U ;qLeæ/ã@sŒddlZddlZddlmZmZddlmZddlmZm Z ddl m Z ddl m Z ddlmZGdd „d eƒZd d „ZGd d „d eƒZdS)éN)Ú_sympifyÚsympify)ÚExpr)ÚBasicÚTuple)ÚImmutableDenseNDimArray)ÚSymbol)ÚIntegerc@sÈeZdZdZdd„Zedd„ƒZedd„ƒZedd „ƒZed d „ƒZ ed d „ƒZ edd„ƒZ edd„ƒZ dd„Z dd„Zedd„ƒZedd„ƒZedd„ƒZdd„Zdd„Zd d!„Zd"d#„Zd$d%„Zd&S)'ÚArrayComprehensiona Generate a list comprehension. Explanation =========== If there is a symbolic dimension, for example, say [i for i in range(1, N)] where N is a Symbol, then the expression will not be expanded to an array. Otherwise, calling the doit() function will launch the expansion. Examples ======== >>> from sympy.tensor.array import ArrayComprehension >>> from sympy import symbols >>> i, j, k = symbols('i j k') >>> a = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, 3)) >>> a ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, 3)) >>> a.doit() [[11, 12, 13], [21, 22, 23], [31, 32, 33], [41, 42, 43]] >>> b = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, k)) >>> b.doit() ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, k)) cOs„tdd„|Dƒƒrtdƒ‚t|ƒg}| | ||¡¡tj|f|ž|Ž}|jdd…|_|  |j¡|_ t |j ƒ|_ |  |j ¡|_|S)Ncss|]}t|ƒdkpdVqdS©éN©Úlen©Ú.0Úl©rú}/home/p21-0144/sympy/latex2sympy2solve-back-end/sympyEq/lib/python3.8/site-packages/sympy/tensor/array/array_comprehension.pyÚ %sz-ArrayComprehension.__new__..úKArrayComprehension requires values lower and upper bound for the expressioné)ÚanyÚ ValueErrorrÚextendÚ_check_limits_validityrÚ__new__Ú_argsÚ_limitsÚ_calculate_shape_from_limitsÚ_shaperÚ_rankÚ_calculate_loop_sizeÚ _loop_size©ÚclsÚfunctionÚsymbolsÚ assumptionsZarglistÚobjrrrr$s  zArrayComprehension.__new__cCs |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©Úselfrrrr%1szArrayComprehension.functioncCs|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)) ©rr)rrrÚlimitsAszArrayComprehension.limitscCs@|jj}|jD],\}}}| |¡|j |j¡}| |¡}q|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%Ú free_symbolsrÚdiscardÚunion)r*Z expr_free_symÚvarÚinfÚsupZcurr_free_symsrrrr-Rs   zArrayComprehension.free_symbolscCsdd„|jDƒS)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] cSsg|] }|d‘qS)rrrrrrÚ {sz0ArrayComprehension.variables..r+r)rrrÚ variablesmszArrayComprehension.variablescCsdd„|jDƒS)z¿The list of dummy variables. Note ==== Note that all variables are dummy variables since a limit without lower bound or upper bound is not accepted. cSs g|]}t|ƒdkr|d‘qS)rrr rrrrr3‡s z4ArrayComprehension.bound_symbols..r+r)rrrÚ bound_symbols}s z ArrayComprehension.bound_symbolscCs|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) )rr)rrrÚshape‰szArrayComprehension.shapecCs,|jD] \}}}t||ƒ t¡rdSqdS)aø 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)rrÚatomsr)r*Ú_r1r2rrrÚis_shape_numeric£sz#ArrayComprehension.is_shape_numericcCs|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 r)rrrÚrank»s zArrayComprehension.rankcCs|jjrtdƒ‚|jS)aÔ 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-rr)rrrÚ__len__ÊszArrayComprehension.