a Эмd.dДd/Ьd0d1ДZ?d2d3ДZ@d4d5ДZAe-e@eAГZBe-ee e2Гe e3ГГe"e2e3ГГZCe-ee d%e2Гe d%e3ГГe#e2e3Гed%ГГZDee/e8e9fZEeEeCeDfe7ZFe=fZGd6S)7a° Classes and functions useful for rewriting expressions for optimized code generation. Some languages (or standards thereof), e.g. C99, offer specialized math functions for better performance and/or precision. Using the ``optimize`` function in this module, together with a collection of rules (represented as instances of ``Optimization``), one can rewrite the expressions for this purpose:: >>> from sympy import Symbol, exp, log >>> from sympy.codegen.rewriting import optimize, optims_c99 >>> x = Symbol('x') >>> optimize(3*exp(2*x) - 3, optims_c99) 3*expm1(2*x) >>> optimize(exp(2*x) - 1 - exp(-33), optims_c99) expm1(2*x) - exp(-33) >>> optimize(log(3*x + 3), optims_c99) log1p(x) + log(3) >>> optimize(log(2*x + 3), optims_c99) log(2*x + 3) The ``optims_c99`` imported above is tuple containing the following instances (which may be imported from ``sympy.codegen.rewriting``): - ``expm1_opt`` - ``log1p_opt`` - ``exp2_opt`` - ``log2_opt`` - ``log2const_opt`` щ)┌ expand_log)┌S)┌Wild)┌sign)┌exp┌log)┌Max┌Min)┌cos┌sin┌sinc)┌Q┌ask)┌log1p┌log2┌exp2┌expm1)┌MatrixSolve)┌UnevaluatedExpr)┌Pow)┌ logaddexp┌ logaddexp2)┌cosm1)┌Mul)┌MatrixSymbol)┌siftc@s"eZdZdZdddДZddДZdS) ┌Optimizationzэ Abstract base class for rewriting optimization. Subclasses should implement ``__call__`` taking an expression as argument. Parameters ========== cost_function : callable returning number priority : number NщcCs||_||_dSйN)┌ cost_function┌priority)┌selfrr йr"·g/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/sympy/codegen/rewriting.py┌__init__@szOptimization.__init__cGst||jdНdS)N)┌keyr)┌sortedr)r!┌argsr"r"r#┌cheapestDszOptimization.cheapest)Nr)┌__name__┌ __module__┌__qualname__┌__doc__r$r(r"r"r"r#r4s rcs(eZdZdZЗfddДZddДZЗZS)┌ReplaceOptima╒ Rewriting optimization calling replace on expressions. Explanation =========== The instance can be used as a function on expressions for which it will apply the ``replace`` method (see :meth:`sympy.core.basic.Basic.replace`). Parameters ========== query : First argument passed to replace. value : Second argument passed to replace. Examples ======== >>> from sympy import Symbol >>> from sympy.codegen.rewriting import ReplaceOptim >>> from sympy.codegen.cfunctions import exp2 >>> x = Symbol('x') >>> exp2_opt = ReplaceOptim(lambda p: p.is_Pow and p.base == 2, ... lambda p: exp2(p.exp)) >>> exp2_opt(2**x) exp2(x) cs"tГjfi|дО||_||_dSr)┌superr$┌query┌value)r!r/r0┌kwargsй┌ __class__r"r#r$hszReplaceOptim.__init__cCs|а|j|jбSr)┌replacer/r0)r!┌exprr"r"r#┌__call__mszReplaceOptim.__call__)r)r*r+r,r$r6┌ __classcell__r"r"r2r#r-Hsr-cCs@t|ddДddНD](}||Г}|jdur.