\hQ9SSKJr SSKJr SSKJr SSKJr SSKJ r SSK J r SSK J r Jr SS KJr SS KJrJrJrJr SS KJrJr "S S \5r"SS\\ 5r\rg))Callable)Dict)sympy_deprecation_warning is_sequence)as_int) MatrixBase)MutableRepMatrix RepMatrix)_iszero)_liupc _row_structure_symbolic_cholesky_cholesky_sparse_LDLdecomposition_sparse)_lower_triangular_solve_sparse_upper_triangular_solve_sparsec^\rSrSrSr\U4Sj5r\S5rSr Sr Sr Sr S r S rS rS rSS jrSSjr\"\SSS5r\"\ SSS5rSrSrSSjrSSjrSrSr\R\l\R\l\R\l\R\l\R\l\R\lSrU=r $)SparseRepMatrixa A sparse matrix (a matrix with a large number of zero elements). Examples ======== >>> from sympy import SparseMatrix, ones >>> SparseMatrix(2, 2, range(4)) Matrix([ [0, 1], [2, 3]]) >>> SparseMatrix(2, 2, {(1, 1): 2}) Matrix([ [0, 0], [0, 2]]) A SparseMatrix can be instantiated from a ragged list of lists: >>> SparseMatrix([[1, 2, 3], [1, 2], [1]]) Matrix([ [1, 2, 3], [1, 2, 0], [1, 0, 0]]) For safety, one may include the expected size and then an error will be raised if the indices of any element are out of range or (for a flat list) if the total number of elements does not match the expected shape: >>> SparseMatrix(2, 2, [1, 2]) Traceback (most recent call last): ... ValueError: List length (2) != rows*columns (4) Here, an error is not raised because the list is not flat and no element is out of range: >>> SparseMatrix(2, 2, [[1, 2]]) Matrix([ [1, 2], [0, 0]]) But adding another element to the first (and only) row will cause an error to be raised: >>> SparseMatrix(2, 2, [[1, 2, 3]]) Traceback (most recent call last): ... ValueError: The location (0, 2) is out of designated range: (1, 1) To autosize the matrix, pass None for rows: >>> SparseMatrix(None, [[1, 2, 3]]) Matrix([[1, 2, 3]]) >>> SparseMatrix(None, {(1, 1): 1, (3, 3): 3}) Matrix([ [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 3]]) Values that are themselves a Matrix are automatically expanded: >>> SparseMatrix(4, 4, {(1, 1): ones(2)}) Matrix([ [0, 0, 0, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 0, 0, 0]]) A ValueError is raised if the expanding matrix tries to overwrite a different element already present: >>> SparseMatrix(3, 3, {(0, 0): ones(2), (1, 1): 2}) Traceback (most recent call last): ... ValueError: collision at (1, 1) See Also ======== DenseMatrix MutableSparseMatrix ImmutableSparseMatrix c  >^[U5S:XaM[US[5(a5USRnUSRnUSR 5mX4T4$0m[U5S:XaUScSSUS/n[U5S:XGaUSSupVXVs=LacO OS=p4O-SXV4;a [ S5e[US5[US5pC[US[5(aUSnSX44;a[ SRX455e[U5Vs/sHoRU5PM n n[U5V s/sHoRU 5PM n n U H:nU H1n URU"X55n XR:wdM+U TX4'M3 M< X4T4$[US[[45(aU4Sjn USR5HuupVn[U[5(a:UR 5R5HuupnU "XX-Xj-U5 M MW[U[ ["45(a6UR$"U40UD6u nmTHupU "XX-Xj-TX45 M MURU5nU "XVURU55 M O['US5(a[)SUS55(+nU(dUR$"US40UD6u nmOUSn[U5X4-:wa$[ S R[U5X455e[U5HGn[U5H5n UX-U -n URU 5n XR:wdM/U TX4'M7 MI UcMTR+5nU(a[-S U55S-OSnU(a[-S U55S-OSnOXTR+5HDupU(aX:dU (dMX:dM![ S RX4SUS- SUS- 55e X4T4$[U5S:Xa[US[ ["45(aUSnSn[/U5Hsunn[U[ ["45(dU/n[/U5H+upXR:wdMURU5TX4'M- [-U[U55nMu U(a [U5OSnUnX4T4$[0TU]H"U6up4n[U5H6n[U5H$n UXH-U -n XR:wdMU TX4'M& M8 X4T4$s snfs sn f) Nr rz*Pass rows=None and no cols for autosizing.z2{} and {} must be integers for this specification.c >U(a9X4T;a+UTX4:wa![SRX4UTX455eUTX4'gg)Nz)There is a collision at {} for {} and {}.) ValueErrorformat)ijvsmats M/var/www/auris/envauris/lib/python3.13/site-packages/sympy/matrices/sparse.pyupdate7SparseRepMatrix._handle_creation_inputs..updatesS6T>a4:o", K!'4:!