o
    Eb_                     @   s  d 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mZ ddlmZmZm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$ Z+d%d& Z,d'd( Z-d)d* Z.d+d, Z/G d-d. d.Z0G d/d0 d0e0Z1G d1d2 d2e0Z2G d3d4 d4e0Z3G d5d6 d6e0Z4G d7d8 d8e0Z5d9d: Z6d;d< Z7d=d> Z8d?d@ Z9dAdB Z:dS )Cz"
Tests for numerical integration.
    N)arangezerosarraydotsqrtcossineyepiexpallclose)assert_assert_array_almost_equalassert_allcloseassert_array_equalassert_equalassert_warns)raises)odeintodecomplex_odec                   @   s   e Zd Zdd Zdd ZdS )
TestOdeintc                    s   t d jd}t j j|dd\}}t || t fdd j|ddd\}}t || t drmt j j| jdd	\}}t || t fd
d j| fddddd\}}t || d S d S )N        g?Tfull_outputc                         || S Nftyproblem F/usr/lib/python3/dist-packages/scipy/integrate/tests/test_integrate.py<lambda>       z(TestOdeint._do_problem.<locals>.<lambda>)r   tfirstjac)Dfunr   c                    r   r   r   r   r"   r$   r%   r&   *   r'   c                    r   r   r)   r   r"   r$   r%   r&   +   r'   )r*   r   r(   )	r   stop_tr   r   z0r   verifyhasattrr)   )selfr#   r    zZinfodictr$   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$   r%   test_odeint/   s   zTestOdeint.test_odeintN)__name__
__module____qualname__r2   r7   r$   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r) 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                    r   r   r   r    r1   r"   r$   r%   r&   >   r'   z*TestODEClass._do_problem.<locals>.<lambda>r)   c                    r   r   r+   r=   r"   r$   r%   r&   A   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$   r"   r%   r2   ;   s,   


"zTestODEClass._do_problem)r<   )r8   r9   r:   rD   r2   r$   r$   r$   r%   r;   7   s    r;   c                   @   sH   e Z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S )TestOdec                 C   s>   t D ]}| }|jrq|js| |dd | |dd qd S Nvoder<   bdf)r4   r5   stiffr2   r6   r$   r$   r%   	test_vode\   s   zTestOde.test_vodec                 C   s6   t D ]}| }|js| |dd | |dd qd S )Nzvoder<   rM   r4   rN   r2   r6   r$   r$   r%   
test_zvodef   s   zTestOde.test_zvodec                 C   s(   t D ]}| }|jrq| |d qd S Nlsodar3   r6   r$   r$   r%   
test_lsodan   s   zTestOde.test_lsodac                 C   <   t D ]}| }|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_dopri5v      
zTestOde.test_dopri5c                 C   rV   Nr)   dop853rY   r6   r$   r$   r%   test_dop853   r[   zTestOde.test_dop853c                 C   s~   dD ]:}dd }t ||}|dd t ||}|dd ||jd  ||jd  tt|j|jd  qd S )N)rL   rP   rT   c                 S      dS N      ?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$   r%   test_concurrent_fail   s   zTestOde.test_concurrent_failc                 C   sF  dd }t dD ]}dD ]@}t||}|dd t||}|dd ||jd  ||jd  ||jd  t|jd t|jd qdD ]P}t||}|dd t||}|dd ||jd  ||jd  ||jd  ||jd  ||jd  t|jd	 t|jd qOqd S )
Nc                 S   r_   r`   r$   r   r$   r$   r%   r&      rb   z,TestOde.test_concurrent_ok.<locals>.<lambda>   )rL   rP   rT   rX   r]   r   rc   g?rX   r]   g333333?)ranger   rE   rF   rG   r    r   r!   )r0   r   krf   rg   rh   r$   r$   r%   test_concurrent_ok   s4   zTestOde.test_concurrent_okN)r8   r9   r:   r   rD   rO   rR   rU   rZ   r^   ri   rn   r$   r$   r$   r%   rJ   X   s    
rJ   c                   @   s0   e Zd ZeZdd Zdd Zdd Zdd Zd	S )
TestComplexOdec                 C   s8   t D ]}| }|js| |dd q| |dd qd S rK   rQ   r6   r$   r$   r%   rO      s   zTestComplexOde.test_vodec                 C   s    t D ]}| }| |d qd S rS   )r4   r2   r6   r$   r$   r%   rU      s   zTestComplexOde.test_lsodac                 C   4   t D ]}| }|jrqt|drq| |d qd S rW   r4   rN   r/   r2   r6   r$   r$   r%   rZ         
zTestComplexOde.test_dopri5c                 C   rp   r\   rq   r6   r$   r$   r%   r^      rr   zTestComplexOde.test_dop853N)	r8   r9   r:   r   rD   rO   rU   rZ   r^   r$   r$   r$   r%   ro      s    	
ro   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         $@ra          @c                         |   |  d S r   appendcopyr   tsysr$   r%   solout      
z+TestSolout._run_solout_test.<locals>.soloutc                 S      |d |d  |d d  gS Nr         r$   r   r$   r$   r%   rhs      z(TestSolout._run_solout_test.<locals>.rhsr   )r   rE   
set_soloutrF   rG   r   r   	r0   rH   t0tendy0r}   r   rI   retr$   rz   r%   _run_solout_test   s   

