\h/SSKrSSKrSSKJrJr SSKJr SSKJrJ r SSK J r SSK J r SSKJr "SS \5rS r"S S \5rg) N)_sympifysympify)Expr)BasicTuple)ImmutableDenseNDimArray)Symbol)Integerc\rSrSrSrSr\S5r\S5r\S5r \S5r \S5r \S 5r \S 5r S rS r\S 5r\S5r\S5rSrSrSrSrSrSrg)ArrayComprehension a Generate a list comprehension. Explanation =========== If there is a symbolic dimension, for example, say [i for i in range(1, N)] where N is a Symbol, then the expression will not be expanded to an array. Otherwise, calling the doit() function will launch the expansion. Examples ======== >>> from sympy.tensor.array import ArrayComprehension >>> from sympy import symbols >>> i, j, k = symbols('i j k') >>> a = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, 3)) >>> a ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, 3)) >>> a.doit() [[11, 12, 13], [21, 22, 23], [31, 32, 33], [41, 42, 43]] >>> b = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, k)) >>> b.doit() ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, k)) c[SU55(a [S5e[U5/nURUR X55 [ R "U/UQ70UD6nURSSUlURUR5Ul [UR5Ul URUR5UlU$)Nc3P# UHn[U5S:g=(d Sv M g7fNlen.0ls ^/var/www/auris/envauris/lib/python3.13/site-packages/sympy/tensor/array/array_comprehension.py -ArrayComprehension.__new__..% 4Gqs1v{"d"G$&KArrayComprehension requires values lower and upper bound for the expression)any ValueErrorrextend_check_limits_validityr__new___args_limits_calculate_shape_from_limits_shaper_rank_calculate_loop_size _loop_sizeclsfunctionsymbols assumptionsarglistobjs rr"ArrayComprehension.__new__$s 4G4 4 445 58$%s11(DEmmC9'9[9iim 55ckkB  O 11#**= c URS$)zThe function applied across limits. Examples ======== >>> from sympy.tensor.array import ArrayComprehension >>> from sympy import symbols >>> i, j = symbols('i j') >>> a = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, 3)) >>> a.function 10*i + j r)r#selfs rr,ArrayComprehension.function1szz!}r2cUR$)a% The list of limits that will be applied while expanding the array. Examples ======== >>> from sympy.tensor.array import ArrayComprehension >>> from sympy import symbols >>> i, j = symbols('i j') >>> a = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, 3)) >>> a.limits ((i, 1, 4), (j, 1, 3)) r$r4s rlimitsArrayComprehension.limitsAs||r2cURRnURHMup#nURU5 URR UR5nUR U5nMO U$)a The set of the free_symbols in the array. Variables appeared in the bounds are supposed to be excluded from the free symbol set. Examples ======== >>> from sympy.tensor.array import ArrayComprehension >>> from sympy import symbols >>> i, j, k = symbols('i j k') >>> a = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, 3)) >>> a.free_symbols set() >>> b = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, k+3)) >>> b.free_symbols {k} )r, free_symbolsr$discardunion)r5 expr_free_symvarinfsupcurr_free_symss rr<ArrayComprehension.free_symbolsRsg( 22 !\\MCc  ! !