B &]\@sdZddlmZmZmZgZddlmZddlZddl Z ddl m Z ddlmZddlmZmZmZdd lmZmZdd lmZdd lmZdd lmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'Gd ddeee#Z(dS)z>Base class for sparse matrix formats using compressed storage.)divisionprint_functionabsolute_import)warnN)zip) _prune_array)spmatrix isspmatrixSparseEfficiencyWarning) _data_matrix _minmax_mixin) dia_matrix) _sparsetools) upcast upcast_char to_nativeisdenseisshapegetdtype isscalarlike IndexMixinget_index_dtypedowncast_intp_index get_sum_dtype check_shapec@s eZdZdZdgddZdhddZejje_didd Zdjd d Zd dZ ddZ ddZ ddZ ddZ ddZddZddZddZdd Zd!d"Zd#d$Zd%d&Zd'd(Zd)d*Zdkd,d-Zejje_d.d/Zd0d1Zejje_d2d3Zejje_dld4d5Zejje_dmd6d7Zd8d9Zd:d;Zdd?Z!d@dAZ"dBdCZ#dDdEZ$dFdGZ%dndHdIZ&ej&je&_dodJdKZ'ej'je'_dLdMZ(dNdOZ)dPdQZ*e+e)e*dRZ,dSdTZ-dUdVZ.dWdXZ/e+e.e/dRZ0dYdZZ1d[d\Z2d]d^Z3d_d`Z4ej4je4_dpdadbZ5dcddZ6dedfZ7dS)q _cs_matrixzAbase matrix class for compressed row and column oriented matricesNFcCst|t|rF|j|jkr,|r,|}n ||j}||nt|trt |rt ||_ |j \}}t t||d}tdt|td|_td||_tj|||fdd|d|_nt|dkrddlm}||||d} || nt|d krt|\} } } d} |dk r*t|} t | | f| d d }tj| ||d |_tj| ||d |_tj| ||d |_ntd |jnZyt|}Wn&tk rtd |jYnXddlm}|||||d|dk rt ||_ n`|j dkrVy t|jd}|jd}Wntk r@tdYnXt |||f|_ |dk rrtj|j|d|_|jdddS)N)maxvalr)defaultr)dtype) coo_matrix)shapeT)rZcheck_contents)copyrz(unrecognized {}_matrix constructor usagez!unable to infer matrix dimensionsF) full_check) r __init__r formatr$asformat _set_self isinstancetuplerr_shaper"rmaxnpzerosrfloatdataindices_swapindptrlencoor! __class__array ValueErrorasarray Exception check_format)selfZarg1r"rr$MN idx_dtyper!otherr1r2r4r major_dim minor_dimrD6lib/python3.7/site-packages/scipy/sparse/compressed.pyr&sj                    z_cs_matrix.__init__cCs|dkrt|jdS|dkr&|d7}||d|f\}}||j\}}|dkrhtjt|j|dS|dkr|t|jSt ddS)Nrr r)Z minlengthzaxis out of bounds) intr4r3r"r.Zbincountrr2diffr9)r=axis_r?rDrDrEgetnnzis  z_cs_matrix.getnnzcCs4|r |}|j|_|j|_|j|_t|j|_dS)z:take the member variables of other and assign them to selfN)r$r1r2r4rr"r,)r=rAr$rDrDrEr)zs z_cs_matrix._set_selfTcCs|d\}}||j\}}|jjjdkrDtd|jjjdd|jjjdkrjtd|jjjddt |j|jf}t j |j|d|_t j |j|d|_t |j |_ x.