o
    EbR                     @   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 )z3 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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      $@)int
ValueErrordivmodnppowerdiag)npabZlargeZsmall r$   I/usr/lib/python3/dist-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   
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$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Zd3d4 Zd5d6 Zd7d8 Zd9d: Zd;d< Z d=S )>TestExpMc                 C   2   t ddgddgg}tt|ddgddgg d S N        r   r(   )r   r	   r   selfr"   r$   r$   r%   test_zero_ndarrayH      zTestExpM.test_zero_ndarrayc                 C   s6   t ddgddgg}tt| ddgddgg d S r3   )r   r	   r   toarrayr5   r$   r$   r%   test_zero_sparseL   s   "zTestExpM.test_zero_sparsec                 C   r2   r3   )r   r	   r   r5   r$   r$   r%   test_zero_matrixP   r8   zTestExpM.test_zero_matrixc                 C   s   t tdgg}tt d| tt dgg| tt tdgg| tt tdgg| tt tdggj| t tdgg}tt d| tt dgg| tt tdgg| tt tdggj| d S )Nr(   ))r(                 ?))r<   )r   r   r   r   r   r   A)r6   r=   Br$   r$   r%   test_misc_typesT   s   zTestExpM.test_misc_typesc                 C   s   t g dg dg dgtd}td}td}tj|d| d|d|   gd	|d
||  gd	d	|ggtd}t| }t|| d S )N)r(      r   )r   r(   r)   )r   r   r   dtyper(   r   r@      r   r)   )	r   floatmathr   r   r   r   r9   r	   )r6   r=   Ze1Ze2r/   r.   r$   r$   r%   test_bidiagonal_sparsea   s$   

zTestExpM.test_bidiagonal_sparsec                 C   Z   t jt jfD ]$}dD ]}|td|d }t|}t|td|d }t||dd q
qd S N{Gz?皙?g      ?r(   
   r@   rA   d   Znulp)r   Zfloat32float64r   r   r   r   r6   rB   scaler=   r.   r/   r$   r$   r%   test_padecases_dtype_floato      z#TestExpM.test_padecases_dtype_floatc                 C   rG   rH   )r   Z	complex64
complex128r   r   r   r   rP   r$   r$   r%   test_padecases_dtype_complexw   rS   z%TestExpM.test_padecases_dtype_complexc              	   C   s   t j}dD ]M}|tdd|dd }t|td|d }t }|td t|dd	 }t|d	d	 }W d    n1 s?w   Y  t
||d
d t
||d
d qd S )NrI   r@   cscrB   formatrA   =Changing the sparsity structure of a csc_matrix is expensive.T)Zuse_exact_onenormFrM   rN   )r   rO   speyer   r   r   filterr   r   r9   r   )r6   rB   rQ   r"   esupZexact_onenormZinexact_onenormr$   r$   r%   !test_padecases_dtype_sparse_float   s   z*TestExpM.test_padecases_dtype_sparse_floatc              	   C   s   t j}dD ]:}|tdd|dd }t|td|d }t }|td tt	|
 |dd W d    n1 s:w   Y  qd S )	NrI   r@   rV   rW   rA   rY   rM   rN   )r   rT   rZ   r   r   r   r[   r   r   r   r9   )r6   rB   rQ   r"   r\   r]   r$   r$   r%   #test_padecases_dtype_sparse_complex   s   z,TestExpM.test_padecases_dtype_sparse_complexc              	   C   s   t d tjtjfD ]8}tddD ]0}dD ]+}t|t |||  |}t	|r8|dt || |  }t
tt|| qqqd S )Nr'   r(   rL   )-C6?MbP?rJ   rK   r(   r   g      Y@r<   )r   r*   r   rO   rT   r+   r   ZrandZastypeZiscomplexobjr	   r   r   )r6   rB   r    rQ   r=   r$   r$   r%   test_logm_consistency   s   

zTestExpM.test_logm_consistencyc                 C   s<   t g dg dg dg dg}tt|td|  d S )N)r(   r(   r(   )r(   rc   r(   r(   )r(   r(   rc   r(   )r(   r(   r(   rc         ?)r   r   r   r   r6   Qr$   r$   r%   test_integer_matrix   s   zTestExpM.test_integer_matrixc                 C   sd   t jg dg dg dg dgt jd}tt|td|  t|}tt|jtd| j d S )N)ii  r   r   )r   iih     )r   iv  ir   r   r   r   r   rA   rd   )r   r   Zint16r   r   r   r=   re   r$   r$   r%   test_integer_matrix_2   s   
zTestExpM.test_integer_matrix_2c           	      C   s   t jg dg dg dg dgtd}t jg dg dg dg d	gtd}tt||d
d td d}| }||d< t }|	t
d t|}W d    n1 sVw   Y  d
}d| }tt j||||d  d S )N)g3d?     L@rk   rk   )r   gRal!A?rk   rk   )r   r   gQI?rk   )r   r   r   g^?rA   )g<gGgx@g9=g[dB)r4   g'V7gZ@g2p)r4   r4   gѤT g\GeE@)r4   r4   r4   gPǆ!r`   )rtolr'   gFFg<)r(   r   zIll-conditioned.*rM   )rl   atol)r   r   rD   r   r   r   r*   copyr   r[   RuntimeWarningr   Zallclose)	r6   r=   ZA_logmZtinyZA_logm_perturbedr]   ZA_expm_logm_perturbedrl   rm   r$   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   rA   r   r   r   rD   r   r   )r6   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   rA   gkQC@gb]IG@gd]IG@gJ[K@r   r   rD   r   r   r6   r=   rs   rt   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   iirA   &   i)r   r   r   rD   Zexpm1r   r   )r6   rr   Zexp39r=   rs   rt   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   rA   r@   r(      r         g      ?ir{   )r   r   rD   dotr   r   r   )r6   r=   UVwrs   rt   r$   r$   r%   test_burkardt_4%  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      r   r   )r   r   r   r   )r   r   r   r   ri   rA   )r(   r      $   )r   r(   r   r   )r   r   r(   r   r   r   r   r(   rv   rw   r$   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   rA   rq   )r6   rr   r=   rs   rt   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   rD   r   r   )r6   rr   Zepsr=   rs   rt   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   )r{   i)r   r   r   rA      r)   r   ir   g      ?rq   )r6   Zexp4Zexp16r=   rs   rt   r$   r$   r%   test_burkardt_8j  s(   

