o i(@sddlZddlZddlmZddlmZddlmZddlZddZeddd dZ ed d d dZ dddZ ddZ dddZ ddZdddZdS)N)_core)_decomposition)_utilcCs,t|||fd}|tj|dddd}|S)N)F compute_uvraxis)cupymoveaxisrsvd)xrow_axiscol_axisopyresultrO/home/ubuntu/veenaModal/venv/lib/python3.10/site-packages/cupy/linalg/_norms.py_multi_svd_norm sr _norm_ord2)z?->lzb->lzB->Lzh->lzH->Lzi->lzI->Lzl->lzL->Lzq->qzQ->Q)ze->e)NNNfloatzf->fzd->d)z in0 * in0a + bout0 = sqrt(type_out0_raw(a))N_norm_ord2_complex)zF->fzD->d)z1in0.real() * in0.real() + in0.imag() * in0.imag()rrNFcCslt|jjtjs |t}|durT|j}|dus(|dkr |dks(|dkrT|dvrT|jjdkr@t | }||9}t | }n t || }|rR|d|}|S|j}|durbtt|}nt|ts|zt|}Wn tyxtdw|f}t|dkr|tjkrt |j||dS|tj krt |j||dS|d kr|d k|jjj ||dS|dkrt |j ||dS|dus|dkr|jjdkrt|||dSt|||dSzt|Wn tytd wt |}||C}|j ||d}|t j||jd C}|St|dkr2|\} } | d kr| |7} | d kr%| |7} d | kr1|kr@nn d | kr?|ksIntd ||jf| | krRtd |dkrgtj t j!d d} t"|| | | }n|dkr|tj t j!dd} t"|| | | }n|dkr| | kr| d8} t |j | dj| d}n|tjkr| | kr| d8} t |j | dj| d}nd|dkr| | kr| d8} t |j | dj| d}nI|tj kr| | kr| d8} t |j | dj| d}n,|dvr|jjdkrt||d}nt||d}n|dkrt"|| | t j }ntd|r0t#|j} d| |d <d| |d<|| }|Std)aReturns one of matrix norms specified by ``ord`` parameter. See numpy.linalg.norm for more detail. Args: x (cupy.ndarray): Array to take norm. If ``axis`` is None, ``x`` must be 1-D or 2-D. ord (non-zero int, inf, -inf, 'fro'): Norm type. axis (int, 2-tuple of ints, None): 1-D or 2-D norm is cumputed over ``axis``. keepdims (bool): If this is set ``True``, the axes which are normed over are left. Returns: cupy.ndarray N)ffroc)rz6'axis' must be None, an integer or a tuple of integersr keepdimsrzInvalid norm order for vectors.)dtypez*Invalid axis %r for an array with shape %rzDuplicate axes given.)indicesrrr )Nrrnucz Invalid norm order for matrices.z&Improper number of dimensions to norm.)$ issubclassr#typenumpyinexactastyperndimkindabsravelr sqrtsumreshapetuplerange isinstanceint Exception TypeErrorleninfmaxminrealrr ValueError reciprocalshape functoolspartialtakerlist)rordr r"r+sretndabsxrrop_maxop_min ret_shaperrrnorms             6                rLcCst|\}}|t|S)aReturns the determinant of an array. Args: a (cupy.ndarray): The input matrix with dimension ``(..., N, N)``. Returns: cupy.ndarray: Determinant of ``a``. Its shape is ``a.shape[:-2]``. .. seealso:: :func:`numpy.linalg.det` )slogdetr exp)asignlogdetrrrdets rRcCst|jdkr|dktStj|dd}|dur0|jdddt|jd dt |j j }||kj dtj d S) aBReturn matrix rank of array using SVD method Args: M (cupy.ndarray): Input array. Its `ndim` must be less than or equal to 2. tol (None or float): Threshold of singular value of `M`. When `tol` is `None`, and `eps` is the epsilon value for datatype of `M`, then `tol` is set to `S.max() * max(M.shape) * eps`, where `S` is the singular value of `M`. It obeys :func:`numpy.linalg.matrix_rank`. Returns: cupy.ndarray: Rank of `M`. .. seealso:: :func:`numpy.linalg.matrix_rank` rrFrNrTr!r)r r#)r+anyr*r5rr r:r?r(finfor#epsr0intp)MtolSrrr matrix_ranks  rZcCsxt|t|t|\}}t|j}|j}|dd}|d}|j dkr;t ||}t ||}||fSt ||\} } } t j| ddd} t t | jdd}t j| t d|dkdd} |jdkrw| t j| dkdd7} | d dd}|jd kr|t j| t | dd}||}|j|d d }| dk}t ||d||t ||d ||fS)aReturns sign and logarithm of the determinant of an array. It calculates the natural logarithm of the determinant of a given value. Args: a (cupy.ndarray): The input matrix with dimension ``(..., N, N)``. Returns: tuple of :class:`~cupy.ndarray`: It returns a tuple ``(sign, logdet)``. ``sign`` represents each sign of the determinant as a real number ``0``, ``1`` or ``-1``. 'logdet' represents the natural logarithm of the absolute of the determinant. If the determinant is zero, ``sign`` will be ``0`` and ``logdet`` will be ``-inf``. The shapes of both ``sign`` and ``logdet`` are equal to ``a.shape[:-2]``. .. warning:: This function calls one or more cuSOLVER routine(s) which may yield invalid results if input conditions are not met. To detect these invalid results, you can set the `linalg` configuration to a value that is not `ignore` in :func:`cupyx.errstate` or :func:`cupyx.seterr`. .. warning:: To produce the same results as :func:`numpy.linalg.slogdet` for singular inputs, set the `linalg` configuration to `raise`. .. seealso:: :func:`numpy.linalg.slogdet` Nrrr)axis1axis2r rrrr F)copyz-inf)r_assert_stacked_2d_assert_stacked_squarelinalg_common_typer(r#charlowerr?sizer oneszerosr _lu_factordiagonallogr-r0 count_nonzeroaranger,prodr*wherer'r1)rOr# sign_dtype logdet_dtypea_shaper?nrPrQluipivdev_infodiagnon_zerosingularrrrrMs4        rMrcCs||||||S)aReturns the sum along the diagonals of an array. It computes the sum along the diagonals at ``axis1`` and ``axis2``. Args: a (cupy.ndarray): Array to take trace. offset (int): Index of diagonals. Zero indicates the main diagonal, a positive value an upper diagonal, and a negative value a lower diagonal. axis1 (int): The first axis along which the trace is taken. axis2 (int): The second axis along which the trace is taken. dtype: Data type specifier of the output. out (cupy.ndarray): Output array. Returns: cupy.ndarray: The trace of ``a`` along axes ``(axis1, axis2)``. .. seealso:: :func:`numpy.trace` )trace)rOoffsetr[r\r#outrrrrwsrw)NNF)N)rrrNN)r(r r cupy.linalgrrr@rcreate_reduction_funcrrrLrRrZrMrwrrrrs0     N