a
    .'aR                     @   s   d Z ddlZddlZddl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mZ ddl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Z dd
lmZ ddl m!Z!m"Z" ddlZ#ddl$Z#dd Z%dd Z&G dd dZ'G dd dZ(dS )z2 Test functions for scipy.linalg.matfuncs module

    N)arrayeyeexprandom)matrix_power)assert_allcloseassert_assert_array_almost_equalassert_equalassert_array_almost_equal_nulpsuppress_warnings)
csc_matrixSparseEfficiencyWarning)r   )expm_expmProductOperatorMatrixPowerOperator_onenorm_matrix_power_nnm)matrix)logm)	factorialbinomc                 C   s   | t | ks| dk rtdt | } |t |ks8|dk r@tdt |}t|| \}}td|  | }|td|   }t|g| |  |t|g| ||   S )aj  
    A helper function for testing matrix functions.

    Parameters
    ----------
    n : integer greater than 1
        Order of the square matrix to be returned.
    p : non-negative integer
        Power of the matrix.

    Returns
    -------
    out : ndarray representing a square matrix
        A Forsythe matrix of order n, raised to the power p.

       z#n must be an integer greater than 1r   z p must be a non-negative integer      $@)int
ValueErrordivmodnppowerdiag)npabZlargeZsmall r$   Flib/python3.9/site-packages/scipy/sparse/linalg/tests/test_matfuncs.py_burkardt_13_power   s    r&   c                  C   sn   t jd tddD ]R} tdD ]D}t j| | f}t j||}t||}t j|d}t|| q"qd S )N        )	r   r   seedrangelinalgr   r   Znormr   )r    r!   MZMpobservedexpectedr$   r$   r%   test_onenorm_matrix_power_nnm<   s    
r0   c                   @   s   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd Z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$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Zd3d4 Zd5d6 Zd7d8 Zd9d: Zd;d< Z d=S )>TestExpMc                 C   s2   t ddgddgg}tt|ddgddgg d S N        r   r(   )r   r	   r   selfr"   r$   r$   r%   test_zero_ndarrayH   s    zTestExpM.test_zero_ndarrayc                 C   s6   t ddgddgg}tt| ddgddgg d S r2   )r   r	   r   toarrayr4   r$   r$   r%   test_zero_sparseL   s    zTestExpM.test_zero_sparsec                 C   s2   t ddgddgg}tt|ddgddgg d S r2   )r   r	   r   r4   r$   r$   r%   test_zero_matrixP   s    zTestExpM.test_zero_matrixc                 C   s   t tdgg}tt d| tt dgg| tt tdgg| tt tdgg| tt tdggj| t tdgg}tt d| tt dgg| tt tdgg| tt tdggj| d S )Nr(   ))r(                 ?))r:   )r   r   r   r   r   r   A)r5   r;   Br$   r$   r%   test_misc_typesT   s    zTestExpM.test_misc_typesc                 C   s   t g dg dg dgtd}td}td}tj|d| d|d|   gd	|d
||  gd	d	|ggtd}t| }t|| d S )N)r(      r   )r   r(   r)   )r   r   r   dtyper(   r   r>      r   r)   )	r   floatmathr   r   r   r   r7   r	   )r5   r;   Ze1Ze2r/   r.   r$   r$   r%   test_bidiagonal_sparsea   s$    

