o i^@sddlZddlZddlZddlmZddlmZddZddZddZ d d Z d d Z d dZ dddZ ddZdddZ   dddZdS)N)linalgcCs(tj|}tt|rtjj|S)zk Wrapper around `cupy.linalg.cholesky` that raises LinAlgError if there are NaNs in the output )cupyrcholeskyanyisnannumpy LinAlgError)BRr ^/home/ubuntu/veenaModal/venv/lib/python3.10/site-packages/cupyx/scipy/sparse/linalg/_lobpcg.py _cholesky s r cCsTt|}t|d}ddg}t|D]}|d||djd7<qt|D]}|d|d|jd7<q(tjdd|D}tdd|D}tdd|D}|r\|s\dnd } tjt||| d } d} d} d} d}t|D]3}| ||djd} d} t|D]}| |||jd}|||| | | | |f<|} q| } qt| S) ze Helper function to create a block matrix in cupy from a list of smaller 2D dense arrays rcSsg|] }|D]}|jqqSr dtype.0 list_iterarrr r r %s  z_bmat..cs$|] }|D]}|jdVqqdS) F_CONTIGUOUSNflagsrr r r ( z_bmat..csr) C_CONTIGUOUSNrrr r r r*rFC)rorder)lenrangeshaper result_typeallemptytuple)list_objn_rowsn_cols final_shapeijrF_orderC_orderrresult start_idx_row start_idx_col end_idx_row end_idx_colr r r _bmatsD         r4c Cs||j}t|d}dt|jj}|tdt t|d9}||kr?t j d|d|jd|d|d t dd d Sd S) zA Report if `M` is not a hermitian matrix given its type. r zMatrix z of the type z is not Hermitian: condition: z < z fails.) stacklevelN) Tconjrnormrfinforepsmaxfloatwarningswarn UserWarning)Mnamemdnmdtolr r r _report_nonhermitian?s  rGcCs0|jdkr|Stj|dd}|jddf|_|S)zm If the input array is 2D return it, if it is 1D, append a dimension, making it a column vector. F)copyrr)ndimrarrayr")arauxr r r _as2dPs rNcCs,|durdSt|}|j|krtd|S)zTakes a dense numpy array or a sparse matrix or a function and makes an operator performing matrix * blockvector products. Nzoperator has invalid shape)splinalgaslinearoperatorr" ValueError) operatorInput expectedShapeoperatorr r r _makeOperator]s   rUcCs2t|j|}t||}|t||8}dS)zChanges blockVectorV in place.N)rdotr8r9rsolve) blockVectorVYBY blockVectorBY blockVectorYYBVtmpr r r _applyConstraintsms r^FcCs|jddt|jj}||}|dur!|dur||}n|}n||}t|j|}zt|}t |j}t||}|durJt||}nd}Wnt j j y^d}d}d}Ynw|rg||||fS||fS)z7B-orthonormalize the given block vector using Cholesky.r)axisN) r=rr;rr<matmulr8r9r rinvrr)r rX blockVectorBVretInvR normalizationVBVr r r _b_orthonormalizevs8     rfcCs6t|}|r|d| dd}|S|d|}|S)z?Get `num` indices into `_lambda` depending on `largest` option.Nr)rargsort)_lambdanumlargestiir r r _get_indxs  rmc Csr|durt|\}}||fSt|}t|}t|j}t|t||}t|\}}t||}||fS)z Helper function for converting a generalized eigenvalue problem A(X) = lambda(B(X)) to standard eigen value problem using cholesky transformation N)reighr rar8rr`) Ar valsvecsr RTiRireigVecr r r _eighs   ruTc Ks |} |} |} |dur d}| dur| jd}nd}t| jdkr#td| j\}}rsd}|dur5|d7}n|d 7}|d 7}|durE|d 7}|d 7}|d |7}|d|7}| dur^|d7}n|dkri|d|7}n|d|7}t|t|||f}t|||f}t|||f}||d|krt||}| durtd|tj||j d}|durdn |tj||j d}t ||\}}|r|ddd}|dddddf}|d|}|ddd|f}||fS| dus| dkrt d|} | dur|dur|| }n| }t | j |}t| ||| t|| \} }|| }t | j |}t |\}}t|||}||}t|dd|f}t | |} t ||}|dur\t ||}tj|ftd}|g}g} |}!tj||j d}"tj||j d}#d}$d}%d}&d}'d}(d})|'|krx|'d7}'|dur||tjddf}n | |tjddf}||}*t|*|*d}t |}+| |+t|+| kdd}||@}t|},|,|!kr|,}!tj|,|j d}"|,dkrndkr td|'td|,td|td|+dkrt|t|*dd|f}-|'dkrHt|$dd|f}.t|%dd|f}/|durHt|&dd|f}0|durQ||-}-| dur]t|-||| |durr|-t| t|j |-}-n|-t| t| j |-}-t||-}|\}-}1||-}2|'dkr|durt||.|0dd}|\}.}0}3}4n t||.dd}|\}.