>#&'QT c38# UHn[U5v M g7fNr).0rs r! :SparseRepMatrix._handle_creation_inputs..s?w!{1~~wszMThe length of the flat list ({}) does not match the specified size ({} * {}).c3*# UH upUv M g7fr&)r'r_s r!r(r).1c3*# UH upUv M g7fr&r+)r'r-cs r!r(r)r.r/z?The location {} is out of the designated range[{}, {}]x[{}, {}])len isinstancer rowscolstodokrrrrrange_sympifyzerodictritemslisttuple_handle_creation_inputsranykeysmax enumeratesuper)clsargskwargsr4r5r,r1opr row_indicesr col_indicesvaluer"rvvr-flat flat_listr@rowmatr __class__s @r!r>'SparseRepMatrix._handle_creation_inputsks t9>ja*==7<d1go$Q(D t9>8DA~~""t! @BB$DG_fT!Wod$q'8,,!WD<'$))/);==9>d D 1||A D8=d D 1||A D$A( # RX 6 HH,).DJ)% 4''DGdD\22'"&aIFQA!!Z00*+'')//*;JFQB"15!%4+<#Ae}55%(%@%@%Mf%M 1d$(DA"15!%ad<%) LLOqS\\!_5"1T!W%%?tAw???33DGFvFAq$!%QI9~4(B#VC ND? #4[!&tA$-afqj$9E$'LL$7E$0-2QT "-)|yy{6:s...26:s...2!IIKDAQY!! (0#VQFAtaxD1HE(t# # Y!^ 47T5M B BQAA#A,3!#e}55%C&s^EAXX~%(\\"%5QT ,3s8$ '3q6ADDt# #$g=tDOD4[tA OE(%*QT %! t# #AEDs U&U+c8[SSSS9 UR5$)Nz The private _smat attribute of SparseMatrix is deprecated. Use the .todok() method instead. z1.9z$deprecated-private-matrix-attributes)deprecated_since_versionactive_deprecations_target)rr6selfs r!_smatSparseRepMatrix._smats' " &+'M  zz|r$c URURSS5URS[5URSS5S9$)NmethodLDL iszerofunctry_block_diagF)rZr\r])invgetr )rVrFs r! _eval_inverseSparseRepMatrix._eval_inversesDxxvzz(E:#)::lG#D'-zz2BE'JL Lr$c[U5(d [S5e0nUR5R5Hup4U"U5nUS:wdMXRU'M UR UR UR U5$)zApply a function to each element of the matrix. Examples ======== >>> from sympy import SparseMatrix >>> m = SparseMatrix(2, 2, lambda i, j: i*2+j) >>> m Matrix([ [0, 1], [2, 3]]) >>> m.applyfunc(lambda i: 2*i) Matrix([ [0, 2], [4, 6]]) z`f` must be callable.r)callable TypeErrorr6r;_newr4r5)rVfdokkrfvs r! applyfuncSparseRepMatrix.applyfuncso${{34 4 JJL&&(DA1BQwA) yyDIIs33r$cSSKJn U"U5$)z,Returns an Immutable version of this Matrix.r )ImmutableSparseMatrix) immutablerm)rVrms r! as_immutableSparseRepMatrix.as_immutables4$T**r$c[U5$)zReturns a mutable version of this matrix. Examples ======== >>> from sympy import ImmutableMatrix >>> X = ImmutableMatrix([[1, 2], [3, 4]]) >>> Y = X.as_mutable() >>> Y[1, 1] = 5 # Can set values in Y >>> Y Matrix([ [1, 2], [3, 5]]) )MutableSparseMatrixrUs r! as_mutableSparseRepMatrix.as_mutable$s#4((r$c[UR5R5SS9Vs/sHn[XU4-5PM sn$s snf)a3Returns a column-sorted list of non-zero elements of the matrix. Examples ======== >>> from sympy 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 ======== sympy.matrices.sparse.SparseMatrix.row_list c*[[U55$r&)r<reversed)rhs r!