a
    RG5dJ                     @   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Zd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$d%d&d'd(d)d*d+d,d-d.d/d0d1d2d3d4d5d6d7d8d9Zd:dd;Zd<d e D Zd=d e D ZG d>d? d?eZ eD ]Zee d"e e
 qeD ]Zee d"e e	 qd@d e D Z!dAd e D Z"G dBdC dCeZ#e!D ]Zee#d"e e
 qe"D ]Zee#d"e e	 qdDd e D Z$dEd e D Z%G dFdG dGeZ&e$D ]Zee&d"e e
 qfe%D ]Zee&d"e e	 qdHS )I    )S)Lambda)Pow   )PythonCodePrinter_known_functions_math_print_known_const_print_known_func_unpack_integral_limitsArrayPrinter)CodePrinterz!erf erfc factorial gamma loggammac                 C   s    g | ]\}}|t vr||fqS  )_not_in_numpy.0kvr   r   P/var/www/html/django/DPS/env/lib/python3.9/site-packages/sympy/printing/numpy.py
<listcomp>	       r   arccosarccosharcsinarcsinharctanarctan2arctanhexp2sign	logaddexp
logaddexp2)acosacoshasinasinhatanatan2atanhr   r   r   r    epieuler_gammananPINFNINF)Exp1Pi
EulerGammaNaNInfinityNegativeInfinityc                 C   s   i | ]\}}|d | qS znumpy.r   r   r   r   r   
<dictcomp>    r   r5   c                 C   s   i | ]\}}|d | qS r4   r   r   r   r   r   r5   !   r   c                       s`  e Zd ZdZdZeZeZdL fdd	Z	dd Z
dd	 Zd
d Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zd d! Zd"d# Zd$d% Z fd&d'Zd(d) Zd*d+ Zd,d- ZdMd/d0Zd1d2 Zd3d4 Z d5d6 Z!d7d8 Z"d9d: Z#d;d< Z$d=d> Z%d?d@ Z&dAdB Z'dCdD Z(dEdF Z)dGZ*dHZ+dIZ,dJZ-dKZ.e/j0Z1e/j0Z2e/j0Z3e/j0Z4  Z5S )NNumPyPrinterza
    Numpy printer which handles vectorized piecewise functions,
    logical operators, etc.
    numpyNc                    s@   d | j| _d | j| _i tj| j| _t j|d dS )z
        `settings` is passed to CodePrinter.__init__()
        `module` specifies the array module to use, currently 'NumPy', 'CuPy'
        or 'JAX'.
        zPython with {}z_{}codesettingsN)format_modulelanguageprintmethodr   _kfsuper__init__selfr9   	__class__r   r   r@   -   s    zNumPyPrinter.__init__c                    s"   d}d | fdd|D S )z+General sequence printer: converts to tuple, z({},)c                 3   s   | ]}  |V  qd S N_print)r   itemrB   r   r   	<genexpr>@   r   z*NumPyPrinter._print_seq.<locals>.<genexpr>)r:   join)rB   seq	delimiterr   rJ   r   
_print_seq;   s    zNumPyPrinter._print_seqc                    sj   |  d tjurJ|  d |  d g }dd fdd|D S dd fdd|jD S )zMatrix multiplication printerr   r   ({})z).dot(c                 3   s   | ]}  |V  qd S rF   rG   r   irJ   r   r   rK   F   r   z-NumPyPrinter._print_MatMul.<locals>.<genexpr>c                 3   s   | ]}  |V  qd S rF   rG   rQ   rJ   r   r   rK   G   r   )Zas_coeff_matricesr   Oner:   rL   args)rB   expr	expr_listr   rJ   r   _print_MatMulB   s    zNumPyPrinter._print_MatMulc                 C   s2   d | | jd | |jd | |jd S )zMatrix power printerz
{}({}, {})z.linalg.matrix_powerr   r   r:   _module_formatr;   rH   rT   rB   rU   r   r   r   _print_MatPowI   s    zNumPyPrinter._print_MatPowc                 C   s$   d | | jd | |jd S )zMatrix inverse printer{}({})z.linalg.invr   rX   rZ   r   r   r   _print_InverseN   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)rT   shapeTrY   r;   rH   )rB   rU   arg1arg2r   r   r   _print_DotProductS   s    
zNumPyPrinter._print_DotProductc                 C   s*   d|  | jd | |j| |jf S )Nr^   z.linalg.solve)rY   r;   rH   matrixvectorrZ   r   r   r   _print_MatrixSolve`   s    

zNumPyPrinter._print_MatrixSolvec                 C   s    d | | jd | |jS )Nr\   z.zerosr:   rY   r;   rH   r_   rZ   r   r   r   _print_ZeroMatrixe   s    