|j j|jj|jjgD]}|dkrtd qWt|j|dkrtd t|j|d|jd d kr td t|jt|j kr>td |jdt|jkr\td||r|jd kr|j|krtd|||jd krtd|t |jd krtddS)zcheck whether the matrix format is valid Parameters ---------- full_check : bool, optional If `True`, rigorous check, O(N) operations. Otherwise basic check, O(1) operations (default True). )rowcolumniz'indptr array has non-integer dtype ({})r#) stacklevelz(indices array has non-integer dtype ({}))rrz'data, indices, and indptr should be 1-Dz&index pointer size ({}) should be ({})rz!index pointer should start with 0z*indices and data should have the same sizerFzQLast value of index pointer should be less than the size of index and data arraysz{} index values must be < {}z{} index values must be >= 0z8index pointer values must form a non-decreasing sequenceN)r3r"r4rkindrr'namer2rr.r:rr1ndimr9r5prunennzr-minrH)r=r%Z major_nameZ minor_namerBrCr@xrDrDrEr<sF     z_cs_matrix.check_formatcCs*||j||j|dd}||S)zScalar version of self._binopt, for cases in which no new nonzeros are added. Produces a new spmatrix in canonical form. T)r$)sum_duplicates _with_datar1eliminate_zeros)r=rAopresrDrDrE_scalar_binoptsz_cs_matrix._scalar_binoptcCst|rxt|r$|j|jtjdS|dkrhtdtdd|tj|jtjd}| |t j }||S| |t j Snt |r||kSt|rtdtdd|j|jkrdS|j|jkr||j}||d}|tj|jtjd}||SdSdS) N)rrzOComparing a sparse matrix with 0 using == is inefficient, try using != instead.r#)rOzHComparing sparse matrices using == is inefficient, try using != instead.F_ne_)rr.isnanr7r"bool_rr onesr\operatorneeqrtodenser r'r(_binopt)r=rAall_trueinvr[rDrDrE__eq__s0       z_cs_matrix.__eq__cCst|rt|r= and <= don't work with 0.)rzinconsistent shapes)rkrjzUComparing sparse matrices using >= and <= is inefficient, using <, >, or !=, instead.rj_gt__lt_zOperands could not be compared.)rNotImplementedErrorrr r.emptyr"Z result_typefillr7rer\rrdr r9r'r(r`r_)r=rArZop_nameZbad_scalar_msg other_arrrfr[rDrDrE _inequalitys2            z_cs_matrix._inequalitycCs||tjddS)NrmzgComparing a sparse matrix with a scalar greater than zero using < is inefficient, try using >= instead.)rsralt)r=rArDrDrE__lt__6s z_cs_matrix.__lt__cCs||tjddS)NrlzdComparing a sparse matrix with a scalar less than zero using > is inefficient, try using <= instead.)rsragt)r=rArDrDrE__gt__<s z_cs_matrix.__gt__cCs||tjddS)NrjzgComparing a sparse matrix with a scalar greater than zero using <= is inefficient, try using > instead.)rsrale)r=rArDrDrE__le__Bs z_cs_matrix.__le__cCs||tjddS)NrkzdComparing a sparse matrix with a scalar less than zero using >= is inefficient, try using < instead.)rsrage)r=rArDrDrE__ge__Hs z_cs_matrix.