a
    .'a\a                     @   s*  d Z ddlZddlZddlZ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 ddlmZmZmZmZmZmZ ddlZddlmZ ddlmZmZmZ ejdkoe dkZG d	d
 d
Z G dd dZ!G dd de!Z"G dd de!Z#G dd dZ$G dd dZ%G dd dZ&G dd de&Z'G dd de&Z(G dd de&Z)G dd de&Z*e'e(e)e*gZ+dd  Z,d!d" Z-d#d$ Z.d%d& Z/d'd( Z0d)d* Z1d+d, Z2d-d. Z3G d/d0 d0Z4G d1d2 d2e4Z5G d3d4 d4e4Z6G d5d6 d6e4Z7G d7d8 d8e4Z8G d9d: d:e4Z9d;d< Z:d=d> Z;d?d@ Z<dAdB Z=dCdD Z>dS )Ez"
Tests for numerical integration.
    N)arangezerosarraydotsqrtcossineyepiexpallclose)assert_assert_array_almost_equalassert_allcloseassert_array_equalassert_equalassert_warns)raises)odeintodecomplex_odedarwinZarm64c                   @   s   e Zd Zdd Zdd ZdS )
TestOdeintc                    s   t d jd}t j j|dd\}}t || t fdd j|ddd\}}t || t drt j j| jdd	\}}t || t fd
d j| fddddd\}}t || d S )N        g?Tfull_outputc                    s     || S Nftyproblem Clib/python3.9/site-packages/scipy/integrate/tests/test_integrate.py<lambda>&       z(TestOdeint._do_problem.<locals>.<lambda>)r   tfirstjac)Dfunr   c                    s     || S r   r   r   r"   r$   r%   r&   1   r'   c                    s     || S r   r)   r   r"   r$   r%   r&   2   r'   )r*   r   r(   )	r   stop_tr   r   z0r   verifyhasattrr)   )selfr#   r    zZinfodictr$   r"   r%   _do_problem   s"    




zTestOdeint._do_problemc                 C   s&   t D ]}| }|jrq| | qd S r   PROBLEMScmplxr2   r0   Zproblem_clsr#   r$   r$   r%   test_odeint6   s
    zTestOdeint.test_odeintN)__name__
__module____qualname__r2   r7   r$   r$   r$   r%   r      s   r   c                   @   s   e Zd ZdZdddZdS )TestODEClassNadamsc           	         s    fdd}d }t  dr& fdd}i } jd us> jd urR j|d<  j|d< | ||}|j|f jd  jd |d| |j jd	d
 |	 j
}t||j t|  |f t| dk |f t t|g j
 |f d S )Nc                    s     || S r   r   r    r1   r"   r$   r%   r&   E   r'   z*TestODEClass._do_problem.<locals>.<lambda>r)   c                    s     || S r   r+   r=   r"   r$   r%   r&   H   r'   ubandlband
   )atolrtolmethodr   )r    r   )r/   r?   r>   	ode_classset_integratorrA   rB   set_initial_valuer-   	integrater,   r   r!   r   Z
successfulZget_return_coder.   r   )	r0   r#   
integratorrC   r   r)   Zintegrator_paramsigr1   r$   r"   r%   r2   B   s,    