|}q|а||б}q|S)aы Apply optimizations to an expression. Parameters ========== expr : expression optimizations : iterable of ``Optimization`` instances The optimizations will be sorted with respect to ``priority`` (highest first). Examples ======== >>> from sympy import log, Symbol >>> from sympy.codegen.rewriting import optims_c99, optimize >>> x = Symbol('x') >>> optimize(log(x+3)/log(2) + log(x**2 + 1), optims_c99) log1p(x**2) + log2(x + 3) cSs|jSr)r )┌optr"r"r#┌Жєzoptimize..T)r%┌reverseN)r&rr()r5Z optimizationsZoptimZnew_exprr"r"r#┌optimizeqs r<cCs|jo|jdkS)Nщ)┌is_Pow┌baseй┌pr"r"r#r9Рr:r9cCs t|jГSr)rrr@r"r"r#r9Сr:┌dcCs|jSr)Zis_Dummyй┌xr"r"r#r9Хr:)Z properties┌ucCs|jo|jSr)┌ is_number┌is_AddrCr"r"r#r9Цr:┌v┌w┌ncCs|jSrйrFrCr"r"r#r9Щr:r=cCs|аddДбS)NcSs*|jr|jjp(t|ttfГo(|jdjS)Nr)r>rZis_negative┌ isinstancerrr'rFй┌er"r"r#r9дs·..)┌countйr5r"r"r#r9гs йrcCsDt|tГoB|jdjoBt|jdjГdkoBtddД|jdjDГГS)Nrr=css|]}t|tГVqdSr)rLr)┌.0┌tr"r"r#┌ ░r:z..)rLrr'rG┌len┌allй┌lr"r"r#r9нs ■cCs<tddД|jdjDГОtttddД|jdjDГОГГS)NcSsg|]}|jdСqSйrйr'йrSrNr"r"r#┌ ▓r:z..rcSsg|]}|jdСqSrZr[r\r"r"r#r]│r:)rr'rrr rXr"r"r#r9▒s cs>eZdZdZdЗfddД ZddДZddДZЗfd d ДZЗZS)┌FuncMinusOneOptimaэSpecialization of ReplaceOptim for functions evaluating "f(x) - 1". Explanation =========== Numerical functions which go toward one as x go toward zero is often best implemented by a dedicated function in order to avoid catastrophic cancellation. One such example is ``expm1(x)`` in the C standard library which evaluates ``exp(x) - 1``. Such functions preserves many more significant digits when its argument is much smaller than one, compared to subtracting one afterwards. Parameters ========== func : The function which is subtracted by one. func_m_1 : The specialized function evaluating ``func(x) - 1``. opportunistic : bool When ``True``, apply the transformation as long as the magnitude of the remaining number terms decreases. When ``False``, only apply the transformation if it completely eliminates the number term. Examples ======== >>> from sympy import symbols, exp >>> from sympy.codegen.rewriting import FuncMinusOneOptim >>> from sympy.codegen.cfunctions import expm1 >>> x, y = symbols('x y') >>> expm1_opt = FuncMinusOneOptim(exp, expm1) >>> expm1_opt(exp(x) + 2*exp(5*y) - 3) expm1(x) + 2*expm1(5*y) Tcs<dЙtГjddД|jЗЗfddДdН||_И|_||_dS)Nщ cSs|jSr)rGrMr"r"r#r9сr:z,FuncMinusOneOptim.__init__..cs|абИ|аИбSr)Z count_opsrPrQй┌func_m_1Zweightr"r#r9тr:rR)r.r$┌replace_in_Add┌funcra┌ opportunistic)r!rcrardr2r`r#r$▀s zFuncMinusOneOptim.__init__csDt|jddДddН\}}t|Г}t|ЗfddДddН\}}|||fS)NcSs|jSrrKй┌argr"r"r#r9шr:z4FuncMinusOneOptim._group_Add_terms..Tй┌binarycs|аИjбSr)Zhasrcreйr!r"r#r9ъr:)rr'┌sum)r!