o jg/@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$d%Zd&S)'ArrayComprehensiona Generate a list comprehension. Explanation =========== If there is a symbolic dimension, for example, say [i for i in range(1, N)] where N is a Symbol, then the expression will not be expanded to an array. Otherwise, calling the doit() function will launch the expansion. Examples ======== >>> from sympy.tensor.array import ArrayComprehension >>> from sympy import symbols >>> i, j, k = symbols('i j k') >>> a = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, 3)) >>> a ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, 3)) >>> a.doit() [[11, 12, 13], [21, 22, 23], [31, 32, 33], [41, 42, 43]] >>> b = ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, k)) >>> b.doit() ArrayComprehension(10*i + j, (i, 1, 4), (j, 1, k)) cOstdd|Dr tdt|g}||||tj|g|Ri|}|jdd|_| |j|_ t |j |_ | |j |_|S)Ncs |] }t|dkp dVqdSNlen.0lr^/var/www/html/zoom/venv/lib/python3.10/site-packages/sympy/tensor/array/array_comprehension.py %z-ArrayComprehension.__new__..KArrayComprehension requires values lower and upper bound for the expression)any ValueErrorrextend_check_limits_validityr__new___args_limits_calculate_shape_from_limits_shaper_rank_calculate_loop_size _loop_sizeclsfunctionsymbols assumptionsarglistobjrrrr$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'1s zArrayComprehension.functioncC|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- expr_free_symvarinfsupcurr_free_symsrrrr1Rs   zArrayComprehension.free_symbolscCdd|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.variablescCr9)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)rrrrrrrr:s z4ArrayComprehension.bound_symbols..r/r,rrr bound_symbols}s z ArrayComprehension.bound_symbolscCr.)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!r,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-_r6r7rrris_shape_numerics z#ArrayComprehension.is_shape_numericcCr.)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$r1rr,rrr__len__szArrayComprehension.__len__cCsg}|D]K\}}}t|}t|}t|trt|}nt|}|t|||tdd||fDr7td||kdkrAtd||jvsK||jvrOtdq|S)Ncss0|]}t|t p|tt|kVqdSN) isinstancerr>rr )rirrrrs(z.zABounds should be an Expression(combination of Integer and Symbol)Tz-Lower bound should be inferior to upper boundz)Variable should not be part of its bounds) rrDlistrappendr TypeErrorrr1)r&r'r0 new_limitsr5r6r7rrrrs$   z)ArrayComprehension._check_limits_validitycCstdd|DS)NcSsg|] \}}}||dqSrr)rr?r6r7rrrr:szCArrayComprehension._calculate_shape_from_limits..)tuple)r&r0rrrr sz/ArrayComprehension._calculate_shape_from_limitscCs"|sdSd}|D]}||}q|S)Nrrr)r&r= loop_sizerrrrr#s  z'ArrayComprehension._calculate_loop_sizecKs|js|S|SrC)r@ _expand_array)r-hintsrrrdoitszArrayComprehension.doitcCs<g}tjdd|jDD] }|||q t||jS)NcSs g|] \}}}t||dqSrJ)range)rr5r6r7rrrr:sz4ArrayComprehension._expand_array..) itertoolsproductrrG _get_elementrr=)r-resvaluesrrrrM s    z ArrayComprehension._expand_arraycCs,|j}t|j|D] \}}|||}q |SrC)r'zipr;subs)r-rUtempr5valrrrrSszArrayComprehension._get_elementcCs|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)r@rMtolistrr,rrrrZs zArrayComprehension.tolistcCs<ddlm}|js td|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.matricesr[r@rr"rMtomatrix)r-r[rrrr^3s  zArrayComprehension.tomatrixN)__name__ __module__ __qualname____doc__rpropertyr'r0r1r;r<r=r@rArB classmethodrr r#rOrMrSrZr^rrrrr s<             r cCs"dd}t|t|o|j|jkS)NcSsdS)NrrrrrrUszisLambda..)rDtyper_)vLAMBDArrrisLambdaTsric@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|Dr tdt|std|||}tj|g|Ri|}|j|_||j|_ t |j |_ | |j |_ ||_|S)Ncsr r rrrrrrrrz0ArrayComprehensionMap.__new__..rzData type not supported)rrrirrrrrr r!rr"r#r$_lambdar%rrrrqs  zArrayComprehensionMap.__new__csGfdddt}|S)NcseZdZfddZdS)z%ArrayComprehensionMap.func.._cstjg|Ri|SrC)rjrk)r&argskwargsr,rrrsz-ArrayComprehensionMap.func.._.__new__N)r_r`rarrr,rrr?sr?)rj)r-r?rr,rfuncszArrayComprehensionMap.funccCsD|j}|jjjdkr|}|S|jjjdkr |tdd|}|S)NrrcSs||SrCr)abrrrresz4ArrayComprehensionMap._get_element..)rk__code__ co_argcount functoolsreduce)r-rUrXrrrrSsz"ArrayComprehensionMap._get_elementN)r_r`rarbrrcrnrSrrrrrjXs   rj)rsrQsympy.core.sympifyrrsympy.core.exprr sympy.corerrsympy.tensor.arrayrsympy.core.symbolrsympy.core.numbersr r rirjrrrrs    L