ó î&]\c@`sdZddlmZmZmZdZddgZddlmZddl Z ddl m Z d d lmZmZmZd d lmZmZmZd d lmZmZd d lmZmZmZmZmZmZm Z m!Z!m"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_indext check_shapetcheck_reshape_kwargscB`sveZdZdZdded„Zd„Zejje_dd„Z ej je _d„Z ded„Z ej je _d„Z ej je _ddd„Z ed „Zed „Zed „Zejje_ed „Zejje_ed „Zejje_dd„Zejje_d„Zed„Zd„Zd„Zd„Zd„Zd„Zd„ZRS(sÛ 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 -------- >>> # Constructing an empty matrix >>> 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) >>> # Constructing a matrix using ijv format >>> 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]]) >>> # Constructing a matrix with duplicate indices >>> 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 = coo_matrix((data, (row, col)), shape=(4, 4)) >>> # Duplicate indices are maintained until implicitly or explicitly summed >>> np.max(coo.data) 1 >>> coo.toarray() array([[3, 0, 1, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1]]) tcooc C`stj|ƒt|tƒrt|ƒr¾|\}}t||fƒ|_tdt||ƒƒ}t j gd|ƒ|_ t j gd|ƒ|_ t j gt |dtƒƒ|_t|_qIy|\}\} } Wn#ttfk rùtdƒ‚nX|dkrwt| ƒdks*t| ƒdkr9tdƒ‚nt j| ƒd}t j| ƒd}t||fƒ|_n!|\}}t||fƒ|_tdt|jƒƒ}t j | d|d|ƒ|_ t j | d|d|ƒ|_ t j |d|ƒ|_t|_n9t|ƒrÇt|ƒry|ry|j jƒ|_ |j jƒ|_ |jjƒ|_t|jƒ|_nB|jƒ} | j |_ | j |_ | j|_t| jƒ|_t|_n‚t jt j|ƒƒ}|jd krýtd ƒ‚nt|jƒ|_|jƒ\|_ |_ ||j |j f|_t|_|dk rs|jj |dtƒ|_n|j!ƒdS( Ntmaxvaltdtypetdefaultsinvalid input formatis4cannot infer dimensions from zero sized index arraysitcopyis'expected dimension <= 2 array or matrix("R t__init__t isinstancettupleRRt_shapeRtmaxtnptarraytrowtcolRtfloattdatatTruethas_canonical_formatt TypeErrort ValueErrortNonetlentshapetFalseR RRttocoot atleast_2dtasarraytndimtnonzerotastypet_check( tselftarg1R.RRtMtNt idx_dtypetobjR$R%R((s/lib/python2.7/site-packages/scipy/sparse/coo.pyR~sb   !  $          c O`sžt||jƒ}t|ƒ\}}||jkrJ|rC|jƒS|Sn|j\}}|dkrÔtd|td|dƒtd|dƒƒ}tj||jd|ƒ|j } t | |dƒ\} } n‡|dkrOtd|td|dƒtd|dƒƒ}tj||j d|ƒ|j} t | |dƒ\} } n t dƒ‚|rs|j jƒ} n |j } t | | | ffd|d tƒS( NtCRiiRtFs'order' must be 'C' or 'F'R.R(RR.RRRR!R"tmultiplyR$R%tdivmodR+R'RR/( R7targstkwargsR.torderRtnrowstncolsRt flat_indicestnew_rowtnew_coltnew_data((s/lib/python2.7/site-packages/scipy/sparse/coo.pytreshapeÂs*  1" 1"  cC`s*|dkr£t|jƒ}|t|jƒksE|t|jƒkrTtdƒ‚n|jjdksŠ|jjdksŠ|jjdkr™tdƒ‚nt|ƒS|dkr¼|d7}n|dkrëtj t |jƒd|j dƒS|dkrtj t |jƒd|j dƒStdƒ‚dS(Ns7row, column, and data array must all be the same lengthis(row, column, and data arrays must be 1-Diit minlengthsaxis out of bounds( R,R-R'R$R%R+R3tintR"tbincountRR.(R7taxistnnz((s/lib/python2.7/site-packages/scipy/sparse/coo.pytgetnnzës" *$     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$RtkindRtnameR%RR!R.R"R2RR'ROR+tmin(R7R;((s/lib/python2.7/site-packages/scipy/sparse/coo.pyR6s&cC`s[|dk rtdƒ‚n|j\}}t|j|j|jffd||fd|ƒS(NsoSparse matrices do not support an 'axes' parameter because swapping dimensions is the only logical permutation.R.R(R,R+R.RR'R%R$(R7taxesRR9R:((s/lib/python2.7/site-packages/scipy/sparse/coo.pyt transposes  cG`s²t|ƒ}|\}}|j\}}||ks?