((zTestExpM.test_burkardt_8c                 C   r   )
N)r(   r   r   r   )r@   r(   r(   r   )r@   r   r(   r   )r@   r@   r@   r(   rA   )fa%@@X21@g鷯g)@)^Iچ@|Pk܂@g'@r   )v@gBfg;@r   r   )gDl{3@r   r   r   rv   rw   r$   r$   r%   test_burkardt_9{  s$   zTestExpM.test_burkardt_9c                 C   l   t jg dg dg dgtd}tttj|d t jg dg dg dgtd}t|}t|| d S )	N)r   r   r   )r(   r   r(   )r(   r(   r   rA   )r@   r@   r   )gl$^{b@
|f@g.Q@)g\"N_@r   g
|V@)g\"N_@gLud@gs[@	r   r   rD   r   sortedscipyr,   Zeigvalsr   rw   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@rA   )      (   )gJކ3Cg;%s1PMSUc[)g;%s1Pgcx
MjCO}vC)r   r   g˂C)r   r   rD   r   r   r,   Zeigvalshr   rw   r$   r$   r%   test_burkardt_11  s"   zTestExpM.test_burkardt_11c                 C   r   )	N)i}   r   )iz8   6   )i}9   4   rA   )ir   r{   )g)'g13V?g-RR?)gǣg׃4V?g3?)gWNx`gp?g}mR?r   rw   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 )Nr   r(   )r   r(   r   r   )r   r   r(   r   r   )r`   r   r   r   )r   r@   r   rL   r   rA   r   rL   )r&   r   maxr   r   ZceilzerosrD   r+   r
   minr   Zfloorr   r   )	r6   Z	A4_actualZ
A4_desiredr    krs   r!   ZAprt   r$   r$   r%   test_burkardt_13  s$   


(zTestExpM.test_burkardt_13c                 C   sV   t jg dg dg dgtd}t jg dg dg dgtd}t|}t|| d S )N)r   g:0yE>r   )g"Drc   g    _B)gP@r   gPrA   )g .?gzDv>g1O?)gvUg԰gLg@sDQ)g F~?gg=>gcE?rv   rw   r$   r$   r%   test_burkardt_14  s    zTestExpM.test_burkardt_14c           	   	   C   s   dD ]k}t dddD ]b}|t|dd }t|dk r nOttd|d d| }t|}|}tt|d d d d f t|d d d d f |d d d f  |d d d f  }dt|  }t	|||d	 q
qd S )
N)rd   ra   gư>r   P   r@   r{   gYnr(   gvIh%<=)rm   )
r+   r   Zarangeanyr   r   r   absr   r   )	r6   rQ   r    Zscr=   r>   Zgotr/   rm   r$   r$   r%   test_pascal  s&   zTestExpM.test_pascalc                 C   st   t d}d|d< t|}t }|td |td tt |}W d    n1 s.w   Y  t|| d S )N)   r   r(   )r{   r   zthe matrix subclass.*)	r   r   r   r   r[   DeprecationWarningPendingDeprecationWarningr   r   )r6   r=   ZB0r]   r>   r$   r$   r%   test_matrix_input  s   
zTestExpM.test_matrix_inputc              
   C   sr   t g dg dg dg dg dg dg dg}t| }td| }|}tdD ]}|| }q+t|| d S )N)rd   r   r   r4   r4   r4   r4   )r4   rd   r4   r   r   r4   r4   )r4   r4   rd   r4   r4   r   r   )r4   r4   r4   r4   r4   r4   r4   i    )r   r   r   r+   r   )r6   LZE0ZE1ZE2jr$   r$   r%   test_exp_sinch_overflow  s   


z TestExpM.test_exp_sinch_overflowN)!__name__
__module____qualname__r7   r:   r;   r?   rF   rR   rU   r^   r_   rb   rg   rj   rp   ru   rx   r|   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r$   r$   r$   r%   r1   G   s>    $(r1   c                   @   s   e Zd Zdd Zdd ZdS )TestOperatorsc           
      C   s   t d d}d}d}t|D ]H}tj ||}tj ||}tj ||}tj ||}t|||}	t|	||||| t|	j	||||j	| qd S )Nr'   r)   r   rL   )
r   r*   r+   r   randnr   r   matmatr   T)
r6   r    r   nsamplesir=   r>   CDopr$   r$   r%   test_product_operator,  s   
"(z#TestOperators.test_product_operatorc           	      C   s   t d d}d}d}d}t|D ]3}tj ||}tj ||}t||}t||t||	| t|j
|t||j
	| qd S )Nr'   r)   r   r@   rL   )r   r*   r+   r   r   r   r   r   r   r   r   )	r6   r    r   r!   r   r   r=   r>   r   r$   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__rE   Znumpyr   r   r   r   r   Znumpy.linalgr   Znumpy.testingr   r   r	   r
   r   r   Zscipy.sparser   r   Zscipy.sparse._constructrZ   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