B [o@sddlmZmZddlZddlmZddlmZddlm Z ddl m Z m Z m Z mZddlmZddlmZdd lmZdd lmZdd lmZd d lmZmZd dlmZd dlmZGdddeZ Gddde eZ!dS))print_functiondivisionN) defaultdict)Dict)Expr) is_sequenceas_intrangeCallable) fuzzy_and)S)Abs)sqrt)uniq) MatrixBase ShapeError)Matrix)a2idxc@seZdZdZddZddZddZdd Zd d Zd d Z ddZ ddZ ddZ ddZ ddZddZddZeddZddZd d!Zd"d#Zd$d%Zd&d'Zd(d)Zd*d+Zd,d-Zd.d/Zed0d1Zd2d3Zd4d5Zd6d7Ze d8d9Z!d:d;Z"dd?Z$d@dAZ%dBdCZ&dDdEZ'dFdGZ(dHdIZ)dJdKZ*dLdMZ+dNdOZ,dPdQZ-dRdSZ.d[dUdVZ/d\dWdXZ0e e,dYdYdZZ1e e'dYdYdZZ2dYS)] SparseMatrixaj A sparse matrix (a matrix with a large number of zero elements). Examples ======== >>> from sympy.matrices import SparseMatrix >>> SparseMatrix(2, 2, range(4)) Matrix([ [0, 1], [2, 3]]) >>> SparseMatrix(2, 2, {(1, 1): 2}) Matrix([ [0, 0], [0, 2]]) See Also ======== sympy.matrices.dense.Matrix c OsZt|}t|dkrPt|dtrP|dj|_|dj|_t|dj|_|Si|_t|dkrt |d|_t |d|_t|dt r|d}xTt |jD]F}x@t |jD]2}| || || |}|r||j||f<qWqWnt|dtt fr>x|dD](}|d|} | r| | |j|<qWnt|drVt|d|j|jkrtdt|d|j|jf|d} xt |jD]H}x@t |jD]2}| | ||j|}|r||j||f<qWqWnntj|\} } } | |_| |_xPt |jD]B}x:t |jD],}| |j||}|r ||j||f<q WqW|S)Nrrz%List length (%s) != rows*columns (%s))object__new__len isinstancerrowscolsdict_smatrr r _sympifyrkeysr ValueErrorrZ_handle_creation_inputs)clsargskwargsselfopijvaluekeyvZ flat_listrcZ_listr/4lib/python3.7/site-packages/sympy/matrices/sparse.pyr*sV    zSparseMatrix.__new__cCs^yD|j|jkrdSt|tr(|j|jkSt|trB|jt|jkSWntk rXdSXdS)NF)shaperrrrMutableSparseMatrixAttributeError)r&otherr/r/r0__eq__]s    zSparseMatrix.__eq__c Cst|tr0|\}}y"||\}}|j||ftjSttfk r.t|t rjt t |j |}nJt |rtn@t|tr|jsddlm}||||S||j krtd|g}t|t rt t |j|}nPt |rnFt|tr|jsddlm}||||S||jkrtd|g}|||SXt|t r|t|dd\}}g}x>t ||D]0}t||j\}} ||j|| ftjqfW|Stt|t||j\}}|j||ftjS)Nr) MatrixElementzRow index out of boundszCol index out of boundsr)rtupleZkey2ijrgetr Zero TypeError IndexErrorslicelistr rrrZ is_numberZ"sympy.matrices.expressions.matexprr6rextractindicesrdivmodappendr) r&r+r(r)r6lohiLmnr/r/r0 __getitem__hsH           zSparseMatrix.__getitem__cCs tdS)N)NotImplementedError)r&r+r*r/r/r0 __setitem__szSparseMatrix.__setitem__cCs"|}||}|j|}|S)N)_cholesky_sparse_lower_triangular_solveT_upper_triangular_solve)r&rhsrDYrvr/r/r0_cholesky_solves  zSparseMatrix._cholesky_solvec Csr|}||j}xVtt|D]D}x<||D].}||kr|||f|||f<d}x\||D]P}||krfxB||D]4}||kr||kr||||f|||f7}q|Pq|WPqfW|||f|8<|||f|||f<q6|||f|||f<d}x4||D](}||kr2||||fd7}nPqW|||f|8<t|||f|||f<q6Wq$W|S)z@Algorithm for numeric Cholesky factorization of a sparse matrix.rr)row_structure_symbolic_choleskyzerosrr rr) r&Z CrowstrucCr(r)summp1p2kr/r/r0rJs4   zSparseMatrix._cholesky_sparsecsjdfddS)zDiagonal solve.rcs|df||fS)Nrr/)r(r))rNr&r/r0sz.SparseMatrix._diagonal_solve..)