┌addZnumbersZnon_num┌numsum┌terms_with_func┌otherr"rir#┌_group_Add_termsчsz"FuncMinusOneOptim._group_Add_termscs:Иа|б\}}}|dkr|Sgg}}|D]Ї}|jrВt|jЗfddДddН\}} t|Гdkr|t| Гdkr||d| d}} qаd} n|jИjkrЬ|tj}} nd} | duРr| jРrt | Гt |ГkРrИj rтt| |Гt|Гk} n| |dk} | Рr|| 7}|а| Иj |jОбq*|а|бq*|j|g|в|в|вRОS)z1 passed as second argument to Basic.replace(...) rcs|jИjkSr)rcrerir"r#r9їr:z2FuncMinusOneOptim.replace_in_Add..TrgrN)roZis_Mulrr'rVrcrZOnerFrrd┌abs┌appendra)r!rNrlrmZother_non_num_termsZsubstitutedZ untouchedZ with_funcrcZcoeffZ do_substituter"rir#rbэs. &z FuncMinusOneOptim.replace_in_Addcs(tГа|б}tГа|абб}|а||бSr)r.r6┌factorr()r!r5Zalt1Zalt2r2r"r#r6 szFuncMinusOneOptim.__call__)T) r)r*r+r,r$rorbr6r7r"r"r2r#r^╕s & r^cCs t|tГSr)rLrrMr"r"r#r9r:cCs(t|аtddДбГаttdГttГбS)NcSst|абГSr)rrrrer"r"r#r9r:rOr)rr4r┌_urrXr"r"r#r9s ■cCs|jSr)Z is_symbol)┌br"r"r#r9r:)┌base_reqcstЗЗfddДddДГS)a Creates an instance of :class:`ReplaceOptim` for expanding ``Pow``. Explanation =========== The requirements for expansions are that the base needs to be a symbol and the exponent needs to be an Integer (and be less than or equal to ``limit``). Parameters ========== limit : int The highest power which is expanded into multiplication. base_req : function returning bool Requirement on base for expansion to happen, default is to return the ``is_symbol`` attribute of the base. Examples ======== >>> from sympy import Symbol, sin >>> from sympy.codegen.rewriting import create_expand_pow_optimization >>> x = Symbol('x') >>> expand_opt = create_expand_pow_optimization(3) >>> expand_opt(x**5 + x**3) x**5 + x*x*x >>> expand_opt(x**5 + x**3 + sin(x)**3) x**5 + sin(x)**3 + x*x*x >>> opt2 = create_expand_pow_optimization(3, base_req=lambda b: not b.is_Function) >>> opt2((x+1)**2 + sin(x)**2) sin(x)**2 + (x + 1)*(x + 1) cs&|jo$И|jГo$|jjo$t|jГИkSr)r>r?rZ is_IntegerrprMйru┌limitr"r#r9Ar:z0create_expand_pow_optimization..cSsJ|jdkr(tt|jg|j ddiОГSdtt|jg|jddiОГS)Nr┌evaluateFr)rrrr?r@r"r"r#r9Bs()r-)rwrur"rvr#┌create_expand_pow_optimizations#■rycCsZ|jrVt|jГdkrV|j\}}|jrV|jddkrV|j}t|tГrVtt t а|jбГГSdS)Nr=rF)Z is_MatMulrVr'Z is_Inverse┌shaperfrLr┌boolrr Zfullrankйr5┌left┌rightZinv_argr"r"r#┌_matinv_predicateHs rcCs|j\}}|j}t||ГSr)r'rfrr|r"r"r#┌_matinv_transformSs rАN)Hr,Zsympy.core.functionrZsympy.core.singletonrZsympy.core.symbolrZ$sympy.functions.elementary.complexesrZ&sympy.functions.elementary.exponentialrrZ(sympy.functions.elementary.miscellaneousrr Z(sympy.functions.elementary.trigonometricr rrZsympy.assumptionsr rZsympy.codegen.cfunctionsrrrrZsympy.codegen.matrix_nodesrZsympy.core.exprrZsympy.core.powerrZsympy.codegen.numpy_nodesrrZsympy.codegen.scipy_nodesrZsympy.core.mulrZ"sympy.matrices.expressions.matexprrZsympy.utilities.iterablesrrr-r<Zexp2_optZ_drsZ_v┌_wZ_nZ sinc_opt1Z sinc_opt2Z sinc_optsZlog2_optZ log2const_optZlogsumexp_2terms_optr^Z expm1_optZ cosm1_optZ log1p_optryrrАZ matinv_optZ logaddexp_optZlogaddexp2_optZ optims_c99Zoptims_numpyZoptims_scipyr"r"r"r#┌st )■ *√[ ■+ ,