o
    i                     @   sj  d dl Zd dlmZmZmZ d dlm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mZmZmZmZmZ d dlmZ d dlmZmZm Z m!Z!m"Z" d dl#m$  m%Z& d dl'Z'G dd dZ(dd	 Z)d
d Z*dd Z+dd Z,dd Z-dd Z.d*ddZ/d+ddZ0dd Z1G dd dZ2G dd dZ3d d! Z4d,d"d#Z5G d$d% d%Z6d&d' Z7G d(d) d)Z8dS )-    N)assert_equalassert_allcloseassert_)raises)BSplineBPolyPPolymake_interp_splinemake_lsq_spline_bsplsplevsplrepsplprepsplder
splantidersprootsplintinsertCubicSplinemake_smoothing_spline)_not_a_knot_augknt_woodbury_algorithm_periodic_knots_make_interp_per_full_matrc                   @   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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$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Zd3d4 Zd5d6 Zd7d8 Zej !d9e"d:d;d<d= Z#d>d? Z$d@dA Z%ej !dBg dCej !dDe"dEdFdG Z&dHdI Z'dJdK Z(dLdM Z)ej !dNg dOdPdQ Z*ej !dNg dOdRdS Z+dTdU Z,dVdW Z-dXS )YTestBSplinec              	   C   s  t ttftfi tddgdgdd tjdd t ttfi tdtjgdgdd W d    n1 s6w   Y  t ttfi tdtjgdgdd t ttfi tddgdgdd t ttfi tdgdggdgdd t ttfi tg d	dgdd t ttfi tg d
ddgdd t ttfi tg dg ddd t ttfi tg dg ddd t ttfi tg dg ddd d\}}t	|| d }tj

|}t|||}t||j t||j t||j d S )N                 ?      ?r   tckignore)invalidr   r      r   r   r'         r'   )        r+   r          @      @      @)r   r   r   Zcubic      @)r+   r   r   r   r'   r)   )r   r   r   )   r)   )assert_raises	TypeError
ValueErrorr   dictnpZerrstatenaninfarangerandomr   r    r!   r   r"   )selfnr"   r    r!   b r=   t/var/www/html/eduruby.in/lip-sync/lip-sync-env/lib/python3.10/site-packages/scipy/interpolate/tests/test_bsplines.py	test_ctor   s:   &$"&"