zTestExpM.test_bidiagonal_sparsec                 C   sZ   t jt jfD ]H}dD ]>}|td|d }t|}t|td|d }t||dd qqd S N{Gz?皙?g      ?r(   
   r>   r?   d   Znulp)r   Zfloat32float64r   r   r   r   r5   r@   scaler;   r.   r/   r$   r$   r%   test_padecases_dtype_floato   s    z#TestExpM.test_padecases_dtype_floatc                 C   sZ   t jt jfD ]H}dD ]>}|td|d }t|}t|td|d }t||dd qqd S rE   )r   Z	complex64
complex128r   r   r   r   rM   r$   r$   r%   test_padecases_dtype_complexw   s    z%TestExpM.test_padecases_dtype_complexc              	   C   s   t j}dD ]}|tdd|dd }t|td|d }t <}|td t|dd	 }t|d	d	 }W d    n1 s~0    Y  t
||d
d t
||d
d q
d S )NrF   r>   cscr@   formatr?   =Changing the sparsity structure of a csc_matrix is expensive.T)Zuse_exact_onenormFrJ   rK   )r   rL   speyer   r   r   filterr   r   r7   r   )r5   r@   rN   r"   esupZexact_onenormZinexact_onenormr$   r$   r%   !test_padecases_dtype_sparse_float   s    .z*TestExpM.test_padecases_dtype_sparse_floatc              	   C   s   t j}dD ]t}|tdd|dd }t|td|d }t 2}|td tt	|
 |dd W d    q
1 st0    Y  q
d S )	NrF   r>   rR   rS   r?   rU   rJ   rK   )r   rP   rV   r   r   r   rW   r   r   r   r7   )r5   r@   rN   r"   rX   rY   r$   r$   r%   #test_padecases_dtype_sparse_complex   s    z,TestExpM.test_padecases_dtype_sparse_complexc              	   C   s   t d tjtjfD ]p}tddD ]`}dD ]V}t|t |||  |}t	|rp|dt || |  }t
tt|| q,q$qd S )Nr'   r(   rI   )-C6?MbP?rG   rH   r(   r   g      Y@r:   )r   r*   r   rL   rP   r+   r   ZrandZastypeZiscomplexobjr	   r   r   )r5   r@   r    rN   r;   r$   r$   r%   test_logm_consistency   s    

zTestExpM.test_logm_consistencyc                 C   s<   t g dg dg dg dg}tt|td|  d S )N)r(   r(   r(   )r(   r_   r(   r(   )r(   r(   r_   r(   )r(   r(   r(   r_         ?)r   r   r   r   r5   Qr$   r$   r%   test_integer_matrix   s    zTestExpM.test_integer_matrixc                 C   sd   t jg dg dg dg dgt jd}tt|td|  t|}tt|jtd| j d S )N)ii  r   r   )r   iih     )r   iv  ir   r   r   r   r   r?   r`   )r   r   Zint16r   r   r   r;   ra   r$   r$   r%   test_integer_matrix_2   s    
zTestExpM.test_integer_matrix_2c           	      C   s   t jg dg dg dg dgtd}t jg dg dg dg d	gtd}tt||d
d td d}| }||d< t $}|	t
d t|}W d    n1 s0    Y  d
}d| }tt j||||d  d S )N)g3d?     L@rg   rg   )r   gRal!A?rg   rg   )r   r   gQI?rg   )r   r   r   g^?r?   )g<gGgx@g9=g[dB)r3   g'V7gZ@g2p)r3   r3   gѤT g\GeE@)r3   r3   r3   gPǆ!r\   )rtolr'   gFFg<)r(   r   zIll-conditioned.*rJ   )rh   atol)r   r   rB   r   r   r   r*   copyr   rW   RuntimeWarningr   Zallclose)	r5   r;   ZA_logmZtinyZA_logm_perturbedrY   ZA_expm_logm_perturbedrh   ri   r$   r$   r%   test_triangularity_perturbation   s6    	

&z(TestExpM.test_triangularity_perturbationc                 C   s^   t d}t d}t jddgddggtd}t j|dgd|ggtd}t|}t|| d S )Nr(   r   r   r?   r   r   r   rB   r   r   )r5   exp1Zexp2r;   desiredactualr$   r$   r%   test_burkardt_1   s     

zTestExpM.test_burkardt_1c                 C   sJ   t jddgddggtd}t jddgddggtd}t|}t|| d S )	Nr(   r>   r   r?   gkQC@gb]IG@gd]IG@gJ[K@r   r   rB   r   r   r5   r;   ro   rp   r$   r$   r%   test_burkardt_2  s    zTestExpM.test_burkardt_2c                 C   s   t d}t d}t jddgddggtd}t jdd|  dd|   t d d|  gdt d d|  d	d|  dd|   ggtd}t|}t|| d S )
Nr(   '   r   iir?   &   i)r   r   r   rB   Zexpm1r   r   )r5   rn   Zexp39r;   ro   rp   r$   r$   r%   test_burkardt_3  s(    

zTestExpM.test_burkardt_3c                 C   s   t jddgddggtd}t jddgdd	ggtd}t jdd
gddggtd}t jddgtd}t |t | |}t|}t|| d S )Ni   i   r?   r>   r(      r         g      ?irw   )r   r   rB   dotr   r   r   )r5   r;   UVwro   rp   r$   r$   r%   test_burkardt_4%  s    zTestExpM.test_burkardt_4c                 C   sb   t jg dg dg dg dgtd}t jg dg dg dg d	gtd}t|}t|| d S )
N)r      r   r   )r   r   r   r   )r   r   r   r   re   r?   )r(   r      $   )r   r(   r   r   )r   r   r(   r   r   r   r   r(   rr   rs   r$   r$   r%   test_burkardt_54  s$    zTestExpM.test_burkardt_5c                 C   sT   t d}t jddgddggtd}t j||gd|ggtd}t|}t|| d S Nr(   r   r?   rm   )r5   rn   r;   ro   rp   r$   r$   r%   test_burkardt_6H  s    
zTestExpM.test_burkardt_6c                 C   sf   t d}t d}t jd| dgdd| ggtd}t j||gd|ggtd}t|}t|| d S r   )r   r   Zspacingr   rB   r   r   )r5   rn   Zepsr;   ro   rp   r$   r$   r%   test_burkardt_7X  s     



zTestExpM.test_burkardt_7c                 C   s   t d}t d}t jg dg dg dgtd}t jd| | d| d|  d	| d	|  gd
| | d
| d|  d| d	|  gd| d| d| ggtdd }t|}t|| d S )Nr{      )      r   )rw   i)r{   r{   r   r?      r)   r   ir}   g      ?rm   )r5   Zexp4Zexp16r;   ro   rp   r$   r$   r%   test_burkardt_8j  s(    

((zTestExpM.test_burkardt_8c                 C   sb   t jg dg dg dg dgtd}t jg dg dg dg d	gtd}t|}t|| d S )
N)r(   r   r   r   )r>   r(   r(   r   )r>   r   r(   r   )r>   r>   r>   r(   r?   )fa%@@X21@g鷯g)@)^Iچ@|Pk܂@g'@r   )v@gBfg;@r   r   )gDl{3@r   r   r   rr   rs   r$   r$   r%   test_burkardt_9{  s$    zTestExpM.test_burkardt_9c                 C   sl   t jg dg dg dgtd}tttj|d t jg dg dg dgtd}t|}t|| d S )	N)r{   r   r   )r(   r{   r(   )r(   r(   r{   r?   )r>   r>   r   )gl$^{b@
|f@g.Q@)g\"N_@r   g
|V@)g\"N_@gLud@gs[@	r   r   rB   r   sortedscipyr,   Zeigvalsr   rs   r$   r$   r%   test_burkardt_10  s"    zTestExpM.test_burkardt_10c                 C   sh   t jg dg dg dgtd}ttj|d t jg dg dg dgtd}t|}t|| d S )	N)g!=@l?QP)r   gt 9@猽誉\!@)r   r   g0n2A@r?   )      (   )gJކ3Cg;%s1PMSUc[)g;%s1Pgcx
MjCO}vC)r   r   g˂C)r   r   rB   r   r   r,   Zeigvalshr   rs   r$   r$   r%   test_burkardt_11  s"    zTestExpM.test_burkardt_11c                 C   sl   t jg dg dg dgtd}tttj|d t jg dg dg dgtd}t|}t|| d S )	N)i}   r   )iz8   6   )i}9   4   r?   )ir}   rw   )g)'g13V?g-RR?)gǣg׃4V?g3?)gWNx`gp?g}mR?r   rs   r$   r$   r%   test_burkardt_12  s"    zTestExpM.test_burkardt_12c           	      C   s   t dd}g dg dg dg dg}t|| dD ]}tdttd| }tj||ftd	}t|| D ]V}t ||}t	t
|d
 tt|tdt||  |  ||t| 7 }qntt |d}t|| q4d S )Nr{   r(   )r   r(   r   r   )r   r   r(   r   r   )r\   r   r   r   )r   r>   r{   rI   r   r?   r   rI   )r&   r   maxr   r   ZceilzerosrB   r+   r
   minr   Zfloorr   r   )	r5   Z	A4_actualZ
A4_desiredr    kro   r!   ZAprp   r$   r$   r%   test_burkardt_13  s"    


