o
    Ebjz                     @   s   d dl Z d dlmZ d dlZd dlmZmZmZ d dl	m
Z d dlmZmZmZ d dlmZmZmZmZmZmZ dd Zd	d
 ZG dd dZG dd dZG dd dZG dd dZdd Zdd ZdS )    N)product)assert_allcloseassert_equalassert_)raises)
csr_matrix
csc_matrix
lil_matrix)_adjust_scheme_to_boundsapprox_derivativecheck_derivativegroup_columns_eps_for_method_compute_absolute_stepc                  C   s   g dg dg dg dg dg dg dg} t jtttfD ]1}|| }t d}t g d	}t||}t|| g d
}t g d}t||}t|| qt|}t|}t|| d S )N)   r   r   r   r   r   )r   r   r   r   r   r   )r   r   r   r   r   r   )r   r   r   r   r   r   )r   r   r   r   r   r   )r   r   r   r   r   r   )r   r   r   r   r   r      )r   r      r   r   r   )r   r            r   )r   r   r   r   r   r   )	npasarrayr   r   r	   arangearrayr   r   )	structureZ	transformAorderZgroups_truegroupsgroups_1groups_2 r    D/usr/lib/python3/dist-packages/scipy/optimize/tests/test__numdiff.pytest_group_columns   s*   	



r"   c                  C   s   t t jj} | d | d | d d}dD ]}ttt jt j|||  ttt jt j|||  qt t jj} | d | d | d d}dD ])}ttt jt j|||  ttt jt j|||  ttt jt j|||  qGd S )N      ?UUUUUU?2-pointz3-pointcs)r   finfofloat64epsr   r   Z
complex128float32)EPSrelative_stepmethodr    r    r!   test_correct_fp_eps+   sB   r/   c                   @   s$   e Zd Zdd Zdd Zdd ZdS )TestAdjustSchemeToBoundsc                 C   s  t d}t dd}t |}t |}|t j  |t j t||dd||\}}t|| tt 	| t||dd||\}}t|| tt 	| t||dd||\}}t|| tt 	|  t||dd||\}}t|| tt 	|  d S )Nr   {Gz?r   1-sidedr   2-sided)
r   zerosZfullZ
empty_likefillinfr
   r   r   all)selfx0hZ	inf_lowerZ	inf_upper
h_adjusted	one_sidedr    r    r!   test_no_boundsP   s4   






z'TestAdjustSchemeToBounds.test_no_boundsc                 C   s   t g d}t d }t d}t g dd }t||dd||\}}t|| t||dd||\}}t|t g dd  t||dd	||\}}t|t | tt |  t||dd	||\}}t|t g dd  t|t g d
 d S )N)        g333333?g333333r   )r   r   皙?r   r2   r   )r   r?   r   r3   )FTT)	r   r   onesr
   r   absr   r7   r   )r8   r9   lbubr:   r;   _r<   r    r    r!   test_with_boundl   s$   