# & --33C4D4DEN)//?M*r2cJURVs/sHoSPM sn$s snf)aThe tuples of the variables in the limits. Examples ======== >>> from sympy.tensor.array import ArrayComprehension >>> from sympy import symbols >>> i, j, k = symbols('i j k') >>> a = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, 3)) >>> a.variables [i, j] rr8r5rs r variablesArrayComprehension.variablesms"#ll+l!l+++s cnURVs/sHn[U5S:wdMUSPM sn$s snf)zThe list of dummy variables. Note ==== Note that all variables are dummy variables since a limit without lower bound or upper bound is not accepted. rr)r$rrFs r bound_symbols ArrayComprehension.bound_symbols}s0#ll:lc!fk!l:::s2 2cUR$)a The shape of the expanded array, which may have symbols. Note ==== Both the lower and the upper bounds are included while calculating the shape. Examples ======== >>> from sympy.tensor.array import ArrayComprehension >>> from sympy import symbols >>> i, j, k = symbols('i j k') >>> a = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, 3)) >>> a.shape (4, 3) >>> b = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, k+3)) >>> b.shape (4, k + 3) )r&r4s rshapeArrayComprehension.shapes0{{r2czURH+upn[X#5R[5(dM+ g g)a Test if the array is shape-numeric which means there is no symbolic dimension. Examples ======== >>> from sympy.tensor.array import ArrayComprehension >>> from sympy import symbols >>> i, j, k = symbols('i j k') >>> a = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, 3)) >>> a.is_shape_numeric True >>> b = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, k+3)) >>> b.is_shape_numeric False FT)r$ratomsr )r5_rArBs ris_shape_numeric#ArrayComprehension.is_shape_numerics3& <>> from sympy.tensor.array import ArrayComprehension >>> from sympy import symbols >>> i, j, k = symbols('i j k') >>> a = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, 3)) >>> a.rank() 2 )r'r4s rrankArrayComprehension.rankszzr2cfURR(a [S5eUR$)ad The length of the expanded array which means the number of elements in the array. Raises ====== ValueError : When the length of the array is symbolic Examples ======== >>> from sympy.tensor.array import ArrayComprehension >>> from sympy import symbols >>> i, j = symbols('i j') >>> a = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, 3)) >>> len(a) 12 z Symbolic length is not supported)r)r<rr4s r__len__ArrayComprehension.__len__s'( ?? ' '?@ @r2c/nUHupEn[U5n[U5n[U[5(a [U6nO [U5nUR [XEU55 [ SXV455(a [ S5eXV:S:Xa [S5eXER;dXFR;dM[S5e U$)Nc3# UHLn[U[5(+=(d+ UR[[5UR5:gv MN g7fN) isinstancerrPr r )ris rr.s@UISA#1d++U0HAGGI0UUISsAAzABounds should be an Expression(combination of Integer and Symbol)Tz-Lower bound should be inferior to upper boundz)Variable should not be part of its bounds) rr]listrappendr TypeErrorrr<)r+r,r9 new_limitsr@rArBs rr!)ArrayComprehension._check_limits_validitys #MCc3-C3-C#t$$Sksm   eCc2 3UJMUUU cdd d" !PQQ&&A1A*A !LMM!$"r2c `[UVVVs/sH up#oDU- S-PM snnn5$s snnnfNr)tuple)r+r9rQrArBs rr%/ArrayComprehension._calculate_shape_from_limitss)v>v Ci!mv>??>s) c4U(dgSnUHnX#-nM U$)Nrr)r+rM loop_sizers rr('ArrayComprehension._calculate_loop_sizes& A! Ir2c HUR(dU$UR5$r\)rR _expand_array)r5hintss rdoitArrayComprehension.doits$$K!!