__len__cCs¤g}|D]–\}}}t|ƒ}t|ƒ}t|tƒr6t|Ž}nt|ƒ}| t|||ƒ¡tdd„||fDƒƒrntdƒ‚||kdkr‚tdƒ‚||jks–||jkrtdƒ‚q|S)Ncss.|]&}t|tƒ p$| tt¡| ¡kVqdS©N)Ú isinstancerr7rr )rÚirrrrðsÿz.zABounds should be an Expression(combination of Integer and Symbol)Tz-Lower bound should be inferior to upper boundz)Variable should not be part of its bounds) rr=ÚlistrÚappendrÚ TypeErrorrr-)r$r%r,Z new_limitsr0r1r2rrrrâs"  ÿ  z)ArrayComprehension._check_limits_validitycCstdd„|DƒƒS)NcSsg|]\}}}||d‘qS©rr)rr8r1r2rrrr3ûszCArrayComprehension._calculate_shape_from_limits..)Útuple)r$r,rrrrùsz/ArrayComprehension._calculate_shape_from_limitscCs"|sdSd}|D] }||}q|S)Nrrr)r$r6Ú loop_sizerrrrr!ýs  z'ArrayComprehension._calculate_loop_sizecKs|js |S| ¡Sr<)r9Ú _expand_array)r*ÚhintsrrrÚdoitszArrayComprehension.doitcCs<g}tjdd„|jDƒŽD]}| | |¡¡qt||jƒS)NcSs g|]\}}}t||dƒ‘qSrB)Úrange)rr0r1r2rrrr3sÿz4ArrayComprehension._expand_array..)Ú itertoolsÚproductrr@Ú _get_elementrr6)r*ÚresÚvaluesrrrrE s  þ z ArrayComprehension._expand_arraycCs,|j}t|j|ƒD]\}}| ||¡}q|Sr<)r%Úzipr4Úsubs)r*rMÚtempr0ÚvalrrrrKszArrayComprehension._get_elementcCs|jr| ¡ ¡Stdƒ‚dS)aÍTransform 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 listN)r9rEÚtolistrr)rrrrRs zArrayComprehension.tolistcCs<ddlm}|jstdƒ‚|jdkr,tdƒ‚|| ¡ ¡ƒS)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)ÚMatrixz/A symbolic array cannot be expanded to a matrixézDimensions must be of size of 2)Úsympy.matricesrSr9rr rEÚtomatrix)r*rSrrrrV3s   zArrayComprehension.tomatrixN)Ú__name__Ú __module__Ú __qualname__Ú__doc__rÚpropertyr%r,r-r4r5r6r9r:r;Ú classmethodrrr!rGrErKrRrVrrrrr s:            r cCs"dd„}t|t|ƒƒo |j|jkS)NcSsdS)NrrrrrrÚUózisLambda..)r=ÚtyperW)ÚvZLAMBDArrrÚisLambdaTsrac@s,eZdZdZdd„Zedd„ƒZdd„ZdS) ÚArrayComprehensionMapa[ 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] cOs‚tdd„|Dƒƒrtdƒ‚t|ƒs*tdƒ‚| ||¡}tj|f|ž|Ž}|j|_| |j¡|_ t |j ƒ|_ |  |j ¡|_ ||_|S)Ncss|]}t|ƒdkpdVqdSr r rrrrrrsz0ArrayComprehensionMap.__new__..rzData type not supported)rrrarrrrrrrrr r!r"Ú_lambdar#rrrrqs  zArrayComprehensionMap.__new__csG‡fdd„dtƒ}|S)NcseZdZ‡fdd„ZdS)z%ArrayComprehensionMap.func.._cstˆjf|ž|ŽSr<)rbrc)r$ÚargsÚkwargsr)rrr…sz-ArrayComprehensionMap.func.._.__new__N)rWrXrYrrr)rrr8„sr8)rb)r*r8rr)rÚfunc‚szArrayComprehensionMap.funccCsB|j}|jjjdkr|ƒ}n"|jjjdkr>|t dd„|¡ƒ}|S)NrrcSs||Sr<r)ÚaÚbrrrr]Žr^z4ArrayComprehensionMap._get_element..)rcÚ__code__Ú co_argcountÚ functoolsÚreduce)r*rMrPrrrrK‰s z"ArrayComprehensionMap._get_elementN)rWrXrYrZrr[rfrKrrrrrbXs  rb)rkrIÚsympy.core.sympifyrrÚsympy.core.exprrÚ sympy.corerrÚsympy.tensor.arrayrÚsympy.core.symbolrÚsympy.core.numbersr r rarbrrrrÚs    L