_newr)r&rNr/)rNr&r0_diagonal_solveszSparseMatrix._diagonal_solvec  s|}|}||j|sF|j}|dddf}||}||dd}|dkrb|jn|dkrr|jn td||j fddt j D}|s||dddfd }||}| |S) aReturn the matrix inverse using Cholesky or LDL (default) decomposition as selected with the ``method`` keyword: 'CH' or 'LDL', respectively. Examples ======== >>> from sympy import SparseMatrix, Matrix >>> A = SparseMatrix([ ... [ 2, -1, 0], ... [-1, 2, -1], ... [ 0, 0, 2]]) >>> A.inv('CH') Matrix([ [2/3, 1/3, 1/6], [1/3, 2/3, 1/3], [ 0, 0, 1/2]]) >>> A.inv(method='LDL') # use of 'method=' is optional Matrix([ [2/3, 1/3, 1/6], [1/3, 2/3, 1/3], [ 0, 0, 1/2]]) >>> A * _ Matrix([ [1, 0, 0], [0, 1, 0], [0, 0, 1]]) rNmethodLDLZCHz$Method may be "CH" or "LDL", not %s.cs g|]}dd|fqS)Nr/).0r()Isolver/r0 sz.SparseMatrix._eval_inverse..)rr) is_symmetric as_mutableeyerrLr8 _LDL_solverQrHZhstackr rrZ) r&r%ZsymMtZr1r\rPZscaler/)r_r`r0 _eval_inverses(    zSparseMatrix._eval_inversecCs|ddS)NcSst|S)N)r )xr/r/r0rYsz(SparseMatrix._eval_Abs..) applyfunc)r&r/r/r0 _eval_AbsszSparseMatrix._eval_AbscCst|ts|||Si}|d}xNt|j|jD]0}|j|||j||}|dkrB|||<qBW||j |j |S)zWIf `other` is a SparseMatrix, add efficiently. Otherwise, do standard addition.r) rrrZr setunionrr!r8rr)r&r4smatZzeror+sumr/r/r0 _eval_adds    zSparseMatrix._eval_addcCst|tst|}i}x<|jD].\}}|\}}||krD||j7}||||f<q"Wx.|jD] \}}|\}}|||||f<q`W||j|j|j|S)N)rrritemsrrZr)r&Zicolr4new_smatr+valrowcolr/r/r0_eval_col_inserts  zSparseMatrix._eval_col_insertcCs&dd|jD}||j|j|S)NcSsi|]\}}||qSr/) conjugate)r^r+rsr/r/r0 sz0SparseMatrix._eval_conjugate..)rrqrZrr)r&rnr/r/r0_eval_conjugateszSparseMatrix._eval_conjugatecCsztt|}tt|}i}t|t|t|jkr~xt|D]8\}}x.t|D]"\}} |j|| fd|||f<qRWq@WnFxD|jD]:\} } | |kr| |kr|j| | f||| || f<qW|t|t||} t|t|kr&x8t|D],\}}||} | |kr| || | } qWt|t|krvx.)r minrZ)r#rrentriesr/r/r0 _eval_eyeBszSparseMatrix._eval_eyecsDtjj}tjjjkr&d}tfddjDpB|S)NFc3s|]}|jVqdS)N)has)r^r+)patternsr&r/r0 Nsz)SparseMatrix._eval_has..)r r9rrrrrany)r&rZzhasr/)rr&r0 _eval_hasGs zSparseMatrix._eval_hascs0tfddtjDs dStjjkS)Nc3s|]}||fdkVqdS)rNr/)r^r()r&r/r0rQsz1SparseMatrix._eval_is_Identity..F)allr rrr)r&r/)r&r0_eval_is_IdentityPszSparseMatrix._eval_is_IdentitycCs ||j|}t|dkS)Nr)rLrjrvalues)r&ZsimpfuncZdiffr/r/r0_eval_is_symmetricUszSparseMatrix._eval_is_symmetriccst|ts|||Sttx&|jD]\\}}}|||<q,Wttx&|jD]\\}}}|||<q\Wi}xnD]bx\D]Ptt@}|rt fdd|D}||f<qWqW||j |j |S)z:Fast multiplication exploiting the sparsity of the matrix.c3s&|]}||VqdS)Nr/)r^rX)ru col_lookuprt row_lookupr/r0rnsz0SparseMatrix._eval_matrix_mul..) rrrZrrrrqr!rlrorr)r&r4r(r)rsrnr?r/)rurrtrr0_eval_matrix_mulYs   zSparseMatrix._eval_matrix_mulcCst|tst|}i}x<|jD].