zTestSolout._run_solout_testc                 C      dD ]}|  | qd S Nrk   r   r0   rH   r$   r$   r%   test_solout     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   rt   ra   ru   c                    rv   r   rw   r   rz   r$   r%   r}     r~   z9TestSolout._run_solout_after_initial_test.<locals>.soloutc                 S   r   r   r$   r   r$   r$   r%   r     r   z6TestSolout._run_solout_after_initial_test.<locals>.rhsr   r   )r   rE   rF   r   rG   r   r   r   r$   rz   r%   _run_solout_after_initial_test  s   

z)TestSolout._run_solout_after_initial_testc                 C   r   r   )r   r   r$   r$   r%   test_solout_after_initial  r   z$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   rt   ra   ru   c                    ,    |   |  |  d krdS d S Nru   r   rw   r   r   r{   r|   r$   r%   r}   *  
   
z1TestSolout._run_solout_break_test.<locals>.soloutc                 S   r   r   r$   r   r$   r$   r%   r   0  r   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$   r   r%   _run_solout_break_test"  s    

z!TestSolout._run_solout_break_testc                 C   r   r   r   r   r$   r$   r%   test_solout_break=  r   zTestSolout.test_solout_breakN)	r8   r9   r:   r   r   r   r   r   r   r$   r$   r$   r%   rs      s    rs   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                    rv   r   rw   r   rz   r$   r%   r}   L  r~   z2TestComplexSolout._run_solout_test.<locals>.soloutc                 S      d| d d  gS Nra   rt                 ?r$   r   r$   r$   r%   r   P     z/TestComplexSolout._run_solout_test.<locals>.rhsr   r   )r   rE   r   rF   rG   r   r   r   r$   rz   r%   r   D  s   

z"TestComplexSolout._run_solout_testc                 C   r   r   r   r   r$   r$   r%   r   \  r   zTestComplexSolout.test_soloutc                    s   g g d}d dg} fdd}dd }t ||}|| ||| | }td | td | td | td  d	 k td  k  d S )
Nr   r   c                    r   r   rw   r   r   r$   r%   r}   h  r   z8TestComplexSolout._run_solout_break_test.<locals>.soloutc                 S   r   r   r$   r   r$   r$   r%   r   n  r   z5TestComplexSolout._run_solout_break_test.<locals>.rhsr   r   ru   )r   rE   r   rF   rG   r   r   r   r   r$   r   r%   r   `  s    

