Wolfram mathematica [[i]]的未估价形式
考虑下面的简单示例Wolfram mathematica [[i]]的未估价形式,wolfram-mathematica,operator-precedence,Wolfram Mathematica,Operator Precedence,考虑下面的简单示例 cf = Block[{a, x, degree = 3}, With[{expr = Product[x - a[[i]], {i, degree}]}, Compile[{{x, _Real, 0}, {a, _Real, 1}}, expr] ] ] 这是在编译语句体中传输代码的可能方法之一。它产生Part:：partd错误，因为[[i]]在求值时不是列表 简单的解决方法是忽略此消息或将其关闭。当然还有其他的方法。例如，可以通过在编译前在编译体中替
cf = Block[{a, x, degree = 3},
With[{expr = Product[x - a[[i]], {i, degree}]},
Compile[{{x, _Real, 0}, {a, _Real, 1}}, expr]
]
]
cf = ReleaseHold[Block[{a, x, degree = 3},
With[{expr = Product[x - a[i], {i, degree}]},
Hold[Compile[{{x, _Real, 0}, {a, _Real, 1}}, expr]] /.
a[i_] :> a[[i]]]
]
]
#define<< CompiledFunctionTools`
cf = Block[{a, x, degree = 3},
With[{expr := Product[x - a[[i]], {i, degree}]},
Compile[{{x, _Real, 0}, {a, _Real, 1}}, expr]]];
CompilePrint[cf]
Block[{a, x}, With[
{expr := D[Product[x - a[[i]], {i, 3}], x]},
Compile[{{x, _Real, 0}, {a, _Real, 1}}, expr]
]
]
11 R1 = MainEvaluate[ Hold[D][ R5, R0]]
Block[{a, x}, With[
{expr = D[Quiet@Product[x - a[[i]], {i, 3}], x]},
Compile[{{x, _Real, 0}, {a, _Real, 1}}, expr]
]
]
wherenewtonC = Function[{degree, f, df, colors},
Compile[{{x0, _Complex, 0}, {a, _Complex, 1}},
Block[{x = x0, xn = 0.0 + 0.0 I, i = 0, maxiter = 256,
eps = 10^(-6.), zeroId = 1, j = 1},
For[i = 0, i < maxiter, ++i,
xn = x - f/(df + eps);
If[Abs[xn - x] < eps,
Break[]
];
x = xn;
];
For[j = 1, j <= degree, ++j,
If[Abs[xn - a[[j]]] < eps*10^2,
zeroId = j + 1;
Break[];
];
];
colors[[zeroId]]*(1 - (i/maxiter)^0.3)*1.5
],
CompilationTarget -> "C", RuntimeAttributes -> {Listable},
RuntimeOptions -> "Speed", Parallelization -> True]]@@
(Quiet@Block[{degree = 3, polynomial, a, x},
polynomial = HornerForm[Product[x - a[[i]], {i, degree}]];
{degree, polynomial, HornerForm[D[polynomial, x]],
List @@@ (ColorData[52, #] & /@ Range[degree + 1])}])
cf = Block[{a, x, degree = 3},
With[{expr = Quiet[Product[x - a[[i]], {i, degree}]]},
Compile[{{x, _Real, 0}, {a, _Real, 1}}, expr]]]
和或函数的代码注入到使用一些编译
的局部变量的编译
中是不可靠的！考虑以下事项：
In[63]:= With[{y=x},Compile[x,y]]
Out[63]= CompiledFunction[{x$},x,-CompiledCode-]
In[64]:= With[{y=x},Compile[{{x,_Real}},y]]
Out[64]= CompiledFunction[{x},x,-CompiledCode-]
注意在第一种情况下，x
重命名为x$
。我建议您阅读有关本地化和本地化的内容。（是的，这是令人困惑的！）我们可以猜测为什么这只发生在第一种情况而不是第二种情况，但我的观点是，这种行为可能不是故意的（称之为bug、暗角或未定义的行为），因此依赖它是脆弱的
替换基于
的解决方案，比如我的do work（这不是我对该功能的预期用途，但它非常适合这里…）
原始答案
您可以将中的：=
与一起使用，如下所示：
cf = Block[{a, x, degree = 3},
With[{expr := Product[x - a[[i]], {i, degree}]},
Compile[{{x, _Real, 0}, {a, _Real, 1}}, expr]
]
]
cf = Block[{a, x, degree = 3},
With[{expr := Product[x - a[[i]], {i, degree}]},
Compile[{{x, _Real, 0}, {a, _Real, 1}}, expr,
CompilationOptions -> {"InlineExternalDefinitions" -> True}]]];
CompilePrint[cf]
它将避免评估expr
和部分的错误
通常，=
和：=
在所有与、模块和块中都能正常工作
您能告诉我为什么在这里使用和
吗？（我相信你有一个很好的理由，从这个简化的例子中我看不出来。）
附加答案
解决@halirutan对编译过程中度未内联的担忧
我认为这与我们在编译中定义的全局变量完全相同。例如：
In[18]:= global=1
Out[18]= 1
In[19]:= cf2=Compile[{},1+global]
Out[19]= CompiledFunction[{},1+global,-CompiledCode-]
In[20]:= CompilePrint[cf2]
Out[20]=
No argument
3 Integer registers
Underflow checking off
Overflow checking off
Integer overflow checking on
RuntimeAttributes -> {}
I0 = 1
Result = I2
1 I1 = MainEvaluate[ Function[{}, global][ ]]
