o
    g                     @   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,dVS )W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   cubic      @)r+   r   r   r   r'   r)   )r   r   r   )   r)   )assert_raises	TypeError
ValueErrorr   dictnperrstatenaninfarangerandomr   r    r!   r   r"   )selfnr"   r    r!   b r?   c/home/ubuntu/cloudmapper/venv/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'   foo)
_make_random_splinetckr   r    r!   r   r"   pytestr   AttributeError)r<   r>   rH   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*   rM   )r6   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'   +=rD   )r   r6   rN   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,   rL   TextrapolaterU   rV   )r6   asarrayr   reshaper   rN   r   r   )r<   r"   r    r!   bpbsplrQ   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   rT   c                       g | ]	}t | qS r?   _naive_eval.0rX   r!   r"   r    r?   r@   
<listcomp>n       z4TestBSpline.test_rndm_naive_eval.<locals>.<listcomp>rU   rV   c                    rb   r?   )_naive_eval_2re   rg   r?   r@   rh   q   ri   )rG   rH   r6   rN   r   )r<   r>   rQ   y_by_ny_n2r?   rg   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   rT   rU   rV   rG   rH   r6   rN   r   r   r<   r>   r    r!   r"   rQ   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   rU   rV   )r6   r;   seedsortr   r   r    r"   rN   r   r   )r<   rX   yrH   r>   r    r"   rQ   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   )rG   r6   	ones_liker!   rN   r    r"   r   )r<   r>   rQ   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   r~   r   )r6   rv   r;   r   r   shape)	r<   r=   r"   r    r!   r>   tmtprQ   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   rT   rU   rV   )r6   rv   r;   r_r   rN   r   r   )
r<   r=   r"   r    r!   c_padr>   b_paddtrQ   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|=&.>rV   rG   rH   r   )r<   r>   r    _r"   r   r   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   rV   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   rT   Tr[   F)extro   )r<   r>   r    r!   r"   r   rQ   maskr?   r?   r@   test_extrap   s   $zTestBSpline.test_extrapc                 C   sL   t  }|j\}}}|d d |d d g}||}ttt|  d S )Nr   r   r%   )rG   rH   r   r6   allisnan)r<   r>   r    r   r"   rQ   yyr?   r?   r@   test_default_extrap   s
   zTestBSpline.test_default_extrapc           	      C   s  t jd t t jd}t jd}d}t|||dd}|j|d  }|d |d	  }t || | || | d
}|| |||  || ||    }t||t||||f g d}|| |||  || ||    }t	||dd||dd d S )Nrr      r*   r)   periodicr[   r   r%   r   rT   )r%   r         ?r   T)
r6   r;   ru   rv   r   r   rN   r   r   r   )	r<   r    r!   r"   r>   r=   r   rQ   xyr?   r?   r@   test_periodic_extrap   s   $$z TestBSpline.test_periodic_extrapc                 C   sV   t  }|j\}}}t|||f}t|| ||  d}t||||ddd d S )Nry   rU   rC   )rG   rH   r   from_spliner6   rN   r   )r<   r>   r    r!   r"   pprQ   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%   rT   r   dernurU   rV   )rG   rH   r6   rN   r   ranger   r   )r<   r>   r    r!   r"   rQ   r   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*   r~   r~   r~   r   r   rr   r   r   )r   r)   r*   r~   r~   r   g2H@gη   @r)   r*   r   r   )
r6   r;   ru   r   r   r]   r   r   allcloser   )r<   r"   r    r!   r>   rX   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*   rs   r   r   r'   r)   )r    rU   rV   r   r   r   r'   r   r'   rL   r   r,   )r6   rN   r   basis_elementr   r   r    r!   r"   B_0123rO   rP   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   rs   rU   rV   )rG   rH   r6   rN   r   _sum_basis_elementsrp   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   rs   rU   rV   )	rG   rH   r   r!   realimagr6   rN   r   )	r<   r>   r    r!   r"   ccb_reb_imrQ   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   r6   r   r8   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   rs   -q=rC   )rG   rH   r   r6   rN   r   
derivativer   )r<   r>   r    r!   r"   b0rQ   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   rs   rU   rC   )
rG   rH   r6   rN   r   antiderivativer   c_dstackr   rp   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%   Tr[   Fr   r'   iii      ?r)   g      +@   r~   ir*   )	r   r   r   	integrate_implr   rH   r\   r   )r<   r>   i
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	   r\   r   r   r   r   )r<   rX   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 )Nr|   r   r   )r~   r   r   r*   r   r   r   )r    r!   r"   r   r'   )r6   rN   r   r;   r   r   r!   r   listndimr2   	AxisErrorr5   r   r   r   )r<   r   r=   r"   r    shpos_axisr!   r>   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   r~   )r%   r'   r   r%   )r'   r   r   r%   r   r   r   r0   )r6   arrayr   r   )r<   r"   r    r!   splspl0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.