z(TestComplexSolout._run_solout_break_testc                 C   r   r   r   r   r$   r$   r%   r   {  r   z#TestComplexSolout.test_solout_breakN)r8   r9   r:   r   r   r   r   r$   r$   r$   r%   r   B  s
    r   c                   @   s0   e Zd ZdZdZdZdZg ZdZdZ	dZ
dZdS )ODEz
    ODE problem
    Fr   Ngư>gh㈵>)r8   r9   r:   __doc__rN   r5   r,   r-   r?   r>   rA   rB   r$   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   rc   g      @c                 C   s.   t dt}d|d< | j | j |d< t||S )N)r   r   ra   r   r   )r   r   )r   floatrm   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   rm   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-   rm   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        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$   r%   r        zPi.fc                 C   s.   dt d }t||dd d f | j| jdS )Ny              r@   r   r   )npZarctanr   rA   rB   r   r$   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   rj   FZ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$   r%   f1     r   c                 C   s   t d|g| dgg}|S Nr   r   r    r   r   r   r$   r$   r%   jac1!     r   c                 C   s   ||d  | |d  g}|S r   r$   )r    r   omega1omega2r   r$   r$   r%   f2'  r   r   c                 C   s   t d|g| dgg}|S r   r   )r    r   r   r   r   r$   r$   r%   jac2,  r   r   c                 C   s&   |d |d  |d  |d  g}|S )Nr   r   r$   r   r$   r$   r%   fv2  s   "r   c                 C   s"   t d|d g|d  dgg}|S )Nr   r   r   r   r   r$   r$   r%   jacv7  s   r   c                   @   sP   e Zd ZdZdZdZdd Zdd Zdd	 Zd
d Z	dd Z
dd Zdd ZdS )ODECheckParameterUsez=Call an ode-class solver with several cases of parameter use. Fc                 C   s@   t ||}| jr|j| jdd| jd |S |j| jddd |S )Ng&.>gHz>)rA   rB   Zwith_jacobianr   )r   solver_uses_jacrE   solver_name)r0   r   r)   solverr$   r$   r%   _get_solverF  s   
z ODECheckParameterUse._get_solverc                 C   s2   ddg}| |d |t t|jddg d S )Nra   r   r   )rF   rG   r
   r   r!   r0   r   Zicr$   r$   r%   _check_solverR  s   
z"ODECheckParameterUse._check_solverc                 C   s   |  tt}| | d S r   )r   r   r)   r   )r0   r   r$   r$   r%   test_no_paramsX  s   z#ODECheckParameterUse.test_no_paramsc                 C   s8   |  tt}d}|| | jr|| | | d S r`   )r   r   r   set_f_paramsr   set_jac_paramsr   r0   r   r   r$   r$   r%   test_one_scalar_param\  s   

z*ODECheckParameterUse.test_one_scalar_paramc                 C   s@   |  tt}d}d}||| | jr||| | | d S r`   )r   r   r   r   r   r   r   )r0   r   r   r   r$   r$   r%   test_two_scalar_paramsd  s   z+ODECheckParameterUse.test_two_scalar_paramsc                 C   s<   |  tt}ddg}|| | jr|| | | d S r`   )r   r   r   r   r   r   r   r   r$   r$   r%   test_vector_paramm  s   