||kr¥tj|j|k|j|kƒ}|jƒs¥|j||_|j||_|j||_q¥n||_dS(N( RR.R"t logical_andR$R%tallR'R (R7R.tnew_Mtnew_NR9R:tmask((s/lib/python2.7/site-packages/scipy/sparse/coo.pytresize+s  $ 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_argsRLtflagst f_contiguoust c_contiguousR+R.RROR$R%R'travel(R7RCtouttBtfortranR9R:((s/lib/python2.7/site-packages/scipy/sparse/coo.pyttoarray;s!c C`sQddlm}|jdkr5||jd|jƒS|j\}}t|j|jfdt|j|ƒƒ}|jj |dt ƒ}|jj |dt ƒ}t j |dd|ƒ}t j |d|ƒ} t j |jdt|jƒƒ} t|||j|||j|| | ƒ || | |fd|jƒ} |jsI| jƒn| SdS( sMConvert this matrix to Compressed Sparse Column format Duplicate entries will be summed together. Examples -------- >>> from numpy import array >>> from scipy.sparse import coo_matrix >>> row = array([0, 0, 1, 3, 1, 0, 0]) >>> col = array([0, 2, 1, 3, 1, 0, 0]) >>> data = array([1, 1, 1, 1, 1, 1, 1]) >>> A = coo_matrix((data, (row, col)), shape=(4, 4)).tocsc() >>> A.toarray() array([[3, 0, 1, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1]]) i(t csc_matrixiRRRR.N(tcscRgROR.RRR%R$R!R5R/R"temptyt empty_likeR'RRR)tsum_duplicates( R7RRgR9R:R;R$R%tindptrtindicesR'tx((s/lib/python2.7/site-packages/scipy/sparse/coo.pyttocscFs"!   c C`sQddlm}|jdkr5||jd|jƒS|j\}}t|j|jfdt|j|ƒƒ}|jj |dt ƒ}|jj |dt ƒ}t j |dd|ƒ}t j |d|ƒ} t j |jdt|jƒƒ} t|||j|||j|| | ƒ || | |fd|jƒ} |jsI| jƒn| SdS( sJConvert this matrix to Compressed Sparse Row format Duplicate entries will be summed together. Examples -------- >>> from numpy import array >>> from scipy.sparse import coo_matrix >>> row = array([0, 0, 1, 3, 1, 0, 0]) >>> col = array([0, 2, 1, 3, 1, 0, 0]) >>> data = array([1, 1, 1, 1, 1, 1, 1]) >>> A = coo_matrix((data, (row, col)), shape=(4, 4)).tocsr() >>> A.toarray() array([[3, 0, 1, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1]]) i(t csr_matrixiRRRR.N(tcsrRpROR.RRR$R%R!R5R/R"RiRjR'RRR)Rk( R7RRpR9R:R;R$R%RlRmR'Rn((s/lib/python2.7/site-packages/scipy/sparse/coo.pyttocsrps"!   cC`s|r|jƒS|SdS(N(R(R7R((s/lib/python2.7/site-packages/scipy/sparse/coo.pyR0šs cC`sþddlm}|jƒ|j|j}tj|dtƒ\}}t|ƒdkrqt dt|ƒt ƒn|j j dkržtj d d|jƒ}nGtj t|ƒ|jjƒdfd|jƒ}|j |||jf<|||fd|jƒS( Ni(t dia_matrixtreturn_inverseids:Constructing a DIA matrix with %d diagonals is inefficientiRR.(ii(tdiaRsRkR%R$R"tuniqueR(R-RR R'tsizetzerosRR!R.