zTestODEClass._do_problem)r<   )r8   r9   r:   rD   r2   r$   r$   r$   r%   r;   >   s   r;   c                   @   sh   e Zd ZeZdd Zejje	dddd Z
dd Zd	d
 Zdd Zdd Zejje	dddd ZdS )TestOdec                 C   s>   t D ]4}| }|jrq|js*| |dd | |dd qd S Nvoder<   bdf)r4   r5   stiffr2   r6   r$   r$   r%   	test_vodec   s    zTestOde.test_vodezvode failing, see gh-15077reasonc                 C   s6   t D ],}| }|js"| |dd | |dd qd S )Nzvoder<   rM   r4   rN   r2   r6   r$   r$   r%   
test_zvodem   s
    zTestOde.test_zvodec                 C   s(   t D ]}| }|jrq| |d qd S Nlsodar3   r6   r$   r$   r%   
test_lsodav   s
    zTestOde.test_lsodac                 C   s<   t D ]2}| }|jrq|jrqt|dr*q| |d qd S Nr)   dopri5r4   r5   rN   r/   r2   r6   r$   r$   r%   test_dopri5~   s    
zTestOde.test_dopri5c                 C   s<   t D ]2}| }|jrq|jrqt|dr*q| |d qd S Nr)   dop853r[   r6   r$   r$   r%   test_dop853   s    
zTestOde.test_dop853c                 C   s~   dD ]t}dd }t ||}|dd t ||}|dd ||jd  ||jd  tt|j|jd  qd S )N)rL   rS   rW   c                 S   s   dS N      ?r$   r   r$   r$   r%   r&      r'   z.TestOde.test_concurrent_fail.<locals>.<lambda>r   皙?)r   rE   rF   rG   r    assert_raisesRuntimeError)r0   solr   rr2r$   r$   r%   test_concurrent_fail   s    zTestOde.test_concurrent_failc                 C   sH  dd }t dD ]0}dD ]}t||}|dd t||}|dd ||jd  ||jd  ||jd  t|jd t|jd qdD ]}t||}|dd t||}|dd ||jd  ||jd  ||jd  ||jd  ||jd  t|jd	 t|jd qqd S )
Nc                 S   s   dS r`   r$   r   r$   r$   r%   r&      r'   z,TestOde.test_concurrent_ok.<locals>.<lambda>   )rL   rS   rW   rZ   r^   r   rb   g?rZ   r^   g333333?)ranger   rE   rF   rG   r    r   r!   )r0   r   kre   rf   rg   r$   r$   r%   test_concurrent_ok   s0    zTestOde.test_concurrent_okN)r8   r9   r:   r   rD   rO   pytestmarkskipifIS_MACOS_ARM64rU   rX   r\   r_   rh   rm   r$   r$   r$   r%   rJ   _   s   

rJ   c                   @   s0   e Zd ZeZdd Zdd Zdd Zdd Zd	S )
TestComplexOdec                 C   s8   t D ].}| }|js$| |dd q| |dd qd S rK   rT   r6   r$   r$   r%   rO      s
    zTestComplexOde.test_vodec                 C   s    t D ]}| }| |d qd S rV   )r4   r2   r6   r$   r$   r%   rX      s    zTestComplexOde.test_lsodac                 C   s4   t D ]*}| }|jrqt|dr"q| |d qd S rY   r4   rN   r/   r2   r6   r$   r$   r%   r\      s    
zTestComplexOde.test_dopri5c                 C   s4   t D ]*}| }|jrqt|dr"q| |d qd S r]   rs   r6   r$   r$   r%   r_      s    
zTestComplexOde.test_dop853N)	r8   r9   r:   r   rD   rO   rX   r\   r_   r$   r$   r$   r%   rr      s
   	
rr   c                   @   s<   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd ZdS )
TestSoloutc           	         s   g  g d}d}ddg} fdd}dd }t ||}|| ||| ||}td	 | td
 | t d	 | t d
 | d S )Nr         $@ra          @c                    s     |   |  d S r   appendcopyr   tsysr$   r%   solout   s    
z+TestSolout._run_solout_test.<locals>.soloutc                 S   s   |d |d  |d d  gS Nr         r$   r   r$   r$   r%   rhs   s    z(TestSolout._run_solout_test.<locals>.rhsr   )r   rE   
set_soloutrF   rG   r   r   	r0   rH   t0tendy0r}   r   rI   retr$   rz   r%   _run_solout_test   s    

zTestSolout._run_solout_testc                 C   s   dD ]}|  | qd S Nrj   r   r0   rH   r$   r$   r%   test_solout  s    zTestSolout.test_soloutc           	         s   g  g d}d}ddg} fdd}dd }t ||}||| || ||}td	 | td
 | t d	 | t d
 | d S )Nr   ru   ra   rv   c                    s     |   |  d S r   rw   r   rz   r$   r%   r}     s    
z9TestSolout._run_solout_after_initial_test.<locals>.soloutc                 S   s   |d |d  |d d  gS r~   r$   r   r$   r$   r%   r     s    z6TestSolout._run_solout_after_initial_test.<locals>.rhsr   r   )r   rE   rF   r   rG   r   r   r   r$   rz   r%   _run_solout_after_initial_test  s    

