g/ddlZddlZddlmZmZddlmZddlmZm Z ddl m Z ddl m Z ddlmZGdd eZd ZGd d eZdS) N)_sympifysympify)Expr)BasicTuple)ImmutableDenseNDimArray)Symbol)IntegerceZdZdZdZedZedZedZedZ edZ edZ ed Z d Z d Zed Zed ZedZdZdZdZdZdZdS)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|Drtdt|g}||||t j|g|Ri|}|jdd|_| |j|_ t|j |_ | |j |_|S)Nc3@K|]}t|dkpdVdSNlen.0ls b/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/tensor/array/array_comprehension.py z-ArrayComprehension.__new__..%144qs1vv{"d444444KArrayComprehension 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 44G444 4 4 5455 58$$%s11(GDDEEEmC9'999[99im 55ckBB  OO 11#*== rc|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.function1sz!}rc|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"r0s rlimitszArrayComprehension.limitsAs |rc|jj}|jD]O\}}}|||j|j}||}P|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)r1 expr_free_symvarinfsupcurr_free_symss rr6zArrayComprehension.free_symbolsRso( 2 !\ @ @MCc  ! !# & & & -33C4DEEN)//??MMrc$d|jDS)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] cg|] }|d S)rrs r z0ArrayComprehension.variables..{s+++!+++rr3r0s r variableszArrayComprehension.variablesms,+dl++++rc$d|jDS)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. cDg|]}t|dk|dS)rrrrs rrAz4ArrayComprehension.bound_symbols..s':::c!ffkk!kkkrr3r0s r bound_symbolsz ArrayComprehension.bound_symbols}s;:dl::::rc|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$r0s rshapezArrayComprehension.shapes 0{rcx|jD]1\}}}t||trdS2dS)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 )r1_r;r<s ris_shape_numericz#ArrayComprehension.is_shape_numericsJ& <  KAsCS#$$V,, uu trc|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%r0s rrankzArrayComprehension.ranks zrcF|jjrtd|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'r6rr0s r__len__zArrayComprehension.__len__s)( ? ' A?@@ @rcg}|D]\}}}t|}t|}t|tr t|}nt|}|t|||t d||fDrt d||kdkrtd||jvs ||jvrtd|S)Nc3K|]P}t|t p5|tt|kVQdSN) isinstancerrIr r )ris rrz.skUUDE#1d+++U0H0HAGGII0UUUUUUUrzABounds 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) rrSlistrappendr TypeErrorrr6)r)r*r4 new_limitsr:r;r<s rrz)ArrayComprehension._check_limits_validitys # N NMCc3--C3--C#t$$ $Sksmm   eCc22 3 3 3UUJMsUUUUU e cdddc d"" !PQQQc&&&#1A*A*A !LMMM+Brc4td|DS)Nc&g|]\}}}||z dzSrr@)rrJr;r<s rrAzCArrayComprehension._calculate_shape_from_limits..s&>>> 3cCi!m>>>r)tuple)r)r4s rr#z/ArrayComprehension._calculate_shape_from_limitss>>v>>>???rc&|sdSd}|D]}||z}|S)Nrrr@)r)rG loop_sizers rr&z'ArrayComprehension._calculate_loop_sizes4 1  & &A!A IIrc <|js|S|SrR)rK _expand_array)r1hintss rdoitzArrayComprehension.doits$$ K!!###rcg}tjd|jDD]*}|||+t ||jS)Nc<g|]\}}}t||dzSr[)range)rr:r;r<s rrAz4ArrayComprehension._expand_array..s<*9*9*9,9Cc+0SU*;*;*9*9*9r) itertoolsproductr"rV _get_elementrrG)r1resvaluess rr`z ArrayComprehension._expand_array ss'*9*9+/<*9*9*9: 2 2F JJt((00 1 1 1 1&sDJ777rcv|j}t|j|D]\}}|||}|SrR)r*ziprBsubs)r1rjtempr:vals rrhzArrayComprehension._get_elementsB}DNF33 ' 'HC99S#&&DD rcz|jr&|Std)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)rKr`tolistrr0s rrqzArrayComprehension.tolists<$   1%%''..00 0HIIIrcddlm}|jstd|jdkrtd||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.matricesrsrKrr%r`tomatrix)r1rss rrvzArrayComprehension.tomatrix3ss. *)))))$ PNOO O :??>?? ?vd((**3355666rN)__name__ __module__ __qualname____doc__r propertyr*r4r6rBrErGrKrMrO classmethodrr#r&rbr`rhrqrvr@rrr r s2     X X X4 , ,X , ; ;X ;X2X.   0[,@@[@[$$$ 888 JJJ.77777rr cbd}t|t|o|j|jkS)NcdS)Nrr@r@rrzisLambda..UsQr)rStyperw)vLAMBDAs risLambdarTs- YF af & & H1:+HHrc4eZdZdZdZedZdZdS)ArrayComprehensionMapa[ A subclass of ArrayComprehension dedicated to map external function lambda. Notes ===== Only the lambda function is considered. At most one argument in lambda function is accepted in order to avoid ambiguity in value assignment. Examples ======== >>> from sympy.tensor.array import ArrayComprehensionMap >>> from sympy import symbols >>> i, j, k = symbols('i j k') >>> a = ArrayComprehensionMap(lambda: 1, (i, 1, 4)) >>> a.doit() [1, 1, 1, 1] >>> b = ArrayComprehensionMap(lambda a: a+1, (j, 1, 4)) >>> b.doit() [2, 3, 4, 5] ctd|Drtdt|std|||}t j|g|Ri|}|j|_||j|_ t|j |_ | |j |_ ||_|S)Nc3@K|]}t|dkpdVdSrrrs rrz0ArrayComprehensionMap.__new__..rrrrzData type not supported)rrrrrr r!r"r#r$rr%r&r'_lambdar(s rr zArrayComprehensionMap.__new__qs 44G444 4 4 5455 5!! 8677 7,,Xw??mC9'999[99i 55ckBB  OO 11#*==  rc2Gfddt}|S)NceZdZfdZdS)%ArrayComprehensionMap.func.._c.tjg|Ri|SrR)rr)r)argskwargsr1s rr z-ArrayComprehensionMap.func.._.__new__s#,T\KDKKKFKKKrN)rwrxryr r0srrJrs5 L L L L L L LrrJ)r)r1rJs` rfunczArrayComprehensionMap.funcsI L L L L L L L% L L Lrc|j}|jjjdkr |}n4|jjjdkr|tjd|}|S)Nrrc ||zSrRr@)abs rrz4ArrayComprehensionMap._get_element..s acr)r__code__ co_argcount functoolsreduce)r1rjrns rrhz"ArrayComprehensionMap._get_elementsa| < , 1 1466DD \ " .! 3 34 ()9)96BBCCD rN)rwrxryrzr r{rrhr@rrrrXsW0"X rr)rrfsympy.core.sympifyrrsympy.core.exprr sympy.corerrsympy.tensor.arrayrsympy.core.symbolr sympy.core.numbersr r rrr@rrrs00000000 ########666666$$$$$$&&&&&&G7G7G7G7G7G7G7G7T III77777.77777r