a
    kh6                     @   s6  d dl mZmZmZmZmZmZmZmZm	Z	m
Z
mZmZmZmZmZ d dl mZmZmZmZmZmZ d dlmZmZmZmZmZmZ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*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5 d dlm6Z6 d d	l7m8Z8 ed
\Z9Z:Z;dd Z<dd Z=dd Z>dd Z?dd Z@dd ZAdd ZBdd ZCdd ZDdd ZEdd  ZFd!d" ZGd#d$ ZHd%d& ZId'd( ZJd)d* ZKe6d+d, ZLd-d. ZMd/d0 ZNd1d2 ZOd3d4 ZPd5d6 ZQd7d8 ZRd9d: ZSd;d< ZTd=d> ZUd?d@ ZVdAdB ZWdCdD ZXdEdF ZYdGdH ZZdIdJ Z[dKdL Z\dMdN Z]dOS )P    )SpioosymbolsFunctionRationalIntegerTupleSymbolEqNeLeLtGtGe)
EulerGammaGoldenRatioCatalanLambdaMulPow)	Piecewisesqrtceilingexpsincossinc)raises)implemented_function)eyeMatrixMatrixSymbolIdentityHadamardProductSparseMatrix)jnynbesseljbesselybesselibesselkhankel1hankel2airyaiairybiairyaiprimeairybiprime)XFAIL
julia_codezx,y,zc                   C   s,   t tddksJ t tddks(J d S )NC   Z67z-1)r4   r    r7   r7   M/var/www/auris/lib/python3.9/site-packages/sympy/printing/tests/test_julia.pytest_Integer   s    r9   c                   C   s   t tdddksJ t tdddks,J t tdddksBJ t td	ddksXJ t ttdd d
ksrJ t tddt dksJ d S )N      z3 // 7   	   2iz-3 // 7z
x + 3 // 7z(3 // 7) * x)r4   r   xr7   r7   r7   r8   test_Rational   s    rA   c                   C   s   t tttdksJ t tttdks,J t tttdksBJ t tttdksXJ t tttdksnJ t tttdksJ d S )Nzx == yzx != yzx <= yzx < yzx > yzx >= y)	r4   r   r@   yr   r   r   r   r   r7   r7   r7   r8   test_Relational!   s    rC   c                   C   sH   t tttt dksJ t ttdks0J t ttdksDJ d S )Nzsin(x) .^ cos(x)zabs(x)zceil(x))r4   r   r@   r   absr   r7   r7   r7   r8   test_Function*   s    rE   c               
   C   s   t td dksJ t ttd  dks,J t ttdd dksFJ tdttdt } t d| td ttt    td t  d	ksJ t td
tttttddddddddksJ d S )Nr:   zx .^ 3zx .^ (y .^ 3)   zx .^ (2 // 3)g   g      @z.(3.5 * 2 * x) .^ (-x + y .^ x) ./ (x .^ 2 + y)F)evaluater6   z-2 * x ./ (y .* y))r4   r@   rB   r   r   r   r   r   )rG   r7   r7   r8   test_Pow0   s    *rK   c                   C   sR   t tt dksJ t tt dks(J t tt dks<J t t dksNJ d S )Nx .* yzx + yzx - yz-x)r4   r@   rB   r7   r7   r7   r8   test_basic_ops<   s    rM   c                   C   s  t dt dksJ t td t td   kr8dks>n J t dtt dksVJ t ttj  t td   kr~dksn J t ttdksJ t ttj t td   krdksn J t dt d	ksJ t td t td   krd	ksn J t td d
ksJ d S )NrH   z1 ./ xr6   g      z1 ./ sqrt(x)g      zsqrt(x)g      ?z1 / piz1 / sqrt(pi))r4   r@   r   r   Halfr   r7   r7   r7   r8   test_1_over_x_and_sqrtC   s    *.,,rO   c                   C   s^  t dt dksJ t tt dks(J t dt dks<J t tt dksPJ t td dksdJ t tt dksxJ t tt dksJ t dt t d	ksJ t dt t t d
ksJ t tt dksJ t dt t dksJ t tt t dksJ t tt t dks J t dt t dks:J t dt t t t dks\J t dt t dksvJ t tdd dksJ t tdd t dksJ t tt t dksJ t tt t dksJ t tt tt  dks J t tt t dksJ t td t dks4J t tdd t t t dksZJ d S )Nr:   z3 * xzpi * xz3 ./ xzpi ./ xzx / 3zx / pirL   z