z)TestSolout._run_solout_after_initial_testc                 C   s   dD ]}|  | qd S r   )r   r   r$   r$   r%   test_solout_after_initial'  s    z$TestSolout.test_solout_after_initialc                    s   g g d}d ddg} fdd}dd }t ||}|| ||| | }td	 | td
 | td	 | td
  d k td
  k  d S )Nr   ru   ra   rv   c                    s,    |   |  |  d kr(dS d S Nrv   r   rw   r   r   r{   r|   r$   r%   r}   3  s    
z1TestSolout._run_solout_break_test.<locals>.soloutc                 S   s   |d |d  |d d  gS r~   r$   r   r$   r$   r%   r   9  s    z.TestSolout._run_solout_break_test.<locals>.rhsr   r   )r   rE   r   rF   rG   r   r   r   r0   rH   r   r   r}   r   rI   r   r$   r   r%   _run_solout_break_test+  s     

z!TestSolout._run_solout_break_testc                 C   s   dD ]}|  | qd S r   r   r   r$   r$   r%   test_solout_breakF  s    zTestSolout.test_solout_breakN)	r8   r9   r:   r   r   r   r   r   r   r$   r$   r$   r%   rt      s   rt   c                   @   s,   e Zd Zdd Zdd Zdd Zdd Zd	S )
TestComplexSoloutc           	         s   g  g d}d}dg} fdd}dd }t ||}|| ||| ||}td | td | t d | t d | d S )	Nr         4@c                    s     |   |  d S r   rw   r   rz   r$   r%   r}   U  s    
z2TestComplexSolout._run_solout_test.<locals>.soloutc                 S   s   d| d d  gS Nra   ru                 ?r$   r   r$   r$   r%   r   Y  s    z/TestComplexSolout._run_solout_test.<locals>.rhsr   r   )r   rE   r   rF   rG   r   r   r   r$   rz   r%   r   M  s    

z"TestComplexSolout._run_solout_testc                 C   s   dD ]}|  | qd S r   r   r   r$   r$   r%   r   e  s    zTestComplexSolout.test_soloutc                    s   g g d}d dg} fdd}dd }t ||}|| ||| | }td | td | td | td  d	 k td  k  d S )
Nr   r   c                    s,    |   |  |  d kr(dS d S r   rw   r   r   r$   r%   r}   q  s    
z8TestComplexSolout._run_solout_break_test.<locals>.soloutc                 S   s   d| d d  gS r   r$   r   r$   r$   r%   r   w  s    z5TestComplexSolout._run_solout_break_test.<locals>.rhsr   r   rv   )r   rE   r   rF   rG   r   r   r   r   r$   r   r%   r   i  s     