__ge__cCs|j|jkrtdt|jj|jj}|dd}tj|||dd}||j\}}|jj rb|n|j }t |||j |j|j|tj|ddS)NzIncompatible shapes.ZCFrT)rorderr$F)r$)r"r9rrcharr3r.r8flags c_contiguousTr csr_todenser4r2r1matrix)r=rArr|resultr>r?yrDrDrE _add_denseRs z_cs_matrix._add_densecCs ||dS)NZ_plus_)re)r=rArDrDrE _add_sparse]sz_cs_matrix._add_sparsecCs ||dS)NZ_minus_)re)r=rArDrDrE _sub_sparse`sz_cs_matrix._sub_sparsecCs2t|r||St|r:|j|jkr>||}||dS|jdkrZ||dS|jdkrv||dS|jddkr|jddkr||S|jddkr|jddkr||S|jddkr$|jd|jdkr$t | dgf|jd|jdfd}||S|jddkr~|jd|jdkr~t | dgf|jd|jdfd}||S|jddkr|jd|jdkrt | dgf|jd|jdfd}||S|jddkr2|jd|jdkr2t | dgf|jd|jdfd}||St dt |}|jdkr`t ||S|jdkr|||jdS|jdkrt |d|Sdd lm}|}|j|jkrt |j||j|jf}n@|jddkr|jddkr t |j|}n<|jd|jdkr@t |j|d d |jf}nt dt t |jdt|j}t |j|jd}||t j ||ff|jd|jdfd d S|jddkr|jddkrt |jd d d f|}n@|jd|jdkr t |jd d d f||j}nt dt |j|jd}t t |jdt|j}||t j ||ff|jd|jdfd d S|jddkr|jd|jdkrt |j|d d |jf }nH|jddkr|jd|jdkrt |j||j }nt d|t j |_|S) zPPoint-wise multiplication by another matrix, vector, or scalar. Z_elmul_)rr)rrrr)r"zinconsistent shapesr )r!NF)r"r$)rZ _mul_scalarr r"r7retoarray_mul_sparse_matrixtocscrravelr9r.Z atleast_2drRmultiplysizeZflatr6r!tocoor1rLcolrepeataranger5tileZviewZndarray)r=rAr$r!retr1rLrrDrDrErcs       & & & &      "&"&z_cs_matrix.multiplycCsT|j\}}tj|t|jj|jjd}tt|jd}||||j |j |j |||S)N)rZ_matvec) r"r.r/rrr}getattrrr'r4r2r1)r=rAr>r?rfnrDrDrE _mul_vectors  z_cs_matrix._mul_vectorc Csl|j\}}|jd}tj||ft|jj|jjd}tt|jd}|||||j |j |j | | |S)Nr)rZ_matvecs) r"r.r/rrr}rrr'r4r2r1r)r=rAr>r?Zn_vecsrrrDrDrE_mul_multivectors   z_cs_matrix._mul_multivectorc Cs|j\}}|j\}}|||fd}||}t|j|j|j|jf||d}tj|d|d}tt |j d} | ||tj |j|dtj |j|dtj |j|dtj |j|d||d} t|j|j|j|jf| d}tj ||d}tj| |d} tj| t |j |j d} tt |j d} | ||tj |j|dtj |j|d|jtj |j|dtj |j|d|j|| | |j| | |f||fdS) Nr)rr)rZ _matmat_pass1rFZ _matmat_pass2)r")r"r3r7rr4r2r.rorrr'r:rrr1) r=rAr>ZK1ZK2r?Z major_axisr@r4rrTr2r1rDrDrErs>         z_cs_matrix._mul_sparse_matrixrcCs|j\}}|| ks||kr$tdtt|jd}tjt|t|d|t|dt |j d}|||jd|jd|j |j |j ||S)Nzk exceeds matrix dimensionsZ _diagonalr)rr)r"r9rrr'r.rorUr-rrr4r2r1)r=kZrowsZcolsrrrDrDrEdiagonal s   z_cs_matrix.diagonalcCst|r||rVtdtddtj|jt|jd}||| |}| ||S| ||j t|}|j ||j |jf|j|jd}|Sn2t|r|||St|r| ||StddS)NzITaking maximum (minimum) with > 0 (< 0) number results to a dense matrix.r#)rO)r)rr"zOperands not compatible.)rrr r.ror"r:rrpr7rerWr1r2r4rrdr r9)r=rAZnpoprqZ dense_checkrrZnew_dataZmatrDrDrE_maximum_minimums&    z_cs_matrix._maximum_minimumcCs||tjdddS)NZ _maximum_cSst|dkS)Nr)r.r:)rVrDrDrE7sz$_cs_matrix.maximum..)rr.maximum)r=rArDrDrEr5s z_cs_matrix.maximumcCs||tjdddS)NZ _minimum_cSst|dkS)Nr)r.r:)rVrDrDrEr=sz$_cs_matrix.minimum..)rr.minimum)r=rArDrDrEr;s z_cs_matrix.minimumcCst|ds||ddkrt|j}tjt|jd|d}|tj \}}|||<t |}|ddkrr|j }|dk r|j |j krt d|jd ||d