(zTestExpM.test_burkardt_13c                 C   sV   t jg dg dg dgtd}t jg dg dg dgtd}t|}t|| d S )N)r   g:0yE>r   )g"Dr_   g    _B)gP@r   gPr?   )g .?gzDv>g1O?)gvUg԰gLg@sDQ)g F~?gg=>gcE?rr   rs   r$   r$   r%   test_burkardt_14  s     zTestExpM.test_burkardt_14c           	   	   C   s   dD ]}t dddD ]}|t|dd }t|dk r< qttd|d d| }t|}|}tt|d d d d f t|d d d d f |d d d f  |d d d f  }dt|  }t	|||d	 qqd S )
N)r`   r]   gư>r   P   r>   rw   gYnr(   gvIh%<=)ri   )
r+   r   Zarangeanyr   r   r   absr   r   )	r5   rN   r    Zscr;   r<   Zgotr/   ri   r$   r$   r%   test_pascal  s"    zTestExpM.test_pascalc                 C   st   t d}d|d< t|}t 6}|td |td tt |}W d    n1 s\0    Y  t|| d S )N)   r   r(   )rw   r   zthe matrix subclass.*)	r   r   r   r   rW   DeprecationWarningPendingDeprecationWarningr   r   )r5   r;   ZB0rY   r<   r$   r$   r%   test_matrix_input  s    
,zTestExpM.test_matrix_inputc              
   C   sr   t g dg dg dg dg dg dg dg}t| }td| }|}tdD ]}|| }qVt|| d S )N)r`   r|   r|   r3   r3   r3   r3   )r3   r`   r3   r|   r|   r3   r3   )r3   r3   r`   r3   r3   r|   r|   )r3   r3   r3   r3   r3   r3   r3   i    )r   r   r   r+   r   )r5   LZE0ZE1ZE2jr$   r$   r%   test_exp_sinch_overflow  s    


z TestExpM.test_exp_sinch_overflowN)!__name__
__module____qualname__r6   r8   r9   r=   rD   rO   rQ   rZ   r[   r^   rc   rf   rl   rq   rt   rx   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r$   r$   r$   r%   r1   G   s<   $(r1   c                   @   s   e Zd Zdd Zdd ZdS )TestOperatorsc           
      C   s   t d d}d}d}t|D ]}tj ||}tj ||}tj ||}tj ||}t|||}	t|	||||| t|	j	||||j	| qd S )Nr'   r)   r   rI   )
r   r*   r+   r   randnr   r   matmatr~   T)
r5   r    r   nsamplesir;   r<   CDopr$   r$   r%   test_product_operator,  s    
"z#TestOperators.test_product_operatorc           	      C   s   t d d}d}d}d}t|D ]f}tj ||}tj ||}t||}t||t||	| t|j
|t||j
	| q"d S )Nr'   r)   r   r>   rI   )r   r*   r+   r   r   r   r   r   r   r~   r   )	r5   r    r   r!   r   r   r;   r<   r   r$   r$   r%   test_matrix_power_operator:  s    

z(TestOperators.test_matrix_power_operatorN)r   r   r   r   r   r$   r$   r$   r%   r   *  s   r   ))__doc__rC   Znumpyr   r   r   r   r   Znumpy.linalgr   Znumpy.testingr   r   r	   r
   r   r   Zscipy.sparser   r   Zscipy.sparse.constructrV   Zscipy.sparse.linalg.matfuncsr   r   r   r   r   Zscipy.sparse.sputilsr   Zscipy.linalgr   Zscipy.specialr   r   r   Zscipy.sparse.linalgr&   r0   r1   r   r$   r$   r$   r%   <module>   s(        f