zTestBSpline.test_ctorc                 C   s~   t  }|j}t|j|d ddd t|j|d ddd t|j|d  tt	 d|_W d    d S 1 s8w   Y  d S )Nr   V瞯<atolrtolr   r'   Zfoo)
_make_random_splinetckr   r    r!   r   r"   pytestr   AttributeError)r:   r<   rE   r=   r=   r>   test_tck8   s   "zTestBSpline.test_tckc                 C   sf   t ddd}tddgdgdd}t||d tg dddgdd}t||t |d	k dd d S )
Nr   r   
   r-   r   r)   )r   ffffff?r   r*   rJ   )r5   linspacer   r   wherer:   xxr<   r=   r=   r>   test_degree_0D   s
    zTestBSpline.test_degree_0c                 C   s   g d}g d}d}t |||}tddd}t|d t| |d t|d   |d t|d   ||dd	 tt||||f||dd	 d S )
Nr(   r   r'   r)   r   r)   2   r   r'   +=rB   )r   r5   rK   r   B_012r   )r:   r    r!   r"   r<   xr=   r=   r>   test_degree_1M   s   8"zTestBSpline.test_degree_1c                 C   s   d}t dg|d  dg|d   }t g d}t|ddddg}t|||}t ddd}t||d	d
||d	d
dd tt||||f||dd d S )Nr)   r   r   r   r,   r-   r.   r%   g      r,   rI   TextrapolaterR   rS   )r5   asarrayr   reshaper   rK   r   r   )r:   r"   r    r!   bpbsplrN   r=   r=   r>   test_bernsteinX   s   "
zTestBSpline.test_bernsteinc                    s   t  }|j\ t  d  d}||} fdd|D }t||dd  fdd|D }t||dd d S )Nr   rQ   c                       g | ]	}t | qS r=   _naive_eval.0rU   r!   r"   r    r=   r>   
<listcomp>n       z4TestBSpline.test_rndm_naive_eval.<locals>.<listcomp>rR   rS   c                    r_   r=   )_naive_eval_2rb   rd   r=   r>   re   q   rf   )rD   rE   r5   rK   r   )r:   r<   rN   Zy_bZy_nZy_n2r=   rd   r>   test_rndm_naive_evalf   s   z TestBSpline.test_rndm_naive_evalc                 C   sP   t  }|j\}}}t|| || d  d}t||t||||fdd d S )Nr   rQ   rR   rS   rD   rE   r5   rK   r   r   r:   r<   r    r!   r"   rN   r=   r=   r>   test_rndm_splevt   s   "zTestBSpline.test_rndm_splevc                 C   s   t jd t t jd}t jd}t||}t| }|j|j}}t || || d  d}t	||t
||dd d S )N     r   P   rR   rS   )r5   r9   seedsortr   r   r    r"   rK   r   r   )r:   rU   yrE   r<   r    r"   rN   r=   r=   r>   test_rndm_splrepz   s   
zTestBSpline.test_rndm_splrepc                 C   sJ   t  }t|j|_t|j|j |j|j d  d}t||d d S )Nr   d   r   )rD   r5   	ones_liker!   rK   r    r"   r   )r:   r<   rN   r=   r=   r>   test_rndm_unity   s   $zTestBSpline.test_rndm_unityc           	      C   s~   d\}}t t j|}t jj|ddfd}t|||}|| || d  }}||| t jd  }t||jd d S )N   r)         sizer   r)   r*      )r)   r*   r}   rx   ry   )r5   rp   r9   r   r   shape)	r:   r;   r"   r    r!   r<   tmtprN   r=   r=   r>   test_vectorization   s   zTestBSpline.test_vectorizationc           
      C   s   d\}}t t j|| d }t j|}t j|t j|d f }t|||t|||}}|d |d  }t |d | |d | d}	t||	||	dd t||	t|	|||fdd t||	t|	|||fdd d S )N)!   r)   r   r%   r   rQ   rR   rS   )r5   rp   r9   r_r   rK   r   r   )
r:   r;   r"   r    r!   Zc_padr<   Zb_paddtrN   r=   r=   r>   
test_len_c   s   "zTestBSpline.test_len_cc                 C   sb   t  }|j\}}}|| || d  }}dD ]}t|||g|||d |d g|dd qd S )Nr   )TF绽|=&.>rS   rD   rE   r   )r:   r<   r    _r"   r   r   Zextrapr=   r=   r>   test_endpoints   s   zTestBSpline.test_endpointsc                 C   sX   t  }|j\}}}t|||d | d  d |||d | d  d dd d S )Nr   r   r   rS   r   )r:   r<   r    r   r"   r=   r=   r>   test_continuity   s
   :
zTestBSpline.test_continuityc                 C   s   t  }|j\}}}|d |d  }t|| | || d  | d}|| |k ||| d  k @ }t||| dd||| dd t||ddt||||fdd d S )	Nr%   r   r   rQ   TrX   F)extri   )r:   r<   r    r!   r"   r   rN   maskr=   r=   r>   test_extrap   s   $zTestBSpline.test_extrapc                 C   sL   t  }|j\}}}|d d |d d g}||}ttt|  d S )Nr   r   r%   )rD   rE   r   r5   allisnan)r:   r<   r    r   r"   rN   yyr=   r=   r>   test_default_extrap   s
   zTestBSpline.test_default_extrapc           	      C   s  t jd t t jd}t jd}d}t|||dd}|j|d  }|d |d	  }t || | || | d
}|| |||  || ||    }t||t||||f g d}|| |||  || ||    }t	||dd||dd d S )Nrl      r*   r)   periodicrX   r   r%   r   rQ   )r%   r         ?r   T)
r5   r9   ro   rp   r   r{   rK   r   r   r   )	r:   r    r!   r"   r<   r;   r   rN   Zxyr=   r=   r>   test_periodic_extrap   s   $$z TestBSpline.test_periodic_extrapc                 C   sV   t  }|j\}}}t|||f}t|| ||  d}t||||ddd d S )Nrs   rR   rA   )rD   rE   r   from_spliner5   rK   r   )r:   r<   r    r!   r"   pprN   r=   r=   r>   
test_ppoly   s
   zTestBSpline.test_ppolyc                 C   s   t  }|j\}}}t|d |d d}tj||f }td|d D ]}t||||f|d}t||||ddd q"t|||d dddd d S )	Nr   r%   rQ   r   dernurR   rS   )rD   rE   r5   rK   r   ranger   r   )r:   r<   r    r!   r"   rN   r   Zydr=   r=   r>   test_derivative_rndm   s   z TestBSpline.test_derivative_rndmc              
   C   s4  d}g d}t jd t jddt jdddf }t|||}t g d}t|||dk d |||dk d  tt |d	|d
  t ddg}t||d dd||d dd t ddg}tt 	t ||d dd||d dd  tt 	t ||d dd||d dd  d S )Nr'   )r%   r%   r   r   r   r)   r*   rx   rx   rx   ry   ry   rl   r   r}   )r   r)   r*   rx   rx   r   g2H@gη   @r)   r*   r   r   )
r5   r9   ro   r   r   rZ   r   r   Zallcloser   )r:   r"   r    r!   r<   rU   x0x1r=   r=   r>   test_derivative_jumps   s*   
z!TestBSpline.test_derivative_jumpsc                 C   s   t ddd}tjg dd}t||t||j|j|jfdd t||t	|dd tjg dd}t d	d
d}t||t 
|dk || d| d
 dd d S )Nr%   r*   rm   r   r   r'   r)   )r    rR   rS   r   r   r   r'   r   r'   rI   r   r,   )r5   rK   r   basis_elementr   r   r    r!   r"   B_0123rL   rM   r=   r=   r>   test_basis_element_quadratic  s   
z(TestBSpline.test_basis_element_quadraticc                 C   sN   t  }|j\}}}t|| || d  d}t||t||||dd d S )Nr   rm   rR   rS   )rD   rE   r5   rK   r   _sum_basis_elementsrj   r=   r=   r>   test_basis_element_rndm  s    z#TestBSpline.test_basis_element_rndmc           	      C   s   t  }|j\}}}|d }t|||}t||jj|}t||jj|}t|| || d  d}t||j||dd t||j||dd d S )Ny      ?      @r   rm   rR   rS   )	rD   rE   r   r!   realimagr5   rK   r   )	r:   r<   r    r!   r"   ccb_reb_imrN   r=   r=   r>   
test_cmplx$  s   zTestBSpline.test_cmplxc                 C   s&   t g d}tt|tj d S )Nr   )r   r   r   r5   r   r6   r:   r<   r=   r=   r>   test_nan1  s   zTestBSpline.test_nanc                 C   st   t dd}|j\}}}t|||}t|| || d  d}td|D ]}| }t|||||ddd q$d S )Nr}   r"   r   rm   -q=rA   )rD   rE   r   r5   rK   r   
derivativer   )r:   r<   r    r!   r"   Zb0rN   jr=   r=   r>   test_derivative_method6  s   
z"TestBSpline.test_derivative_methodc                 C   s   t  }|j\}}}t|| || d  d}t|  |||ddd tj|||f }t||f}t	|||}t|  |||ddd d S )Nr   rm   rR   rA   )
rD   rE   r5   rK   r   antiderivativer   c_dstackr   rj   r=   r=   r>   test_antiderivative_method?  s   


z&TestBSpline.test_antiderivative_methodc                 C   s>  t g d}t|ddd t|ddd t|ddd t|ddd t|jddddd t|jddd	dd t|jddd	dd t|jddd	dtdd|j d
|_| }|d|d }t|dd| t|ddd|  t|dd| t|ddd|  t|dd|d|d  t|dd|d|d |d |d  t|dd|d|d |d |d  t|dd|d|d |d |d d|   t|dd|d|d  t|dd|d|d  t|dd|d|d d|   d S )Nr&   r   r   r   g      r%   TrX   Fr   r'   iii      ?r)   g      +@   rx   ir*   )	r   r   r   	integrate_implr   rE   rY   r   )r:   r<   iZ
period_intr=   r=   r>   test_integralM  s:   .&*zTestBSpline.test_integralc                 C   sN   g d}t ||}d|_t|}dD ]\}}t|||||| qd S )Nr(   r   ))r   )r   r}   )r      )r	   rY   r   r   r   r   )r:   rU   r<   pr   r   r=   r=   r>   test_integrate_ppolyr  s   


