ó ʽ÷Xc@`sdZddlmZmZmZdZddgZddlmZddl Z ddl m Z d d lmZmZmZd d lmZmZmZd d lmZmZd d lmZmZmZmZmZmZm Z deefd„ƒYZ!d„Z"dS(s2 A sparse matrix in COOrdinate or 'triplet' formati(tdivisiontprint_functiontabsolute_importsrestructuredtext ent coo_matrixtisspmatrix_coo(twarnN(tzipi(t coo_tocsrt coo_todenset coo_matvec(t isspmatrixtSparseEfficiencyWarningtspmatrix(t _data_matrixt _minmax_mixin(tupcastt upcast_chart to_nativetisshapetgetdtypetget_index_dtypetdowncast_intp_indexcB`s:eZdZdZdded„Zdd„Zejje_d„Z ded„Z ej je _ddd„Z ed„Z ed„Z ed „Zejje_ed „Zejje_ed „Zejje_d „Zejje_d „Zed„Zd„Zd„Zd„Zd„Zd„ZRS(sç A sparse matrix in COOrdinate format. Also known as the 'ijv' or 'triplet' format. This can be instantiated in several ways: coo_matrix(D) with a dense matrix D coo_matrix(S) with another sparse matrix S (equivalent to S.tocoo()) coo_matrix((M, N), [dtype]) to construct an empty matrix with shape (M, N) dtype is optional, defaulting to dtype='d'. coo_matrix((data, (i, j)), [shape=(M, N)]) to construct from three arrays: 1. data[:] the entries of the matrix, in any order 2. i[:] the row indices of the matrix entries 3. j[:] the column indices of the matrix entries Where ``A[i[k], j[k]] = data[k]``. When shape is not specified, it is inferred from the index arrays Attributes ---------- dtype : dtype Data type of the matrix shape : 2-tuple Shape of the matrix ndim : int Number of dimensions (this is always 2) nnz Number of nonzero elements data COO format data array of the matrix row COO format row index array of the matrix col COO format column index array of the matrix Notes ----- Sparse matrices can be used in arithmetic operations: they support addition, subtraction, multiplication, division, and matrix power. Advantages of the COO format - facilitates fast conversion among sparse formats - permits duplicate entries (see example) - very fast conversion to and from CSR/CSC formats Disadvantages of the COO format - does not directly support: + arithmetic operations + slicing Intended Usage - COO is a fast format for constructing sparse matrices - Once a matrix has been constructed, convert to CSR or CSC format for fast arithmetic and matrix vector operations - By default when converting to CSR or CSC format, duplicate (i,j) entries will be summed together. This facilitates efficient construction of finite element matrices and the like. (see example) Examples -------- >>> from scipy.sparse import coo_matrix >>> coo_matrix((3, 4), dtype=np.int8).toarray() array([[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]], dtype=int8) >>> row = np.array([0, 3, 1, 0]) >>> col = np.array([0, 3, 1, 2]) >>> data = np.array([4, 5, 7, 9]) >>> coo_matrix((data, (row, col)), shape=(4, 4)).toarray() array([[4, 0, 9, 0], [0, 7, 0, 0], [0, 0, 0, 0], [0, 0, 0, 5]]) >>> # example with duplicates >>> row = np.array([0, 0, 1, 3, 1, 0, 0]) >>> col = np.array([0, 2, 1, 3, 1, 0, 0]) >>> data = np.array([1, 1, 1, 1, 1, 1, 1]) >>> coo_matrix((data, (row, col)), shape=(4, 4)).toarray() array([[3, 0, 1, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1]]) tcooc C`s]tj|ƒt|tƒrþt|ƒr¸|\}}||f|_tdt||ƒƒ}tj gd|ƒ|_ tj gd|ƒ|_ tj gt |dt ƒƒ|_t|_q%y|\}\} } Wn#ttfk rótdƒ‚nX|dkrkt| ƒdks$t| ƒdkr3tdƒ‚ntj| ƒd}tj| ƒd}||f|_n|\}}||f|_tdt|jƒƒ}tj | d|d|ƒ|_ tj | d|d|ƒ|_ tj |d|ƒ|_t|_n't|ƒr©t|ƒra|ra|j jƒ|_ |j jƒ|_ |jjƒ|_|j|_n<|jƒ} | j |_ | j |_ | j|_| j|_t|_n|tjtj|ƒƒ}|jd krßtd ƒ‚n |j|_|jƒ\|_ |_ ||j |j f|_t|_|dk rO|jj|dtƒ|_n|jƒdS( Ntmaxvaltdtypetdefaultsinvalid input formatis4cannot infer dimensions from zero sized index arraysitcopyis'expected dimension <= 2 array or matrix( R t__init__t isinstancettupleRtshapeRtmaxtnptarraytrowtcolRtfloattdatatTruethas_canonical_formatt TypeErrort ValueErrortNonetlentFalseR RRttocoot atleast_2dtasarraytndimtnonzerotastypet_check( tselftarg1RRRtMtNt idx_dtypetobjR"R#R((s//tmp/pip-build-7oUkmx/scipy/scipy/sparse/coo.pyRvsb   !  $            cC`s*|dkr£t|jƒ}|t|jƒksE|t|jƒkrTtdƒ‚n|jjdksŠ|jjdksŠ|jjdkr™tdƒ‚nt|ƒS|dkr¼|d7}n|dkrëtj t |jƒd|j dƒS|dkrtj t |jƒd|j dƒStdƒ‚dS(Ns7row, column, and data array must all be the same lengthis(row, column, and data arrays must be 1-Diit minlengthsaxis out of bounds( R*R+R%R"R#R)R0tintR tbincountRR(R4taxistnnz((s//tmp/pip-build-7oUkmx/scipy/scipy/sparse/coo.pytgetnnzºs" *$     cC`sr|jjjdkr/td|jjjƒn|jjjdkr^td|jjjƒntdt|jƒƒ}t j |jd|ƒ|_t j |jd|ƒ|_t |j ƒ|_ |j dkrn|jjƒ|jdkrøtdƒ‚n|jjƒ|jdkr#td ƒ‚n|jjƒdkrGtd ƒ‚n|jjƒdkrntd ƒ‚qnnd S( s' Checks data structure for consistency tis,row index array has non-integer dtype (%s) s+col index array has non-integer dtype (%s) RRis#row index exceeds matrix dimensionsis&column index exceeds matrix dimensionssnegative row index foundsnegative column index foundN(R"RtkindRtnameR#RRRR R/RR%R>R)tmin(R4R8((s//tmp/pip-build-7oUkmx/scipy/scipy/sparse/coo.pyR3Ôs&cC`s[|dk rtdƒ‚n|j\}}t|j|j|jffd||fd|ƒS(NsoSparse matrices do not support an 'axes' parameter because swapping dimensions is the only logical permutation.RR(R*R)RRR%R#R"(R4taxesRR6R7((s//tmp/pip-build-7oUkmx/scipy/scipy/sparse/coo.pyt transposeîs  c C`sŽ|j||ƒ}t|jjƒ}| rG|jj rGtdƒ‚n|j\}}t|||j|j |j |j |j dƒ|ƒ|S(s)See the docstring for `spmatrix.toarray`.s&Output array must be C or F contiguoustA( t_process_toarray_argsR;tflagst f_contiguoust c_contiguousR)RRR>R"R#R%travel(R4tordertouttBtfortranR6R7((s//tmp/pip-build-7oUkmx/scipy/scipy/sparse/coo.pyttoarrayús!c C`s?ddlm}|jdkr5||jd|jƒS|j\}}|jƒt|j|jfdt |j|ƒƒ}|jj |dt ƒ}|jj |dt ƒ}t j |dd|ƒ}t j|d|ƒ} t j|jdt|jƒƒ} t|||j|||j|| | ƒ || | |fd|jƒSdS( sMConvert this matrix to Compressed Sparse Column format Duplicate entries will be summed together. Examples -------- >>> from numpy import array >>> from scipy.sparse import coo_matrix >>> row = array([0, 0, 1, 3, 1, 0, 0]) >>> col = array([0, 2, 1, 3, 1, 0, 0]) >>> data = array([1, 1, 1, 1, 1, 1, 1]) >>> A = coo_matrix((data, (row, col)), shape=(4, 4)).tocsc() >>> A.toarray() array([[3, 0, 1, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1]]) i(t csc_matrixiRRRRN(tcscRQR>RRtsum_duplicatesRR#R"RR2R,R temptyt empty_likeR%RR( R4RRQR6R7R8R"R#tindptrtindicesR%((s//tmp/pip-build-7oUkmx/scipy/scipy/sparse/coo.pyttocscs ! c C`s?ddlm}|jdkr5||jd|jƒS|j\}}|jƒt|j|jfdt |j|ƒƒ}|jj |dt ƒ}|jj |dt ƒ}t j |dd|ƒ}t j|d|ƒ} t j|jdt|jƒƒ} t|||j|||j|| | ƒ || | |fd|jƒSdS( sJConvert this matrix to Compressed Sparse Row format Duplicate entries will be summed together. Examples -------- >>> from numpy import array >>> from scipy.sparse import coo_matrix >>> row = array([0, 