Stj||||d SdS) z~Sum the matrix over the given axis. If the axis is None, sum over both rows and columns, returning a scalar. blocksize))rrF)rr rr)rr Nzdimensions do not matchrD)rIrout)hasattrr3rrr.r/r5r4 _minor_reduceaddZasmatrixrr"r9sumr )r=rIrrZ res_dtyper major_indexvaluerDrDrErEs    z_cs_matrix.sumcCs>|dkr|j}tt|j}||t|j|}||fS)aReduce nonzeros with a ufunc over the minor axis when non-empty Can be applied to a function of self.data by supplying data parameter. Warning: this does not call sum_duplicates() Returns ------- major_index : array of ints Major indices where nonzero value : array of self.dtype Reduce result for nonzeros in each major_index N)r1r.Z flatnonzerorHr4Zreduceatr)r=Zufuncr1rrrDrDrErbs z_cs_matrix._minor_reducec Cs||\}}|||\}}t|r|jddkoB|jddk}|jddko^|jddk}|sx|jd|jdkr|s|jd|jdkstd|||f\}}||||jdd}| |j |j } } t j |j|jd}|r8t t |jdt| } t | |jd} t ||jd}|r~t | |jd} t t |jdt| } t ||jd}|| | f}|| | f}n6t j ||jd}t ||\}} |j|jkrtdt |dkrdS|||f\}}||||dS)Nrrzshape mismatch in assignmentT)r$)r)Z _unpack_indexZ_index_to_arraysr r"r9r3r _zero_manyrrWrLrr.r:r1rrrr5rZbroadcast_arraysr _set_many) r=indexrVrNjZ broadcast_rowZ broadcast_colZciZcjrcrJrDrDrE __setitem__|s@    z_cs_matrix.__setitem__c Csd|jkrdS|j\}}|jdk}|dkr|r>t|||}nt|||t|}tj||jjd}tj||jjd}||8}nT|rt|||}nt|||t|}tj||jjd}tj||jjd}||7}|s|dt|}||||f<dS)Nr)r)r"rRrUr5r.rr2r) r=valuesrr>r?Z broadcastZ max_indexrNrrDrDrE_setdiags(    z_cs_matrix._setdiagcCs\||j\}}dd}||||||tj||jjd}tj||jjd}||||fS)NcSsF|}||kr td||f|}|| krBtd||fdS)Nzindex (%d) out of range (>= %d)zindex (%d) out of range (< -%d))r- IndexErrorrU)r2ZboundidxrDrDrE check_boundss  z1_cs_matrix._prepare_indices..check_bounds)r)r3r"r.r:r2r)r=rNrr>r?rrDrDrE_prepare_indicess  z_cs_matrix._prepare_indicesc Cs|||\}}}}t|}tj||jjd}t|||j|j||||}|dkrv| t|||j|j||||d|kr||j |<dSt d |j t dd|dk} || |j || <| } || }||dk|7<|| }||dk|7<||||| dS) zSets value at each (i, j) to x Here (i,j) index major and minor respectively, and must not contain duplicate entries. )rrrFNzZChanging the sparsity structure of a {}_matrix is expensive. lil_matrix is more efficient.r#)rOr)rr5r.ror2rrcsr_sample_offsetsr4rWr1rr'r _insert_many) r=rNrrVr>r? n_samplesoffsetsrmaskrDrDrErs0     z_cs_matrix._set_manyc Cs|||\}}}}t|}tj||jjd}t|||j|j||||}|dkrv| t|||j|j||||d|j ||dk<dS)zSets value at each (i, j) to zero, preserving sparsity structure. Here (i,j) index major and minor respectively. )rrrrFN) rr5r.ror2rrrr4rWr1)r=rNrr>r?rrrrDrDrErs   