z&ODECheckParameterUse.test_vector_paramc                 C   sB   |  tt}|j| jdd ddg}||d tt|jt	 d S )Nr   )Znstepsra   r   )
r   r   r)   rE   r   rF   r   UserWarningrG   r
   r   r$   r$   r%   test_warns_on_failureu  s
   z*ODECheckParameterUse.test_warns_on_failureN)r8   r9   r:   r   r   r   r   r   r   r   r   r   r   r$   r$   r$   r%   r   =  s    	r   c                   @      e Zd ZdZdZdS )TestDOPRI5CheckParameterUserX   FNr8   r9   r:   r   r   r$   r$   r$   r%   r   ~      r   c                   @   r   )TestDOP853CheckParameterUser]   FNr   r$   r$   r$   r%   r     r   r   c                   @   r   )TestVODECheckParameterUserL   TNr   r$   r$   r$   r%   r     r   r   c                   @   r   )TestZVODECheckParameterUserP   TNr   r$   r$   r$   r%   r     r   r   c                   @   r   )TestLSODACheckParameterUserT   TNr   r$   r$   r$   r%   r     r   r   c                  C   s:   d} dg}t dd | |dd\}}t|t| gg d S )Nr   r   c                 S   s   |  S r   r$   )r!   r    r$   r$   r%   r&     s    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$   r%   func     
z)test_odeint_banded_jacobian.<locals>.funcc                 S   s   |S r   r$   r   r$   r$   r%   r)        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$   r%   	bjac_cols  r   z.test_odeint_banded_jacobian.<locals>.bjac_cols)i3{Gz?r   r   )rc   g      g{Gz?r   )gMbP?r   g       r   )r   r   rc   r      )r   r   r@   d   TgvIh%<=gdy=i'  )argsr   rA   rB   mxstepr*   )r   r   rA   rB   r   r*   	col_derivr   r   )r   r   rA   rB   r   r*   mlmu)	r   r   rA   rB   r   r*   r   r  r   zsol1 != sol2)err_msg-q=zsol1 != sol3)rA   r  zsol3 != sol4Znjec                        || |S r   r$   r    r!   r   )r   r$   r%   r&     r'   z-test_odeint_banded_jacobian.<locals>.<lambda>c                    r  r   r$   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      d|  S Nr$   r   r    r$   r$   r%   sys1d  r   z!test_odeint_errors.<locals>.sys1dc                 S      dd S Nra   r   r$   r  r$   r$   r%   bad1  r   z test_odeint_errors.<locals>.bad1c                 S   r_   NZfoor$   r  r$   r$   r%   bad2  r   z test_odeint_errors.<locals>.bad2c                 S   r  r  r$   r  r$   r$   r%   bad_jac1  r   z$test_odeint_errors.<locals>.bad_jac1c                 S   s   dggS r  r$   r  r$   r$   r%   bad_jac2  r   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$   r%   sys2d_bad_jac  s   z)test_odeint_errors.<locals>.sys2d_bad_jacra   r   r   r*   )rd   ZeroDivisionErrorr   
ValueError)r  r  r  r  r  r  r  r$   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  r   z&test_odeint_bad_shapes.<locals>.badrhsc                 S   r  r	  r$   r  r$   r$   r%   sys1  r   z$test_odeint_bad_shapes.<locals>.sys1c                 S   s
   g dgS )N)r   r   r   r$   r  r$   r$   r%   badjac  r   z&test_odeint_bad_shapes.<locals>.badjacr   r   r   rj   rt   r@   r  )rd   r  r   re   )r  r  r  Zbad_y0Zbad_tr$   r$   r%   test_odeint_bad_shapes	  s    r  c                  C   s  dd } t d}t| dg|}t|t t|df dt d }dgd	 |d| d| d
| g }t| ddg|ddd}t ddggd	 ddgddgddgddgg }t|| t| dgg }t|t jg t j	d
d ttt| dgg d ttt| g dg d dS )zRegression test for gh-8217.c                 S   r  )Ng      пr$   r  r$   r$   r%   r   '  r   z$test_repeated_t_values.<locals>.funcr@   ra   r   r   r   r   	   rj   r  )rB   rA   ru   r   g      ?g      ?)Zdtyper   )r   r   r   r   )r   r   rj   )r   r   r   rj   N)r   r   r   r   r  lenlogr   r   Zfloat64Zreshaperd   r  )r   r    rf   ZtauZexpected_solr$   r$   r%   test_repeated_t_values$  s&   
"
r"  );r   Znumpyr   r   r   r   r   r   r   r   r	   r
   r   r   Znumpy.testingr   r   r   r   r   r   Zpytestr   rd   Zscipy.integrater   r   r   r   r;   rJ   ro   rs   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>   sJ   4 #!h(ZC?A	I 