z(TestAdjustSchemeToBounds.test_with_boundc                 C   s  t ddg}t ddg}t ddg}t ddg}t||dd||\}}t|t ddg t||d	d||\}}t|t d
dg t||dd||\}}t|t ddg t|t ddg t||d	d||\}}t|t ddg t|t ddg d S )NgQg?r>   gQ?皙r   r2   gQr   g?r3   FTgQ?gQ)r   r   r
   r   r   )r8   rC   rD   r9   r:   r;   rE   r<   r    r    r!   test_tight_bounds   s$   z*TestAdjustSchemeToBounds.test_tight_boundsN)__name__
__module____qualname__r=   rF   rH   r    r    r    r!   r0   O   s    r0   c                   @   s  e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd ZdFddZdGddZdd Zdd Zdd Zdd  Zd!d" Zd#d$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/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#dES )HTestApproxDerivativesDensec                 C   
   t |S Nr   Zsinhr8   xr    r    r!   fun_scalar_scalar      
z,TestApproxDerivativesDense.fun_scalar_scalarc                 C   rM   rN   r   ZcoshrP   r    r    r!   jac_scalar_scalar   rS   z,TestApproxDerivativesDense.jac_scalar_scalarc                 C   ,   t |d d t |d t |d gS Nr   r   r   r   ZtanexprP   r    r    r!   fun_scalar_vector      ,z,TestApproxDerivativesDense.fun_scalar_vectorc                 C   8   t d|d  t |d d t |d gddS Nr   r   r?   r   r   r   cosrY   ZreshaperP   r    r    r!   jac_scalar_vector   
   (z,TestApproxDerivativesDense.jac_scalar_vectorc                 C   $   t |d |d  t |d  S Nr   r   r   sinlogrP   r    r    r!   fun_vector_scalar      $z,TestApproxDerivativesDense.fun_vector_scalarc                 C   s    t |d t |t |gS Nr   rX   rP   r    r    r!   wrong_dimensions_fun   s    z/TestApproxDerivativesDense.wrong_dimensions_func              	   C   |   t |d t |d |d   t |d  t |d |d  |d   |d t |d |d   t |d  gS Nr   r   r   r   r`   rg   rf   rP   r    r    r!   jac_vector_scalar      **z,TestApproxDerivativesDense.jac_vector_scalarc                 C   H   t |d t |d  |d t |d  |d d |d d  gS Nr   r   r         ࿩r   r   rf   r`   rP   r    r    r!   fun_vector_vector   
   z,TestApproxDerivativesDense.fun_vector_vectorc                 C      t t |d |d t |d  g|d  t |d  t |d gd|d d  |d d  d|d d  |d d  ggS Nr   r   r   r   rs   g      rt   rP   r    r    r!   jac_vector_vector   
   "$6z,TestApproxDerivativesDense.jac_vector_vector      ?c                 C   s*   t t ||d  t ||d  gS rd   r   r   rY   r8   rQ   c0c1r    r    r!   fun_parametrized   s   *z+TestApproxDerivativesDense.fun_parametrizedr@   c              
   C   s:   t |t ||d   dgd|t ||d   ggS rd   r|   r}   r    r    r!   jac_parametrized   s   z+TestApproxDerivativesDense.jac_parametrizedc                 C   s   t |dkr	|S t jS )N:0yE>r   rB   nanrP   r    r    r!   fun_with_nan      z'TestApproxDerivativesDense.fun_with_nanc                 C   s   t |dkr	dS t jS )Nr   r{   r   rP   r    r    r!   jac_with_nan   r   z'TestApproxDerivativesDense.jac_with_nanc                 C   s,   t |d |d  t |d |d  gS rd   )r   r   r`   rP   r    r    r!   fun_zero_jacobian   r[   z,TestApproxDerivativesDense.fun_zero_jacobianc              
   C   sV   t |d |d g|d  t |d |d   |d  t |d |d   ggS rm   )r   r   rf   rP   r    r    r!   jac_zero_jacobian   s   >z,TestApproxDerivativesDense.jac_zero_jacobianc                 C   rM   rN   )mathrY   rP   r    r    r!   fun_non_numpy   rS   z(TestApproxDerivativesDense.fun_non_numpyc                 C   s   t | }t|S rN   )r   r   itemr   rY   )r8   rQ   Zxpr    r    r!   jac_non_numpy   s   
z(TestApproxDerivativesDense.jac_non_numpyc                 C   sh   d}t | j|dd}t | j|}t | j|dd}| |}t||dd t||dd t||dd d S )	Nr{   r&   r.   r'   ư>rtol&.>-q=r   rR   rU   r   r8   r9   
jac_diff_2
jac_diff_3
jac_diff_4jac_truer    r    r!   test_scalar_scalar   s   
z-TestApproxDerivativesDense.test_scalar_scalarc                 C   sp   d}t | j|ddd}t | j|dd}t | j|ddd}| |}t||dd t||d	d t||d
d d S )Nr{   r&   "\O>r.   abs_step)r   r'   r   r   r   r   r   r   r    r    r!   test_scalar_scalar_abs_step   s   
z6TestApproxDerivativesDense.test_scalar_scalar_abs_stepc                 C   sn   d}t | j|dd}t | j|}t | j|dd}| t|}t||dd t||dd t||dd d S )	Nr#   r&   r   r'   r   r   r   r   )r   rZ   ra   r   
atleast_1dr   r   r    r    r!   test_scalar_vector   s   z-TestApproxDerivativesDense.test_scalar_vectorc                 C   r   t ddg}t| j|dd}t| j|}t| j|dd}| |}t||dd t||dd t||d	d d S )
N      Y@rs   r&   r   r'   r   r   Hz>r   )r   r   r   rh   ro   r   r   r    r    r!   test_vector_scalar	     
z-TestApproxDerivativesDense.test_vector_scalarc                 C   s~   t ddg}t| j|ddd}t| j|dt jd}t| j|ddd}| |}t||dd	 t||d
d	 t||dd	 d S )Nr   rs   r&   r   r   )r   rel_stepr'   r   r   A:)>r   )r   r   r   rh   r6   ro   r   r   r    r    r!   test_vector_scalar_abs_step  s   
z6TestApproxDerivativesDense.test_vector_scalar_abs_stepc                 C   r   )
N      Y皙?r&   r   r'   h㈵>r   r   r   r   r   r   ru   ry   r   r   r    r    r!   test_vector_vector#  r   z-TestApproxDerivativesDense.test_vector_vectorc                 C   s<   d}t tt| j| | t|}t tt| j||d d S )Nr{   )f0)assert_raisesRuntimeErrorr   rk   r   r   
ValueError)r8   r9   r   r    r    r!   test_wrong_dimensions/  s   
z0TestApproxDerivativesDense.test_wrong_dimensionsc                 C   sZ   t ddg}t| j|ddd}t| j|dd}| |}t||dd t||dd d S )	NrG   r@   r&   g-C6?)r.   r   )r   r1   r   r   )r8   r9   r   r   r   r    r    r!   test_custom_rel_step7  s   
z/TestApproxDerivativesDense.test_custom_rel_stepc              
   C   s   t ddg}d}d}d}d}| j|||d}t ddg}| |||}t| j|d|||ft|d||fd	}	t| j||||ft|d||fd
}
t|	|dd t|
|dd d S )Nr{         r>          @)r   gưr   r&   )r.   r   r   argskwargsbounds)r   r   r   r   r   r   r   r   )r   r   r   r   r   dictr   )r8   r9   r~   r   rC   rD   r   r   r   r   r   r    r    r!   test_optionsA  s$   
z'TestApproxDerivativesDense.test_optionsc                 C   s|   t d }t d}t ddg}ttt| j|||fd t ddg}t| j|d||fd}| |}t||d	d
 d S )Nr   g       r   r   r   r{   r&   r.   r   r   r   )	r   rA   r   r   r   r   ru   ry   r   )r8   rC   rD   r9   jac_diffr   r    r    r!   test_with_bounds_2_pointS  s   

