s   t |\}}t|dkr< d}dtt j|d  }n( d}dd fdd	|D }d
|dt j| |jd |S )Nr   zscipy.integrate.quadz%s, %sr   zscipy.integrate.nquadrJ   r;   c                 3   s"   | ]}d t t j| V  qdS )z(%s, %s)N)tuplemapr>   )r   lr@   r   r   rA     s   z/SciPyPrinter._print_Integral.<locals>.<genexpr>z{}(lambda {}: {}, {})[0])	r
   rl   rP   r   r   r>   r0   rB   rM   )r8   r#   Zintegration_varsZlimitsZ
module_strZ	limit_strr   r@   r   _print_Integral  s    


zSciPyPrinter._print_Integralc                 C   s   d | d| |jd S )Nr   scipy.special.sicir   r   rG   r   r   r   	_print_Si  s    zSciPyPrinter._print_Sic                 C   s   d | d| |jd S )Nr   r   r   r   rG   r   r   r   	_print_Ci  s    zSciPyPrinter._print_Ci)N)r   r   r   r,   r4   _scipy_known_functionsr   _scipy_known_constantsr6   r   Z_print_ImmutableSparseMatrixr   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r9   r   r   \  s*   r   c                 C   s   i | ]\}}|d | qS zcupy.r   r   r   r   r   r+     r   c                 C   s   i | ]\}}|d | qS r   r   r   r   r   r   r+     r   c                       s.   e Zd ZdZdZeZeZd fdd	Z	  Z
S )CuPyPrinterz`
    CuPy printer which handles vectorized piecewise functions,
    logical operators, etc.
    ZcupyNc                    s   t  j|d d S )Nr.   )r5   r6   r7   r9   r   r   r6     s    zCuPyPrinter.__init__)N)r   r   r   r   r1   _cupy_known_functionsr4   _cupy_known_constantsr   r6   r   r   r   r9   r   r     s
   r   c                 C   s   i | ]\}}|d | qS z
jax.numpy.r   r   r   r   r   r+     r   c                 C   s   i | ]\}}|d | qS r   r   r   r   r   r   r+     r   c                       s>   e Zd ZdZdZeZeZd
 fdd	Z	dd Z
dd	 Z  ZS )
JaxPrinterz_
    JAX printer which handles vectorized piecewise functions,
    logical operators, etc.
    z	jax.numpyNc                    s   t  j|d d| _d S )Nr.   Z_jaxcode)r5   r6   r3   r7   r9   r   r   r6     s    zJaxPrinter.__init__c              	      s8   d   jd   jd fdd|jD S )r   {}({}.asarray([{}]), axis=0)z.allrx   c                 3   s   | ]}  |V  qd S r<   r=   rK   r@   r   r   rA     r   z(JaxPrinter._print_And.<locals>.<genexpr>r   rG   r   r@   r   r   	  s
    
zJaxPrinter._print_Andc              	      s8   d   jd   jd fdd|jD S )r   r   z.anyrx   c                 3   s   | ]}  |V  qd S r<   r=   rK   r@   r   r   rA     r   z'JaxPrinter._print_Or.<locals>.<genexpr>r   rG   r   r@   r   r     s
    
zJaxPrinter._print_Or)N)r   r   r   r   r1   _jax_known_functionsr4   _jax_known_constantsr   r6   r   r   r   r   r   r9   r   r     s   r   N)'Z
sympy.corer   Zsympy.core.functionr   Zsympy.core.powerr   Zpycoder   r   r   r	   r
   r   Zcodeprinterr   splitr   r   Z	_in_numpydictZ_known_functions_numpyZ_known_constants_numpyr   r   r,   rg   setattrconstZ_known_functions_scipy_specialZ _known_constants_scipy_constantsr   r   r   r   r   r   r   r   r   r   r   r   r   <module>   s    
  }