z TestBSpline.test_integrate_ppolyc                 C   sN   G dd dt }|g d}t|j| t| j| t| j| d S )Nc                   @   s   e Zd ZdS )z'TestBSpline.test_subclassing.<locals>.BN)__name__
__module____qualname__r=   r=   r=   r>   B  s    r   )r   r   r'   r'   )r   r   r   	__class__r   r   )r:   r   r<   r=   r=   r>   test_subclassing}  s
   zTestBSpline.test_subclassingaxisr   r*   c              
   C   sf  d\}}t dd|| d }g d}|d }||| t jj|d}t||||d}t|jj|| g|d |  ||d d    t jd}	t||	j|d | t|	j ||d d    |j	 d |j	fD ]}
t
t jtfi t||||
d	 qlt||||d t||||dd
t||||d t||||dd
fD ]	}t|j|j qd S )Nrv   r   r   )rx   ry   r   r*   rz   r   r|   )r    r!   r"   r   r'   )r5   rK   r   r9   r   r   r!   r~   listndimr1   Z	AxisErrorr4   r   r   r   )r:   r   r;   r"   r    shZpos_axisr!   r<   Zxpaxb1r=   r=   r>   	test_axis  s2   $
$zTestBSpline.test_axisc                 C   sp   d}g d}t g dg dg}t|||dd}t||d |}t||d |}t|d	|d	|d	g d S )
Nr'   )r   r   r'   r)   r*   r}   rx   )r%   r'   r   r%   )r'   r   r   r%   r   r   r   r/   )r5   arrayr   r   )r:   r"   r    r!   splZspl0Zspl1r=   r=   r>   test_neg_axis  s   zTestBSpline.test_neg_axisc                 C   sh   dd }d}d}dD ]}|||| q
t dddD ]}|||d qd	}t dd
D ]}|||d q)dS )a7  
        Splines with different boundary conditions are built on different
        types of vectors of knots. As far as design matrix depends only on
        vector of knots, `k` and `x` it is useful to make tests for different
        boundary conditions (and as following different vectors of knots).
        c           	      S   s   t jd t t j| d d }t j| d d }|dkr'|d |d< t||||d}t t|j| d }t	|j|||}t	
||j| }t||j |d	d
 t||d	d
 dS )zY
            To avoid repetition of code the following function is provided.
            rl   (   rm   r   r%   r   r"   bc_typer   rR   rS   N)r5   r9   ro   rp   random_sampler	   eyelenr    r   design_matrixtoarrayr   r!   )	r;   r"   r   rU   rq   r]   r!   Zdes_matr_defdes_matr_csrr=   r=   r>   run_design_matrix_tests  s    zHTestBSpline.test_design_matrix_bc_types.<locals>.run_design_matrix_testsr0   r)   clampednaturalr   r'   
not-a-knotr}   ry   r   N)r   )r:   r   r;   r"   bcr=   r=   r>   test_design_matrix_bc_types  s   z'TestBSpline.test_design_matrix_bc_typesrY   )FTr   degreer}   c           
   	   C   sJ  t jd t jd|d  }t |t |}}|}t jt |d |d |t ||d|d  t |d |d |f }t t	|| d }t
||||}	t|	|t
||||  t |d |d |d |d g}|stt t
|||| W d   dS 1 sw   Y  dS t|	|t
||||  dS )z;Test that design_matrix(x) is equivalent to BSpline(..)(x).rl   rI   r   r'   r   N)r5   r9   ro   r   ZaminZamaxr   rK   r   r   r   r   r   r   r   rF   r   r3   )
r:   rY   r   rU   ZxminZxmaxr"   r    r!   Zbspliner=   r=   r>   'test_design_matrix_same_as_BSpline_call  s,   ""z3TestBSpline.test_design_matrix_same_as_BSpline_callc           
      C   s   t jd d}d}t t j|d d }t j|d d }t|||d}tddD ]"}|d | }|d | }t||j	|
 }	t|	|j |d	d
 q-d S )Nrl   rI   r)   r   rm   r   r   r*   rR   rS   )r5   r9   ro   rp   r   r	   r   r   r   r    r   r   r!   )
r:   r;   r"   rU   rq   r]   r   Zxcycr   r=   r=   r>   test_design_matrix_x_shapes  s"   z'TestBSpline.test_design_matrix_x_shapesc                 C   s2   g d}t d|d }t|g dgdd d S )N)r   r   r   r,   r-   r.   r.   r.   r,   r)   )g      ?gmਪ?gK}\UU?r+   rR   rS   )r   r   r   r   )r:   r    Zdes_matrr=   r=   r>   test_design_matrix_t_shapes  s   
z'TestBSpline.test_design_matrix_t_shapesc                 C   s   t jd d}d}t t j|d d }t j|d d }t|||d}tt t	||j
d d d | W d    n1 sDw   Y  d}g d	}g d
}tt t	||| W d    d S 1 sjw   Y  d S )Nrl   rI   r)   r   rm   r   r%   r'   )r+   r   r,   r-   r.   g      @rW   )r5   r9   ro   rp   r   r	   r1   r3   r   r   r    )r:   r;   r"   rU   rq   r]   r    r=   r=   r>   test_design_matrix_asserts  s   

"z&TestBSpline.test_design_matrix_assertsr   )r   r   r   r   c                 C   s   t jd t t jd}t jd}|dkr|d |d< t|||d}tj||d}t ddd}t||||dd	 t	|||d}t|j
|j
dd	 d S )
Nrl   rm   r   r   r%   r   r   r@   rS   )r5   r9   ro   rp   r   r   from_power_basisrK   r   r	   r!   )r:   r   rU   rq   cbr]   rN   Zbspl_newr=   r=   r>   test_from_power_basis   s   z!TestBSpline.test_from_power_basisc                 C   s   t jd t t jd}t jdt jdd  }|dkr'|d |d< t|||d}tj||d}t||j|d}t||j	|d}t
|jj|jd|j  j t|j|jd|j  dd	 d S )
Nrl   rm   r   r   r   r%   r   r@   rS   )r5   r9   ro   rp   r   r   r   r	   r   r   r   r!   dtyper   )r:   r   rU   rq   r   r]   Zbspl_new_realZbspl_new_imagr=   r=   r>   test_from_power_basis_complex/  s&   

z)TestBSpline.test_from_power_basis_complexc                 C   sL   t g d}t g d}tjt||dddd}t|jg ddd dS )	a}  
        For x = [0, 1, 2, 3, 4] and y = [1, 1, 1, 1, 1]
        the coefficients of Cubic Spline in the power basis:

        $[[0, 0, 0, 0, 0],\$
        $[0, 0, 0, 0, 0],\$
        $[0, 0, 0, 0, 0],\$
        $[1, 1, 1, 1, 1]]$

        It could be shown explicitly that coefficients of the interpolating
        function in B-spline basis are c = [1, 1, 1, 1, 1, 1, 1]
        r(   )r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r@   rS   N)r5   r   r   r   r   r   r!   )r:   rU   rq   r]   r=   r=   r>   test_from_power_basis_exmp@  s   z&TestBSpline.test_from_power_basis_exmpc                 C   sl   t ddg}t dg}|jdd |jdd t ddd}|jdd t||dd}t||d d S )	Nr   r   r-   FwriterI   r   r)   )r5   r   setflagsrK   r   r   )r:   r    r!   rN   r<   r=   r=   r>   test_read_onlyS  s   zTestBSpline.test_read_onlyN).r   r   r   r?   rH   rO   rV   r^   rh   rk   rr   ru   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   rF   markparametrizer   r   r   r   r   r   r   r   r   r   r   r   r=   r=   r=   r>   r      sZ    #				%


