U L?h/@sddlZddlZddlmZmZddlmZddlmZm Z ddl m Z ddl m Z ddlmZGdd d eZd d ZGd d d eZdS)N)_sympifysympify)Expr)BasicTuple)ImmutableDenseNDimArray)Symbol)Integerc@seZdZdZddZeddZeddZedd Zed d Z ed d Z eddZ eddZ ddZ ddZeddZeddZeddZddZddZd d!Zd"d#Zd$d%Zd&S)'ArrayComprehensiona Generate a list comprehension. Explanation =========== If there is a symbolic dimension, for example, say [i for i in range(1, N)] where N is a Symbol, then the expression will not be expanded to an array. Otherwise, calling the doit() function will launch the expansion. Examples ======== >>> from sympy.tensor.array import ArrayComprehension >>> from sympy import symbols >>> i, j, k = symbols('i j k') >>> a = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, 3)) >>> a ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, 3)) >>> a.doit() [[11, 12, 13], [21, 22, 23], [31, 32, 33], [41, 42, 43]] >>> b = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, k)) >>> b.doit() ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, k)) cOstdd|Drtdt|g}||||tj|f||}|jdd|_| |j|_ t |j |_ | |j |_|S)Ncss|]}t|dkpdVqdSNlen.0lrX/var/www/html/venv/lib/python3.8/site-packages/sympy/tensor/array/array_comprehension.py %sz-ArrayComprehension.__new__..KArrayComprehension requires values lower and upper bound for the expression)any ValueErrorrextend_check_limits_validityr__new___args_limits_calculate_shape_from_limits_shaper_rank_calculate_loop_size _loop_sizeclsfunctionsymbolsZ assumptionsZarglistobjrrrr$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)rselfrrrr%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(rrrlimitsAszArrayComprehension.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% free_symbolsrdiscardunion)r)Z expr_free_symvarinfsupZcurr_free_symsrrrr,Rs   zArrayComprehension.free_symbolscCsdd|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] cSsg|] }|dqS)rrrrrr {sz0ArrayComprehension.variables..r*r(rrr variablesmszArrayComprehension.variablescCsdd|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. cSs g|]}t|dkr|dqS)rrr rrrrr2s z4ArrayComprehension.bound_symbols..r*r(rrr 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(rrrshapeszArrayComprehension.shapecCs,|jD] \}}}t||trdSqdS)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)rratomsr)r)_r0r1rrris_shape_numericsz#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(rrrranks zArrayComprehension.rankcCs|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"r,rr(rrr__len__szArrayComprehension.__len__cCsg}|D]\}}}t|}t|}t|tr6t|}nt|}|t|||tdd||fDrntd||kdkrtd||jks||jkrtdq|S)Ncss.|]&}t|t p$|tt|kVqdSN) isinstancerr6rr )rirrrrsz.zABounds should be an Expression(combination of Integer and Symbol)Tz-Lower bound should be inferior to upper boundz)Variable should not be part of its bounds) rr<listrappendr TypeErrorrr,)r$r%r+Z new_limitsr/r0r1rrrrs"    z)ArrayComprehension._check_limits_validitycCstdd|DS)NcSsg|]\}}}||dqSrr)rr7r0r1rrrr2szCArrayComprehension._calculate_shape_from_limits..)tuple)r$r+rrrrsz/ArrayComprehension._calculate_shape_from_limitscCs"|sdSd}|D] }||}q|S)Nrrr)r$r5Z loop_sizerrrrr!s  z'ArrayComprehension._calculate_loop_sizecKs|js |S|Sr;)r8 _expand_array)r)hintsrrrdoitszArrayComprehension.doitcCs<g}tjdd|jDD]}|||qt||jS)NcSs g|]\}}}t||dqSrA)range)rr/r0r1rrrr2sz4ArrayComprehension._expand_array..) itertoolsproductrr? _get_elementrr5)r)resvaluesrrrrC s   z ArrayComprehension._expand_arraycCs,|j}t|j|D]\}}|||}q|Sr;)r%zipr3subs)r)rKtempr/valrrrrIszArrayComprehension._get_elementcCs|jr|StddS)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 listN)r8rCtolistrr(rrrrPs zArrayComprehension.tolistcCs<ddlm}|jstd|jdkr,td||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)Zsympy.matricesrQr8rr rCtomatrix)r)rQrrrrS3s   zArrayComprehension.tomatrixN)__name__ __module__ __qualname____doc__rpropertyr%r+r,r3r4r5r8r9r: classmethodrrr!rErCrIrPrSrrrrr s:            r cCs"dd}t|t|o |j|jkS)NcSsdS)NrrrrrrUzisLambda..)r<typerT)vZLAMBDArrrisLambdaTsr^c@s,eZdZdZddZeddZddZdS) 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] cOstdd|Drtdt|s*td|||}tj|f||}|j|_||j|_ t |j |_ | |j |_ ||_|S)Ncss|]}t|dkpdVqdSr r rrrrrrsz0ArrayComprehensionMap.__new__..rzData type not supported)rrr^rrrrrrrrr r!r"_lambdar#rrrrqs  zArrayComprehensionMap.__new__csGfdddt}|S)NcseZdZfddZdS)z%ArrayComprehensionMap.func.._cstjf||Sr;)r_r`)r$argskwargsr(rrrsz-ArrayComprehensionMap.func.._.__new__N)rTrUrVrrr(rrr7sr7)r_)r)r7rr(rfuncszArrayComprehensionMap.funccCsB|j}|jjjdkr|}n"|jjjdkr>|tdd|}|S)NrrcSs||Sr;r)abrrrrZr[z4ArrayComprehensionMap._get_element..)r`__code__ co_argcount functoolsreduce)r)rKrNrrrrIs z"ArrayComprehensionMap._get_elementN)rTrUrVrWrrXrcrIrrrrr_Xs  r_)rhrGZsympy.core.sympifyrrZsympy.core.exprrZ sympy.corerrZsympy.tensor.arrayrZsympy.core.symbolrZsympy.core.numbersr r r^r_rrrrs    L