z(TestComplexSolout._run_solout_break_testc                 C   s   dD ]}|  | qd S r   r   r   r$   r$   r%   r     s    z#TestComplexSolout.test_solout_breakN)r8   r9   r:   r   r   r   r   r$   r$   r$   r%   r   K  s   r   c                   @   s0   e Zd ZdZdZdZdZg ZdZdZ	dZ
dZdS )ODEz
    ODE problem
    Fr   Ngư>gh㈵>)r8   r9   r:   __doc__rN   r5   r,   r-   r?   r>   rA   rB   r$   r$   r$   r%   r     s   r   c                   @   s:   e Zd ZdZdZeddgeZdZdZ	dd Z
dd	 Zd
S )SimpleOscillatorz
    Free vibration of a simple oscillator::
        m \ddot{u} + k u = 0, u(0) = u_0 \dot{u}(0) \dot{u}_0
    Solution::
        u(t) = u_0*cos(sqrt(k/m)*t)+\dot{u}_0*sin(sqrt(k/m)*t)/sqrt(k/m)
    gq=
ףp?ra   rb   g      @c                 C   s.   t dt}d|d< | j | j |d< t||S )N)r   r   ra   r   r   )r   r   )r   floatrl   mr   )r0   r1   r    tmpr$   r$   r%   r     s    
zSimpleOscillator.fc                 C   s`   t | j| j }| jd t||  | jd t||  |  }t||d d df | j| jdS )Nr   r   rA   rB   )	r   rl   r   r-   r   r   r   rA   rB   )r0   zsr    omegaur$   r$   r%   r.     s    0zSimpleOscillator.verifyN)r8   r9   r:   r   r,   r   r   r-   rl   r   r   r.   r$   r$   r$   r%   r     s   r   c                   @   s@   e Zd ZdZde Zeg dZdZdd Z	dd Z
d	d
 ZdS )
ComplexExpzThe equation :lm:`\dot u = i u`gGz?)r   y               @y              @y              @y              @Tc                 C   s   d| S )Nr   r$   r0   r1   r    r$   r$   r%   r     s    zComplexExp.fc                 C   s   dt d S )Nr      )r	   r   r$   r$   r%   r)     s    zComplexExp.jacc                 C   s&   | j td|  }t||| j| jdS )Nr   r   )r-   r   r   rA   rB   r0   r   r    r   r$   r$   r%   r.     s    zComplexExp.verifyN)r8   r9   r:   r   r
   r,   r   r-   r5   r   r)   r.   r$   r$   r$   r%   r     s   r   c                   @   s.   e Zd ZdZdZdgZdZdd Zdd Zd	S )
Piz'Integrate 1/(t + 1j) from t=-10 to t=10   r   Tc                 C   s   t d|d d  gS )Nra   r@   r   r   r   r$   r$   r%   r     s    zPi.fc                 C   s.   dt d }t||dd d f | j| jdS )Ny              r@   r   r   )npZarctanr   rA   rB   r   r$   r$   r%   r.     s    z	Pi.verifyN)	r8   r9   r:   r   r,   r-   r5   r   r.   r$   r$   r$   r%   r     s   r   c                   @   sH   e Zd ZdZdZdZg dZdZdZg dZ	dd	 Z
d
d Zdd ZdS )CoupledDecayze
    3 coupled decays suited for banded treatment
    (banded mode makes it necessary when N>>3)
    T      ?)g      @g      @g      *@r   r   )g(\?gq=
ףp?g(\?c                 C   s`   | j }t|d  |d  |d  |d  |d |d   |d  |d  |d |d   gS r~   )lmbdr   r   )r0   r1   r    r   r$   r$   r%   r     s
      zCoupledDecay.fc                    s   j }tjjj d dfdd  fdd}|dd|d   |dd|d  |dd|d   |dd|d  |dd|d    S )	Nr   ri   Forderc                    s   | j |  | |f< d S r   )r>   )ZriZcivaljr0   r$   r%   set_j  s    zCoupledDecay.jac.<locals>.set_jr   r   )r   r   r   r?   r>   )r0   r1   r    r   r   r$   r   r%   r)     s    zCoupledDecay.jacc              
   C   s8  t | j}|d |d  }|d |d  }|d |d  }t |d  | }t |d  | }t |d  | }	t | jd | | jd | | jd |d  | ||   | jd |	 | jd |d  | ||	   |d |d  | jd  | d| ||	  d| ||	     f }
t|
|| j| j	dS )Nr   r   r   r   )
r   r   r   r   Zvstackr-   Z	transposer   rA   rB   )r0   r   r    r   Zd10Zd21Zd20Ze0Ze1Ze2r   r$   r$   r%   r.     s"    **
zCoupledDecay.verifyN)r8   r9   r:   r   rN   r,   r-   r?   r>   r   r   r)   r.   r$   r$   r$   r%   r     s   r   c                 C   s   |d |d  g}|S Nr   r   r$   )r    xdxdtr$   r$   r%   r     s    r   c                 C   s   t ddgddgg}|S )Nr   ra         r   )r    r   r   r$   r$   r%   r)     s    r)   c                 C   s   ||d  | |d  g}|S r   r$   r    r   r   r   r$   r$   r%   f1%  s    r   c                 C   s   t d|g| dgg}|S Nr   r   r    r   r   r   r$   r$   r%   jac1*  s    r   c                 C   s   ||d  | |d  g}|S r   r$   )r    r   omega1omega2r   r$   r$   r%   f20  s    r   c                 C   s   t d|g| dgg}|S r   r   )r    r   r   r   r   r$   r$   r%   jac25  s    r   c                 C   s&   |d |d  |d  |d  g}|S )Nr   r   r$   r   r$   r$   r%   fv;  s    "r   c                 C   s"   t d|d g|d  dgg}|S )Nr   r   r   r   r   r$   r$   r%   jacv@  s    r   c                   @   s   e Zd ZdZdZdZdd Zdd Zej	j
edd	d
d Zej	j
edd	dd Zej	j
edd	dd Zej	j
edd	dd Zdd ZdS )ODECheckParameterUsez=Call an ode-class solver with several cases of parameter use. Fc                 C   s>   t ||}| jr(|j| jdd| jd n|j| jddd |S )Ng&.>gHz>)rA   rB   Zwith_jacobianr   )r   solver_uses_jacrE   solver_name)r0   r   r)   solverr$   r$   r%   _get_solverO  s    
z ODECheckParameterUse._get_solverc                 C   s2   ddg}| |d |t t|jddg d S )Nra   r   r   )rF   rG   r
   r   r!   r0   r   Zicr$   r$   r%   _check_solver[  s    
z"ODECheckParameterUse._check_solverrP   rQ   c                 C   s   |  tt}| | d S r   )r   r   r)   r   )r0   r   r$   r$   r%   test_no_paramsa  s    z#ODECheckParameterUse.test_no_paramsc                 C   s8   |  tt}d}|| | jr*|| | | d S r`   )r   r   r   set_f_paramsr   set_jac_paramsr   r0   r   r   r$   r$   r%   test_one_scalar_paramf  s    