*

r   c               	   C   sf   d	dd} dD ])}t |d}tt|D ]\}}| || td|d D ]
}| |||dd q$qqd S )
Nr   rR   c           	   	   S   s   | j \}}}t|}tj|d d d|dd  |d d   |d d f }tt||||f|| ||||d| d| j d d S )	Nr   g?r   r   r%   zder = z  k = )rB   rC   err_msg)rE   r5   uniquer   r   r   r"   )	r<   r   r   rB   rC   r    r!   r"   rU   r=   r=   r>   check_spleve  s   
8
z,test_knots_multiplicity.<locals>.check_splev)r   r'   r)   r*   r}   r   r   r   )r   rR   rR   )rD   	enumerate_make_multiplesr   )r   r"   r<   r   r   r   r=   r=   r>   test_knots_multiplicitya  s   



r   c                 C   s   |dkr|| |   kr||d  k rdS  dS |||  || kr%d}n| ||  |||  ||   t | |d || }||| d  ||d  krRd}|| S ||| d  |  ||| d  ||d    t | |d |d | }|| S )zw
    Naive way to compute B-spline basis functions. Useful only for testing!
    computes B(x; t[i],..., t[i+k+1])
    r   r   r   r+   _naive_B)rU   r"   r   r    c1c2r=   r=   r>   r  x  s   (2Fr  c                    s    kr	nt d    kr"d  ks%J  J kr1t k s3J t fddtdd D S )z=
    Naive B-spline evaluation. Useful only for testing!
    r   c                 3   s.    | ]} |  t |  V  qd S Nr  )rc   r   r!   r   r"   r    rU   r=   r>   	<genexpr>  s   , z_naive_eval.<locals>.<genexpr>r   )r5   searchsortedr   sumr   )rU   r    r!   r"   r=   r  r>   ra     s   ((ra   c                    st   t d  }|d ksJ t  |ksJ    kr'| ks*J  J t fddt|D S )z'Naive B-spline evaluation, another way.r   c                 3   s&    | ]} | t | V  qd S r  r  )rc   r   r!   r"   r    rU   r=   r>   r    s   $ z _naive_eval_2.<locals>.<genexpr>)r   r	  r   )rU   r    r!   r"   r;   r=   r
  r>   rg     s
   $ rg   c                 C   s~   t ||d  }||d ksJ t ||ksJ d}t|D ]}tj|||| d  dd| }||| t| 7 }q|S )Nr   r+   r'   FrX   )r   r   r   r   r5   Z
nan_to_num)rU   r    r!   r"   r;   sr   r<   r=   r=   r>   r     s   "r   c                 C   sT   t | } t | | dk | dkB | dk| dk @ | dk| dk@ gdd dd dd gS )z+ A linear B-spline function B(x | 0, 1, 2).r   r'   r   c                 S      dS )Nr+   r=   rU   r=   r=   r>   <lambda>      zB_012.<locals>.<lambda>c                 S   s   | S r  r=   r  r=   r=   r>   r    r  c                 S   s   d|  S Nr,   r=   r  r=   r=   r>   r    s    )r5   
atleast_1d	piecewiser  r=   r=   r>   rT     s   
rT   c                 C   s   t | } | dk | dk| dk @ | dkg}|dkr$dd dd dd g}n|dkr4dd d	d d
d g}ntd| t | ||}|S )z0A quadratic B-spline function B(x | 0, 1, 2, 3).r   r'   r   c                 S   s   | |  d S r  r=   r  r=   r=   r>   r    s    zB_0123.<locals>.<lambda>c                 S   s   d| d d  S )Ng      ?r   r'   r=   r  r=   r=   r>   r        c                 S   s   d|  d d S )Nr-   r'   r=   r  r=   r=   r>   r    r  c                 S   r  Nr   r=   r  r=   r=   r>   r    r  c                 S   r  )Ng       r=   r  r=   r=   r>   r    r  c                 S   r  r  r=   r  r=   r=   r>   r    r  znever be here: der=%s)r5   r  r3   r  )rU   r   Zcondsfuncspiecesr=   r=   r>   r     s   
r   #   r)   c                 C   s@   t jd t t j| | d }t j| }t|||S )N{   r   )r5   r9   ro   rp   r   Zconstruct_fast)r;   r"   r    r!   r=   r=   r>   rD     s   rD   c                 c   s    | j | j}}| j }|d |dd< |d |d< t|||V  | j }|d |d|d < t|||V  | j }|d || d d< t|||V  dS )	zIncrease knot multiplicity.         rw   r   Nr   r%   )r!   r"   r    copyr   )r<   r!   r"   t1r=   r=   r>   r     s   


r   c                   @   sd   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S )TestInteropc                 C   s   t ddt j d}t |}t||}|j|j|jf| _|||| _	| _
| _t ddt j d| _t j|j|j|jf }t ||f| _t|j| j|j| _d S )Nr   r.   )   r  )r5   rK   picosr	   r    r!   r"   rE   rN   r   r<   xnewr   r   r  r   b2)r:   rN   r   r<   r  r=   r=   r>   setup_method  s   

zTestInterop.setup_methodc                    s   | j | j| j} }tt|  |ddd tt| j |ddd t fdd|D  |ddd ttdd t|| W d    n1 sMw   Y  tt	d|j
jd }|j
|}|j||jf}tt|||||ddd d S )	Nr@   rA   c                    s   g | ]}t | qS r=   )r   rb   r<   r=   r>   re     s    z*TestInterop.test_splev.<locals>.<listcomp>zCalling splev.. with BSplinematchr   r   )r"  r<   r#  r   r   rE   r1   r3   tupler   r!   r   	transposer    r"   )r:   r"  r#  r   r   rE   r=   r%  r>   
test_splev  s&   





zTestInterop.test_splevc                 C   s   | j | j}}t||}t||\}}}t|d |dd t|d |dd t|d | t||dd\}}}}t|d |dd t|d |dd t|d | t||}	t||	dd t| }
t||
|dd d S )Nr   r@   rS   r   r'   T)full_output)rN   r   r   r   r   r   r   r   )r:   rU   rq   rE   r    r!   r"   Ztck_fr   r   r<   r=   r=   r>   test_splrep  s   

zTestInterop.test_splrepc                 C   s  | j | j}}tj||f }tt t|| W d    n1 s"w   Y  tt t|| W d    n1 s<w   Y  ttdd t|d d |d d  W d    n1 s_w   Y  ttdd t|d d |d d  W d    d S 1 sw   Y  d S )Nm > k must holdr&  r)   )	rN   r   r5   r   r1   r3   r   r   r2   )r:   rU   rq   y2r=   r=   r>   test_splrep_errors$  s   

