OtjQ9ddlmZddlmZddlmZddlmZddlm Z ddl m Z ddl m Z mZdd lmZdd lmZmZmZmZdd lmZmZGd d eZGddee ZeZdS))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_sparsecxeZdZdZefdZedZdZdZ dZ dZ dZ d Z d Zd Zdd ZddZeedddZee dddZdZdZddZddZdZdZeje_eje_eje_eje_eje_eje_xZS)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  t|dkrTt|dtr9|dj}|dj}|d||fSit|dkr|d dd|dg}t|dkr|dd\}}||cxurnndx}}n?d||fvrt dt|dt|d}}t|dtr|d}d||fvr#t d ||fdt|D}fdt|D} |D]8} | D]3} || | } | j kr| | | f<49||fSt|dttfrfd } |dD]\\}}}t|trC|D]\\} } }| || z|| z|`t|t t"fr6j|fi|\}}D] \} } | || z|| z| | f! |}| || |nt'|drt)d |dD }|sj|dfi|\}}n|d}t|||zkr1t d t|||t|D]I} t|D]7} || |z| z} | } | j kr| | | f<8J|U}|rt-d |Ddznd}|rt-d |Ddznd}nXD]C\} } | r| |ks| r4| |kr.t d | | fd|dz d|dz D||fSt|dkrt|dt t"fr|d}d}t/|D]{\} }t|t t"fs|g}t/|D]*\} }|j kr || | f<+t-|t|}||rt|nd}|}||fSt1j|\}}}t|D]4} t|D]"} ||| z| z} | j kr| | | f<#5||fS)Nr rz*Pass rows=None and no cols for autosizing.z2{} and {} must be integers for this specification.c:g|]}|S_sympify).0iclss S/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/sympy/matrices/sparse.py z;SparseRepMatrix._handle_creation_inputs..#DDD1s||ADDDc:g|]}|Srr)rjrs r r!z;SparseRepMatrix._handle_creation_inputs..r"r#c |rK||fvr<|||fkr.td||f|||f|||f<dSdS)Nz)There is a collision at {} for {} and {}.) ValueErrorformat)rr%vsmats r updatez7SparseRepMatrix._handle_creation_inputs..updatesw'q6T>>a41:oo", K!'A41:!>!>##&'QT ''r#c34K|]}t|VdSNr)rrs r z:SparseRepMatrix._handle_creation_inputs..s(??!{1~~??????r#zMThe length of the flat list ({}) does not match the specified size ({} * {}).c3 K|] \}}|V dSr-r)rr_s r r.z:SparseRepMatrix._handle_creation_inputs..&..A1......r#c3 K|] \}}|V dSr-r)rr1cs r r.z:SparseRepMatrix._handle_creation_inputs..r2r#z?The location {} is out of the designated range[{}, {}]x[{}, {}])len isinstancer rowscolstodokr'rrr(rangerzerodictritemslisttuple_handle_creation_inputsranykeysmax enumeratesuper)rargskwargsr7r8r0r4op row_indices col_indicesrr%valuer+r)vvr1flat flat_listrBrowmatr* __class__s` @r r@z'SparseRepMatrix._handle_creation_inputsks t99>>ja*==>7>d1go$Q(D t99>>8DAqA~~~~~~~~""tt!Q @BBB$DG__fT!Wood$q'8,,> 3!WD$<''$))/d););===EDDDd DDD DDDDd DDD $//A(// # RR1XX 6 6 CH,,).DAJ/ T4''DGdD\22+ 3'''''"&a 6 6IFQA!!Z00 6*+''))//*;*;55JFQB"F1q5!a%44445#Ae}556%@S%@%M%Mf%M%M 1d$(==DAq"F1q5!a%ad<<<<= LLOOq!S\\!__5555 6T!W%% 3??tAw??????333DGFFvFFAq$$!%QI9~~44(B#VC NND$?? #4[[33!&t33A$-afqj$9E$'LL$7$7E$00-2QT 3 |yy{{6:As.......226:As.......22!IIKKDAqQ$YY!YT (0#VQFAtaxD1HEE t# # YY!^^ 47T5M B B^QAA#A,, % %3!#e}55 %C&s^^66EArSX~~%(\\"%5%5QT 3s88$$%3q666ADDt# #>egg=tDOD$4[[ + +t++AQ OE((%*QT + t# #r#cNtddd|S)Nz The private _smat attribute of SparseMatrix is deprecated. Use the .todok() method instead. z1.9z$deprecated-private-matrix-attributes)deprecated_since_versionactive_deprecations_target)rr9selfs r _smatzSparseRepMatrix._smats8 " &+'M     zz||r#c ||dd|dt|ddS)NmethodLDL iszerofunctry_block_diagF)rYr[r\)invgetr )rVrGs r _eval_inversezSparseRepMatrix._eval_inversesSxxvzz(E::#)::lG#D#D'-zz2BE'J'JLL Lr#ct|stdi}|D]\}}||}|dkr|||<||j|j|S)aXApply 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 TypeErrorr9r=_newr7r8)rVfdokkr)fvs r applyfunczSparseRepMatrix.applyfuncs${{ 5344 4 JJLL&&((  DAq1BQwwAyyDIs333r#c$ddlm}||S)z,Returns