\}}|\}}||krD||j7}||||f<q"Wx.|jD] \}}|\}}|||||f<q`W||j|j|j|S)N)rrrrqrrZr)r&Zirowr4rrr+rsrtrur/r/r0_eval_row_insertrs  zSparseMatrix._eval_row_insertcs|fddS)Ncs|S)Nr/)ri)r4r/r0rYsz/SparseMatrix._eval_scalar_mul..)rj)r&r4r/)r4r0_eval_scalar_mulszSparseMatrix._eval_scalar_mulcs|fddS)Ncs|S)Nr/)ri)r4r/r0rYsz0SparseMatrix._eval_scalar_rmul..)rj)r&r4r/)r4r0_eval_scalar_rmulszSparseMatrix._eval_scalar_rmulcCs&dd|jD}||j|j|S)aKReturns the transposed SparseMatrix of this SparseMatrix. Examples ======== >>> from sympy.matrices import SparseMatrix >>> a = SparseMatrix(((1, 2), (3, 4))) >>> a Matrix([ [1, 2], [3, 4]]) >>> a.T Matrix([ [1, 3], [2, 4]]) cSsi|]\\}}}|||fqSr/r/)r^r(r)rsr/r/r0rxsz0SparseMatrix._eval_transpose..)rrqrZrr)r&rnr/r/r0_eval_transposeszSparseMatrix._eval_transposecCsdd|jDS)NcSsg|]\}}|js|qSr/)Zis_zero)r^rXr,r/r/r0rasz-SparseMatrix._eval_values..)rrq)r&r/r/r0 _eval_valuesszSparseMatrix._eval_valuescCs|||iS)N)rZ)r#rrr/r/r0 _eval_zerosszSparseMatrix._eval_zeroscCs,|\}}||}||}|j|S)N) _LDL_sparserKr[rLrM)r&rNrDDZrOr/r/r0res   zSparseMatrix._LDL_solvec Cs|}||j}||j|j}xbtt|D]P}xH||D]:}||kr |||f|||f<d}xj||D]^}||krxP||D]@}||kr||kr||||f|||f|||f7}qPqWqxPqxW|||f|8<|||f|||f<qF||krF|||f|||f<d}x@||D]4} | |krf|||| fd|| | f7}nPq6W|||f|8<qFWq4W||fS)zLAlgorithm for numeric LDL factization, exploiting sparse structure. rr)rRrdrrSrr r) r&Z LrowstrucrDrr(r)rUrVrWrXr/r/r0rs6  * "zSparseMatrix._LDL_sparsec Csddt|jD}x0|D]$\}}}||kr||||fqW|}xdt|jD]V}x4||D](\}}||df|||df8<qhW||df|||f<qZW||S)zsFast algorithm for solving a lower-triangular system, exploiting the sparsity of the given matrix. cSsg|]}gqSr/r/)r^r(r/r/r0rasz8SparseMatrix._lower_triangular_solve..r)r rrow_listrAcopyrZ)r&rNrr(r)r,Xr/r/r0rKs$ z$SparseMatrix._lower_triangular_solvecCst|S)zsReturn a list of matrix elements. Some routines in DenseMatrix use `_mat` directly to speed up operations.)r=)r&r/r/r0_matszSparseMatrix._matc Csddt|jD}x0|D]$\}}}||kr||||fqW|}xxt|jdddD]b}||x4||D](\}}||df|||df8<q|W||df|||f<qbW||S)ztFast algorithm for solving an upper-triangular system, exploiting the sparsity of the given matrix. cSsg|]}gqSr/r/)r^r(r/r/r0rasz8SparseMatrix._upper_triangular_solve..rr)r rrrArreverserZ)r&rNrr(r)r,rr/r/r0rMs $ z$SparseMatrix._upper_triangular_solvecCsZt|std|}x<|jD].