zNumPyPrinter._print_ZeroMatrixc                 C   s    d | | jd | |jS )Nr\   z.onesrg   rZ   r   r   r   _print_OneMatrixi   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   )rR   jz{}(lambda {}: {}, {})z.fromfunctionrE   c                 3   s   | ]}  |V  qd S rF   rG   r   argrJ   r   r   rK   s   r   z5NumPyPrinter._print_FunctionMatrix.<locals>.<genexpr>r   )	sympy.abcrR   rj   lamda
isinstancer   r:   rY   r;   rL   rT   rH   r_   )rB   rU   rR   rj   rn   r   rJ   r   _print_FunctionMatrixm   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r:   rH   rk   funcrB   r   r   rK   x   s   z6NumPyPrinter._print_HadamardProduct.<locals>.<genexpr>{}{})r   rY   r;   rL   rT   r:   rH   lenrZ   r   ru   r   _print_HadamardProductv   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.kronrr   c                 3   s    | ]}d   |V  qdS rs   rt   rk   ru   r   r   rK   ~   s   z7NumPyPrinter._print_KroneckerProduct.<locals>.<genexpr>rw   rx   ry   r   rz   rZ   r   ru   r   _print_KroneckerProduct|   s    z$NumPyPrinter._print_KroneckerProductc                 C   s2   d | | jd | | jd | |jd S )Nz
{}({}({}))z
.conjugatez
.transposer   rX   rZ   r   r   r   _print_Adjoint   s
    zNumPyPrinter._print_Adjointc                 C   s8   d | | jd | |j}d | | jd |S )Nr\   z.diagz{}({}, (-1, 1))z.reshape)r:   rY   r;   rH   rl   )rB   rU   vectr   r   r   _print_DiagonalOf   s    
zNumPyPrinter._print_DiagonalOfc                 C   s$   d | | jd | |jd S )Nr\   z	.diagflatr   rX   rZ   r   r   r   _print_DiagMatrix   s    zNumPyPrinter._print_DiagMatrixc              
   C   sJ   d | | jd | |j| | jd | |jd | |jd S )Nz{}({}, {}({}, {}))rq   .eyer   r   )r:   rY   r;   rH   rl   r_   rZ   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)hasrH   cond)r   rB   r   r   r   
print_cond   s    
z1NumPyPrinter._print_Piecewise.<locals>.print_condz[{}],c                 3   s   | ]}  |jV  qd S rF   )rH   rU   rk   rJ   r   r   rK      r   z0NumPyPrinter._print_Piecewise.<locals>.<genexpr>c                 3   s   | ]} |j V  qd S rF   r   rk   )r   r   r   rK      r   z{}({}, {}, default={})z.select)sympy.logic.boolalgr   r   r:   rL   rT   rY   r;   rH   r   r1   )rB   rU   exprscondsr   )r   r   rB   r   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_equalless
less_equalgreatergreater_equal)z==z!=<z<=>z>=z{op}({lhs}, {rhs}).)oplhsrhs)	rel_oprH   r   r   r:   rY   r;   r?   _print_Relational)rB   rU   r   r   r   rC   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_andr   c                 3   s   | ]}  |V  qd S rF   rG   rQ   rJ   r   r   rK      r   z*NumPyPrinter._print_And.<locals>.<genexpr>r:   rY   r;   rL   rT   rZ   r   rJ   r   
_print_And   s    zNumPyPrinter._print_Andc                    s.   d   jd d fdd|jD S )Logical Or printerr   z.logical_orr   c                 3   s   | ]}  |V  qd S rF   rG   rQ   rJ   r   r   rK      r   z)NumPyPrinter._print_Or.<locals>.<genexpr>r   rZ   r   rJ   r   	_print_Or   s    zNumPyPrinter._print_Orc                    s.   d   jd d fdd|jD S )zLogical Not printerr\   z.logical_notr   c                 3   s   | ]}  |V  qd S rF   rG   rQ   rJ   r   r   rK      r   z*NumPyPrinter._print_Not.<locals>.<genexpr>r   rZ   r   rJ   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_integeris_negativer   baseevalf_hprint_Powr;   )rB   rU   r   r   r   r   
_print_Pow   s    zNumPyPrinter._print_Powc                    s.   d   jd d fdd|jD S )N{}(({}), axis=0)z.aminr   c                 3   s   | ]}  |V  qd S rF   rG   rQ   rJ   r   r   rK      r   z*NumPyPrinter._print_Min.<locals>.<genexpr>r   rZ   r   rJ   r   