"zTestInterop.test_splrep_errorsc           	      C   s   t dd}t|\}}t|\}}t||dd tt|||dd tt|||dd t|ddd\\}}}}}t||dd tt|||dd d S )Nr   r)   r}   r@   rS   r   T)r  r,  )r5   r8   r[   r   r   r   r   )	r:   rU   r<   urE   u1Zb_fZu_fr   r=   r=   r>   test_splprep4  s   zTestInterop.test_splprepc                 C   s  t dd}ttdd t| W d    n1 sw   Y  ttdd t| W d    n1 s8w   Y  t jdddd}ttd	d t|g W d    n1 s[w   Y  ttd	d t|g W d    n1 sww   Y  g d
}ttdd t|g W d    n1 sw   Y  ttdd t|g W d    n1 sw   Y  g d}g d}ttdd t|gd |g  W d    d S 1 sw   Y  d S )N<   r|   ztoo many values to unpackr&  r   r   r)   )numr.  ) >Ir7   >Kr8  zInvalid inputs)r   r)   r'   r*   )r   g333333?g?r   )	r5   r8   r[   r1   r3   r   r   rK   r2   )r:   rU   r2  r=   r=   r>   test_splprep_errorsC  s4   
"zTestInterop.test_splprep_errorsc                 C   s   | j | j}}tg dtj }tt||ddd tt|j|j|j	f|ddd t
tdd t|dd W d    n1 sBw   Y  |jdd	d
}tt|j||j	fdd}t|jd t|| d
dd d S )N)r   r   r/   g      @gHz>rA   zCalling sproot.. with BSpliner&  rQ   )Zmestr   r'   r   )r)   r'   r*   r   rS   )r<   r#  r5   r   r   r   r   r    r!   r"   r1   r3   r*  rZ   r   r~   )r:   r<   r#  rootsc2rrrr=   r=   r>   test_sproot`  s    zTestInterop.test_sprootc                 C   s   | j | j}}ttdd|tdd|jdd ttdd||dddd ttdd tdd| W d    n1 s=w   Y  |j	ddd}t
tdd|j||jf}t|jd t|tdd|dd d S )	Nr   r   rR   rS   zCalling splint.. with BSpliner&  r'   )r)   r'   )r<   r#  r   r   rE   r   r1   r3   r!   r*  r5   rZ   r    r"   r   r~   )r:   r<   r#  r;  Zintegrr=   r=   r>   test_splintq  s    
zTestInterop.test_splintc              	   C      | j | jfD ]c}t|jt|j }|dkr+tj|jt|f|jjdd   f |_dD ];}t	|}t
	|j|j|jf}t|j|d dd t|j|d dd t|j|d  tt|t tt|t q-qd S Nr   r   rP   r@   rS   r'   )r<   r#  r   r    r!   r5   r   zerosr~   r   r   r"   r   r   r   
isinstancer   r)  r:   r<   ctr;   ZbdZtck_dr=   r=   r>   test_splder     *zTestInterop.test_splderc              	   C   r?  r@  )r<   r#  r   r    r!   r5   r   rA  r~   r   r   r"   r   r   r   rB  r   r)  rC  r=   r=   r>   test_splantider  rF  zTestInterop.test_splantiderc                 C   s$  | j | j| j}}}|jjd }d|j| |j|d    }t||t||j|j|jf}}tt	||t	||dd t
t|t t
t|t tt|jj}|j|dd  d }	t||j|	|jf}
t||}ttt	||
ddd||dd t
t|t t
t|
t d S )Nr'   r   r   r@   rS   r(  r   )r<   r#  rN   r    r{   r   r!   r"   r   r   r   rB  r   r)  r   r   r*  r5   rZ   )r:   r<   r#  rN   r   tnZbnZtck_nr   r   Ztck_n2Zbn2r=   r=   r>   test_insert  s$   "