z*ODECheckParameterUse.test_one_scalar_paramc                 C   s@   |  tt}d}d}||| | jr2||| | | d S r`   )r   r   r   r   r   r   r   )r0   r   r   r   r$   r$   r%   test_two_scalar_paramso  s    z+ODECheckParameterUse.test_two_scalar_paramsc                 C   s<   |  tt}ddg}|| | jr.|| | | d S r`   )r   r   r   r   r   r   r   r   r$   r$   r%   test_vector_paramy  s    

z&ODECheckParameterUse.test_vector_paramc                 C   sB   |  tt}|j| jdd ddg}||d tt|jt	 d S )Nr   )Znstepsra   r   )
r   r   r)   rE   r   rF   r   UserWarningrG   r
   r   r$   r$   r%   test_warns_on_failure  s
    z*ODECheckParameterUse.test_warns_on_failureN)r8   r9   r:   r   r   r   r   r   rn   ro   rp   rq   r   r   r   r   r   r$   r$   r$   r%   r   F  s   


	
r   c                   @   s   e Zd ZdZdZdS )TestDOPRI5CheckParameterUserZ   FNr8   r9   r:   r   r   r$   r$   r$   r%   r     s   r   c                   @   s   e Zd ZdZdZdS )TestDOP853CheckParameterUser^   FNr   r$   r$   r$   r%   r     s   r   c                   @   s   e Zd ZdZdZdS )TestVODECheckParameterUserL   TNr   r$   r$   r$   r%   r     s   r   c                   @   s   e Zd ZdZdZdS )TestZVODECheckParameterUserS   TNr   r$   r$   r$   r%   r     s   r   c                   @   s   e Zd ZdZdZdS )TestLSODACheckParameterUserW   TNr   r$   r$   r$   r%   r     s   r   c                  C   s:   d} dg}t dd | |dd\}}t|t| gg d S )Nr   r   c                 S   s   |  S r   r$   )r!   r    r$   r$   r%   r&     r'   z*test_odeint_trivial_time.<locals>.<lambda>Tr   )r   r   r   r   )r   r    r!   infor$   r$   r%   test_odeint_trivial_time  s    r   c                     s  dd dd dd } dd   fd	d
}t g dg dg dg dg}td}t g d}t|||fddddd	\}}t|||fdddd| dd
\}}t|||fdddd ddd\}	}
t|||fdddd|dddd\}}t||dd t||	ddd t|	|d d t|d! |d!  t|
d! |d!  tfd"d#|||fddddfd$d#dd%
\}}t||dd&d' d S )(Nc                 S   s
   | | S r   )r   r!   r    cr$   r$   r%   func  s    z)test_odeint_banded_jacobian.<locals>.funcc                 S   s   |S r   r$   r   r$   r$   r%   r)     s    z(test_odeint_banded_jacobian.<locals>.jacc                 S   s   |j jddS NCr   Try   r   r$   r$   r%   jac_transpose  s    z2test_odeint_banded_jacobian.<locals>.jac_transposec              
   S   sT   t t jdt |df t |t jt |ddf t jt |dddf f}|S )Nr   r   r   )r   Z	row_stackZr_Zdiag)r!   r    r   r)   r$   r$   r%   	bjac_rows  s    z.test_odeint_banded_jacobian.<locals>.bjac_rowsc                    s    | ||j jddS r   r   r   )r   r$   r%   	bjac_cols  s    z.test_odeint_banded_jacobian.<locals>.bjac_cols)i3{Gz?r   r   )rb   g      g{Gz?r   )gMbP?r   g       r   )r   r   rb   r      )r   r   r@   d   TgvIh%<=gdy=i'  )argsr   rA   rB   mxstepr*   )r   r   rA   rB   r   r*   	col_derivr   r   )r   r   rA   rB   r   r*   mlmu)	r   r   rA   rB   r   r*   r   r   r   zsol1 != sol2)err_msg-q=zsol1 != sol3)rA   r   zsol3 != sol4Znjec                    s    || |S r   r$   r    r!   r   )r   r$   r%   r&     r'   z-test_odeint_banded_jacobian.<locals>.<lambda>c                    s    || |S r   r$   r   r+   r$   r%   r&     r'   )r   r   rA   rB   r   r*   r(   zsol1 != sol1ty)rB   r   )r   r   onesr   r   r   )r   r   r   r   r    Zsol1Zinfo1Zsol2Zinfo2Zsol3Zinfo3Zsol4Zinfo4Zsol1tyZinfo1tyr$   )r   r   r)   r%   test_odeint_banded_jacobian  sN    