_print_Min   s    zNumPyPrinter._print_Minc                    s.   d   jd d fdd|jD S )Nr   z.amaxr   c                 3   s   | ]}  |V  qd S rF   rG   rQ   rJ   r   r   rK      r   z*NumPyPrinter._print_Max.<locals>.<genexpr>r   rZ   r   rJ   r   
_print_Max   s    zNumPyPrinter._print_Maxc                 C   s$   d|  | jd | |jd f S )N%s(%s)z.angler   rY   r;   rH   rT   rZ   r   r   r   
_print_arg   s    zNumPyPrinter._print_argc                 C   s$   d|  | jd | |jd f S )Nr   z.imagr   r   rZ   r   r   r   	_print_im   s    zNumPyPrinter._print_imc                    s.   d   jd dt fdd|jf S )Nr   z.modrE   c                    s
     | S rF   rG   )rl   rJ   r   r   <lambda>   r   z)NumPyPrinter._print_Mod.<locals>.<lambda>)rY   r;   rL   maprT   rZ   r   rJ   r   
_print_Mod   s    zNumPyPrinter._print_Modc                 C   s$   d|  | jd | |jd f S )Nr   z.realr   r   rZ   r   r   r   	_print_re   s    zNumPyPrinter._print_rec                 C   s*   d|  | jd | |jd tj f S )Nr   z.sincr   )rY   r;   rH   rT   r   r/   rZ   r   r   r   _print_sinc   s    zNumPyPrinter._print_sincc                 C   s@   | j |jjd }|d u r*| | jd }d|| | f S )Nz.arrayr   )known_functionsgetrD   __name__rY   r;   rH   tolist)rB   rU   rv   r   r   r   _print_MatrixBase   s    zNumPyPrinter._print_MatrixBasec                 C   sH   |j }tdd |D r<d| | jd | |j d f S tdd S )Nc                 s   s   | ]}|j V  qd S rF   )
is_Integer)r   dimr   r   r   rK      r   z/NumPyPrinter._print_Identity.<locals>.<genexpr>r   r   r   zFSymbolic matrix dimensions are not yet supported for identity matrices)r_   allrY   r;   rH   NotImplementedError)rB   rU   r_   r   r   r   _print_Identity   s    $zNumPyPrinter._print_Identityc                 C   s(   d | | jd | |jd  S )Nr\   z.blockr   )r:   rY   r;   rH   rT   r   rZ   r   r   r   _print_BlockMatrix   s    zNumPyPrinter._print_BlockMatrixc                 C   sT   t |jdkr,| jd | |jd  d S t |jdkrH| | S t| |S )Nr   z.array(r   ry      )r{   r_   r;   rH   rT   tomatrixr   _print_not_supportedrZ   r   r   r   _print_NDimArray   s
    zNumPyPrinter._print_NDimArrayaddeinsum	transposeoneszeros)N)F)6r   
__module____qualname____doc__r;   _numpy_known_functionsr>   _numpy_known_constants_kcr@   rO   rW   r[   r]   rc   rf   rh   ri   rp   r|   r}   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   _add_einsum
_transpose_ones_zerosr   r   _print_lowergamma_print_uppergamma_print_fresnelc_print_fresnels__classcell__r   r   rC   r   r6   #   s\   	
r6   _print_erferfcZjvZyvivkvcosm1	factorialgammagammalnpsiZpochZeval_jacobiZeval_gegenbauerZeval_chebytZeval_chebyuZeval_legendreZeval_hermiteZeval_laguerreZeval_genlaguerrebetalambertw)r   r   besseljbesselybesselibesselkr   r   r   loggammadigammaRisingFactorialjacobi
gegenbauer
chebyshevt
chebyshevulegendrehermitelaguerreassoc_laguerrer   LambertWZgolden_ratio)GoldenRatior/   c                 C   s   i | ]\}}|d | qS )zscipy.special.r   r   r   r   r   r5   5  r   c                 C   s   i | ]\}}|d | qS )zscipy.constants.r   r   r   r   r   r5   6  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  ZS )SciPyPrinterNc                    s   t  j|d d| _d S )Nr8   zPython with SciPy and NumPy)r?   r@   r<   rA   rC   r   r   r@   =  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datarR   rj   r_   )todokitemsappendr:   rY   r_   )rB   rU   rR   rj   r   rcr   r   r   r   _print_SparseRepMatrixA  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   r   r:   rY   rH   rT   rZ   r   r   r   _print_assoc_legendreP  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  rZ   r   r   r   r   W  s    zSciPyPrinter._print_lowergammac              	   C   s4   d | d| d| |jd | |jd S )Nr  r  zscipy.special.gammainccr   r   r  rZ   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   rG   rk   rJ   r   r   r   h  r   z/SciPyPrinter._print_betainc.