\}}||}|rD||j|<q$|j|dq$W|S)aaApply a function to each element of the matrix. Examples ======== >>> from sympy.matrices import SparseMatrix >>> m = SparseMatrix(2, 2, lambda i, j: i*2+j) >>> m Matrix([ [0, 1], [2, 3]]) >>> m.applyfunc(lambda i: 2*i) Matrix([ [0, 2], [4, 6]]) z`f` must be callable.N)callabler:rrrqpop)r&foutrXr,fvr/r/r0rjs zSparseMatrix.applyfunccCsddlm}||S)z,Returns an Immutable version of this Matrix.r)ImmutableSparseMatrix)Z immutabler)r&rr/r/r0 as_immutables zSparseMatrix.as_immutablecCst|S)aCReturns a mutable version of this matrix. Examples ======== >>> from sympy import ImmutableMatrix >>> X = ImmutableMatrix([[1, 2], [3, 4]]) >>> Y = X.as_mutable() >>> Y[1, 1] = 5 # Can set values in Y >>> Y Matrix([ [1, 2], [3, 5]]) )r2)r&r/r/r0rcszSparseMatrix.as_mutablecCsRddlm}m}|s td|}||s@||rHtd||S)a Returns the Cholesky decomposition L of a matrix A such that L * L.T = A A must be a square, symmetric, positive-definite and non-singular matrix Examples ======== >>> from sympy.matrices import SparseMatrix >>> A = SparseMatrix(((25,15,-5),(15,18,0),(-5,0,11))) >>> A.cholesky() Matrix([ [ 5, 0, 0], [ 3, 3, 0], [-1, 1, 3]]) >>> A.cholesky() * A.cholesky().T == A True r)nanooz:Cholesky decomposition applies only to symmetric matrices.zACholesky decomposition applies only to positive-definite matrices) sympy.core.numbersrrrbr"rcrJrrZ)r&rrrfr/r/r0cholesky,s zSparseMatrix.choleskycs(fddttjdddDS)aReturns a column-sorted list of non-zero elements of the matrix. Examples ======== >>> from sympy.matrices import SparseMatrix >>> a=SparseMatrix(((1, 2), (3, 4))) >>> a Matrix([ [1, 2], [3, 4]]) >>> a.CL [(0, 0, 1), (1, 0, 3), (0, 1, 2), (1, 1, 4)] See Also ======== col_op row_list csg|]}t||fqSr/)r7)r^rX)r&r/r0ra`sz)SparseMatrix.col_list..cSs tt|S)N)r=reversed)rXr/r/r0rY`sz'SparseMatrix.col_list..)r+)sortedr=rr!)r&r/)r&r0col_listLszSparseMatrix.col_listcCs||j|j|jS)N)rZrrr)r&r/r/r0rbszSparseMatrix.copycCstddlm}m}|s td|\}}||sX||sX||sX||r`td||||fS)a Returns the LDL Decomposition (matrices ``L`` and ``D``) of matrix ``A``, such that ``L * D * L.T == A``. ``A`` must be a square, symmetric, positive-definite and non-singular. This method eliminates the use of square root and ensures that all the diagonal entries of L are 1. Examples ======== >>> from sympy.matrices import SparseMatrix >>> A = SparseMatrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11))) >>> L, D = A.LDLdecomposition() >>> L Matrix([ [ 1, 0, 0], [ 3/5, 1, 0], [-1/5, 1/3, 1]]) >>> D Matrix([ [25, 0, 0], [ 0, 9, 0], [ 0, 0, 9]]) >>> L * D * L.T == A True r)rrz5LDL decomposition applies only to symmetric matrices.z>> from sympy.matrices import SparseMatrix >>> S = SparseMatrix([ ... [1, 0, 3, 2], ... [0, 0, 1, 0], ... [4, 0, 