zTestInterop.test_insertN)r   r   r   r$  r+  r-  r0  r4  r9  r=  r>  rE  rG  rI  r=   r=   r=   r>   r    s    r  c                   @   s  e Zd Zeddej ZeeZdd Z	dd Z
dd Zejd	g d
dd Zejd	g d
dd Zdd Zdd Zejd	g ddd Zdd Zdd Zdd Zejd	g ddd Zdd  Zd!d" Zd#d$ Zd%d& Zd'd( Zejjd)d*d+d, Zd-d. Zd/d0 Z d1d2 Z!d3d4 Z"d5d6 Z#d7d8 Z$d9d: Z%ejd	g d;d<d= Z&d>d? Z'd@dA Z(dBdC Z)dDdE Z*dFdG Z+dHS )I
TestInterpr+   r,   c                 C   s@   t t t| j| jdd W d    d S 1 sw   Y  d S )Nr/   r   )r1   r2   r	   rN   r   )r:   r=   r=   r>   test_non_int_order  s   
"zTestInterp.test_non_int_orderc                 C   Z   t | j| jdd}t|| j| jddd t | j| jddd}t|| j| jddd d S )Nr   r   rR   rA   r%   r"   r   r	   rN   r   r   r   r=   r=   r>   test_order_0     zTestInterp.test_order_0c                 C   rL  )Nr   r   rR   rA   r%   rM  rN  r   r=   r=   r>   test_linear  rP  zTestInterp.test_linearr"   r   c                 C   sP   g d}g d}t tdd t|||d W d    d S 1 s!w   Y  d S )Nr   r   r'   r)   r*   r}   )r   r   r'   r)   r*   r}   rx   ry   zShapes of xr&  r   r1   r3   r	   r:   r"   rU   rq   r=   r=   r>   test_incompatible_x_y  s
   "z TestInterp.test_incompatible_x_yc                 C   s   g d}g d}t tdd t|||d W d    n1 s w   Y  g d}t tdd t|||d W d    n1 sAw   Y  g d}t|d}t tdd t|||d W d    d S 1 skw   Y  d S )	N)r   r   r   r'   r)   r*   rR  zx to not have duplicatesr&  r   )r   r'   r   r)   r*   r}   zExpect x to be a 1D strictly)r   r%   )r1   r3   r	   r5   rZ   r[   rT  r=   r=   r>   test_broken_x  s   "zTestInterp.test_broken_xc                 C   s6   dD ]}t | j| j|}t|| j| jddd qd S )Nr1  rR   rA   rN  )r:   r"   r<   r=   r=   r>   test_not_a_knot  s   zTestInterp.test_not_a_knotc                 C   s   t | j| jddd}t|| j| jddd tddD ]}t|| jd |d|| jd	 |dd
d qt | j| jddd	d}t|| j| jddd tddD ]}t|| jd |d|| jd	 |dd
d qOd S )Nr}   r   r   rR   rA   r   r   r   r%   gdy=rS   r"   r   r   )r	   rN   r   r   r   )r:   r<   r   r=   r=   r>   test_periodic  s   ,,zTestInterp.test_periodic)r'   r)   r*   r}   rx   ry   c                 C   sh   d}t jd t t j|d }t j|d }|d |d< t|||dd}t|||d	d
 d S )Nr}   rl   rI   rs   r%   r   r   r   rR   rS   )r5   r9   ro   rp   r   r	   r   )r:   r"   r;   rU   rq   r<   r=   r=   r>   test_periodic_random   s   zTestInterp.test_periodic_randomc                 C   s   | j jd }tjd tj|d tj }t|}d|d< dtj |d< td|f}t	||d< t
||d< t||dddd	}t|D ]}t||| |d d |f d
d qIt||d ||d d
d d S )Nr   rl   r'   r+   r%   r   r}   r   rX  rR   rS   )rN   r~   r5   r9   ro   r   r   rp   rA  sinr!  r	   r   r   )r:   r;   rU   rq   r<   r   r=   r=   r>   test_periodic_axis  s   
$"zTestInterp.test_periodic_axisc                 C   s   t jd d}d}t t j|}t j|}|d d |d< tt t|||dd W d    d S 1 s9w   Y  d S )	Nrl   r}   r   r%   r   r   r   r   )r5   r9   ro   rp   r   r1   r3   r	   )r:   r"   r;   rU   rq   r=   r=   r>   test_periodic_points_exception  s   
"z)TestInterp.test_periodic_points_exceptionc                 C   s   t jd d}d}t t j|}t j|}t |d|  }tt t||||d W d    d S 1 s:w   Y  d S )Nrl   r)   ry   r'   r   )	r5   r9   ro   rp   r   rA  r1   r3   r	   )r:   r"   r;   rU   rq   r    r=   r=   r>   test_periodic_knots_exception%  s   
"z(TestInterp.test_periodic_knots_exception)r'   r)   r*   r}   c                 C   s   t | j| j|dd}t| j| jd|d}t| j|}t||| jdd td|D ]}t| j||d}t||| j|d	d
d q)d S )Nr   r   T)Zperr"   rR   rS   r   r   r   r   )r	   rN   r   r   r   r   r   )r:   r"   r<   rE   r   r   r=   r=   r>   test_periodic_splev0  s   zTestInterp.test_periodic_splevc                 C   s   t | j| jddd}t| j| jdd}t|| j|| jdd d}ttj|d }tj|d }|d	 |d
< t ||ddd}t||dd}t||||dd d S )Nr)   r   r   r   rR   rS   rI   rs   r%   r   )	r	   rN   r   r   r   r5   rp   r9   r   )r:   r<   Zcubr;   rU   rq   r=   r=   r>   test_periodic_cubic=  s   zTestInterp.test_periodic_cubicc                    sj   dt | j| jdd}t| jt| j| j t fdd}t|| j|| jdd d S )Nr)   r   r   c                    s   t |  S r  r`   r  rd   r=   r>   r  S  s    z6TestInterp.test_periodic_full_matrix.<locals>.<lambda>rR   rS   )r	   rN   r   r   r   r5   Z	vectorizer   )r:   r<   r   r=   rd   r>   test_periodic_full_matrixL  s   z$TestInterp.test_periodic_full_matrixc                 C   s   dg}t | j| jdd |fd}t|| j| jddd t|| jd d|d d ddd t | j| jd|d fd}t|| j| jddd t|| jd d|d d ddd d S )	Nr   g       @r'   r   rR   rA   r%   r   r   rN  )r:   r   r<   r=   r=   r>   test_quadratic_derivV  s   $(zTestInterp.test_quadratic_derivc                 C   s   d}dgdg}}t | j| j|||fd}t|| j| jddd t|| jd d|| jd	 dg|d d |d d gddd d
gd
g}}t | j| j|||fd}t|| j| jddd d S )Nr)   r   r-   )r   r.   r   rR   rA   r   r   r%   r'   r   rN  )r:   r"   der_lder_rr<   r=   r=   r>   test_cubic_derivc  s    zTestInterp.test_cubic_derivc                 C   s   d\}}t |t j}t |}ddg}ddg}t|||||fd}t|||ddd t||d	 d
||d	 dgdd |D  t||d d
||d dgdd |D  d S )N)r}   ry   )r   g      ()r'   r   rb  )r'   r-   r   rR   rA   r   r   r'   c                 S      g | ]\}}|qS r=   r=   rc   r   valr=   r=   r>   re   {      z2TestInterp.test_quintic_derivs.<locals>.<listcomp>r%   c                 S   ri  r=   r=   rj  r=   r=   r>   re   }  rl  )r5   r8   astypefloat_r[  r	   r   )r:   r"   r;   rU   rq   rf  rg  r<   r=   r=   r>   test_quintic_derivsr  s   
zTestInterp.test_quintic_derivsZunstable)reasonc                 C   sN   d}t | j|}ddg}t| j| j|||d fd}t|| j| jddd d S )Nr)   rd  )r'   r.   r   rR   rA   )r   rN   r	   r   r   )r:   r"   r    rf  r<   r=   r=   r>   test_cubic_deriv_unstable  s
   z$TestInterp.test_cubic_deriv_unstablec                 C   s   d}t j| jd f|d  | jdd  | jd d  d | jd f|d  f }t| j| j||dgdgfd}t|| j| jddd	 t|| jd d|| jd dgd
d
gdd d S )Nr'   r   r   r%   r,   re  r   rR   rA   r+   rS   )r5   r   rN   r	   r   r   )r:   r"   r    r<   r=   r=   r>   test_knots_not_data_sites  s   
&
z$TestInterp.test_knots_not_data_sitesc                 C   sX   d}ddg}ddg}t |||dgdgfd}tdd}|d }t|||ddd d S )	Nr)   r+   r   r   r+   rd  r   rR   rA   )r	   r5   rK   r   )r:   r"   rU   rq   r<   rN   r   r=   r=   r>   test_minimum_points_and_deriv  s   z(TestInterp.test_minimum_points_and_derivc                 C   s4  g d }}t t t||dgd fd W d    n1 sw   Y  t t t||dd W d    n1 s:w   Y  t t t||dgd W d    n1 sVw   Y  t t t||dd W d    n1 sqw   Y  d\}}t t t||||fd W d    d S 1 sw   Y  d S )N)r   r'   r)   r*   r}   rx   rs  r   *   )rs  rs  rS  )r:   rU   rq   lrr=   r=   r>   test_deriv_spec  s"   