            rr   (   rs   r   r%   r   r"   bc_typer   rU   rV   N)r6   r;   ru   rv   random_sampler	   eyelenr    r   design_matrixtoarrayr   r!   )	r=   r"   r   rX   rw   r`   r!   des_matr_defdes_matr_csrr?   r?   r@   run_design_matrix_tests  s    zHTestBSpline.test_design_matrix_bc_types.<locals>.run_design_matrix_testsr1   r)   clampednaturalr   r'   
not-a-knotr   r   r   N)r   )r<   r   r=   r"   bcr?   r?   r@   test_design_matrix_bc_types  s   z'TestBSpline.test_design_matrix_bc_typesr\   )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).rr   rL   r   r'   r   N)r6   r;   ru   r   aminamaxr   rN   r   r   r   r   r   r   r   rI   r   r4   )
r<   r\   r   rX   xminxmaxr"   r    r!   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 )Nrr   rL   r)   r   rs   r   r   r*   rU   rV   )r6   r;   ru   rv   r   r	   r   r   r   r    r   r   r!   )
r<   r=   r"   rX   rw   r`   r   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+   rU   rV   )r   r   r   r   )r<   r    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 )Nrr   rL   r)   r   rs   r   r%   r'   )r+   r   r,   r-   r.   g      @rZ   )r6   r;   ru   rv   r   r	   r2   r4   r   r   r    )r<   r=   r"   rX   rw   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 )
Nrr   rs   r   r   r%   r   r   rB   rV   )r6   r;   ru   rv   r   r   from_power_basisrN   r   r	   r!   )r<   r   rX   rw   cbr`   rQ   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 )
Nrr   rs   r   r   r   r%   r	  rB   rV   )r6   r;   ru   rv   r   r   r
  r	   r   r   r   r!   dtyper   )r<   r   rX   rw   r  r`   bspl_new_real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   rB   rV   N)r6   r   r   r
  r   r   r!   )r<   rX   rw   r`   r?   r?   r@   test_from_power_basis_exmp@  s   z&TestBSpline.test_from_power_basis_exmpN)-r   r   r   rA   rK   rR   rY   ra   rn   rq   rx   r{   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   rI   markparametrizer   r   r   r   r  r  r  r  r  r  r  r?   r?   r?   r@   r      sX    #				%


*

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   rU   c           	      S   s   | j \}}}t|}tj|d d d|dd  |d d   |d d f }tt||||f|| ||||d|| jf d d S )Nr   g?r   r   r%   zder = %s  k = %s)rD   rE   err_msg)rH   r6   uniquer   r   r   r"   )	r>   r   r   rD   rE   r    r!   r"   rX   r?   r?   r@   check_splevX  s   
8
z,test_knots_multiplicity.<locals>.check_splev)r   r'   r)   r*   r   r   r   r   )r   rU   rU   )rG   	enumerate_make_multiplesr   )r  r"   r>   r   r   r   r?   r?   r@   test_knots_multiplicityT  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)rX   r"   r   r    c1c2r?   r?   r@   r  k  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  )rf   r   r!   r   r"   r    rX   r?   r@   	<genexpr>  s   , z_naive_eval.<locals>.<genexpr>r   )r6   searchsortedr   sumr   )rX   r    r!   r"   r?   r   r@   rd   ~  s   ((rd   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  )rf   r   r!   r"   r    rX   r?   r@   r!    s   $ z _naive_eval_2.<locals>.<genexpr>)r   r#  r   )rX   r    r!   r"   r=   r?   r$  r@   rj     s
   $ rj   c                 C   s~   t ||d  }||d ksJ t ||ksJ d}t|D ]}tj|||| d  dd| }||| t| 7 }q|S )Nr   r+   r'   Fr[   )r   r   r   r   r6   