an Immutable version of this Matrix.r )ImmutableSparseMatrix) immutablerj)rVrjs r as_immutablezSparseRepMatrix.as_immutables%444444$$T***r#c t|S)aCReturns a mutable version of this matrix. Examples ======== >>> from sympy import ImmutableMatrix >>> X = ImmutableMatrix([[1, 2], [3, 4]]) >>> Y = X.as_mutable() >>> Y[1, 1] = 5 # Can set values in Y >>> Y Matrix([ [1, 2], [3, 5]]) )MutableSparseMatrixrUs r as_mutablezSparseRepMatrix.as_mutable$s#4(((r#cfdtdDS)aReturns a column-sorted list of non-zero elements of the matrix. Examples ======== >>> from sympy import SparseMatrix >>> a=SparseMatrix(((1, 2), (3, 4))) >>> a Matrix([ [1, 2], [3, 4]]) >>> a.CL [(0, 0, 1), (1, 0, 3), (0, 1, 2), (1, 1, 4)] See Also ======== sympy.matrices.sparse.SparseMatrix.row_list cBg|]}t||fzSrr?rrfrVs r r!z,SparseRepMatrix.col_list..Is+lll!a47*n%%lllr#c:tt|Sr-)r>reversed)rfs r z*SparseRepMatrix.col_list..IsY]^fgh^i^iYjYjr#key)sortedr9rBrUs`r col_listzSparseRepMatrix.col_list5sE(mlllvdjjll6G6G6I6IOjOj/k/k/kllllr#cDt|S)z2Returns the number of non-zero elements in Matrix.)r5r9rUs r nnzzSparseRepMatrix.nnzKs4::<<   r#cfdttDS)aReturns a row-sorted list of non-zero elements of the matrix. Examples ======== >>> from sympy import SparseMatrix >>> a = SparseMatrix(((1, 2), (3, 4))) >>> a Matrix([ [1, 2], [3, 4]]) >>> a.RL [(0, 0, 1), (0, 1, 2), (1, 0, 3), (1, 1, 4)] See Also ======== sympy.matrices.sparse.SparseMatrix.col_list cBg|]}t||fzSrrrrss r r!z,SparseRepMatrix.row_list..cs7333!a47*n%%333r#rw)ryr9rBr>rUs`r row_listzSparseRepMatrix.row_listOsO(3333 4::<<$$&&D 1 1 1333 3r#c ||zS)z"Scalar element-wise multiplicationr)rVscalars r scalar_multiplyzSparseRepMatrix.scalar_multiplyfs }r#rZcN|j}||z||z|zS)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 rY)Tr])rVrhsrYts r solve_least_squaresz#SparseRepMatrix.solve_least_squaresjs.l F$||6|**1,S00r#c|js@|j|jkrtd|j|jkrtddS|||S)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_squarer7r8r'r]multiply)rVrrYs r solvezSparseRepMatrix.solves ~ 9y49$$ !;<<<TY&& "NOOO'&8868**33C88 8r#NzAlternate faster representationc t|Sr-)rrUs r liupczSparseRepMatrix.liupcsd||r#c t|Sr-)rrUs r row_structure_symbolic_choleskyz/SparseRepMatrix.row_structure_symbolic_choleskys/555r#Tc$t||SN) hermitian)rrVrs r choleskyzSparseRepMatrix.choleskys ::::r#c$t||Sr)rrs r LDLdecompositionz SparseRepMatrix.LDLdecompositions' BBBBr#c"t||Sr-)rrVrs r lower_triangular_solvez&SparseRepMatrix.lower_triangular_solve-dC888r#c"t||Sr-)rrs r upper_triangular_solvez&SparseRepMatrix.upper_triangular_solverr#)rZ)T)__name__ __module__ __qualname____doc__ classmethodr@propertyrWr_rhrlrorzr|rrrrRLCLrrrrrrrrrr __classcell__)rQs@r rrsSSj~$~$~$~$[~$@  X LLL 444@+++ )))"mmm,!!!333.71717171r 9 9 9 9 (D$(I J JB (D$(I J JB666;;;;CCCC999999/5nEM.N.V#+.>.FH.F.N.D.L".D.L"""""r#rc$eZdZedZdS)rnc||j|i|\}}}||||}||Sr-)r@_smat_to_DomainMatrix_fromrep)rrFrGr7r8r*reps r rczMutableSparseMatrix._newsI636GGGdD''dD99||C   r#N)rrrrrcrr#r rnrns-!![!!!r#rnN)collections.abcrsympy.core.containersrsympy.utilities.exceptionsrsympy.utilities.iterablesrsympy.utilities.miscr matrixbaser repmatrixr r utilitiesr decompositionsrrrrsolversrrrrn SparseMatrixrr#r rsz$$$$$$&&&&&&@@@@@@111111''''''""""""22222222DDDDDDDDvMvMvMvMvMivMvMvMr !!!!!/+;!!!# r#