(R7RRstkstdiagstdiag_idxR'((s/lib/python2.7/site-packages/scipy/sparse/coo.pyttodia¢s 1cC`s^ddlm}|jƒ||jd|jƒ}|jtt|j|jƒ|j ƒƒ|S(Ni(t dok_matrixR( tdokR}RkR.Rt_updatetizipR$R%R'(R7RR}R~((s/lib/python2.7/site-packages/scipy/sparse/coo.pyttodok¹s  (ic C`sü|j\}}|| ks(||kr7tdƒ‚ntjt|t|dƒ|t|dƒƒd|jƒ}|j||jk}|j r®|j|}|j |}n3|j |j||j||j |ƒ\}}}|||t|dƒ<|S(Nsk exceeds matrix dimensionsiR( R.R+R"RxRTR!RR$R%R)R't_sum_duplicates( R7tktrowstcolstdiagt diag_maskR$R't_((s/lib/python2.7/site-packages/scipy/sparse/coo.pytdiagonalÄs/    c C`sû|j\}}|jr)t|ƒ r)dS|jj}|j|j|k}|dkrÜt|||ƒ}|jr‹t|t|ƒƒ}ntj||j|kƒ}tj | | |d|ƒ} tj |d|ƒ} n€t|||ƒ}|jrt|t|ƒƒ}ntj||j|kƒ}tj |d|ƒ} tj |||d|ƒ} |jrr|| } ntj |d|jƒ} || (tj |j|| fƒ|_tj |j|| fƒ|_tj |j || fƒ|_ t |_dS(NiR(R.R3R-R$RR%RTR"t logical_ortarangeRit concatenateR'R/R)( R7tvaluesRƒR9R:R;t full_keept max_indextkeepRGRHRI((s/lib/python2.7/site-packages/scipy/sparse/coo.pyt_setdiagÙs4      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. R.RN(RR$RR%R.R(R7R'R((s/lib/python2.7/site-packages/scipy/sparse/coo.pyt _with_dataþs 'cC`sP|jr dS|j|j|j|jƒ}|\|_|_|_t|_dS(slEliminate duplicate matrix entries by adding them together This is an *in place* operation N(R)R‚R$R%R'R((R7tsummed((s/lib/python2.7/site-packages/scipy/sparse/coo.pyRk s  cC`sÛt|ƒdkr|||fStj||fƒ}||}||}||}|d|d k|d|d kB}tjt|ƒ}||}||}tj|ƒ\}tjj||d|jƒ}|||fS(NiiiÿÿÿÿR( R-R"tlexsorttappendR(R4taddtreduceatR(R7R$R%R'RCt unique_maskt unique_inds((s/lib/python2.7/site-packages/scipy/sparse/coo.pyR‚s      cC`sC|jdk}|j||_|j||_|j||_dS(sURemove zero entries from the matrix This is an *in place* operation iN(R'R$R%(R7R[((s/lib/python2.7/site-packages/scipy/sparse/coo.pyteliminate_zeros&sc C`s¿|j|jkr!tdƒ‚nt|jj|jjƒ}tj|d|dtƒ}t|j j ƒ}|j\}}t |||j |j |j|j|jdƒ|ƒtj|dtƒS(NsIncompatible shapes.RRR](R.R+RRtcharR"R#R(RLR_R`RROR$R%R'RbtmatrixR/(R7totherRtresultReR9R:((s/lib/python2.7/site-packages/scipy/sparse/coo.pyt _add_dense4s!cC`sZtj|jddt|jj|jjƒƒ}t|j|j|j |j ||ƒ|S(NiR( R"RxR.RRR›R ROR$R%R'(R7RRž((s/lib/python2.7/site-packages/scipy/sparse/coo.pyt _mul_vector?s%c C`s tj|jd|jdfdt|jj|jjƒƒ}xFt|jƒD]5\}}t|j |j |j |j |||ƒqNW|jj dt|ƒƒS(NiiRttype(R"RxR.RRR›t enumeratetTR ROR$R%R'tviewR¡(R7RRžRQR%((s/lib/python2.7/site-packages/scipy/sparse/coo.pyt_mul_multivectorFs  -N(t__name__t __module__t__doc__tformatR,R/RRJR RPR6RVR\RfRoRrR0R|RR‰R R‘R(R’RkR‚RšRŸR R¥(((s/lib/python2.7/site-packages/scipy/sparse/coo.pyRs>eD '     * *     %   cC`s t|tƒS(sÍIs x of coo_matrix type? Parameters ---------- x object to check for being a coo matrix Returns ------- bool True if x is a coo matrix, False otherwise Examples -------- >>> from scipy.sparse import coo_matrix, isspmatrix_coo >>> isspmatrix_coo(coo_matrix([[5]])) True >>> from scipy.sparse import coo_matrix, csr_matrix, isspmatrix_coo >>> isspmatrix_coo(csr_matrix([[5]])) False (RR(Rn((s/lib/python2.7/site-packages/scipy/sparse/coo.pyRNs(%R¨t __future__RRRt __docformat__t__all__twarningsRtnumpyR"tscipy._lib.sixRR€t _sparsetoolsRRR tbaseR R R R'R RtsputilsRRRRRRRRRRR(((s/lib/python2.7/site-packages/scipy/sparse/coo.pyts  @ÿÿ: