o
    iT                     @   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	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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%dd Z&G dd dZ'G dd dZ(dS )z3 Test functions for scipy.linalg._matfuncs module

    N)arrayeyeexprandom)assert_allcloseassert_assert_array_almost_equalassert_equalassert_array_almost_equal_nulpsuppress_warnings)	csc_arraySparseEfficiencyWarning)	eye_array)expm_expmProductOperatorMatrixPowerOperator_onenorm_matrix_power_nnmmatrix_power)matrix)logm)	factorialbinomc                 C   s   | t | ks
| dk rtdt | } |t |ks|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      $@)int
ValueErrordivmodnppowerdiag)npabZlargeZsmall r%   a/home/kim/smarthome/.venv/lib/python3.10/site-packages/scipy/sparse/linalg/tests/test_matfuncs.py_burkardt_13_power   s   ,r'   c                  C   sn   t jd tddD ])} tdD ]"}t j| | f}t j||}t||}t j|d}t|| qqd S )N        )	r   r   seedrangelinalgr   r   Znormr   )r!   r"   MZMpobservedexpectedr%   r%   r&   test_onenorm_matrix_power_nnm;   s   
r1   c            
      C   s   t jd t jjdddd\} }t jjdd}t|| |ffdd}t|| |ffdd}| }d	D ]!}t|| }t|| }t j||}	t||	 t|| q2d S )
Nr(   r      )r      )size)r3   )r2   r2   )shape)r   r*   r3   )	r   r   r+   randintr   toarrayr   r-   r   )
rowcoldataZAmatAZAdenser   ZApowZAmat_powZ
Adense_powr%   r%   r&   test_matrix_powerE   s   
r<   c                   @   s   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd Zdd Zdd Zdd Zdd Zdd Zdd Zdd  Zd!d" Zd#d$ 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   2   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_ndarrayU      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 r?   )r   r   r   r7   rA   r%   r%   r&   test_zero_sparseY   s   "zTestExpM.test_zero_sparsec                 C   r>   r?   )r   r   r   rA   r%   r%   r&   test_zero_matrix]   rD   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 | 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 | d S )Nr)   ))r)                 ?))rG   )r   r   r   r   r   r   r7   )rB   r;   Br%   r%   r&   test_misc_typesa   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   rJ      r   r*   )	r   floatmathr   r   r   r   r7   r   )rB   r;   e1e2r0   r/   r%   r%   r&   test_bidiagonal_sparsen   s$   

zTestExpM.test_bidiagonal_sparsec                 C   ^   t jt jfD ]&}dD ]!}|td|d }t|}t||dtd|d }t||dd q
qd S N{Gz?皙?g      ?r)   
   rJ   rK   d   Znulp)r   Zfloat32float64r   r   r   r
   rB   rL   scaler;   r/   r0   r%   r%   r&   test_padecases_dtype_float|      z#TestExpM.test_padecases_dtype_floatc                 C   rS   rT   )r   Z	complex64
complex128r   r   r   r
   r\   r%   r%   r&   test_padecases_dtype_complex   r_   z%TestExpM.test_padecases_dtype_complexc              	   C   s   t j}dD ]O}|tdd|dd }t||dtd|d }t }|td t|dd	 }t|d	d	 }W d    n1 sAw   Y  t
||d
d t
||d
d qd S )NrU   rJ   cscrL   formatrK   Changing the sparsity structureT)Zuse_exact_onenormFrY   rZ   )r   r[   r   r   r   r   filterr   r   r7   r
   )rB   rL   r]   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dd|dd }t|td|d }t }|td tt	|
 |dd W d    n1 s:w   Y  qd S )	NrU   rJ   rb   rc   rK   re   rY   rZ   )r   r`   r   r   r   r   rf   r   r
   r   r7   )rB   rL   r]   r#   rg   rh   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 ]8}tddD ]0}dD ]+}t|t |||  |}t	|r8|dt || |  }t
tt|| qqqd S )Nr(   r)   rX   )-C6?MbP?rV   rW   r)   r   g      Y@rG   )r   r+   r   r[   r`   r,   r   ZrandZastypeZiscomplexobjr   r   r   )rB   rL   r!   r]   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)   rn   r)   r)   )r)   r)   rn   r)   )r)   r)   r)   rn         ?)r   r   r   r   rB   Qr%   r%   r&   test_integer_matrix   s   zTestExpM.test_integer_matrixc                 C   sh   t jg dg dg dg dgt jd}tt|td|  t|}tt| td|   d S )N)ii  r   r   )r   iih     )r   iv  ir   r   r   r   r   rK   ro   )r   r   Zint16r   r   r   r7   rp   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 sVw   Y  d
}d| }tt j||||d  d S )N)g3d?     L@rv   rv   )r   gRal!A?rv   rv   )r   r   gQI?rv   )r   r   r   g^?rK   )g<gGgx@g9=g[dB)r@   g'V7gZ@g2p)r@   r@   gѤT g\GeE@)r@   r@   r@   gPǆ!rk   )rtolr(   gFFg<)r)   r   zIll-conditioned.*rY   )rw   atol)r   r   rN   r   r   r   r+   copyr   rf   RuntimeWarningr   Zallclose)	rB   r;   ZA_logmZtinyZA_logm_perturbedrh   ZA_expm_logm_perturbedrw   rx   r%   r%   r&   test_triangularity_perturbation   s8   	


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   rK   r   r   r   rN   r   r   )rB   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)   rJ   r   rK   gkQC@gb]IG@gd]IG@gJ[K@r   r   rN   r   r   rB   r;   r~   r   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   iirK   &   i)r   r   r   rN   expm1r   r   )rB   r}   Zexp39r;   r~   r   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   rK   rJ   r)   r2   r         g      ?ir   )r   r   rN   dotr   r   r   )rB   r;   UVwr~   r   r%   r%   r&   test_burkardt_40  s   zTestExpM.test_burkardt_4c                 C   b   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   r3   r   r   )r   r   r3   r   )r   r   r   r3   rt   rK   )r)   r3      $   )r   r)   r3   r   )r   r   r)   r3   r   r   r   r)   r   r   r%   r%   r&   test_burkardt_5?  s$   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   rK   r|   )rB   r}   r;   r~   r   r%   r%   r&   test_burkardt_6S  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   spacingr   rN   r   r   )rB   r}   epsr;   r~   r   r%   r%   r&   test_burkardt_7c  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 )Nr2      )      r3   )r   i)r2   r2   r   rK      r*   r   ir   g      ?r|   )rB   Zexp4Zexp16r;   r~   r   r%   r%   r&   test_burkardt_8u  s(   

((zTestExpM.test_burkardt_8c                 C   r   )
N)r)   r   r   r   )rJ   r)   r)   r   )rJ   r   r)   r   )rJ   rJ   rJ   r)   rK   )fa%@@X21@g鷯g)@)^Iچ@|Pk܂@g'@r   )v@gBfg;@r   r   )gDl{3@r   r   r   r   r   r%   r%   r&   test_burkardt_9  s$   zTestExpM.test_burkardt_9c                 C   l   t jg dg dg dgtd}tttj|d t jg dg dg dgtd}t|}t|| d S )	N)r2   r   r   )r)   r2   r)   )r)   r)   r2   rK   )rJ   rJ   r3   )gl$^{b@
|f@g.Q@)g\"N_@r   g
|V@)g\"N_@gLud@gs[@	r   r   rN   r   sortedscipyr-   Zeigvalsr   r   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@rK   )      (   )gJކ3Cg;%s1PMSUc[)g;%s1Pgcx
MjCO}vC)r   r   g˂C)r   r   rN   r   r   r-   Zeigvalshr   r   r%   r%   r&   test_burkardt_11  s"   zTestExpM.test_burkardt_11c                 C   r   )	N)i}   r   )iz8   6   )i}9   4   rK   )ir   r   )g)'g13V?g-RR?)gǣg׃4V?g3?)gWNx`gp?g}mR?r   r   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 ]U}tdttd| }tj||ftd	}t|| D ]+}t ||}t	t
|d
 tt|tdt||  |  ||t| 7 }q7tt |d}t|| qd S )Nr2   r)   )r   r)   r   r   )r   r   r)   r   r   )rk   r   r   r   )r   rJ   r2   rX   r   rK   r   rX   )r'   r   maxr   r   ceilzerosrN   r,   r	   minr   floorr   r   )	rB   Z	A4_actualZ
A4_desiredr!   kr~   r"   ZApr   r%   r%   r&   test_burkardt_13  s$   


(zTestExpM.test_burkardt_13c                 C   sV   t jg dg dg dgtd}t jg dg dg dgtd}t|}t|| d S )N)r   g:0yE>r   )g"Drn   g    _B)gP@r   gPrK   )g .?gzDv>g1O?)gvUg԰gLg@sDQ)g F~?gg=>gcE?r   r   r%   r%   r&   test_burkardt_14  s    zTestExpM.test_burkardt_14c           	   	   C   s   dD ]k}t dddD ]b}|t|dd }t|dk r nOttd|d d| }t|}|}tt|d d d d f t|d d d d f |d d d f  |d d d f  }dt|  }t	|||d	 q
qd S )
N)ro   rl   gư>r   P   rJ   r   gYnr)   gvIh%<=)rx   )
r,   r   Zarangeanyr    r   r   absr   r   )	rB   r]   r!   scr;   rH   gotr0   rx   r%   r%   r&   test_pascal  s&   zTestExpM.test_pascalc                 C   st   t d}d|d< t|}t }|td |td tt |}W d    n1 s.w   Y  t|| d S )N)   r   r)   )r   r   zthe matrix subclass.*)	r   r   r   r   rf   DeprecationWarningPendingDeprecationWarningr   r   )rB   r;   B0rh   rH   r%   r%   r&   test_matrix_input  s   
zTestExpM.test_matrix_inputc              
   C   sr   t g dg dg dg dg dg dg dg}t| }td| }|}tdD ]}|| }q+t|| d S )N)ro   r   r   r@   r@   r@   r@   )r@   ro   r@   r   r   r@   r@   )r@   r@   ro   r@   r@   r   r   )r@   r@   r@   r@   r@   r@   r@   i    )r   r   r   r,   r   )rB   LZE0ZE1ZE2jr%   r%   r&   test_exp_sinch_overflow"  s   


z TestExpM.test_exp_sinch_overflowN)!__name__
__module____qualname__rC   rE   rF   rI   rR   r^   ra   ri   rj   rm   rr   ru   r{   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r%   r%   r%   r&   r=   T   s>    
$(r=   c                   @   s   e Zd Zdd Zdd ZdS )TestOperatorsc           
      C   s   t d d}d}d}t|D ]H}tj ||}tj ||}tj ||}tj ||}t|||}	t|	||||| t|	j	||||j	| qd S )Nr(   r*   r   rX   )
r   r+   r,   r   randnr   r   matmatr   T)
rB   r!   r   nsamplesir;   rH   CDopr%   r%   r&   test_product_operator7  s   
"(z#TestOperators.test_product_operatorc           	      C   s   t d d}d}d}d}t|D ]7}tj ||}tj ||}t||}t||tj	||
| t|j|tj	||j
| qd S )Nr(   r*   r   rJ   rX   )r   r+   r,   r   r   r   r   r   r-   r   r   r   )	rB   r!   r   r"   r   r   r;   rH   r   r%   r%   r&   test_matrix_power_operatorE  s   

 &z(TestOperators.test_matrix_power_operatorN)r   r   r   r   r   r%   r%   r%   r&   r   5  s    r   ))__doc__rO   numpyr   r   r   r   r   Znumpy.testingr   r   r   r	   r
   r   Zscipy.sparser   r   Zscipy.sparse._constructr   Zscipy.sparse.linalg._matfuncsr   r   r   r   r   r   Zscipy.sparse._sputilsr   Zscipy.linalgr   Zscipy.specialr   r   r   Zscipy.sparse.linalgr'   r1   r<   r=   r   r%   r%   r%   r&   <module>   s*      
   d