3 * x .* yz3 * pi * x .* yzx ./ yz
3 * x ./ yzx .* y ./ zzx .* z ./ yrH   z1 ./ (x .* y)rF   z2 * pi * x ./ (y .* z)z3 * pi ./ x   z3 // 5z(3 // 5) * xzx ./ (y .* z)z(x + y) ./ zz(x + y) ./ (x + z)z(x + y) / eulergammazx / (3 * pi)z(3 // 5) * x .* y / pi)r4   r@   r   rB   zr   r   r7   r7   r7   r8   test_mix_number_mult_symbolsQ   s0    "rR   c                   C   s   t td dksJ t td dks(J t ttd  dks@J t tt dksTJ t ttt  dkslJ t tt t dksJ d S )	Nr:   zpi ^ 3rF   zx .^ 2zx .^ (pi ^ 3)zx .^ yzx .^ (y .^ z)z(x .^ y) .^ z)r4   r   r@   rB   rQ   r7   r7   r7   r8   test_mix_number_pow_symbolsl   s    rS   c                  C   sd   t d} t| dksJ td|  dks,J tt dd |  dksHJ tdd|   d	ks`J d S )
NIZimrP   Z5imr:   rF   z(3 // 2) * im   z3 + 4im)r   r4   )rT   r7   r7   r8   	test_imagu   s
    rV   c                   C   s   t tdksJ t tdks J t t dks2J t tjdksDJ t tjdksVJ t tjdkshJ t tddks|J d S )Nr   ZInfz-InfNaNerH   )r4   r   r   r   NegativeInfinityrW   ZExp1r   r7   r7   r7   r8   test_constants}   s    rZ   c                   C   s@   t dt dksJ t dt dks(J t dt dks<J d S )NrF   z
2 * goldenz2 * catalanz2 * eulergamma)r4   r   r   r   r7   r7   r7   r8   test_constants_other   s    r[   c                   C   s   t tt@ dksJ t ttB dks(J t t dks:J t tt@ t@ dksRJ t ttB tB dksjJ t tt@ tB dksJ t ttB t@ dksJ d S )Nzx && yzx || yz!xzx && y && zzx || y || zzz || x && yzz && (x || y))r4   r@   rB   rQ   r7   r7   r7   r8   test_boolean   s    r\   c                   C   sL   t ttdksJ t ttd dks,J t tttd  dksHJ d S )Nzsinc(x / pi)r:   zsinc((x + 3) / pi)zsinc(x + 3))r4   r   r@   r   r7   r7   r7   r8   	test_sinc   s    r]   c                  C   s   t tdddgdksJ tdttd ttgddtgdtdttgg} d}t | |ksbJ t | d d df dks~J t | dd d f dksJ t tddg d	ksJ t tdd
g dksJ t tttt t ggdksJ d S )NrH   
   z[10]rF   r   zB[1 sin(x / 2)  abs(x);
0          1      pi;
0          e ceil(x)]z	[1, 0, 0]z[1 sin(x / 2) abs(x)]zzeros(0, 0)r:   zzeros(0, 3)z[x x - y -y])	r4   r!   r   r@   rD   r   r   r   rB   Aexpectedr7   r7   r8   test_Matrices   s    rb   c                  C   sJ   t dtdt dt t d gg} t| dks4J t| jdksFJ d S )NrH   rF   r:   rP   z"[1 sin(2 ./ x) (3 // 5) * pi ./ x]z$[1, sin(2 ./ x), (3 // 5) * pi ./ x])r!   r   r@   r   r4   Tr`   r7   r7   r8   test_vector_entries_hadamard   s    $re   c                  C   sH   t dtdt dt t d gddtt gg} d}t| |ksDJ d S )NrH   rF   r:   rP   z.[1 sin(2/x) 3*pi/(5*x);
1        2        x*y])r!   r   r@   r   rB   r4   r_   r7   r7   r8   "test_Matrices_entries_not_hadamard   s    0rf   c                  C   s   t ddd} td| | }td| | }t|| dks8J t|| dksLJ td| | d	ksdJ t|d | d
ks|J t||dt|    dksJ t|td  dksJ t|d dksJ t|tj dksJ d S )NnT)integerr`   BzA * BzB * ArF   z	2 * A * Bz	2 * B * Ar:   zA * (3 * eye(n) + B)zA ^ (x .^ 2)zA ^ 3zA ^ (1 // 2))r