<locals>.<listcomp>(r   rE   r      z) - r   z))             * ry   )rY   rT   )rB   rU   betaincr   rT   r   rJ   r   _print_betaince  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  rZ   r   r   r   _print_betainc_regularizedl  s    z'SciPyPrinter._print_betainc_regularizedc                 C   s   d | d| |jd S )N	{}({})[0]scipy.special.fresnelr   r  rZ   r   r   r   r   t  s    zSciPyPrinter._print_fresnelsc                 C   s   d | d| |jd S )N	{}({})[1]r  r   r  rZ   r   r   r   r   y  s    zSciPyPrinter._print_fresnelcc                 C   s   d | d| |jd S )Nr  scipy.special.airyr   r  rZ   r   r   r   _print_airyai~  s    zSciPyPrinter._print_airyaic                 C   s   d | d| |jd S )Nr  r  r   r  rZ   r   r   r   _print_airyaiprime  s    zSciPyPrinter._print_airyaiprimec                 C   s   d | d| |jd S )Nz	{}({})[2]r  r   r  rZ   r   r   r   _print_airybi  s    zSciPyPrinter._print_airybic                 C   s   d | d| |jd S )Nz	{}({})[3]r  r   r  rZ   r   r   r   _print_airybiprime  s    zSciPyPrinter._print_airybiprimec                    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.nquadrP   rE   c                 3   s"   | ]}d t t j| V  qdS )z(%s, %s)N)tupler   rH   )r   lrJ   r   r   rK     s   z/SciPyPrinter._print_Integral.<locals>.<genexpr>z{}(lambda {}: {}, {})[0])	r
   r{   rY   r  r   rH   r:   rL   rT   )rB   r(   integration_varslimitsZ
module_strZ	limit_strr   rJ   r   _print_Integral  s    


zSciPyPrinter._print_Integral)N)r   r   r   r6   r>   _scipy_known_functionsr   _scipy_known_constantsr@   r  _print_ImmutableSparseMatrixr  r   r   r  r  r   r   r  r  r  r  r  r   r   r   rC   r   r   8  s"   r   c                 C   s   i | ]\}}|d | qS zcupy.r   r   r   r   r   r5     r   c                 C   s   i | ]\}}|d | qS r  r   r   r   r   r   r5     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.
    cupyNc                    s   t  j|d d S Nr8   r?   r@   rA   rC   r   r   r@     s    zCuPyPrinter.__init__)N)r   r   r   r   r;   _cupy_known_functionsr>   _cupy_known_constantsr   r@   r   r   r   rC   r   r    s
   r  c                 C   s   i | ]\}}|d | qS z
jax.numpy.r   r   r   r   r   r5     r   c                 C   s   i | ]\}}|d | qS r%  r   r   r   r   r   r5     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 S r!  r"  rA   rC   r   r   r@     s    zJaxPrinter.__init__c              	      s8   d   jd   jd fdd|jD S )r   {}({}.asarray([{}]), axis=0)z.allr   c                 3   s   | ]}  |V  qd S rF   rG   rQ   rJ   r   r   rK     r   z(JaxPrinter._print_And.<locals>.<genexpr>r   rZ   r   rJ   r   r     s
    
zJaxPrinter._print_Andc              	      s8   d   jd   jd fdd|jD S )r   r'  z.anyr   c                 3   s   | ]}  |V  qd S rF   rG   rQ   rJ   r   r   rK     r   z'JaxPrinter._print_Or.<locals>.<genexpr>r   rZ   r   rJ   r   r     s
    
zJaxPrinter._print_Or)N)r   r   r   r   r;   _jax_known_functionsr>   _jax_known_constantsr   r@   r   r   r   r   r   rC   r   r&    s   r&  N)'
sympy.corer   sympy.core.functionr   sympy.core.powerr   pycoder   r   r   r	   r
   r   codeprinterr   splitr   r   Z	_in_numpydictZ_known_functions_numpyZ_known_constants_numpyr   r   r6   rv   setattrconstZ_known_functions_scipy_specialZ _known_constants_scipy_constantsr  r  r   r#  r$  r  r(  r)  r&  r   r   r   r   <module>   s    
	 om