nan_to_num)rX   r    r!   r"   r=   sr   r>   r?   r?   r@   r     s   "r   c                 C   sT   t | } t | | dk | dkB | dk| dk @ | dk| dk@ gdd dd dd gS )z+ A linear B-spline function B(x | 0, 1, 2).r   r'   r   c                 S      dS )Nr+   r?   rX   r?   r?   r@   <lambda>      zB_012.<locals>.<lambda>c                 S   s   | S r  r?   r(  r?   r?   r@   r)    r*  c                 S   s   d|  S Nr,   r?   r(  r?   r?   r@   r)    s    )r6   
atleast_1d	piecewiser(  r?   r?   r@   rW     s   
rW   c                 C   s   t | } | dk | dk| dk @ | dkg}|dkr$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)r6   r,  r4   r-  )rX   r   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   )r6   r;   ru   rv   r   construct_fast)r=   r"   r    r!   r?   r?   r@   rG     s   rG   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.         r}   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.   )   r8  )r6   rN   picosr	   r    r!   r"   rH   rQ   r   r>   xnewr   r   r  r   b2)r<   rQ   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 )	NrB   rC   c                    s   g | ]}t | qS r?   )r   re   r>   r?   r@   rh     s    z*TestInterop.test_splev.<locals>.<listcomp>zCalling splev.. with BSplinematchr   r   )r?  r>   r@  r   r   rH   r2   r4   tupler   r!   r   	transposer    r"   )r<   r?  r@  r   r   rH   r?   rB  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   rB   rV   r   r'   T)full_output)rQ   r   r   r   r   r   r   r   )r<   rX   rw   rH   r    r!   r"   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 holdrC  r)   )	rQ   r   r6   r   r2   r4   r   r   r3   )r<   rX   rw   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   rB   rV   r   T)r&  rI  )r6   r:   r^   r   r   r   r   )	r<   rX   r>   urH   u1b_fu_fr   r?   r?   r@   test_splprep'  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 unpackrC  r   r   r)   )numrL  ) >IrW   >KrX  zInvalid inputs)r   r)   r'   r*   )r   g333333?g?r   )	r6   r:   r^   r2   r4   r   r   rN   r3   )r<   rX   rP  r?   r?   r@   test_splprep_errors6  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   r0   g      @gHz>rC   zCalling sproot.. with BSplinerC  rT   )mestr   r'   r   )r)   r'   r*   r   rV   )r>   r@  r6   r   r=  r   r   r    r!   r"   r2   r4   rG  r]   r   r   )r<   r>   r@  rootsc2rrrr?   r?   r@   test_sprootS  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   rU   rV   zCalling splint.. with BSplinerC  r'   )r)   r'   )r>   r@  r   r   rH   r   r2   r4   r!   rG  r6   r]   r    r"   r   r   )r<   r>   r@  r\  integrr?   r?   r@   test_splintd  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   rS   rB   rV   r'   )r>   r@  r   r    r!   r6   r   zerosr   r   r   r"   r   r   r   
isinstancer   rF  r<   r>   ctr=   bdtck_dr?   r?   r@   test_splderw     *zTestInterop.test_splderc              	   C   ra  rb  )r>   r@  r   r    r!   r6   r   rc  r   r   r   r"   r   r   r   rd  r   rF  re  r?   r?   r@   test_splantider  rj  zTestInterop.test_splantiderc                 C   s$  | j | j| j}}}|jjd }d|j| |j|d    }t||t||j|j|jf}}tt	||t	||dd t
t|t t
t|t tt|jj}|j|dd  d }	t||j|	|jf}
t||}ttt	||
ddd||dd t
t|t t
t|
t d S )Nr'   r   r   rB   rV   rE  r   )r>   r@  rQ   r    r   r   r!   r"   r   r   r   rd  r   rF  r   r   rG  r6   r]   )r<   r>   r@  rQ   r   tnbntck_nr   r   tck_n2bn2r?   r?   r@   test_insert  s$   "


zTestInterop.test_insertN)r   r   r   rA  rH  rK  rN  rT  rY  r^  r`  ri  rk  rq  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 )Nr0   r   )r2   r3   r	   rQ   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   rU   rC   r%   r"   r   r	   rQ   r   r   r   r?   r?   r@   test_order_0     zTestInterp.test_order_0c                 C   rt  )Nr   r   rU   rC   r%   ru  rv  r   r?   r?   r@   test_linear  rx  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   r~   r   zShapes of xrC  r   r2   r4   r	   r<   r"   rX   rw   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*   rz  zx to not have duplicatesrC  r   )r   r'   r   r)   r*   r   zExpect x to be a 1D strictly)r   r%   )r2   r4   r	   r6   r]   r^   r|  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 )NrO  rU   rC   rv  )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   rU   rC   r   r   r   r%   gdy=rV   r"   r   r   )r	   rQ   r   r   r   )r<   r>   r   r?   r?   r@   test_periodic  s   ,,zTestInterp.test_periodic)r'   r)   r*   r   r~   r   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   rr   rL   ry   r%   r   r   r   rU   rV   )r6   r;   ru   rv   r   r	   r   )r<   r"   r=   rX   rw   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   rr   r'   r+   r%   r   r   r   r  rU   rV   )rQ   r   r6   r;   ru   r   r=  rv   rc  sinr>  r	   r   r   )r<   r=   rX   rw   r>   r   r?   r?   r@   test_periodic_axis  s   
$"zTestInterp.test_periodic_axisc                 C   s   t jd d}d}t t j|}t j|}|d d |d< tt t|||dd W d    d S 1 s9w   Y  d S )	Nrr   r   r   r%   r   r   r   r   )r6   r;   ru   rv   r   r2   r4   r	   )r<   r"   r=   rX   rw   r?   r?   r@   test_periodic_points_exception  s   
"z)TestInterp.test_periodic_points_exceptionc                 C   s   t jd d}d}t t j|}t j|}t |d|  }tt t||||d W d    d S 1 s:w   Y  d S )Nrr   r)   r   r'   r   )	r6   r;   ru   rv   r   rc  r2   r4   r	   )r<   r"   r=   rX   rw   r    r?   r?   r@   test_periodic_knots_exception  s   
"z(TestInterp.test_periodic_knots_exception)r'   r)   r*   r   c                 C   s   t | j| j|dd}t| j| jd|d}t| j|}t||| jdd td|D ]}t| j||d}t||| j|d	d
d q)d S )Nr   r   T)perr"   rU   rV   r   r   r   r   )r	   rQ   r   r   r   r   r   )r<   r"   r>   rH   r   r   r?   r?   r@   test_periodic_splev#  s   zTestInterp.test_periodic_splevc                 C   s   t | j| jddd}t| j| jdd}t|| j|| jdd d}ttj|d }tj|d }|d	 |d
< t ||ddd}t||dd}t||||dd d S )Nr)   r   r   r	  rU   rV   rL   ry   r%   r   )	r	   rQ   r   r   r   r6   rv   r;   r   )r<   r>   cubr=   rX   rw   r?   r?   r@   test_periodic_cubic0  s   zTestInterp.test_periodic_cubicc                    sj   dt | j| jdd}t| jt| j| j t fdd}t|| j|| jdd d S )Nr)   r   r   c                    s   t |  S r  rc   r(  rg   r?   r@   r)  F  s    z6TestInterp.test_periodic_full_matrix.<locals>.<lambda>rU   rV   )r	   rQ   r   r   r   r6   	vectorizer   )r<   r>   r   r?   rg   r@   test_periodic_full_matrix?  s   z$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   rU   rC   r%   r   r   rv  )r<   r   r>   r?   r?   r@   test_quadratic_derivI  s   $(zTestInterp.test_quadratic_derivc                 C   s   d}dgdg}}t | j| j|||fd}t|| j| jddd t|| jd d|| jd	 dg|d d |d d gddd d
gd
g}}t | j| j|||fd}t|| j| jddd d S )Nr)   r   r-   )r   r.   r	  rU   rC   r   r   r%   r'   r   rv  )r<   r"   der_lder_rr>   r?   r?   r@   test_cubic_derivV  s    zTestInterp.test_cubic_derivc                 C   s   d\}}t |t j}t |}ddg}ddg}t|||||fd}t|||ddd t||d	 d
||d	 dgdd |D  t||d d
||d dgdd |D  d S )N)r   r   )r   g      ()r'   r   r  )r'   r-   r   rU   rC   r   r   r'   c                 S      g | ]\}}|qS r?   r?   rf   r   valr?   r?   r@   rh   n      z2TestInterp.test_quintic_derivs.<locals>.<listcomp>r%   c                 S   r  r?   r?   r  r?   r?   r@   rh   p  r  )r6   r:   astypefloat_r  r	   r   )r<   r"   r=   rX   rw   r  r  r>   r?   r?   r@   test_quintic_derivse  s   
zTestInterp.test_quintic_derivsunstable)reasonc                 C   sN   d}t | j|}ddg}t| j| j|||d fd}t|| j| jddd d S )Nr)   r  )r'   r.   r	  rU   rC   )r   rQ   r	   r   r   )r<   r"   r    r  r>   r?   r?   r@   test_cubic_deriv_unstabler  s
   z$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,   r  r	  rU   rC   r+   rV   )r6   r   rQ   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+   r  r	  rU   rC   )r	   r6   rN   r   )r<   r"   rX   rw   r>   rQ   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   r~   r  r	  *   )r  r  r{  )r<   rX   rw   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	  rU   rC   r   r   r%   )r   r   r   )rQ   r   r	   r   )r<   r"   rQ   r   r  r  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 )NrL   r   r   )r6   r:   r  int_r	   )r<   rX   rw   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   ry   r   r   r   )r6   rN   r	   )r<   rQ   rX   rw   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 )NrL   r'   r%   )	r6   r:   r  floatr8   r9   r2   r4   r	   )r<   rX   rw   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 )NrL   c                 S   s   g | ]}|d  qS )r'   r?   )rf   ar?   r?   r@   rh     r  z.TestInterp.test_list_input.<locals>.<listcomp>r   )r   r   r	   r|  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   rU   rC   r   r%   )r6   r   r  rQ   r>  r	   r   )r<   r   r  r  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 )
Nrr   r)   r}   r   r   r~   r   r   r   r~   r   r	  )r6   r;   ru   rv   r	   r   r!   r   )r<   r"   r=   rX   rw   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   r  rB   rV   )r   r   )r   r   r'   )Nr   r  r   typor   r+   r   rr   r  r   r   r~   r   r  r	  r   )r6   r  rQ   r	   r   r!   r2   r4   r   r>  r;   ru   rv   rc  )r<   r   r   r@  r  r  r"   r=   rX   rw   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 )Nrr   )r)   r   r   rU   rC   )	r6   r;   ru   rv   r   r	   make_interp_full_matrr   r!   )r<   r"   r=   rX   rw   r    r>   cfr?   r?   r@   test_full_matrix4  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.
        rr      r)       r'   r   Nr%   r   )offsetrU   rV   )r6   r;   ru   r   intdiagflatrc  r  diagonalr   r   linalgsolve)r<   r=   r"   r  r  r   urlldr   r>   r?   r?   r@   test_woodbury?  s,   46zTestInterp.test_woodburyN),r   r   r   r6   rN   r=  rQ   r  r   rs  rw  ry  rI   r  r  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  xfailr  r  r  r  r  r  r  r  r  r  r  r  r  r  r?   r?   r?   r@   rr    sP    









	

3rr  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   r6   rc  r  r   r"  r   evaluate_all_bsplslr  )rX   rw   r    r"   r=   Ar   xvalleftbbr!   r?   r?   r@   r  \  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$t
|j|}t
|j|}t||}|||ffS )z,Make the least-square spline, full matrices.r   r  )mapr6   r]   r   rc  r  r   r"  r   r  dotTr  r  )rX   rw   r    r"   mr=   r  r   r  r  r  r   Yr!   r?   r?   r@   make_lsq_full_matrixx  s   r  c                   @   s   e Zd Zejd d\ZZeejeZ	ejeZ
eee	d e	d deZdd Zdd	 Zd
d Zdd Zdd Zdd Zdd ZdS )TestLSQrr   )r   r)   r   r%   r   c                 C   s   | j | j| j| jf\}}}}t||||\}}t||||}t|j| t|jj	|j
| d f |\}}	tjj||dd\}
}}}t|j|
 d S )Nr   r%   )rcond)rX   rw   r    r"   r  r
   r   r!   r   r   r   r6   r  lstsq)r<   rX   rw   r    r"   c0AYr>   aar   r  r   r?   r?   r@   
test_lstsq  s   zTestLSQ.test_lstsqc                 C   s|   | j | j| j| jf\}}}}t|}t||||}t|||||d}t|j|jdd t|j|jdd t	|j|j d S )N)wrU   rV   )
rX   rw   r    r"   r6   rz   r
   r   r!   r   )r<   rX   rw   r    r"   r  r>   b_wr?   r?   r@   test_weights  s   
zTestLSQ.test_weightsc                 C   sd   | j | j| j| jf\}}}}tjj|dddfd}t||||}t|jj	|j
| d dddf d S )Nr   r~   r   r   r   )rX   r    r"   r=   r6   r;   r
   r   r!   r   r   )r<   rX   r    r"   r=   rw   r>   r?   r?   r@   r    s   $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   rB   rC   )rX   r    r"   rw   r
   r   r   r   )r<   rX   r    r"   r  r>   r   r   r?   r?   r@   r    s   
(zTestLSQ.test_complexc                 C   sD   t dt j}t dt j}t|dd}t|||dd d S )NrL   r   r   )r6   r:   r  r  r   r
   )r<   rX   rw   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   ry   r)   r   )r6   rN   r   r
   )r<   rQ   rX   rw   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%   )
r6   r:   r  r  r   r8   r9   r2   r4   r
   )r<   rX   rw   r    r  r?   r?   r@   test_checkfinite  s   
zTestLSQ.test_checkfiniteN)r   r   r   r6   r;   ru   r=   r"   rv   rX   rw   r   rN   r    r  r  r  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    d S 1 sw   Y  d S )Nrr   ry   r*   r'   r)   r+   r   r   r%   r   )r6   r;   ru   rv   r   r  normalr2   r4   r   r^   r9  )r<   r=   rX   rw   x_duplr?   r?   r@   test_invalid_input  s*   .





"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.npzrX   rw   y_GCVSPLg-C6?rC   N)r6   loadr  r   r   )r<   r  rX   rw   r  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.
        rr   ry   r*   r'   r)   r+   r   )lamr   r	  r   r%   rB   rV   N)r6   r;   ru   rv   r   r  r  r   r	   rN   r   )r<   r=   rX   rw   
spline_GCVspline_interpgridr?   r?   r@   test_non_regularized_case=  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 )Nrr   ry   r*   r'   r)   r+   r   rL   r   g      >@zJSpline with weights should be closer to the points than the original one: z.4z < )r6   r;   ru   rv   r   r  r  r   choicer   onesabsr4   )
r<   r=   rX   rw   r   indr  spl_worigweightedr?   r?   r@   test_weighted_smoothing_splineP  s&   .

z2TestSmoothingSpline.test_weighted_smoothing_splineN)r   r   r   r  r  r  r  r?   r?   r?   r@   r    s
    6r  rE  )r3  r)   )r)   )9numpyr6   numpy.testingr   r   r   rI   r   r2   scipy.interpolater   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   scipy.linalgr  r  scipy.interpolate._bsplinesr   r   r   r   r   scipy.interpolate._fitpack_implinterpolate_fitpack_implr   r  r   r  r  rd   rj   r   rW   r   rG   r  r;  rr  r  r  r  r  r  r?   r?   r?   r@   <module>   sD    H    E	
	
 `   -
R