0, 5], ... [0, 6, 7, 0]]) >>> S.liupc() ([[0], [], [0], [1, 2]], [4, 3, 4, 4]) References ========== Symbolic Sparse Cholesky Factorization using Elimination Trees, Jeroen Van Grondelle (1999) http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.7582 cSsg|]}gqSr/r/)r^r-r/r/r0rasz&SparseMatrix.liupc..Nr)r rrrAr) r&Rr-r._infparentZvirtualrgr/r/r0liupcs    zSparseMatrix.liupccCs t|jS)z2Returns the number of non-zero elements in Matrix.)rr)r&r/r/r0nnzszSparseMatrix.nnzcs(fddttjdddDS)aReturns a row-sorted list of non-zero elements of the matrix. Examples ======== >>> from sympy.matrices import SparseMatrix >>> a = SparseMatrix(((1, 2), (3, 4))) >>> a Matrix([ [1, 2], [3, 4]]) >>> a.RL [(0, 0, 1), (0, 1, 2), (1, 0, 3), (1, 1, 4)] See Also ======== row_op col_list csg|]}t||fqSr/)r7)r^rX)r&r/r0rasz)SparseMatrix.row_list..cSst|S)N)r=)rXr/r/r0rYsz'SparseMatrix.row_list..)r+)rr=rr!)r&r/)r&r0rs zSparseMatrix.row_listcCs|\}}t|}t|}xht|jD]Z}x<||D]0}x*||krf||krf|||||}q>Wq8Wttt ||||<q*W|S)aSymbolic cholesky factorization, for pre-determination of the non-zero structure of the Cholesky factororization. Examples ======== >>> from sympy.matrices import SparseMatrix >>> S = SparseMatrix([ ... [1, 0, 3, 2], ... [0, 0, 1, 0], ... [4, 0, 0, 5], ... [0, 6, 7, 0]]) >>> S.row_structure_symbolic_cholesky() [[0], [], [0], [1, 2]] References ========== Symbolic Sparse Cholesky Factorization using Elimination Trees, Jeroen Van Grondelle (1999) http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.7582 ) rrrdeepcopyr rrAr=rrl)r&rrrZLrowrXr)r/r/r0rRs  z,SparseMatrix.row_structure_symbolic_choleskycCsP|j|j}|rLx:|jD]0}||j|}|r:||j|<q|j|dqW|S)z"Scalar element-wise multiplicationN)rSr1rr)r&Zscalarrfr(r,r/r/r0scalar_multiplys   zSparseMatrix.scalar_multiplyr]cCs|j}||j|d||S)aReturn the least-square fit to the data. By default the cholesky_solve routine is used (method='CH'); other methods of matrix inversion can be used. To find out which are available, see the docstring of the .inv() method. Examples ======== >>> from sympy.matrices import SparseMatrix, Matrix, ones >>> A = Matrix([1, 2, 3]) >>> B = Matrix([2, 3, 4]) >>> S = SparseMatrix(A.row_join(B)) >>> S Matrix([ [1, 2], [2, 3], [3, 4]]) If each line of S represent coefficients of Ax + By and x and y are [2, 3] then S*xy is: >>> r = S*Matrix([2, 3]); r Matrix([ [ 8], [13], [18]]) But let's add 1 to the middle value and then solve for the least-squares value of xy: >>> xy = S.solve_least_squares(Matrix([8, 14, 18])); xy Matrix([ [ 5/3], [10/3]]) The error is given by S*xy - r: >>> S*xy - r