z_cs_matrix._zero_manycCstj|dd}|j|dd}|j|dd}|j|dd}|j}t|j|jf|jd|jd}tj|j|d|_tj|j|d|_tj||d}tj||d}g}g}tj |dd \} } t | t |} t | } d } xt t| | | d d D]\} \}}}|j| }|j|}| |j||| |j||tj |||d d ddd \}}t |||kr| |||| |||nL| |||d d d|| |||d d d|t || | <|} qW|j|}| |j|d | |j|d t||_t||_tj|jj|d}|d |d <t |j}|| | 7<||d d <tj||d |_|rd|_||jddd S)a:Inserts new nonzero at each (i, j) with value x Here (i,j) index major and minor respectively. i, j and x must be non-empty, 1d arrays. Inserts each major group (e.g. all entries per row) at a time. Maintains has_sorted_indices property. Modifies i, j, x in place. Z mergesort)rPZclip)moderF)r)rT)Z return_indexrrN)rF)r%)r.ZargsortZtakehas_sorted_indicesrr2r4rr:uniqueappendr5rH enumerateizipr1Z concatenateror"cumsum sort_indicesr<)r=rNrrVr|Zdo_sortr@Z indices_partsZ data_partsZuiZ ui_indptrZnew_nnzsprevrZiiZjsZjestartstopZujZ uj_indptrZnnzsZ indptr_diffrDrDrErsZ   *  $         z_cs_matrix._insert_manyc Cs8|j\}}|dkr||7}|dkr*||7}d|kr>|krXnnd|krV|kslntd||||f|||f\}}|j|}|j|d}|jr|jj|}|j||} tj | |dd} | tj | | d|dd} |j || || j |jdSt ||j||k|j ||j |jdSdS)Nrz'index out of bounds: 0<=%d<%d, 0<=%d<%drleft)Zsideright)r) r"rr3r4rr2rtyper.Z searchsortedr1rcompress) r=rLrr>r?rZ minor_indexrend minor_indicesZinsert_pos_leftZinsert_pos_rightrDrDrE_get_single_element^s, .   z_cs_matrix._get_single_elementc Cs|||f\}}||j\}}dd}dd}|||\}}|||\} } |||||| | |t|||j|j|j||| | } | d| d| d} } }|||| | f}|j| | |f|dS) z:Return a submatrix of this matrix (new matrix is created).cSst|tr\|j|j}}|dkr&d}n|dkr6||}|dkrD|}n|dkrT||}||fSt|r|dkrv||7}||dfS|d|dfSdS)Nrr)r*slicerrr.Zisscalar)Zslnumi0i1rDrDrE_process_slices    z1_cs_matrix._get_submatrix.._process_slicecSsPd|kr|kr8nn d|kr,|kr8nn||ksLtdj|||ddS)Nrz._in_boundsr rr)r")r3r"rZget_csr_submatrixr4r2r1r7)r=Zslice0Zslice1Zshape0Zshape1rrrrZj0Zj1Zauxr1r2r4r"rDrDrE_get_submatrix{s   z_cs_matrix._get_submatrixc Csx||j\}}|j}tjt||jjd}t||j ||||f\}}ddl m }||j ||ff|j||jdS)N)rr)r!)r$r) r3r"r2r.ror5rrZ expandptrr4r6r!r1) r=r$rBrCrZ major_indicesrLrr!rDrDrErs z_cs_matrix.tocoocCs|dkr|dkr|dd}|||}|jjsB|jjsBtd|jjrX|}|}n|}|j}||j \}}t |||j |j |j||S)NZcfrz&Output array must be C or F contiguous)r3Z_process_toarray_argsr~r f_contiguousr9Ztocsrrrr"rrr4r2r1)r=r|rrVrr>r?rDrDrErs z_cs_matrix.toarraycCs4||j\}}t|||j|j|j|dS)zURemove zero entries from the matrix This is an *in place* operation N)r3r"rZcsr_eliminate_zerosr4r2r1rS)r=r>r?rDrDrErYsz_cs_matrix.eliminate_zeroscCsBt|ddsd|_n(t|dsr?rDrDrErWsz_cs_matrix.sum_duplicatescCs.t|ds(tt|jd|j|j|_|jS)zDetermine whether the matrix has sorted indices Returns - True: if the indices of the matrix are in sorted order - False: otherwise rr)rrZcsr_has_sorted_indicesr5r4r2r)r=rDrDrEZ __get_sorted s z_cs_matrix.