z3TestApproxDerivativesDense.test_with_bounds_2_pointc                 C   s   t ddg}t ddg}t ddg}| |}t| j|}t||dd t| j||t jfd}t||dd t| j|t j |fd}t||dd t| j|||fd}t||dd d S )Nr{   r   r   r   r   )r   r   ry   r   ru   r   r6   )r8   rC   rD   r9   r   r   r    r    r!   test_with_bounds_3_pointa  s$   

z3TestApproxDerivativesDense.test_with_bounds_3_pointc                 C   s   t ddg}|d }|d }| |}t| j|d||fd}t||dd t| j|dd||fd}t||dd t| j|||fd	}t||dd t| j|d||fd
}t||dd d S )Ng      $@r   g&.!>r&   r   r   r   r.   r   r   r   r   r   )r   r   ry   r   ru   r   )r8   r9   rC   rD   r   r   r    r    r!   rH   w  s*   
z,TestApproxDerivativesDense.test_tight_boundsc                 C   s   d}d}d}|  |}t| j|dd||fd}t| j|d||fd}t||dd t||d	d d}|  |}t| j|dd||fd}t| j|d||fd}t||dd t||d	d d S )
N:0yEr   r>   r&   r   r   r   r   r   )r   r   r   r   )r8   rC   rD   r9   r   r   r   r    r    r!   test_bound_switches  s0   



z.TestApproxDerivativesDense.test_bound_switchesc                 C   sh   d}|  |}t| j |dd}t| j |}t||dd t||dd ttt| j |fi tdd d S )Nr{   r&   r   r   r   r   r'   )r   r   r   r   	TypeErrorr   )r8   r9   r   r   r   r    r    r!   test_non_numpy  s   

z)TestApproxDerivativesDense.test_non_numpyc                    s  t jd dd fdd t jdddt jdt jdt jt d	d	g}t |d
fd}t |t jd
fd} |j	t jksOJ t
||dd  fdd}t||d
d}||j	t jksoJ t
||dd dd }dd }dd }dd }t jt jt jfD ]5}	t |	j}
t d|	}td |||d
}||||||
}t||d
|d||  t |k sJ qd S )Nr   c                 S   s   | d | d |  S rd   r    )prQ   r    r    r!   func  s   z0TestApproxDerivativesDense.test_fp.<locals>.funcc                    s    | || S rN   r    )r   rQ   y)r   r    r!   err     z/TestApproxDerivativesDense.test_fp.<locals>.errr   d   dtyper   r&   )r.   r   gMbP?)atolc                    s    |  tjS rN   )astyper   r+   )r   )r   rQ   r   r    r!   <lambda>  s    z4TestApproxDerivativesDense.test_fp.<locals>.<lambda>r   c                 S   
   t | S rN   r   rf   rQ   r    r    r!   r        
 c                 S   r   rN   )r   r`   r   r    r    r!   r     r   c                 S   s   t |  S rN   r   r   r    r    r!   r     s    c                 S   s\   | d t t||t|||   }||  t t||t|||   }|| S rj   )maxr   rB   )r:   r9   fhessr,   Zt0t1r    r    r!   	calc_atol  s   **z5TestApproxDerivativesDense.test_fp.<locals>.calc_atolr{   r   )r   randomseedZlinspacer)   r   r   r   r+   r   r   Zfloat16r(   r*   r   rB   )r8   Zp0Zjac_fp64Zjac_fpZerr_fp32r   gr   r   r   r,   r9   r:   r   r    )r   r   rQ   r   r!   test_fp  sD   	z"TestApproxDerivativesDense.test_fpc                 C   s   t ddg}t| j| j|}t|dk  t| j| j|}t|dk  t ddg}t| j| j|}t|dk t| j| j|}t|dk d S )Ng      $
   r   r   r>   r   )r   r   r   ru   ry   r   r   r   )r8   r9   accuracyr    r    r!   test_check_derivative  s$   z0TestApproxDerivativesDense.test_check_derivativeN)r{   )r@   )$rI   rJ   rK   rR   rU   rZ   ra   rh   rk   ro   ru   ry   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   rH   r   r   r   r   r    r    r    r!   rL      sD    


5rL   c                   @   sL   e 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d Z
dS )TestApproxDerivativeSparsec                 C   s   t jd d| _ddt | j  | _ddt | j  | _t | j| _d| jd d d  | jd d d< d| jdd d  | jdd d< | 	| j| _
d S )Nr   2   rG   r   r@   gP?r   )r   r   r   nr   rC   rD   emptyr9   jacJ_truer8   r    r    r!   setup_method  s     z'TestApproxDerivativeSparse.setup_methodc                 C   sD   |dd  d |d d d  }t dd| ft d| df S )Nr   r   r?   r   r   )r   Zhstack)r8   rQ   er    r    r!   fun  s    $zTestApproxDerivativeSparse.func                 C   s   |j }t||f}d|d  |d< d|d d  |d< td|d D ]2}d||d   |||d f< d	|| d  d
||   |||f< d||d  d  |||d f< q#d	|d d  |d< d|d  |d< |S )Nr   r   r   r   r   r   r   r   i	   r   r?   r?   r?   r^   r?   r^   )sizer   r4   range)r8   rQ   r   Jir    r    r!   r     s   $"zTestApproxDerivativeSparse.jacc                 C   sb   t j||ftd}d|d< d|d< td|d D ]}d|||d |d f< qd|d< d|d< |S )Nr   r   r   r   r   r   r   )r   r4   intr   )r8   r   r   r   r    r    r!   r     s   z$TestApproxDerivativeSparse.structurec                 C   s  |  | j}t| j}t||}tj| t||}tg d||gtj | j	gtj| j
gD ]O\}}}}t| j| j|||f||fd}	tt|	t t|	 | jdd t| jd}
|
d d d  d9  < t| j| j||
||fd}	t|	 | jd	d q0d S )
Nr%   )r.   r   sparsityr   r   r   r   r?   )r.   r   r   r   )r   r   r   r   r   r   Zshuffler   r6   rC   rD   r   r   r9   r   
isinstancer   r   toarrayr   Z	full_like)r8   r   r   r   r   r.   r   lur   r   r    r    r!   test_all   s*   

z#TestApproxDerivativeSparse.test_allc                 C   s6   |  | j}t| j| j|d}t| | jdd d S )N)r   r   r   )r   r   r   r   r9   r   r   r   )r8   r   r   r    r    r!   test_no_precomputed_groups5  s   z5TestApproxDerivativeSparse.test_no_precomputed_groupsc                 C   sn   t j| j| jftd}t | j}dD ]!}t| j| j|d}t| j| j||f|d}t||	 ddd qd S )Nr   r%   r   )r   r.   gV瞯<gVs<)r   r   )
r   rA   r   r   r   r   r   r9   r   r   )r8   r   r   r.   ZJ_denseZJ_sparser    r    r!   test_equivalence:  s   
z+TestApproxDerivativeSparse.test_equivalencec                    s`    fdd}t  j| j j jfd}t|dk  t  j| j j jfd}t|dk  d S )Nc                    s   t  | S rN   )r   r   r   r   r    r!   r   E  r   z=TestApproxDerivativeSparse.test_check_derivative.<locals>.jacr   r   )r   r   r9   rC   rD   r   )r8   r   r   r    r   r!   r   D  s   