*SparseRepMatrix.col_list..IsY]^fgh^iYjr$key)sortedr6r@r=rVrhs r!col_listSparseRepMatrix.col_list5sB(06djjl6G6G6IOj/kl/k!a7*n%/klllsAc4[UR55$)z2Returns the number of non-zero elements in Matrix.)r2r6rUs r!nnzSparseRepMatrix.nnzKs4::<  r$c[UR5R5[S9Vs/sHn[ XU4-5PM sn$s snf)a2Returns a row-sorted list of non-zero elements of the matrix. Examples ======== >>> from sympy 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 ======== sympy.matrices.sparse.SparseMatrix.col_list rz)r|r6r@r<r=r}s r!row_listSparseRepMatrix.row_listOsL* 4::<$$&D 13 1+,a7*n% 13 33sA c X-$)z"Scalar element-wise multiplicationr+)rVscalars r!scalar_multiplySparseRepMatrix.scalar_multiplyfs }r$cHURnX0-RUS9U-U-$)aReturn the least-square fit to the data. By default the cholesky_solve routine is used (method='CH'); other methods of matrix inversion can be used. To find out which are available, see the docstring of the .inv() method. Examples ======== >>> from sympy import SparseMatrix, Matrix, ones >>> A = Matrix([1, 2, 3]) >>> B = Matrix([2, 3, 4]) >>> S = SparseMatrix(A.row_join(B)) >>> S Matrix([ [1, 2], [2, 3], [3, 4]]) If each line of S represent coefficients of Ax + By and x and y are [2, 3] then S*xy is: >>> r = S*Matrix([2, 3]); r Matrix([ [ 8], [13], [18]]) But let's add 1 to the middle value and then solve for the least-squares value of xy: >>> xy = S.solve_least_squares(Matrix([8, 14, 18])); xy Matrix([ [ 5/3], [10/3]]) The error is given by S*xy - r: >>> S*xy - r Matrix([ [1/3], [1/3], [1/3]]) >>> _.norm().n(2) 0.58 If a different xy is used, the norm will be higher: >>> xy += ones(2, 1)/10 >>> (S*xy - r).norm().n(2) 1.5 rZ)Tr^)rVrhsrZts r!solve_least_squares#SparseRepMatrix.solve_least_squaresjs+l FF||6|*1,S00r$cUR(dKURUR:a [S5eURUR:a [S5egUR US9R U5$)zReturn solution to self*soln = rhs using given inversion method. For a list of possible inversion methods, see the .inv() docstring. zUnder-determined system.z]For over-determined system, M, having more rows than columns, try M.solve_least_squares(rhs).rN) is_squarer4r5rr^multiply)rVrrZs r!solveSparseRepMatrix.solveso ~~yy499$ !;<<TYY& "NOO'8868*33C8 8r$NzAlternate faster representationc[U5$r&)rrUs r!liupcSparseRepMatrix.liupcs d|r$c[U5$r&)rrUs r!row_structure_symbolic_cholesky/SparseRepMatrix.row_structure_symbolic_choleskys /55r$c[XS9$N) hermitian)rrVrs r!choleskySparseRepMatrix.choleskys ::r$c[XS9$r)rrs r!LDLdecomposition SparseRepMatrix.LDLdecompositions 'BBr$c[X5$r&)rrVrs r!lower_triangular_solve&SparseRepMatrix.lower_triangular_solve -d88r$c[X5$r&)rrs r!upper_triangular_solve&SparseRepMatrix.upper_triangular_solverr$r+)r[)T)!__name__ __module__ __qualname____firstlineno____doc__ classmethodr>propertyrWr`rjrorsr~rrrrrRLCLrrrrrrrrrr__static_attributes__ __classcell__)rPs@r!rrsSj~$~$@  L 4@+ )"m,!3.71r 9 (D$(I JB (D$(I JB6;C99/5nnEM.N.V.V#+.>.F.FH.F.N.N.D.L.L".D.L.L""r$rc$\rSrSr\S5rSrg)rricrUR"U0UD6up4nURX4U5nURU5$r&)r>_smat_to_DomainMatrix_fromrep)rDrErFr4r5r reps r!reMutableSparseMatrix._news=66GGD''D9||C  r$r+N)rrrrrrerr+r$r!rrrrs!!r$rrN)collections.abcrsympy.core.containersrsympy.utilities.exceptionsrsympy.utilities.iterablesrsympy.utilities.miscr matrixbaser repmatrixr r utilitiesr decompositionsrrrrsolversrrrrr SparseMatrixr+r$r!rsT$&@1'"2DvMivMr !/+;!# r$