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See its docstring for more information. z2Only floating-point dtypes are allowed in cholesky) �dtyper � TypeError�np�linalg�cholesky�_arrayr �_newZmT)r( r& �Lr r r r. , s r. �����axis�int)�x1�x2r4 r) c C sr | j tvs|j tvr td��| j|jkr0td��| jdkrBtd��| j| dkrXtd��t�tj | j |j |d��S )zz Array API compatible wrapper for :py:func:`np.cross <numpy.cross>`. See its docstring for more information. z(Only numeric dtypes are allowed in crossz"x1 and x2 must have the same shaper z/cross() requires arrays of dimension at least 1� z cross() dimension must equal 3r3 ) r* r r+ �shape� ValueError�ndimr r0 r, �crossr/ )r6 r7 r4 r r r r< < s r< )r( r) c C s& | j tvrtd��t�tj�| j��S )z� Array API compatible wrapper for :py:func:`np.linalg.det <numpy.linalg.det>`. See its docstring for more information. z-Only floating-point dtypes are allowed in det) r* r r+ r r0 r, r- �detr/ �r( r r r r= N s r= )�offset)r( r? r) c C s t �tj| j|ddd��S )z� Array API compatible wrapper for :py:func:`np.diagonal <numpy.diagonal>`. See its docstring for more information. ���r2 )r? �axis1�axis2)r r0 r, �diagonalr/ )r( r? r r r rC [ s rC c C s, | j tvrtd��tttjtj� | j ��� S )z� Array API compatible wrapper for :py:func:`np.linalg.eigh <numpy.linalg.eigh>`. See its docstring for more information. z.Only floating-point dtypes are allowed in eigh) r* r r+ r �mapr r0 r, r- �eighr/ r> r r r rE f s rE c C s& | j tvrtd��t�tj�| j��S )z� Array API compatible wrapper for :py:func:`np.linalg.eigvalsh <numpy.linalg.eigvalsh>`. See its docstring for more information. z2Only floating-point dtypes are allowed in eigvalsh) r* r r+ r r0 r, r- �eigvalshr/ r> r r r rF v s rF c C s& | j tvrtd��t�tj�| j��S )z� Array API compatible wrapper for :py:func:`np.linalg.inv <numpy.linalg.inv>`. See its docstring for more information. z-Only floating-point dtypes are allowed in inv) r* r r+ r r0 r, r- �invr/ r> r r r rG � s rG )r6 r7 r) c C s2 | j tvs|j tvr td��t�t�| j|j��S )z| Array API compatible wrapper for :py:func:`np.matmul <numpy.matmul>`. See its docstring for more information. z)Only numeric dtypes are allowed in matmul)r* r r+ r r0 r, �matmulr/ �r6 r7 r r r rH � s rH Zfro)�keepdims�ordz2Optional[Union[int, float, Literal['fro', 'nuc']]])r( rJ rK r) c C s. | j tvrtd��t�tjj| jd||d��S )�� Array API compatible wrapper for :py:func:`np.linalg.norm <numpy.linalg.norm>`. See its docstring for more information. z5Only floating-point dtypes are allowed in matrix_norm)r@ r2 �r4 rJ rK ) r* r r+ r r0 r, r- �normr/ )r( rJ rK r r r � matrix_norm� s rO )r( �nr) c C s( | j tvrtd��t�tj�| j|��S )z� Array API compatible wrapper for :py:func:`np.matrix_power <numpy.matrix_power>`. See its docstring for more information. zMOnly floating-point dtypes are allowed for the first argument of matrix_power) r* r r+ r r0 r, r- � matrix_powerr/ )r( rP r r r rQ � s rQ )�rtolz Optional[Union[float, Array]])r( rR r) c C s� | j dk rtj�d��tjj| jdd�}|du r`|jddd�t| jd d� � t�|j �j }n2t |t �rp|j}|jddd�t� |�d tjf }t �tj||kdd ��S ) z� Array API compatible wrapper for :py:func:`np.matrix_rank <numpy.matrix_rank>`. See its docstring for more information. r zA1-dimensional array given. Array must