U !?h@* @sddlZddlZddlmZeddddddZeddddd d Zeddddd d ZGd dde Z dddddddddddddg e dddfddZ dS)N)njitzDi8(i8, f8[:], i8[:], i8[:], f8[:], i8[:], i8[:], f8, f8, i8, f8, b1)T)cacheZnogilc !Csd} d} t|tj}t|tj}t|tjd}t|tj}t|tj}t|tj}t|tj}t||tj}t|D]p}t||||dD]T}||}||kr||||7<|d||<||kr||t||7<qqt|D]}t||||dD]\}||}||}|dkr||kr|||7<||sd||<||| <| d7} q||}|dkrF||}||d}||}||}|d7}||kr>|||<||}||||<|||<t||D]L}||}||}||||8<||sd||<||| <| d7} q|}q||dkrZdS| d| | krrdSt ||||<|||| <||| <| d7} | ||<t |d| D]}||||}| r||||8<| ||} t||krFt||| krF| s.||||8<||| <||| <| d7} d||<d||<qd} | ||d<||d||dkr|||d}||||<|||<q| S) z :cite:`jones1995improved` might be slightly interesting for the general idea to use linked list to keep track of the sparse matrix values. But instead of pointers, we have to use indices here, since this is Python and not C. rTNF) npzerosint64float64Zbool_emptyfullrangeabssqrtsort)!nZAvZArZApLvLrLpdiscard_thresholdshiftmax_nnzrelative_discard_thresholddiag_keep_discardednnzZc_nstlarbcdjidxiL_ijkZk0Zk1Zk2ZL_jkZL_ikrelr*P/var/www/html/venv/lib/python3.8/site-packages/pymatting/preconditioner/ichol.py_ichols                  r,z$void(f8[:], i8[:], i8[:], f8[:], i8)c Cszt|D]l}||}||}|||}|||<t||d||dD](}||} ||} || | |8<qJqdS)Nrr) dataindicesindptrxrr$r(ZL_jjtempr&r'r*r*r+_backsub_L_csc_inplacets  r3c Cs~t|dddD]h}||}t||d||dD]$}||}||} || ||8}q6||}||} || ||<qdS)Nrrr-) r.r/r0r1rr&rr(r$ZL_jiZL_iir*r*r+_backsub_LT_csc_inplacesr4c@s,eZdZdZddZeddZddZdS) CholeskyDecompositionaHCholesky Decomposition Calling this object applies the preconditioner to a vector by forward and back substitution. Parameters ---------- Ltuple: tuple of numpy.ndarrays Tuple of array describing values, row indices and row pointers for Cholesky factor in the compressed sparse column format (csc) cCs ||_dSN)Ltuple)selfr7r*r*r+__init__szCholeskyDecomposition.__init__cCs,|j\}}}t|d}tj|j||fS)zReturns the Cholesky factor Returns ------- L: scipy.sparse.csc_matrix Cholesky factor r)r7lenscipysparse csc_matrix)r8rrrrr*r*r+Ls  zCholeskyDecomposition.LcCs@|j\}}}t|}|}t|||||t||||||Sr6)r7r:copyr3r4)r8r!rrrrr1r*r*r+__call__s  zCholeskyDecomposition.__call__N)__name__ __module__ __qualname____doc__r9propertyr>r@r*r*r*r+r5s   r5g-C6?rgMbP?g{Gz?g?g?g?g$@dg@@g@gj@geͭAc CsXt|tjjr|j}t|tjjs*td|js8||j \}}||ksNt t j |t j d}t j |t jd} t j|dt jd} |D]} t||j|jt j|jt j|| | || ||| } | dkrq | dkrtdtdtd|td | td td | d krtd q| dkr2td|d| }| d| } t|| | fS)aQImplements the thresholded incomplete Cholesky decomposition. For reference, a dense ichol implementation with relative threshold would look like this: L = np.tril(A) for j in range(n): col = L[j:, j] col -= np.sum(L[j, :j] * L[j:, :j], axis=1) discard_mask = abs(col[1:]) < relative_discard_threshold * np.sum(np.abs(A[j:, j])) col[1:][discard_mask] = 0 col[0] **= 0.5 col[1:] /= col[0] Parameters ---------- A: scipy.sparse.csc_matrix Matrix for which the preconditioner should be calculated discard_threshold: float Values having an absolute value smaller than this threshold will be discarded while calculating the Cholesky decompositions shifts: array of floats Values to try for regularizing the matrix of interest in case it is not positive definite after discarding the small values max_nnz: int Maximum number of non-zero entries in the Cholesky decomposition. Defaults to 250 million, which should usually be around 4 GB. relative_discard_threshold: float Values with an absolute value of less than :code:`relative_discard_threshold * sum(abs(A[j:, j]))` will be discarded. diag_keep_discarded: bool Whether to update the diagonal with the discarded values. Usually better if :code:`True`. Returns ------- chol: CholeskyDecomposition Preconditioner or solver object. Raises ------ ValueError: If inappropriate parameter values were passed Example ------- >>> from pymatting import * >>> import numpy as np >>> from scipy.sparse import csc_matrix >>> A = np.array([[2.0, 3.0], [3.0, 5.0]]) >>> cholesky_decomposition = ichol(csc_matrix(A)) >>> cholesky_decomposition(np.array([1.0, 2.0])) array([-1., 1.]) z*Matrix A must be a scipy.sparse.csc_matrix)ZdtyperrrzPERFORMANCE WARNING:z{Thresholded incomplete Cholesky decomposition failed due to insufficient positive-definiteness of matrix A with parameters:z discard_threshold = %ez shift = %ez=Try decreasing discard_threshold or start with a larger shiftrzThresholded incomplete Cholesky decomposition failed because more than max_nnz non-zero elements were created. Try increasing max_nnz or discard_threshold.zThresholded incomplete Cholesky decomposition failed due to insufficient positive-definiteness of matrix A and diagonal shifts did not help.N) isinstancer;r<Z csr_matrixTr= ValueErrorZhas_canonical_formatZsum_duplicatesshapeAssertionErrorrr r r r r,r.r/Zastyper0printr5) ArZshiftsrrrmrrrrrrr*r*r+icholsf8          rP) numpyrZ scipy.sparser;Znumbarr,r3r4objectr5intrPr*r*r*r+s&  i    &