B ddY9@sddlmZddlmZddlmZddlmZddlm Z ddl m Z ddl m Z mZdd lmZdd lmZmZmZmZdd lmZmZGd d d eZGdddee 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_sparsecseZdZdZefddZeddZddZdd Z d d Z d d Z ddZ ddZ ddZddZd*ddZd+ddZeedddZee dddZddZdd Zd,d"d#Zd-d$d%Zd&d'Zd(d)Zeje_eje_eje_eje_eje_eje_ZS).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 s@t|dkrDt|dtrD|dj}|dj}|d||fSit|dkrn|ddkrndd|dg}t|dkr|dd\}}||krdkrnn d}}n0d||fkrtdnt|dt|d}}t|dtr|d}d||fkrtd ||fddt |D}fd dt |D} xF|D]>} x6| D].} || | } | j krP| | | f<qPWqFW||fSt|dt tfrfd d } x|dD]\\}}}t|trx|D]"\\} } }| || || |qWnrt|ttfrdj|f|\}}xLD]&\} } | || || | | fq8Wn |}| || |qWnt|drXtd d |dD }|sΈj|df|\}}n|d}t|||krtd t|||xXt |D]L} xDt |D]8} || || } | } | j kr| | | f<qWqW|dkr}|rtdd|Ddnd}|rtdd|Ddnd}nZxXD]L\} } | r| |ks| r| |krtd | | fd|dd|dqW||fSt|dkrt|dttfr|d}d}xpt|D]d\} }t|ttfsf|g}x4t|D](\} }|j krp || | f<qpWt|t|}qHW|rt|nd}|}||fStj|\}}}xNt |D]B} x:t |D].} ||| | } | j kr| | | f<qWqW||fSdS)Nrrz*Pass rows=None and no cols for autosizing.z2{} and {} must be integers for this specification.csg|]}|qS)_sympify).0i)clsrb/work/yifan.wang/ringdown/master-ringdown-env/lib/python3.7/site-packages/sympy/matrices/sparse.py sz;SparseRepMatrix._handle_creation_inputs..csg|]}|qSr)r)rj)rrrrscsN|rJ||fkr>|||fkr>td||f|||f|||f<dS)Nz)There is a collision at {} for {} and {}.) ValueErrorformat)rrv)smatrrupdates z7SparseRepMatrix._handle_creation_inputs..updatecss|]}t|VqdS)N)r)rrrrr sz:SparseRepMatrix._handle_creation_inputs..zMThe length of the flat list ({}) does not match the specified size ({} * {}).cSsg|] \}}|qSrr)rr_rrrrscSsg|] \}}|qSrr)rr$crrrrsz?The location {} is out of the designated range[{}, {}]x[{}, {}])len isinstancerrowscolstodokrrrrrangerzerodictritemslisttuple_handle_creation_inputsranykeysmax enumeratesuper)rargskwargsr(r)r#r%opZ row_indicesZ col_indicesrrvaluer!rvvr$ZflatZ flat_listr3rowmat) __class__)rr rr1ks             $     " " "   z'SparseRepMatrix._handle_creation_inputscCstdddd|S)Nz The private _smat attribute of SparseMatrix is deprecated. Use the .todok() method instead. z1.9z$deprecated-private-matrix-attributes)Zdeprecated_since_versionZactive_deprecations_target)rr*)selfrrr_smats zSparseRepMatrix._smatcKs(|j|dd|dt|dddS)NmethodLDL iszerofunctry_block_diagF)rArCrD)invgetr )r?r8rrr _eval_inverses zSparseRepMatrix._eval_inversecCsXt|stdi}x0|D] \}}||}|dkr"|||<q"W||j|j|S)aXApply a function to each element of the matrix. Examples ======== >>> from sympy import SparseMatrix >>> m = SparseMatrix(2, 2, lambda i, j: i*2+j) >>> m Matrix([ [0, 1], [2, 3]]) >>> m.applyfunc(lambda i: 2*i) Matrix([ [0, 2], [4, 6]]) z`f` must be callable.r)callable TypeErrorr*r._newr(r))r?fZdokkrZfvrrr applyfuncs zSparseRepMatrix.applyfunccCsddlm}||S)z,Returns an Immutable version of this Matrix.r)ImmutableSparseMatrix)Z immutablerN)r?rNrrr as_immutables zSparseRepMatrix.as_immutablecCst|S)aCReturns a mutable version of this matrix. Examples ======== >>> from sympy import ImmutableMatrix >>> X = ImmutableMatrix([[1, 2], [3, 4]]) >>> Y = X.as_mutable() >>> Y[1, 1] = 5 # Can set values in Y >>> Y Matrix([ [1, 2], [3, 5]]) )MutableSparseMatrix)r?rrr as_mutable$szSparseRepMatrix.as_mutablecs*fddttdddDS)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 csg|]}t||fqSr)r0)rrL)r?rrrIsz,SparseRepMatrix.col_list..cSs tt|S)N)r/reversed)rLrrrIz*SparseRepMatrix.col_list..)key)sortedr/r*r3)r?r)r?rcol_list5szSparseRepMatrix.col_listcCs t|S)z2Returns the number of non-zero elements in Matrix.)r&r*)r?rrrnnzKszSparseRepMatrix.nnzcs"fddttdDS)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 csg|]}t||fqSr)r0)rrL)r?rrrcsz,SparseRepMatrix.row_list..)rU)rVr*r3r/)r?r)r?rrow_listOs zSparseRepMatrix.row_listcCs||S)z"Scalar element-wise multiplicationr)r?Zscalarrrrscalar_multiplyfszSparseRepMatrix.scalar_multiplyrBcCs|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 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 )rA)TrE)r?rhsrAtrrrsolve_least_squaresjs6z#SparseRepMatrix.solve_least_squarescCsH|js2|j|jkrtdqD|j|jkrDtdn|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).)rAN)Z is_squarer(r)rrEmultiply)r?r\rArrrsolves     zSparseRepMatrix.solveNzAlternate faster representationcCst|S)N)r )r?rrrliupcszSparseRepMatrix.liupccCst|S)N)r )r?rrrrow_structure_symbolic_choleskysz/SparseRepMatrix.row_structure_symbolic_choleskyTcCs t||dS)N) hermitian)r)r?rcrrrcholeskyszSparseRepMatrix.choleskycCs t||dS)N)rc)r)r?rcrrrLDLdecompositionsz SparseRepMatrix.LDLdecompositioncCs t||S)N)r)r?r\rrrlower_triangular_solvesz&SparseRepMatrix.lower_triangular_solvecCs t||S)N)r)r?r\rrrupper_triangular_solvesz&SparseRepMatrix.upper_triangular_solve)rB)rB)T)T)__name__ __module__ __qualname____doc__ classmethodr1propertyr@rGrMrOrQrWrXrYrZr^r`ZRLZCLrarbrdrerfrgr r rr __classcell__rr)r>rrs8T   9   rc@seZdZeddZdS)rPcOs*|j||\}}}||||}||S)N)r1Z_smat_to_DomainMatrixZ_fromrep)rr7r8r(r)r reprrrrJszMutableSparseMatrix._newN)rhrirjrlrJrrrrrPsrPN)collections.abcrZsympy.core.containersrZsympy.utilities.exceptionsrZsympy.utilities.iterablesrZsympy.utilities.miscrZmatricesrZ repmatrixr r Z utilitiesr Zdecompositionsr r rrZsolversrrrrPZ SparseMatrixrrrrs       <