z0TestApproxDerivativeSparse.test_check_derivativeN)rI   rJ   rK   r   r   r   r   r   r   r   r   r    r    r    r!   r     s    
r   c                   @   st   e 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d Z
dd Zdd Zdd Zdd Zdd ZdS )"TestApproxDerivativeLinearOperatorc                 C   rM   rN   rO   rP   r    r    r!   rR   S  rS   z4TestApproxDerivativeLinearOperator.fun_scalar_scalarc                 C   rM   rN   rT   rP   r    r    r!   rU   V  rS   z4TestApproxDerivativeLinearOperator.jac_scalar_scalarc                 C   rV   rW   rX   rP   r    r    r!   rZ   Y  r[   z4TestApproxDerivativeLinearOperator.fun_scalar_vectorc                 C   r\   r]   r_   rP   r    r    r!   ra   \  rb   z4TestApproxDerivativeLinearOperator.jac_scalar_vectorc                 C   rc   rd   re   rP   r    r    r!   rh   `  ri   z4TestApproxDerivativeLinearOperator.fun_vector_scalarc              	   C   rl   rm   rn   rP   r    r    r!   ro   c  rp   z4TestApproxDerivativeLinearOperator.jac_vector_scalarc                 C   rq   rr   rt   rP   r    r    r!   ru   j  rv   z4TestApproxDerivativeLinearOperator.fun_vector_vectorc                 C   rw   rx   rt   rP   r    r    r!   ry   q  rz   z4TestApproxDerivativeLinearOperator.jac_vector_vectorc                 C   s   d}t | j|ddd}t | j|dd}t | j|ddd}| |}tjd tdD ]/}tjjd	dd
d}t|	||| dd t|	||| dd t|	||| dd q+d S )Nr{   r&   Tr.   as_linear_operatorr   r'   r   r   r   r   r   r   h㈵>)
r   rR   rU   r   r   r   r   uniformr   dotr8   r9   r   r   r   r   r   r   r    r    r!   r   x  s4   
z5TestApproxDerivativeLinearOperator.test_scalar_scalarc                 C   s   d}t | j|ddd}t | j|dd}t | j|ddd}| t|}tjd tdD ]2}tjjd	dd
d}t	|
||
|dd t	|
||
|dd t	|
||
|dd q.d S )Nr#   r&   Tr   r  r'   r   r   r  r  r  r   r   r  )r   rZ   ra   r   r   r   r   r   r  r   r  r  r    r    r!   r     s4   z5TestApproxDerivativeLinearOperator.test_scalar_vectorc                 C   s   t ddg}t| j|ddd}t| j|dd}t| j|ddd}| |}t jd td	D ]<}t jjd
d	|j	d}t
||t ||dd t
||t ||dd t
||t ||dd q0d S )Nr   rs   r&   Tr   r  r'   r   r   r  r  r   r   r  r   )r   r   r   rh   ro   r   r   r   r  shaper   r  r   r  r    r    r!   r     s4   
z5TestApproxDerivativeLinearOperator.test_vector_scalarc                 C   s   t ddg}t| j|ddd}t| j|dd}t| j|ddd}| |}t jd td	D ]3}t jjd
d	|j	d}t
||||dd t
||||dd t
||||dd q0d S )Nr   r   r&   Tr   r  r'   r   r   r  r  r   r   r   r   )r   r   r   ru   ry   r   r   r   r  r	  r   r  r  r    r    r!   r     s(   
z5TestApproxDerivativeLinearOperator.test_vector_vectorc                 C   s.   t ddg}ttt| j|ddt jfd d S )Nr   r   r&   r   r   )r   r   r   r   r   ru   r6   )r8   r9   r    r    r!   test_exception  s
   

z1TestApproxDerivativeLinearOperator.test_exceptionN)rI   rJ   rK   rR   rU   rZ   ra   rh   ro   ru   ry   r   r   r   r   r
  r    r    r    r!   r   Q  s    r   c                  C   s  dd } t | ddgddd}t|ddg t | ddgdd	d}t|ddg t | ddgdddgd}t|ddg t | ddgddd	gd}t|ddg t | ddgdd	dgd}t|ddg t | ddgddtj dfd
}t|ddg t | ddgdd	dtjfd
}t|ddg d S )Nc                 S   s&   t | d d  t | d d  S rd   )r   rB   r   r    r    r!   r     s   &z"test_absolute_step_sign.<locals>.fr?   r&   r   r   r   r{   r   )r.   r   r   )r   r   r   r6   )r   Zgradr    r    r!   test_absolute_step_sign  s4   	
r  c            
      C   sj  g d} t g d}t t jj}|d |d |d d}t d}| D ]A}|| }t ||d |d |t |d  g}td |||}t|| | dkt	d d	 }	td | ||}t||	|  q%t g d
}t |d |d  |d |d d |d t |d  g}t|||d}t|| | dkt	d d	 }	t|| |d}t||	|  d S )Nr%   )r   r   r   g     j@r#   r$   r{   r   r   r   r   )r@   r   r   r   r&   )
r   r   r(   r)   r*   rB   r   r   r   float)
methodsr9   r,   r-   r   r.   r   Zcorrect_stepr   Zsign_x0r    r    r!   test__compute_absolute_step  s>   



r  )r   	itertoolsr   Znumpyr   Znumpy.testingr   r   r   Zpytestr   r   Zscipy.sparser   r   r	   Zscipy.optimize._numdiffr
   r   r   r   r   r   r"   r/   r0   rL   r   r   r  r  r    r    r    r!   <module>   s"     $J  _[5