##r2c /n[R"URVVVs/sHup#n[X4S-5PM snnn6H#nUR UR U55 M% [ XR5$s snnnfrf) itertoolsproductr$rangera _get_elementrrM)r5resr@rArBvaluess rrn ArrayComprehension._expand_array sz''+/<<*9+7-:Cc+0U*;+7*9:F JJt((0 1: 'sJJ77 *9sB c~URn[URU5Hup4URX45nM U$r\)r,ziprGsubs)r5rxtempr@vals rrvArrayComprehension._get_elements5}}DNNF3HC99S&D4 r2cvUR(aUR5R5$[S5e)amTransform the expanded array to a list. Raises ====== ValueError : When there is a symbolic dimension Examples ======== >>> from sympy.tensor.array import ArrayComprehension >>> from sympy import symbols >>> i, j = symbols('i j') >>> a = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, 3)) >>> a.tolist() [[11, 12, 13], [21, 22, 23], [31, 32, 33], [41, 42, 43]] z-A symbolic array cannot be expanded to a list)rRrntolistrr4s rrArrayComprehension.tolists1$  %%'..0 0HIIr2cSSKJn UR(d [S5eURS:wa [S5eU"UR 5R 55$)aTransform the expanded array to a matrix. Raises ====== ValueError : When there is a symbolic dimension ValueError : When the rank of the expanded array is not equal to 2 Examples ======== >>> from sympy.tensor.array import ArrayComprehension >>> from sympy import symbols >>> i, j = symbols('i j') >>> a = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, 3)) >>> a.tomatrix() Matrix([ [11, 12, 13], [21, 22, 23], [31, 32, 33], [41, 42, 43]]) r)Matrixz/A symbolic array cannot be expanded to a matrixzDimensions must be of size of 2)sympy.matricesrrRrr'rntomatrix)r5rs rrArrayComprehension.tomatrix3sP. *$$NO O ::?>? ?d((*33566r2rjN)__name__ __module__ __qualname____firstlineno____doc__r"propertyr,r9r<rGrJrMrRrUrX classmethodr!r%r(rprnrvrr__static_attributes__rjr2rr r s2    4 , , ; ;2. 0,@@$ 8 J.7r2r crSn[U[U55=(a URUR:H$)Ncg)Nrrjrjr2risLambda..UsQr2)r]typer)vLAMBDAs risLambdarTs* F af & H1::+HHr2c4\rSrSrSrSr\S5rSrSr g)ArrayComprehensionMapiXa A subclass of ArrayComprehension dedicated to map external function lambda. Notes ===== Only the lambda function is considered. At most one argument in lambda function is accepted in order to avoid ambiguity in value assignment. Examples ======== >>> from sympy.tensor.array import ArrayComprehensionMap >>> from sympy import symbols >>> i, j, k = symbols('i j k') >>> a = ArrayComprehensionMap(lambda: 1, (i, 1, 4)) >>> a.doit() [1, 1, 1, 1] >>> b = ArrayComprehensionMap(lambda a: a+1, (j, 1, 4)) >>> b.doit() [2, 3, 4, 5] c[SU55(a [S5e[U5(d [S5eURX5n[R "U/UQ70UD6nUR UlURUR5Ul [UR5Ul URUR5Ul XlU$)Nc3P# UHn[U5S:g=(d Sv M g7frrrs rr0ArrayComprehensionMap.__new__..rrrrzData type not supported)rrrr!rr"r#r$r%r&rr'r(r)_lambdar*s rr"ArrayComprehensionMap.__new__qs 4G4 4 445 5!!67 7,,X?mmC9'9[9ii 55ckkB  O 11#**=  r2c,^"U4SjS[5nU$)Nc">\rSrSrU4SjrSrg)%ArrayComprehensionMap.func.._ic6>[TR/UQ70UD6$r\)rr)r+argskwargsr5s rr"-ArrayComprehensionMap.func.._.__new__s,T\\KDKFKKr2rjN)rrrrr"rr4srrQrs L Lr2rQ)r)r5rQs` rfuncArrayComprehensionMap.funcs L% Lr2cURnURRRS:Xa U"5nU$URRRS:XaU"[R"SU55nU$)Nrrc X-$r\rj)abs rr4ArrayComprehensionMap._get_element..sacr2)r__code__ co_argcount functoolsreduce)r5rxr}s rrv"ArrayComprehensionMap._get_elementsh|| << , , 16D \\ " " . .! 3 (()96BCD r2rjN) rrrrrr"rrrvrrjr2rrrXs%0" r2r)rrssympy.core.sympifyrrsympy.core.exprr sympy.corerrsympy.tensor.arrayrsympy.core.symbolr sympy.core.numbersr r rrrjr2rrs<0 #6$&G7G7T I7.7r2