Matrix([ [1/3], [1/3], [1/3]]) >>> _.norm().n(2) 0.58 If a different xy is used, the norm will be higher: >>> xy += ones(2, 1)/10 >>> (S*xy - r).norm().n(2) 1.5 )r\)rLinv)r&rNr\rgr/r/r0solve_least_squaress6z SparseMatrix.solve_least_squarescCsF|js2|j|jkrtdqB|j|jkrBtdn|j|d|SdS)zReturn solution to self*soln = rhs using given inversion method. For a list of possible inversion methods, see the .inv() docstring. zUnder-determined system.z]For over-determined system, M, having more rows than columns, try M.solve_least_squares(rhs).)r\N)Z is_squarerrr"r)r&rNr\r/r/r0r`<s     zSparseMatrix.solveNzAlternate faster representation)r])r])3__name__ __module__ __qualname____doc__rr5rGrIrQrJr[rhrkrprvryr| classmethodrrrrrrrrrrrrerrKpropertyrrMrjrrcrrrrrrrrRrrr`ZRLZCLr/r/r/r0rs\3 . "4    $  (,# 9 rc@seZdZeddZddZddZdZdd Zd d Z d d Z ddZ ddZ ddZ ddZddZddZddZddZddZdS) r2cOs||S)Nr/)r#r$r%r/r/r0rZPszMutableSparseMatrix._newcCsP|||}|dk rL|\}}}|r2||j||f<n||f|jkrL|j||f=dS)a?Assign value to position designated by key. Examples ======== >>> from sympy.matrices import SparseMatrix, ones >>> M = SparseMatrix(2, 2, {}) >>> M[1] = 1; M Matrix([ [0, 1], [0, 0]]) >>> M[1, 1] = 2; M Matrix([ [0, 1], [0, 2]]) >>> M = SparseMatrix(2, 2, {}) >>> M[:, 1] = [1, 1]; M Matrix([ [0, 1], [0, 1]]) >>> M = SparseMatrix(2, 2, {}) >>> M[1, :] = [[1, 1]]; M Matrix([ [0, 0], [1, 1]]) To replace row r you assign to position r*m where m is the number of columns: >>> M = SparseMatrix(4, 4, {}) >>> m = M.cols >>> M[3*m] = ones(1, m)*2; M Matrix([ [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [2, 2, 2, 2]]) And to replace column c you can assign to position c: >>> M[2] = ones(m, 1)*4; M Matrix([ [0, 0, 4, 0], [0, 0, 4, 0], [0, 0, 4, 0], [2, 2, 4, 2]]) N)Z_setitemr)r&r+r*rPr(r)r/r/r0rITs1  zMutableSparseMatrix.__setitem__cCs|S)N)r)r&r/r/r0rcszMutableSparseMatrix.as_mutableNcCsi}t||j}xV|jD]L\}}||kr*q||krN|j||f|||df<q|j||f|||f<qW||_|jd8_dS)a}Delete the given column of the matrix. Examples ======== >>> from sympy.matrices import SparseMatrix >>> M = SparseMatrix([[0, 0], [0, 1]]) >>> M Matrix([ [0, 0], [0, 1]]) >>> M.col_del(0) >>> M Matrix([ [0], [1]]) See Also ======== row_del rN)rrr)r&rXnewDr(r)r/r/r0col_dels zMutableSparseMatrix.col_delc Cs|jdkr,|j|jkr,|d|jg|S||}}|j|jksHt|}t|tsd}|j}xt |jD]@}x:t |jD],}||}|r||j ||j|f<|d7}qWqpWn0x.