   r"   r4   r#   r@   r   rN   )rg   r`   ri   r7   r7   r8   test_MatrixSymbol   s     rj   c                   C   s   t dtd dksJ d S )N   r:   z
6 * eye(3))r4   r#   r7   r7   r7   r8   test_special_matrices   s    rl   c                   C   s   t dddddddggdd	d
gdgdks,J t ddks<J t dgdksNJ t ddks^J t tg d dksvJ t dtt dtd ffdksJ t dtdtddg g fdksJ d S )NrH   rF   r:   rU   rP   rk   r;      r=   r^      z5Any[1, 2, 3, Any[4, 5, Any[6, 7]], 8, Any[9, 10], 11])rH   rF   )r:   rU   z(1, 2, (3, 4))zAny[1])rH   z(1,)rH   rF   r:   z	(1, 2, 3)z(1, x .* y, (3, x .^ 2))r   z.(1, [1 0 0;
0 1 0;
0 0 1], zeros(0, 0), Any[]))r4   r	   r@   rB   r    r!   r7   r7   r7   r8   test_containers   s    ""rp   c                  C   s4   t tt t ddd} dtd }| |ks0J d S )NmeF	assign_toinlinez)const Catalan = %s
me = (x + y) / Catalan   )r4   r@   rB   r   Zevalf)sourcera   r7   r7   r8   test_julia_noninline   s
    rw   c                     s  t ttdk ftd df t dks*J t dddks>J t ddd	d
ksTJ t td tdk ftd tdk ftd tdk ftd df d} t | ksJ t ddd|  ksJ t ddd	dksJ t ttdk ftd tdkftttdkf tt fdd d S )NrH   rF   Tz((x < 1) ? (x) : (x .^ 2))rrs   zr = ((x < 1) ? (x) : (x .^ 2))Frr   z,if (x < 1)
    r = x
else
    r = x .^ 2
endr:   rU   rP   zI((x < 1) ? (x .^ 2) :
(x < 2) ? (x .^ 3) :
(x < 3) ? (x .^ 4) : (x .^ 5))zr = zmif (x < 1)
    r = x .^ 2
elseif (x < 2)
    r = x .^ 3
elseif (x < 3)
    r = x .^ 4
else
    r = x .^ 5
endr   c                      s   t  S )Nr3   r7   exprr7   r8   <lambda>      z&test_julia_piecewise.<locals>.<lambda>)r   r@   r4   r   r   
ValueError)ra   r7   rz   r8   test_julia_piecewise   s"    
:,r   c                  C   sr   t ttdk ftd df} td|  dks.J t| t dksBJ t| tt  dksZJ t| d dksnJ d S )	NrH   rF   Tz2 * ((x < 1) ? (x) : (x .^ 2))z((x < 1) ? (x) : (x .^ 2)) ./ xz&((x < 1) ? (x) : (x .^ 2)) ./ (x .* y)r:   z((x < 1) ? (x) : (x .^ 2)) / 3)r   r@   r4   rB   )pwr7   r7   r8    test_julia_piecewise_times_const  s
    r   c                  C   sN   t g dg} t| dddks"J t ddgddgg} t| d	dd
ksJJ d S )Nro   ary   za = [1 2 3]rH   rF   r:   rU   r`   zA = [1 2;
3 4])r!   r4   rd   r7   r7   r8   test_julia_matrix_assign_to  s    r   c                     sd   t g dg tddd} tdddt | ddks:J tt fd	d
 tt fdd
 d S )Nro   ri   rH   r:   CrF   ry   zB = [1 2 3]c                      s   t  tdS Nry   )r4   r@   r7   rd   r7   r8   r|     r}   z2test_julia_matrix_assign_to_more.<locals>.<lambda>c                      s   t  dS r   r3   r7   r`   r   r7   r8   r|     r}   r!   r"   r4   r   r~   ri   r7   r   r8    test_julia_matrix_assign_to_more  s    r   c                     sP   t dgg tddd} tdddt | ddks8J tt fdd	 d S )
Nr:   ri   rH   r   rF   ry   zB = [3]c                      s   t  dS r   r3   r7   r   r7   r8   r|   '  r}   z'test_julia_matrix_1x1.<locals>.<lambda>r   r   r7   r   r8   test_julia_matrix_1x1   s