__get_sortedcCst||_dS)N)rr)r=rrDrDrEZ __set_sortedsz_cs_matrix.__set_sortedcCs|}||S)z9Return a copy of this matrix with sorted indices )r$r)r=ArDrDrEsorted_indices!sz_cs_matrix.sorted_indicescCs0|js,tt|jd|j|j|jd|_dS)z3Sort the indices of this matrix *in place* rTN)rrZcsr_sort_indicesr5r4r2r1)r=rDrDrEr,s z_cs_matrix.sort_indicescCs||jd}t|j|dkr*tdt|j|jkrBtdt|j|jkrZtdt|jd|j|_t|jd|j|_dS)z8Remove empty space after all non-zero elements. rrz index pointer has invalid lengthz)indices array has fewer than nnz elementsz&data array has fewer than nnz elementsN) r3r"r5r4r9r2rTr1r)r=rBrDrDrErS5sz_cs_matrix.prunec Gst|}t|drz|j\}}t|d|\}}t|d|\}}|sH|rZtd|j|f|jd||jd|}} n||\}}||j\}} ||kr|jd|j||_|j d|j||_ |jd|d|_n<||krt |j|d|_|j|dd |j||| kr|j|k} t | s|j| |_|j | |_ |t j| \} } |j d| |jdd| <t j|j|jd||_dS)Nrrrz.shape must be divisible into %s blocks. Got %s)r)rrrdivmodr9r"r3r2r4r1r.resizerpallrrrr,) r=r"ZbmZbnZnew_MZrmZnew_NZrnr>r?rrrrDrDrErDs8          z_cs_matrix.resizecCsL|r*|j||j|jf|j|jdS|j||j|jf|j|jdSdS)zReturns a matrix with the same sparsity structure as self, but with different data. By default the structure arrays (i.e. .indptr and .indices) are copied. )r"rN)r7r2r$r4r"r)r=r1r$rDrDrErXms  z_cs_matrix._with_datac Cs&||}tt|j||j}|j|j}t|j|j|j|jf|d}tj |jj |d}tj ||d}dddddg}||krtj |tj d} ntj |t |j |j d} ||j d|j d tj|j|dtj|j|d|jtj|j|dtj|j|d|j||| |j| ||f|j d } | | S) z5apply the binary operation fn to two sparse matrices.)r)rr]rmrlrjrkrr)r")r7rrr'rTrr4r2r.ror"r_rrr:r1rS) r=rArZrZmaxnnzr@r4r2Zbool_opsr1rrDrDrEre{s.     z_cs_matrix._binoptcCs|j|jkrtd||d}t|jtjrtj|j|jd}|tj | \}}d|||f<| }|j ||j |jf<t|}n|}|S)z? Divide this matrix by a second sparse matrix. zinconsistent shapesZ_eldiv_)rr)r"r9rer.Z issubdtyperZinexactrorpnanZnonzerorr1rLrr)r=rArrrLrrDrDrE_divide_sparses      z_cs_matrix._divide_sparse)NNF)N)F)T)r)NNN)N)T)NN)T)8__name__ __module__ __qualname____doc__r&rKr r)r<r\rhrirsrurwryr{rrrrrrrrrrrrrrrrrrrrrrrrYZ$_cs_matrix__get_has_canonical_formatZ$_cs_matrix__set_has_canonical_formatpropertyrrWZ_cs_matrix__get_sortedZ_cs_matrix__set_sortedrrrrSrrXrerrDrDrDrErsx P   F !"  h '      ,'H7       "  "r))rZ __future__rrr__all__warningsrraZnumpyr.Zscipy._lib.sixrrZscipy._lib._utilrbaser r r r1r r ZdiarrZsputilsrrrrrrrrrrrrrrDrDrDrEs     8