U
    »mœdª  ã                   @   sš   d Z ddlZddlmZ ddlmZmZmZ ddl	m
Z
mZ ddlZddlmZ 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„ ƒZdS )z1Test functions for linalg._solve_toeplitz module
é    N)Úlevinson)ÚsolveÚtoeplitzÚsolve_toeplitz)Úassert_equalÚassert_allclose)Úraisesc                  C   sà   t j d¡} dD ]Ê}|  |¡}|  ¡ dk r<|d|  |¡  }|  |¡}|  ¡ dk rd|d|  |¡  }|  |¡}|  ¡ dk rŒ|d|  |¡  }t||f|ƒ}tt||d�|ƒ}t||ƒ t||d�}tt|ƒ|ƒ}t||ƒ qd S )NéÒ  )é   é   é   é
   g      à?ù              ð?©Úr©Úb)	ÚnpÚrandomÚRandomStateÚrandnZrandr   r   r   r   )r   ÚnÚcr   ÚyÚactualÚdesired© r   ú_/home/sam/Atlas/atlas_env/lib/python3.8/site-packages/scipy/linalg/tests/test_solve_toeplitz.pyÚtest_solve_equivalence   s"    



r   c                  C   sŠ   t j d¡} |  d¡}|  d¡}dD ]`}dD ]V}| j|Ž | }t||f|d�}tt||d�|ƒ}t|j|ƒ t|j|ƒ t	||ƒ q,q$d S )Nr	   é   )r   r   ))r   )r   r   )r   r   r   r   r   )
r   r   r   r   r   r   r   r   Úshaper   )r   r   r   ÚoffsetZyshaper   r   r   r   r   r   Útest_multiple_rhs%   s    

r"   c                  C   sR   ddddg} ddddg}ddddg}t | |f|ƒ}tt| |d	�|ƒ}t||ƒ d S )
Nr
   r   r   é   r   é	   é   é   r   )r   r   r   r   )r   r   r   r   r   r   r   r   Útest_native_list_arguments3   s    r'   c                  C   sR   t j d¡} d}|  |¡}|  |¡}|  |¡}d|d< tt jjt||f|d� d S )Nr	   r   r   r   ©r   r   r   r   Úassert_raisesZlinalgZLinAlgErrorr   )r   r   r   r   r   r   r   r   Útest_zero_diag_error<   s    


  ÿr*   c                  C   s8   t j d¡} dddg}|  d¡}tt jjt||d� d S )Nr	   r   r
   r   r   r(   )r   r   r   r   r   r   Útest_wikipedia_counterexampleH   s    

r+   c                  C   s0  t j d¡} |  d¡}|  d¡d }dg}dg}tddƒD ]X}| t|d |d … |d|… d�d ¡ | t|d |d … |d|… d�d ¡ q:t  |dd	d… |d d… f¡}t  |dd	d…  ¡ |d d… f¡}t	||dd … d�\}}	t	||dd … d�\}}
t
||	d d… ƒ t
||
d d… ƒ d S )
Nr	   r   r   r
   r   r   éÿÿÿÿéþÿÿÿr   )r   r   r   r   ÚrangeÚappendr   ZconcatenateZconjr   r   )r   Zy_dZy_zZreflection_coeffs_dZreflection_coeffs_zÚiZ
y_d_concatZ
y_z_concatÚ_Zref_dZref_zr   r   r   Útest_reflection_coeffsQ   s    
*, $r2   z!Instability of Levinson iteration)Úreasonc                  C   sT   t j d¡} d}dt  |¡d  }|  |¡}t||d�}tt|ƒ|ƒ}t||ƒ d S )Nr	   éd   gÍÌÌÌÌÌì?r   r   )	r   r   r   Zaranger   r   r   r   r   )r   r   r   r   Z	solution1Z	solution2r   r   r   Útest_unstableg   s    	
r5   )Ú__doc__Únumpyr   Zscipy.linalg._solve_toeplitzr   Zscipy.linalgr   r   r   Znumpy.testingr   r   Zpytestr   r)   r   r"   r'   r*   r+   r2   ÚmarkZxfailr5   r   r   r   r   Ú<module>   s   		