    r   c                  C   s   t tdtt gg} t| d d | d  | d  dks<J tddd} t| dksXJ t| d d t| d  | d  d	ksJ tt| d
ksJ d S )NrF   r   r   )r   rH   )r   rF   zx .^ 2 + x .* y + 2ZAArH   r:   z%sin(AA[1,2]) + AA[1,1] .^ 2 + AA[1,3]zAA[1,1] + AA[1,2] + AA[1,3])r!   r@   rB   r4   r"   r   sumrd   r7   r7   r8   test_julia_matrix_elements*  s    ("r   c                   C   sH   t ddksJ t tjdks"J t ddks2J t tjdksDJ d S )NTtrueFfalse)r4   r   r   r   r7   r7   r7   r8   test_julia_boolean4  s    r   c                  C   s\   t t ttj W d    n1 s(0    Y  td} t| ttdddksXJ d S )NfF)strictz:# Not supported in Julia:
# Derivative
Derivative(f(x), x))r   NotImplementedErrorr4   r   ZComplexInfinityr   r@   diff)r   r7   r7   r8   test_julia_not_supported;  s    
(r   c                  C   sD   t d} t d}t| tdk f|tdkfd}t|dddks@J d S )	NZendlessZ	elsewherer   rH   )rH   TF)rt   zCif (x < 0)
    endless
elseif (x <= 1)
    elsewhere
else
    1
end)r   r   r@   r4   )t1t2r   r7   r7   r8   %test_trick_indent_with_end_else_wordsG  s    
r   c                  C   s   t ddd} t ddd}t ddd}t ddd}t| |}t|dksJJ t|| dks^J t|| | d	ksvJ t||  d
ksJ t|t t dksJ d S )Nr`   r:   ri   vrH   hzA .* Bz(A .* B) * vzh * (A .* B) * vz(A .* B) * Az(x .* y) * (A .* B))r"   r$   r4   r@   rB   )r`   ri   r   r   r   r7   r7   r8   test_haramardV  s    
r   c                  C   sL   t ddi } d| d< d| d< d| d< d	| d
< tt | d< t| dksHJ d S )NrP   rk   r^   )rF   rF      )rH   rF      )rH   r:      )r   r:   )r:   r   zHsparse([4, 2, 3, 1, 2], [1, 3, 3, 4, 4], [x .* y, 20, 10, 30, 22], 5, 6))r%   r@   rB   r4   )Mr7   r7   r8   test_sparsed  s    r   c                  C   s   t d} ttttfD ] }t|| t|jd ksJ qtt	t
tfD ]}t|t|jd ksBJ qBtt| tdksxJ tt| tdksJ tt| tdksJ tt| tdksJ d S )Nrg   z(n, x)z(x)zhankelh1(n, x)zhankelh2(n, x)z?sqrt(2) * sqrt(pi) * sqrt(1 ./ x) .* besselj(n + 1 // 2, x) / 2z?sqrt(2) * sqrt(pi) * sqrt(1 ./ x) .* bessely(n + 1 // 2, x) / 2)r
   r(   r)   r*   r+   r4   r@   __name__r.   r0   r/   r1   r,   r-   r&   r'   )rg   r   r7   r7   r8   test_specfunp  s    r   c                  C   sx   t ddd} t ddd}t ddd}t| d dks8J td| d  dksPJ |d || | }t|d	kstJ d S )
Nr`   rH   r:   ri   r   r   zA[1,1]z
3 * A[1,1]z(A - B)[1,1])r"   r4   subs)r`   ri   r   Fr7   r7   r8   test_MatrixElement_printing|  s    r   N)^Z
sympy.corer   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   Zsympy.functionsr   r   r   r   r   r   r   Zsympy.testing.pytestr   Zsympy.utilities.lambdifyr   Zsympy.matricesr    r!   r"   r#   r$   r%   Zsympy.functions.special.besselr&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   Zsympy.printing.juliar4   r@   rB   rQ   r9   rA   rC   rE   rK   rM   rO   rR   rS   rV   rZ   r[   r\   r]   rb   re   rf   rj   rl   rp   rw   r   r   r   r   r   r   r   r   r   r   r   r   r   r7   r7   r7   r8   <module>   sX   D $ 8			
	

	 