r   c                  C   s   dd } dd }dd }dd }d	d
 }dd }dd }t tt|dddg t tt|dddg t tt| dddg|d t tt| dddg|d t tt|ddgddg|d d S )Nc                 S   s   d|  S Nr$   r   r    r$   r$   r%   sys1d  s    z!test_odeint_errors.<locals>.sys1dc                 S   s   dd S Nra   r   r$   r   r$   r$   r%   bad1  s    z test_odeint_errors.<locals>.bad1c                 S   s   dS NZfoor$   r   r$   r$   r%   bad2  s    z test_odeint_errors.<locals>.bad2c                 S   s   dd S r   r$   r   r$   r$   r%   bad_jac1   s    z$test_odeint_errors.<locals>.bad_jac1c                 S   s   dggS r   r$   r   r$   r$   r%   bad_jac2  s    z$test_odeint_errors.<locals>.bad_jac2c                 S   s   d| d  d| d  gS )Nr   r   皙r   r$   r   r$   r$   r%   sys2d  s    z!test_odeint_errors.<locals>.sys2dc                 S   s   dd dgddggS )Nra   r   r  r$   r   r$   r$   r%   sys2d_bad_jac	  s    z)test_odeint_errors.<locals>.sys2d_bad_jacra   r   r   r*   )rc   ZeroDivisionErrorr   
ValueError)r   r   r   r   r   r  r  r$   r$   r%   test_odeint_errors  s    r  c                  C   s   dd } dd }dd }ddgddgg}t tt||ddg ddgd	d
gg}t tt|dg| t tt| dddg t tt|ddgddg|d d S )Nc                 S   s   ddgS )Nr   r   r$   r   r$   r$   r%   badrhs  s    z&test_odeint_bad_shapes.<locals>.badrhsc                 S   s   d|  S r   r$   r   r$   r$   r%   sys1  s    z$test_odeint_bad_shapes.<locals>.sys1c                 S   s
   g dgS )N)r   r   r   r$   r   r$   r$   r%   badjac  s    z&test_odeint_bad_shapes.<locals>.badjacr   r   r   ri   ru   r@   r  )rc   r  r   rd   )r  r	  r
  Zbad_y0Zbad_tr$   r$   r%   test_odeint_bad_shapes  s    r  c                  C   s  dd } t d}t| dg|}t|t t|df dt d }dgd	 |d| d| d
| g }t| ddg|ddd}t ddggd	 ddgddgddgddgg }t|| t| dgg }t|t jg t j	d
d ttt| dgg d ttt| g dg d dS )zRegression test for gh-8217.c                 S   s   d|  S )Ng      пr$   r   r$   r$   r%   r   4  s    z$test_repeated_t_values.<locals>.funcr@   ra   r   r   r   r   	   ri   r   )rB   rA   rv   r   g      ?g      ?)Zdtyper   )r   r   r   r   )r   r   ri   )r   r   r   ri   N)r   r   r   r   r   lenlogr   r   Zfloat64Zreshaperc   r  )r   r    re   ZtauZexpected_solr$   r$   r%   test_repeated_t_values1  s&    
"
r  )?r   sysplatformZnumpyr   r   r   r   r   r   r   r   r	   r
   r   r   Znumpy.testingr   r   r   r   r   r   rn   r   rc   Zscipy.integrater   r   r   machinerq   r   r;   rJ   rr   rt   r   r   r   r   r   r   r4   r   r)   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r$   r$   r$   r%   <module>   sP   4 #!j(ZC?E	I 