}5}3}4|.dur|/|4}/t |/|3}/d}(nd}(|2j d krd}6n |-j d krd!}6nd"}6|+|6kr|)sd})nd})|dur| }|-}1|(s|.}0t | j |2}7t |-j |2}8|)rE|8|8j d}8t | j |}||j d}t | j |}9t |-j |1}:t | j |1};nt|}|#}9|"}:tjt|t|,f|j d};fd#d$}<|(st | j |/}=t |-j |/}>t |.j |/}?t | j |0}@t |-j |0}A|)r|?|?j d}?t |.j |0}Bn|"}Bt||7|=g|7j |8|>g|=j |>j |?gg}Ct|9|;|@g|;j |:|Ag|@j |Aj |Bgg}D|<|C|Dz t |C|D\}}Wnt j!j"yd}(Ynw|(r3t||7g|7j |8gg}Ct|9|;g|;j |:gg}D|<|C|Dz t |C|D\}}Wnt j!j"y2td%wt|||}dkrFt|t|||}|dd|f}||dkratd&|dkrjt||dur|(s|d|}E||||,}F|||,d}Gt |-|F}H|Ht |.|G7}Ht |2|F}I|It |/|G7}It |1|F}J|Jt |0|G7}Jn|d|}E||d}Ft |-|F}Ht |2|F}It |1|F}Jdkrt|Ht|It|Jt | |E|H} t ||E|I}t ||E|J}|H|I|J}$}%}&np|(s9|d|}E||||,}F|||,d}Gt |-|F}H|Ht |.|G7}Ht |2|F}I|It |/|G7}In|d|}E||d}Ft |-|F}Ht |2|F}Idkr^t|Ht|It | |E|H} t ||E|I}|H|I}$}%|'|ks|dur||tjddf}n | |tjddf}||}*t|*|*d}t |}+dkrtd'|td(|+dkrtd)|td*|+| r| r|| || fS|| |fS| r|| | fS|| fS)+a Locally Optimal Block Preconditioned Conjugate Gradient Method (LOBPCG) LOBPCG is a preconditioned eigensolver for large symmetric positive definite (SPD) generalized eigenproblems. Args: A (array-like): The symmetric linear operator of the problem, usually a sparse matrix. Can be of the following types - cupy.ndarray - cupyx.scipy.sparse.csr_matrix - cupy.scipy.sparse.linalg.LinearOperator X (cupy.ndarray): Initial approximation to the ``k`` eigenvectors (non-sparse). If `A` has ``shape=(n,n)`` then `X` should have shape ``shape=(n,k)``. B (array-like): The right hand side operator in a generalized eigenproblem. By default, ``B = Identity``. Can be of following types: - cupy.ndarray - cupyx.scipy.sparse.csr_matrix - cupy.scipy.sparse.linalg.LinearOperator M (array-like): Preconditioner to `A`; by default ``M = Identity``. `M` should approximate the inverse of `A`. Can be of the following types: - cupy.ndarray - cupyx.scipy.sparse.csr_matrix - cupy.scipy.sparse.linalg.LinearOperator Y (cupy.ndarray): `n-by-sizeY` matrix of constraints (non-sparse), `sizeY < n` The iterations will be performed in the B-orthogonal complement of the column-space of Y. Y must be full rank. tol (float): Solver tolerance (stopping criterion). The default is ``tol=n*sqrt(eps)``. maxiter (int): Maximum number of iterations. The default is ``maxiter = 20``. largest (bool): When True, solve for the largest eigenvalues, otherwise the smallest. verbosityLevel (int): Controls solver output. The default is ``verbosityLevel=0``. retLambdaHistory (bool): Whether to return eigenvalue history. Default is False. retResidualNormsHistory (bool): Whether to return history of residual norms. Default is False. Returns: tuple: - `w` (cupy.ndarray): Array of ``k`` eigenvalues - `v` (cupy.ndarray) An array of ``k`` eigenvectors. `v` has the same shape as `X`. - `lambdas` (list of cupy.ndarray): The eigenvalue history, if `retLambdaHistory` is True. - `rnorms` (list of cupy.ndarray): The history of residual norms, if `retResidualNormsHistory` is True. .. seealso:: :func:`scipy.sparse.linalg.lobpcg` .. note:: If both ``retLambdaHistory`` and ``retResidualNormsHistory`` are `True` the return tuple has the following format ``(lambda, V, lambda history, residual norms history)``. 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