|j D] \\}}}||j ||j|f<qW|j|j7_|S)a,Returns B augmented beneath A (row-wise joining):: [A] [B] Examples ======== >>> from sympy import SparseMatrix, Matrix, ones >>> A = SparseMatrix(ones(3)) >>> A Matrix([ [1, 1, 1], [1, 1, 1], [1, 1, 1]]) >>> B = SparseMatrix.eye(3) >>> B Matrix([ [1, 0, 0], [0, 1, 0], [0, 0, 1]]) >>> C = A.col_join(B); C Matrix([ [1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 0, 0], [0, 1, 0], [0, 0, 1]]) >>> C == A.col_join(Matrix(B)) True Joining along columns is the same as appending rows at the end of the matrix: >>> C == A.row_insert(A.rows, Matrix(B)) True rr) rrrZcol_joinrrrrrr rrq) r&r4ABrXbr(r)r,r/r/r0rs&(   zMutableSparseMatrix.col_joincCs^xXt|jD]J}|j||ftj}|||}|rB||j||f<q |r |j||fq WdS)aIn-place operation on col j using two-arg functor whose args are interpreted as (self[i, j], i) for i in range(self.rows). Examples ======== >>> from sympy.matrices import SparseMatrix >>> M = SparseMatrix.eye(3)*2 >>> M[1, 0] = -1 >>> M.col_op(1, lambda v, i: v + 2*M[i, 0]); M Matrix([ [ 2, 4, 0], [-1, 0, 0], [ 0, 0, 2]]) N)r rrr8r r9r)r&r)rr(r,rr/r/r0col_ops zMutableSparseMatrix.col_opc Cs||kr||}}|}g}xl|D]d\}}}||krV|j||f|||fq$||kr~|j||f||j||f<q$||kr$Pq$Wx|D]\}}||j||f<qWdS)aSwap, in place, columns i and j. Examples ======== >>> from sympy.matrices import SparseMatrix >>> S = SparseMatrix.eye(3); S[2, 1] = 2 >>> S.col_swap(1, 0); S Matrix([ [0, 1, 0], [1, 0, 0], [2, 0, 1]]) N)rrrrA) r&r(r)rtempiijjr,rXr/r/r0col_swap s zMutableSparseMatrix.col_swapcCs$t|std||t|dS)Nz&`value` must be of type list or tuple.)rr: copyin_matrixr)r&r+r*r/r/r0 copyin_list)szMutableSparseMatrix.copyin_listcCs||\}}}}|j}||||}} ||| fkr>tdt|tsxBt|jD]4} x.t|jD] } || | f|| || |f<qdWqTWn||||t|krxt||D]*} x$t||D]} |j | | fdqWqWn^x\| D]P\} } } || kr |krnq|| kr&|krnq|j | | fdqWx<|j D].\} } | \} } || | f|| || |f<qLWdS)NzXThe Matrix `value` doesn't have the same dimensions as the in sub-Matrix given by `key`.) Z key2boundsr1rrrr rrrrrrrq)r&r+r*ZrloZrhiZcloZchir1ZdrZdcr(r)r,rXr/r/r0r.s(  &4z!MutableSparseMatrix.copyin_matrixcs:|s i_n*|tfddtjD_dS)aFill self with the given value. Notes ===== Unless many values are going to be deleted (i.e. set to zero) this will create a matrix that is slower than a dense matrix in operations. Examples ======== >>> from sympy.matrices import SparseMatrix >>> M = SparseMatrix.zeros(3); M Matrix([ [0, 0, 0], [0, 0, 0], [0, 0, 0]]) >>> M.fill(1); M Matrix([ [1, 1, 1], [1, 1, 1], [1, 1, 1]]) cs(g|] }tjD]}||ffqqSr/)r r)r^r(r))r&r,r/r0raesz,MutableSparseMatrix.fill..N)rr rr r)r&r*r/)r&r,r0fillHs  zMutableSparseMatrix.fillcCsi}t||j}xV|jD]L\}}||kr*q||krN|j||f||d|f<q|j||f|||f<qW||_|jd8_dS)agDelete the given row of the matrix. Examples ======== >>> from sympy.matrices import SparseMatrix >>> M = SparseMatrix([[0, 0], [0, 1]]) >>> M Matrix([ [0, 0], [0, 1]]) >>> M.row_del(0) >>> M Matrix([[0, 1]]) See Also ======== col_del rN)rrr)r&rXrr(r)r/r/r0row_delhs zMutableSparseMatrix.row_delc Cs|jdkr,|j|jkr,||jdg|S||}}|j|jksHt|}t|tsd}|j}xt |jD]@}x:t |jD],}||}|r||j |||jf<|d7}qWqpWn0x.