"zTestInterp.test_deriv_specc                 C   s   d}| j }| jd| j  }dgdg}}t|||||fd}t|||ddd t||d d	||d
 d	g|d d	 |d d	 gddd dD ]}t|||d}t|||ddd qHd S )Nr)   r   )r   y              @)r   y      @       @r   rR   rA   r   r   r%   )r   r   r   )rN   r   r	   r   )r:   r"   rN   r   rf  rg  r<   r=   r=   r>   test_complex  s   zTestInterp.test_complexc                 C   sH   t dt j}t dt j}dD ]}t|||d}|| qd S )NrI   r   r   )r5   r8   rm  int_r	   )r:   rU   rq   r"   r<   r=   r=   r>   test_int_xy  s   
zTestInterp.test_int_xyc                 C   sF   t ddd}|d d d }|d d d }dD ]	}t|||d qd S )Nr%   r   rs   r}   r   r   )r5   rK   r	   )r:   rN   rU   rq   r"   r=   r=   r>   test_sliced_input  s   zTestInterp.test_sliced_inputc                 C   sJ   t dt}|d }t jt jt j fD ]}||d< ttt|| qd S )NrI   r'   r%   )	r5   r8   rm  floatr6   r7   r1   r3   r	   )r:   rU   rq   zr=   r=   r>   test_check_finite  s   zTestInterp.test_check_finite)r   r'   r)   r}   c                 C   s,   t td}dd |D }t|||d d S )NrI   c                 S   s   g | ]}|d  qS )r'   r=   )rc   ar=   r=   r>   re     rl  z.TestInterp.test_list_input.<locals>.<listcomp>r   )r   r   r	   rT  r=   r=   r>   test_list_input  s   zTestInterp.test_list_inputc                 C   s   t jt | jt | jf }dddgfg}dddgfg}t| j|d||fd}t|| j|ddd	 t|| jd
 d|d
 d ddd	 t|| jd d|d
 d ddd	 d S )Nr   r   r,   r-   r.   r)   r   rR   rA   r   r%   )r5   r   r[  rN   r!  r	   r   )r:   r   rf  rg  r<   r=   r=   r>   test_multiple_rhs  s   $(zTestInterp.test_multiple_rhsc                 C   s   t jd d\}}t t jj|d}t jj|dddfd}t|||}t|jj|dddf dt jdfg}dt jdfg}t|||||fd	}t|jj|| d dddf d S )
Nrl   r)   rw   rz   r}   rx   ry   r   r}   rx   ry   r   )r5   r9   ro   rp   r	   r   r!   r~   )r:   r"   r;   rU   rq   r<   d_ld_rr=   r=   r>   test_shapes  s   "zTestInterp.test_shapesc                 C   s@  t | j}t| j|ddd}t| j|ddgdgfd}t|j|jdd t| j|ddd}t| j|ddgdgfd}t|j|jdd t| j|d	d
d}t| j|d	d dgfd}t|j|jdd t| j|ddd}t| j|dd d}t|j|jdd tt t| j|ddd W d    n1 sw   Y  t jt | jt 	| jf }dddgfg}d	ddgfg}t| j|d||fd}t| j|ddd}t|j|jdd t j
d d\}}t t j
j
|d}t j
j
|dddfd}	dt dfg}
dt dfg}t||	||
|fd}t||	|dd}t|j|jdd d S )Nr)   r   r   re  r@   rS   )r   r   )r   r   r'   )Nr   rs  r   Ztypor   r+   r   rl   r  rz   r}   rx   ry   r  r   r   )r5   r[  rN   r	   r   r!   r1   r3   r   r!  r9   ro   rp   rA  )r:   r   r   r#  rf  rg  r"   r;   rU   rq   r  r  r=   r=   r>   test_string_aliases  sJ   




zTestInterp.test_string_aliasesc                 C   sr   t jd d\}}t t jj|d}t jj|d}t||}t||||}t||||}t|j|ddd d S )Nrl   )r)   ry   rz   rR   rA   )	r5   r9   ro   rp   r   r	   make_interp_full_matrr   r!   )r:   r"   r;   rU   rq   r    r<   cfr=   r=   r>   test_full_matrixA  s   
zTestInterp.test_full_matrixc                 C   s  t jd d}tdddD ]}t|d d }t t jd|f}td|d D ]6}|d| |df  t t jd|| f7  < ||dd| f  t t jd|| f7  < q*t j||f}||d|| df< t j||f}||| dd|f< t ||f}tt|| d dD ]#\}}	|	d	k rt j||	d
||d|	f< qt j||	d
|||	df< qt j|}
t	t
||||
|t j||
dd qdS )z
        Random elements in diagonal matrix with blocks in the
        left lower and right upper corners checking the
        implementation of Woodbury algorithm.
        rl      r)       r'   r   Nr%   r   )offsetrR   rS   )r5   r9   ro   r   intZdiagflatrA  r   Zdiagonalr   r   linalgsolve)r:   r;   r"   r  r  r   urlldr   r<   r=   r=   r>   test_woodburyL  s,   46zTestInterp.test_woodburyN),r   r   r   r5   rK   r   rN   r[  r   rK  rO  rQ  rF   r   r   rU  rV  rW  rY  rZ  r\  r]  r^  r_  r`  ra  rc  rh  ro  Zxfailrq  rr  rt  rx  ry  r{  r|  r  r  r  r  r  r  r  r=   r=   r=   r>   rJ    sP    









	

3rJ  c                 C   s   | j |j ksJ |j | j | d ksJ | j }tj||ftjd}t|D ]+}| | }||| kr4|}nt||d }t||||}	|	|||| |d f< q%t	||}
|
S )zAssemble an spline order k with knots t to interpolate
    y(x) using full matrices.
    Not-a-knot BC only.

    This routine is here for testing only (even though it's functional).
    r   r   )
r{   r5   rA  rn  r   r  r   evaluate_all_bsplslr  )rU   rq   r    r"   r;   Ar   xvalleftbbr!   r=   r=   r>   r  i  s   r  c                 C   s   t tj| ||f\} }}| j}|j| d }tj||ftjd}t|D ]+}| | }||| kr3|}	nt||d }	t	||||	}
|
|||	| |	d f< q$t
|j|}t
|j|}t||}|||ffS )z,Make the least-square spline, full matrices.r   r  )mapr5   rZ   r{   rA  rn  r   r  r   r  dotTr  r  )rU   rq   r    r"   mr;   r  r   r  r  r  r   Yr!   r=   r=   r>   make_lsq_full_matrix  s   r  c                   @   s   e Zd Zejd d\ZZeejeZ	ejeZ
eee	d e	d deZdd Zdd	 Zd
d Zdd Zdd Zdd Zdd Zdd ZdS )TestLSQrl   )r   r)   r   r%   ry   c                 C   s   | j | j| j| jf\}}}}t||||\}}t||||}t|j| t|jj	|j
| d f |\}}	tjj||dd\}
}}}t|j|
 d S )Nr   r%   )Zrcond)rU   rq   r    r"   r  r
   r   r!   r   r~   r{   r5   r  Zlstsq)r:   rU   rq   r    r"   Zc0ZAYr<   Zaar   r  r   r=   r=   r>   
test_lstsq  s   zTestLSQ.test_lstsqc                 C   s|   | j | j| j| jf\}}}}t|}t||||}t|||||d}t|j|jdd t|j|jdd t	|j|j d S )N)wrR   rS   )
rU   rq   r    r"   r5   rt   r
   r   r!   r   )r:   rU   rq   r    r"   r  r<   Zb_wr=   r=   r>   test_weights  s   
zTestLSQ.test_weightsc                 C   sd   | j | j| j| jf\}}}}tjj|dddfd}t||||}t|jj	|j
| d dddf d S )Nr}   rx   ry   rz   r   )rU   r    r"   r;   r5   r9   r
   r   r!   r~   r{   )r:   rU   r    r"   r;   rq   r<   r=   r=   r>   r    s   $zTestLSQ.test_multiple_rhsc                 C   sv   | j | j| j}}}| jd }t||||}t||j||}t||j||}t||||d||  ddd d S )Ny      ?       @r   r@   rA   )rU   r    r"   rq   r
   r   r   r   )r:   rU   r    r"   r   r<   r   r   r=   r=   r>   ry    s   
(zTestLSQ.test_complexc                 C   sD   t dt j}t dt j}t|dd}t|||dd d S )NrI   r   r   )r5   r8   rm  rz  r   r
   r:   rU   rq   r    r=   r=   r>   r{    s   zTestLSQ.test_int_xyc                 C   sH   t ddd}|d d d }|d d d }t|d}t|||dd d S )Nr%   r   rs   r)   r   )r5   rK   r   r
   )r:   rN   rU   rq   r    r=   r=   r>   r|    s
   
zTestLSQ.test_sliced_inputc                 C   sV   t dt}|d }t|d}t jt jt j fD ]}||d< ttt	||| qd S )N   r'   r)   r%   )
r5   r8   rm  r}  r   r6   r7   r1   r3   r
   )r:   rU   rq   r    r~  r=   r=   r>   test_checkfinite  s   
zTestLSQ.test_checkfinitec                 C   sL   | j | j| j}}}|jdd |jdd |jdd t|||d d S )NFr   )rU   rq   r    )rU   rq   r    r   r
   r  r=   r=   r>   r     s
   zTestLSQ.test_read_onlyN)r   r   r   r5   r9   ro   r;   r"   rp   rU   rq   r   rK   r    r  r  r  ry  r{  r|  r  r   r=   r=   r=   r>   r    s    	
r  c                 C   s    t jt jt jtd| S )Ndata)ospathjoinabspathdirname__file__)basenamer=   r=   r>   	data_file  s   r  c                   @   s,   e Zd Zdd Zdd Zdd Zdd Zd	S )
TestSmoothingSplinec                 C   s  t jd d}t t j|d d }|d t d|  |d  t jdd| }tt t	||dd   W d    n1 sDw   Y  tt t	|dd  | W d    n1 saw   Y  tt t	|
d|| W d    n1 s~w   Y  tt t	|d d d	 | W d    n1 sw   Y  t |}|d |d
< tt t	|| W d    n1 sw   Y  t d}t d}d}tjt|d t	|| W d    d S 1 sw   Y  d S )Nrl   rs   r*   r'   r)   r+   r   r   r%   r   z,``x`` and ``y`` length must be larger than 5r&  )r5   r9   ro   rp   r   r[  normalr1   r3   r   r[   r  r8   onesrF   r   )r:   r;   rU   rq   Zx_duplZexception_messager=   r=   r>   test_invalid_input  s6   .







"z&TestSmoothingSpline.test_invalid_inputc                 C   sH   t td}|d }|d }|d }t|||}t||ddd dS )ae  
        Data is generated in the following way:
        >>> np.random.seed(1234)
        >>> n = 100
        >>> x = np.sort(np.random.random_sample(n) * 4 - 2)
        >>> y = np.sin(x) + np.random.normal(scale=.5, size=n)
        >>> np.savetxt('x.csv', x)
        >>> np.savetxt('y.csv', y)

        We obtain the result of performing the GCV smoothing splines
        package (by Woltring, gcvspl) on the sample data points
        using its version for Octave (https://github.com/srkuberski/gcvspl).
        In order to use this implementation, one should clone the repository
        and open the folder in Octave.
        In Octave, we load up ``x`` and ``y`` (generated from Python code
        above):

        >>> x = csvread('x.csv');
        >>> y = csvread('y.csv');

        Then, in order to access the implementation, we compile gcvspl files in
        Octave:

        >>> mex gcvsplmex.c gcvspl.c
        >>> mex spldermex.c gcvspl.c

        The first function computes the vector of unknowns from the dataset
        (x, y) while the second one evaluates the spline in certain points
        with known vector of coefficients.

        >>> c = gcvsplmex( x, y, 2 );
        >>> y0 = spldermex( x, c, 2, x, 0 );

        If we want to compare the results of the gcvspl code, we can save
        ``y0`` in csv file:

        >>> csvwrite('y0.csv', y0);

        z
gcvspl.npzrU   rq   y_GCVSPLg-C6?rA   N)r5   loadr  r   r   )r:   r  rU   rq   r  Zy_comprr=   r=   r>   test_compare_with_GCVSPL"  s   )z,TestSmoothingSpline.test_compare_with_GCVSPLc                 C   s   t jd d}t t j|d d }|d t d|  |d  t jdd| }t||dd}t||dd	d
}t 	|d |d d| }t
||||dd dS )z
        In case the regularization parameter is 0, the resulting spline
        is an interpolation spline with natural boundary conditions.
        rl   rs   r*   r'   r)   r+   r   )Zlamr   r   r   r%   r@   rS   N)r5   r9   ro   rp   r   r[  r  r   r	   rK   r   )r:   r;   rU   rq   Z
spline_GCVZspline_interpgridr=   r=   r>   test_non_regularized_caseX  s   .
z-TestSmoothingSpline.test_non_regularized_casec           
      C   s   t jd d}t t j|d d }|d t d|  |d  t jdd| }t||}t jjt	ddd	D ]9}t 
|}d
||< t|||}t||| ||  }t||| ||  }	||	k rttd|dd|	dq;d S )Nrl   rs   r*   r'   r)   r+   r   rI   rz   g      >@zJSpline with weights should be closer to the points than the original one: z.4z < )r5   r9   ro   rp   r   r[  r  r   choicer   r  absr3   )
r:   r;   rU   rq   r   indr  Zspl_worigZweightedr=   r=   r>   test_weighted_smoothing_splinek  s&   .

z2TestSmoothingSpline.test_weighted_smoothing_splineN)r   r   r   r  r  r  r  r=   r=   r=   r>   r    s
    6r  r(  )r  r)   )r)   )9numpyr5   Znumpy.testingr   r   r   rF   r   r1   Zscipy.interpolater   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   Zscipy.linalgr  r  Zscipy.interpolate._bsplinesr   r   r   r   r   Zscipy.interpolate._fitpack_implZinterpolateZ_fitpack_implr   r  r   r   r  ra   rg   r   rT   r   rD   r   r  rJ  r  r  r  r  r  r=   r=   r=   r>   <module>   sD    H    R	
	
 `   -
Y