be at least two-dimensionalF�Z compute_uvNr2 T)r4 rJ r@ .r3 )r; r, r- Z LinAlgError�svdr/ �maxr9 �finfor* �eps� isinstancer �asarrayZnewaxisr0 Z count_nonzero)r( rR r% Ztolr r r � matrix_rank� s 0 "rZ c C s( | j dk rtd��t�t�| jdd��S )Nr z5x must be at least 2-dimensional for matrix_transposer2 r@ )r; r: r r0 r, Zswapaxesr/ r> r r r �matrix_transpose� s r[ c C sN | j tvs|j tvr td��| jdks0|jdkr8td��t�t�| j |j ��S )zz Array API compatible wrapper for :py:func:`np.outer <numpy.outer>`. See its docstring for more information. z(Only numeric dtypes are allowed in outerr z/The input arrays to outer must be 1-dimensional) r* r r+ r; r: r r0 r, �outerr/ rI r r r r\ � s r\ c C sR | j tvrtd��|du r:t| jdd� �t�| j �j }t� tj j | j |d��S )z� Array API compatible wrapper for :py:func:`np.linalg.pinv <numpy.linalg.pinv>`. See its docstring for more information. z.Only floating-point dtypes are allowed in pinvNr@ )Zrcond) r* r r+ rU r9 r, rV rW r r0 r- �pinvr/ )r( rR r r r r] � s r] Zreduced��modez Literal['reduced', 'complete'])r( r_ r) c C s0 | j tvrtd��tttjtjj | j |d��� S )z� Array API compatible wrapper for :py:func:`np.linalg.qr <numpy.linalg.qr>`. See its docstring for more information. z,Only floating-point dtypes are allowed in qrr^ ) r* r r+ r rD r r0 r, r- �qrr/ )r( r_ r r r r` s r` c C s, | j tvrtd��tttjtj� | j ��� S )z� Array API compatible wrapper for :py:func:`np.linalg.slogdet <numpy.linalg.slogdet>`. See its docstring for more information. z1Only floating-point dtypes are allowed in slogdet) r* r r+ r! rD r r0 r, r- �slogdetr/ r> r r r ra s ra c C s� ddl m}m}m}m}m}m}m} ddlm } || �\} } || � || � ||�\}} || |�\} } |j dkrx| j }n| j }|| �r�dnd}||�}|| |||d�}| |j | dd ��S ) Nr )� _makearray�_assert_stacked_2d�_assert_stacked_square� _commonType� isComplexType�get_linalg_error_extobj�_raise_linalgerror_singular)� _umath_linalgr zDD->Dzdd->d)� signature�extobjF)�copy)Z linalg.linalgrb rc rd re rf rg rh r- ri r; Zsolve1�solveZastype)�a�brb rc rd re rf rg rh ri �_�wrap�tZresult_tZgufuncrj rk �rr r r �_solve+ s $ rt c C s0 | j tvs|j tvr td��t�t| j|j��S )z� Array API compatible wrapper for :py:func:`np.linalg.solve <numpy.linalg.solve>`. See its docstring for more information. z/Only floating-point dtypes are allowed in solve)r* r r+ r r0 rt r/ rI r r r rm F s rm T�� full_matrices)r( rv r) c C s0 | j tvrtd��tttjtjj | j |d��� S )z� Array API compatible wrapper for :py:func:`np.linalg.svd <numpy.linalg.svd>`. See its docstring for more information. z-Only floating-point dtypes are allowed in svdru ) r* r r+ r# rD r r0 r, r- rT r/ )r( rv r r r rT S s rT z Union[Array, Tuple[Array, ...]]c C s* | j tvrtd��t�tjj| jdd��S )Nz1Only floating-point dtypes are allowed in svdvalsFrS ) r* r r+ r r0 r, r- rT r/ r> r r r �svdvalsd s rw ��axesz/Union[int, Tuple[Sequence[int], Sequence[int]]])r6 r7 ry r) c C s6 | j tvs|j tvr td��t�tj| j|j|d��S )Nz,Only numeric dtypes are allowed in tensordotrx )r* r r+ r r0 r, � tensordotr/ )r6 r7 ry r r r rz l s rz )r? r* zOptional[Dtype])r( r? r* r) c C sZ | j tvrtd��|du r8| j tkr*t}n| j tkr8t}t�t � t j | j |dd|d���S )zz Array API compatible wrapper for :py:func:`np.trace <numpy.trace>`. 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