|j D] \\}}}||j |||jf<qW|j|j7_|S)a,Returns B appended after A (column-wise augmenting):: [A B] Examples ======== >>> from sympy import SparseMatrix, Matrix >>> A = SparseMatrix(((1, 0, 1), (0, 1, 0), (1, 1, 0))) >>> A Matrix([ [1, 0, 1], [0, 1, 0], [1, 1, 0]]) >>> B = SparseMatrix(((1, 0, 0), (0, 1, 0), (0, 0, 1))) >>> B Matrix([ [1, 0, 0], [0, 1, 0], [0, 0, 1]]) >>> C = A.row_join(B); C Matrix([ [1, 0, 1, 1, 0, 0], [0, 1, 0, 0, 1, 0], [1, 1, 0, 0, 0, 1]]) >>> C == A.row_join(Matrix(B)) True Joining at row ends is the same as appending columns at the end of the matrix: >>> C == A.col_insert(A.cols, B) True rr) rrrZrow_joinrrrrrr rrq) r&r4rrrXrr(r)r,r/r/r0rs&$   zMutableSparseMatrix.row_joincCs^xXt|jD]J}|j||ftj}|||}|rB||j||f<q |r |j||fq WdS)aIn-place operation on row ``i`` using two-arg functor whose args are interpreted as ``(self[i, j], j)``. Examples ======== >>> from sympy.matrices import SparseMatrix >>> M = SparseMatrix.eye(3)*2 >>> M[0, 1] = -1 >>> M.row_op(1, lambda v, j: v + 2*M[0, j]); M Matrix([ [2, -1, 0], [4, 0, 0], [0, 0, 2]]) See Also ======== row zip_row_op col_op N)r rrr8r r9r)r&r(rr)r,rr/r/r0row_ops zMutableSparseMatrix.row_opc Cs||kr||}}|}g}xl|D]d\}}}||krV|j||f|||fq$||kr~|j||f||j||f<q$||kr$Pq$Wx|D]\}}||j||f<qWdS)aSwap, in place, columns i and j. Examples ======== >>> from sympy.matrices import SparseMatrix >>> S = SparseMatrix.eye(3); S[2, 1] = 2 >>> S.row_swap(1, 0); S Matrix([ [0, 1, 0], [1, 0, 0], [0, 2, 1]]) N)rrrrA) r&r(r)rrrrr,rXr/r/r0row_swaps zMutableSparseMatrix.row_swapcs|fdddS)aIn-place operation on row ``i`` using two-arg functor whose args are interpreted as ``(self[i, j], self[k, j])``. Examples ======== >>> from sympy.matrices import SparseMatrix >>> M = SparseMatrix.eye(3)*2 >>> M[0, 1] = -1 >>> M.zip_row_op(1, 0, lambda v, u: v + 2*u); M Matrix([ [2, -1, 0], [4, 0, 0], [0, 0, 2]]) See Also ======== row row_op col_op cs||fS)Nr/)r,r))rrXr&r/r0rYsz0MutableSparseMatrix.zip_row_op..N)r)r&r(rXrr/)rrXr&r0 zip_row_opszMutableSparseMatrix.zip_row_op)rrrrrZrIrc__hash__rrrrrrrrrrrrr/r/r/r0r2Os  9#> !:r2)"Z __future__rrr collectionsrZsympy.core.containersrZsympy.core.exprrZsympy.core.compatibilityrrr r Zsympy.core.logicr Zsympy.core.singletonr Zsympy.functionsr Z(sympy.functions.elementary.miscellaneousrZsympy.utilities.iterablesrZmatricesrrZdensercommonrrr2r/r/r/r0s*          A