0, 1, 3, 1, 0, 0]) >>> col = array([0, 2, 1, 3, 1, 0, 0]) >>> data = array([1, 1, 1, 1, 1, 1, 1]) >>> A = coo_matrix((data, (row, col)), shape=(4, 4)).tocsr() >>> A.toarray() array([[3, 0, 1, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1]]) i(t csr_matrixiRRRRN(tcsrRYR>RRRSRR"R#RR2R,R RTRUR%RR( R4RRYR6R7R8R"R#RVRWR%((s//tmp/pip-build-7oUkmx/scipy/scipy/sparse/coo.pyttocsr-s ! cC`s|r|jƒS|SdS(N(R(R4R((s//tmp/pip-build-7oUkmx/scipy/scipy/sparse/coo.pyR-Us cC`sþddlm}|jƒ|j|j}tj|dtƒ\}}t|ƒdkrqt dt|ƒt ƒn|j j dkržtj d d|jƒ}nGtj t|ƒ|jjƒdfd|jƒ}|j |||jf<|||fd|jƒS( Ni(t dia_matrixtreturn_inverseids:Constructing a DIA matrix with %d diagonals is inefficientiRR(ii(tdiaR\RSR#R"R tuniqueR&R+RR R%tsizetzerosRRR(R4RR\tkstdiagstdiag_idxR%((s//tmp/pip-build-7oUkmx/scipy/scipy/sparse/coo.pyttodia]s 1cC`s^ddlm}|jƒ||jd|jƒ}|jtt|j|jƒ|j ƒƒ|S(Ni(t dok_matrixR( tdokRfRSRRtupdatetizipR"R#R%(R4RRfRg((s//tmp/pip-build-7oUkmx/scipy/scipy/sparse/coo.pyttodokts  (cC`sštjt|jƒd|jƒ}|j|jk}|jrY|j|}|j|}n3|j |j||j||j|ƒ\}}}|||<|S(NR( R RaRCRRR"R#R'R%t_sum_duplicates(R4tdiagt diag_maskR"R%t_((s//tmp/pip-build-7oUkmx/scipy/scipy/sparse/coo.pytdiagonals!    c C`sû|j\}}|jr)t|ƒ r)dS|jj}|j|j|k}|dkrÜt|||ƒ}|jr‹t|t|ƒƒ}ntj||j|kƒ}tj | | |d|ƒ} tj |d|ƒ} n€t|||ƒ}|jrt|t|ƒƒ}ntj||j|kƒ}tj |d|ƒ} tj |||d|ƒ} |jrr|| } ntj |d|jƒ} || (tj |j|| fƒ|_tj |j|| fƒ|_tj |j || fƒ|_ t |_dS(NiR(RR0R+R"RR#RCR t logical_ortarangeRTt concatenateR%R,R'( R4tvaluestkR6R7R8t full_keept max_indextkeeptnew_rowtnew_coltnew_data((s//tmp/pip-build-7oUkmx/scipy/scipy/sparse/coo.pyt_setdiags4      cC`sr|r@t||jjƒ|jjƒffd|jd|jƒSt||j|jffd|jd|jƒSdS(sªReturns a matrix with the same sparsity structure as self, but with different data. By default the index arrays (i.e. .row and .col) are copied. RRN(RR"RR#RR(R4R%R((s//tmp/pip-build-7oUkmx/scipy/scipy/sparse/coo.pyt _with_dataµs 'cC`sP|jr dS|j|j|j|jƒ}|\|_|_|_t|_dS(slEliminate duplicate matrix entries by adding them together This is an *in place* operation N(R'RkR"R#R%R&(R4tsummed((s//tmp/pip-build-7oUkmx/scipy/scipy/sparse/coo.pyRSÁs  cC`sÛt|ƒdkr|||fStj||fƒ}||}||}||}|d|d k|d|d kB}tjt|ƒ}||}||}tj|ƒ\}tjj||d|jƒ}|||fS(NiiiÿÿÿÿR( R+R tlexsorttappendR&R1taddtreduceatR(R4R"R#R%RLt unique_maskt unique_inds((s//tmp/pip-build-7oUkmx/scipy/scipy/sparse/coo.pyRkÌs      cC`sC|jdk}|j||_|j||_|j||_dS(sURemove zero entries from the matrix This is an *in place* operation iN(R%R"R#(R4tmask((s//tmp/pip-build-7oUkmx/scipy/scipy/sparse/coo.pyteliminate_zerosÝscC`sZtj|jddt|jj|jjƒƒ}t|j|j|j |j ||ƒ|S(NiR( R RaRRRtcharR R>R"R#R%(R4tothertresult((s//tmp/pip-build-7oUkmx/scipy/scipy/sparse/coo.pyt _mul_vectorës%c C`s tj|jd|jdfdt|jj|jjƒƒ}xFt|jƒD]5\}}t|j |j |j |j |||ƒqNW|jj dt|ƒƒS(NiiRttype(R RaRRRR†t enumeratetTR R>R"R#R%tviewRŠ(R4R‡RˆR@R#((s//tmp/pip-build-7oUkmx/scipy/scipy/sparse/coo.pyt_mul_multivectoròs  -N(t__name__t __module__t__doc__tformatR*R,RR?R R3RERPRXR[R-ReRjRoR R{R&R|RSRkR…R‰RŽ(((s//tmp/pip-build-7oUkmx/scipy/scipy/sparse/coo.pyRs4^D    ( (     %   cC`s t|tƒS(N(RR(tx((s//tmp/pip-build-7oUkmx/scipy/scipy/sparse/coo.pyRús(#R‘t __future__RRRt __docformat__t__all__twarningsRtnumpyR tscipy._lib.sixRRit _sparsetoolsRRR tbaseR R R R%R RtsputilsRRRRRRRRR(((s//tmp/pip-build-7oUkmx/scipy/scipy/sparse/coo.pyts  4ÿæ