sg/ddlZddlZddlmZmZddlmZddlmZm Z ddl m Z ddl m Z ddlmZGdd eZd ZGd d eZy) N)_sympifysympify)Expr)BasicTuple)ImmutableDenseNDimArray)Symbol)IntegerceZdZdZdZedZedZedZedZ edZ edZ ed Z d Z d Zed Zed ZedZdZdZdZdZdZy)ArrayComprehensiona 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)) ctd|Dr tdt|g}|j|j ||t j |g|i|}|jdd|_|j|j|_ t|j|_ |j|j|_|S)Nc3@K|]}t|dk7xsdywNlen.0ls Y/var/www/html/venv/lib/python3.12/site-packages/sympy/tensor/array/array_comprehension.py z-ArrayComprehension.__new__..% 4qs1v{"d"4KArrayComprehension 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 zArrayComprehension.__new__$s 4G4 445 58$%s11(GDEmmC9'9[9iim 55ckkB  O 11#**= c |jdS)aAThe 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*zArrayComprehension.function1szz!}r/c|jS)au 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"r1s rlimitszArrayComprehension.limitsAs||r/c|jj}|jD]M\}}}|j||jj |j}|j |}O|S)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)r2 expr_free_symvarinfsupcurr_free_symss rr7zArrayComprehension.free_symbolsRsp( 22 !\\ @MCc  ! !# & --33C4D4DEN)//?M @r/cF|jDcgc]}|d c}Scc}w)aLThe 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] rr4r2rs r variableszArrayComprehension.variablesms #ll+!+++s cd|jDcgc]}t|dk7s|dc}Scc}w)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"rr@s r bound_symbolsz ArrayComprehension.bound_symbols}s*#ll:c!fk!:::s--c|jS)aE 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$r1s rshapezArrayComprehension.shapes0{{r/cp|jD]'\}}}t||jts'yy)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 )r2_r<r=s ris_shape_numericz#ArrayComprehension.is_shape_numerics9& << KAsCS#$$V, r/c|jS)a9The rank of the expanded array. Examples ======== >>> from sympy.tensor.array import ArrayComprehension >>> from sympy import symbols >>> i, j, k = symbols('i j k') >>> a = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, 3)) >>> a.rank() 2 )r%r1s rrankzArrayComprehension.rankszzr/c\|jjr td|jS)a The length of the expanded array which means the number of elements in the array. Raises ====== ValueError : When the length of the array is symbolic Examples ======== >>> from sympy.tensor.array import ArrayComprehension >>> from sympy import symbols >>> i, j = symbols('i j') >>> a = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, 3)) >>> len(a) 12 z Symbolic length is not supported)r'r7rr1s r__len__zArrayComprehension.__len__s'( ?? ' '?@ @r/c~g}|D]\}}}t|}t|}t|tr t|}n t|}|j t|||t d||fDr t d||kDdk(r td||jvs||jvstd|S)Nc3K|]B}t|t xs+|jtt|jk7DywN) isinstancerrGr r )ris rrz.sBUDE#1d++U0HAGGI0UUUsAA zABounds should be an Expression(combination of Integer and Symbol)Tz-Lower bound should be inferior to upper boundz)Variable should not be part of its bounds) rrQlistrappendr TypeErrorrr7)r)r*r5 new_limitsr;r<r=s rrz)ArrayComprehension._check_limits_validitys # NMCc3-C3-C#t$Sksm   eCc2 3UJMsUU cddc d" !PQQc&&&#1A1A*A !LMM! N"r/c ^t|Dcgc]\}}}||z dzc}}}Scc}}}wNr)tuple)r)r5rHr<r=s rr#z/ArrayComprehension._calculate_shape_from_limitss,v>> 3cCi!m>??>s( c(|syd}|D]}||z} |S)Nrr)r)rE loop_sizers rr&z'ArrayComprehension._calculate_loop_sizes-  &A!A I &r/c >|js|S|jSrP)rI _expand_array)r2hintss rdoitzArrayComprehension.doits$$K!!##r/c g}tj|jDcgc]\}}}t||dzc}}}D]"}|j |j |$t ||jScc}}}wrX) itertoolsproductr"rangerT _get_elementrrE)r2resr;r<r=valuess rr^z ArrayComprehension._expand_array s''+/<<*9*9,9Cc+0SU*;*9: 2F JJt((0 1 2 'sDJJ77 *9sA= c~|j}t|j|D]\}}|j||}|SrP)r*ziprAsubs)r2rgtempr;vals rrezArrayComprehension._get_elements>}}DNNF3 'HC99S#&D ' r/cl|jr|jjStd)aTransform the expanded array to a list. Raises ====== ValueError : When there is a symbolic dimension Examples ======== >>> from sympy.tensor.array import ArrayComprehension >>> from sympy import symbols >>> i, j = symbols('i j') >>> a = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, 3)) >>> a.tolist() [[11, 12, 13], [21, 22, 23], [31, 32, 33], [41, 42, 43]] z-A symbolic array cannot be expanded to a list)rIr^tolistrr1s rrnzArrayComprehension.tolists1$  %%'..0 0HIIr/cddlm}|js td|jdk7r td||j j S)aETransform 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.matricesrprIrr%r^tomatrix)r2rps rrszArrayComprehension.tomatrix3sP. *$$NO O ::?>? ?d((*33566r/N)__name__ __module__ __qualname____doc__r propertyr*r5r7rArCrErIrKrM classmethodrr#r&r`r^rernrsr[r/rr r s2    4 , , ; ;2. 0,@@$ 8 J.7r/r chd}t|t|xr|j|jk(S)Ncy)Nrr[r[r/rzisLambda..Usr/)rQtypert)vLAMBDAs risLambdarTs* F af & H1::+HHr/c,eZdZdZdZedZdZy)ArrayComprehensionMapa[ 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] ctd|Dr tdt|s td|j||}t j |g|i|}|j |_|j|j|_ t|j|_ |j|j|_ ||_|S)Nc3@K|]}t|dk7xsdywrrrs rrz0ArrayComprehensionMap.__new__..rrrrzData type not supported)rrrrrr r!r"r#r$rr%r&r'_lambdar(s rr zArrayComprehensionMap.__new__qs 4G4 445 5!67 7,,Xw?mmC9'9[9ii 55ckkB  O 11#**=  r/c*Gfddt}|S)NceZdZfdZy)%ArrayComprehensionMap.func.._c6tjg|i|SrP)rr)r)argskwargsr2s rr z-ArrayComprehensionMap.func.._.__new__s,T\\KDKFKKr/N)rtrurvr r1srrHrs  Lr/rH)r)r2rHs` rfunczArrayComprehensionMap.funcs L% Lr/c|j}|jjjdk(r |}|S|jjjdk(r|tjd|}|S)Nrrc ||zSrPr[)abs rr|z4ArrayComprehensionMap._get_element..s acr/)r__code__ co_argcount functoolsreduce)r2rgrks rrez"ArrayComprehensionMap._get_elementsh|| << , , 16D \\ " " . .! 3 (()96BCD r/N)rtrurvrwr rxrrer[r/rrrXs%0" r/r)rrbsympy.core.sympifyrrsympy.core.exprr sympy.corerrsympy.tensor.arrayrsympy.core.symbolr sympy.core.numbersr r rrr[r/rrs<0 #6$&G7G7T I7.7r/