2 I2 = I0 + I1
3 Return
这是一个普遍的问题。解决方法是告诉编译，如下所示：
cf = Block[{a, x, degree = 3},
With[{expr := Product[x - a[[i]], {i, degree}]},
Compile[{{x, _Real, 0}, {a, _Real, 1}}, expr]
]
]
cf = Block[{a, x, degree = 3},
With[{expr := Product[x - a[[i]], {i, degree}]},
Compile[{{x, _Real, 0}, {a, _Real, 1}}, expr,
CompilationOptions -> {"InlineExternalDefinitions" -> True}]]];
CompilePrint[cf]
您可以检查，现在没有对主计算器的回调
或者，您可以使用一层额外的With
而不是Block
注入度的值。这会让你非常渴望
Mathematica中的宏展开
这有点不相关，但您在帖子中提到，您使用和
进行宏扩展。这是我在Mathematica中实现宏扩展的第一步（可能是错误的）。这没有经过很好的测试，请尝试打破它并发表评论
Clear[defineMacro, macros, expandMacros]
macros = Hold[];
SetAttributes[defineMacro, HoldAllComplete]
defineMacro[name_Symbol, value_] := (AppendTo[macros, name]; name := value)
SetAttributes[expandMacros, HoldAllComplete]
expandMacros[expr_] := Unevaluated[expr] //. Join @@ (OwnValues /@ macros)
说明：
宏
是要展开的所有符号的（保留）列表。
defineMacro
将生成一个新宏。
expandMacros
将在表达式中展开宏定义
注意：我没有实现宏重新定义，当使用$Pre
进行扩展时，这将不起作用。还要注意递归宏定义和无限循环
用法：Clear[defineMacro, macros, expandMacros]
macros = Hold[];
SetAttributes[defineMacro, HoldAllComplete]
defineMacro[name_Symbol, value_] := (AppendTo[macros, name]; name := value)
SetAttributes[expandMacros, HoldAllComplete]
expandMacros[expr_] := Unevaluated[expr] //. Join @@ (OwnValues /@ macros)
$Pre = expandMacros;
defineMacro[a, 1]
b := a + 1
?b
Global`b
b:=1+1
$Pre =.
ClearAll[symbolToHideQ]
SetAttributes[symbolToHideQ, HoldFirst];
symbolToHideQ[s_Symbol, expandedSymbs_] :=! MemberQ[expandedSymbs, Unevaluated[s]];
ClearAll[globalProperties]
globalProperties[] := {DownValues, SubValues, UpValues (*,OwnValues*)};
ClearAll[getSymbolsToHide];
Options[getSymbolsToHide] = {
Exceptions -> {List, Hold, HoldComplete,
HoldForm, HoldPattern, Blank, BlankSequence, BlankNullSequence,
Optional, Repeated, Verbatim, Pattern, RuleDelayed, Rule, True,
False, Integer, Real, Complex, Alternatives, String,
PatternTest,(*Note- this one is dangerous since it opens a hole
to evaluation leaks. But too good to be ingored *)
Condition, PatternSequence, Except
}
};
getSymbolsToHide[code_Hold, headsToExpand : {___Symbol}, opts : OptionsPattern[]] :=
Join @@ Complement[
Cases[{
Flatten[Outer[Compose, globalProperties[], headsToExpand]], code},
s_Symbol /; symbolToHideQ[s, headsToExpand] :> Hold[s],
Infinity,
Heads -> True
],
Hold /@ OptionValue[Exceptions]];
ClearAll[makeHidingSymbol]
SetAttributes[makeHidingSymbol, HoldAll];
makeHidingSymbol[s_Symbol] :=
Unique[hidingSymbol(*Unevaluated[s]*) (*,Attributes[s]*)];
ClearAll[makeHidingRules]
makeHidingRules[symbs : Hold[__Symbol]] :=
Thread[List @@ Map[HoldPattern, symbs] -> List @@ Map[makeHidingSymbol, symbs]];
ClearAll[reverseHidingRules];
reverseHidingRules[rules : {(_Rule | _RuleDelayed) ..}] :=
rules /. (Rule | RuleDelayed)[Verbatim[HoldPattern][lhs_], rhs_] :> (rhs :> lhs);
FrozenCodeEval[code_Hold, headsToEvaluate : {___Symbol}] :=
Module[{symbolsToHide, hidingRules, revHidingRules, result},
symbolsToHide = getSymbolsToHide[code, headsToEvaluate];
hidingRules = makeHidingRules[symbolsToHide];
revHidingRules = reverseHidingRules[hidingRules];
result =
Hold[Evaluate[ReleaseHold[code /. hidingRules]]] /. revHidingRules;
Apply[Remove, revHidingRules[[All, 1]]];
result];
In[80]:=
FrozenCodeEval[
Hold[Compile[{{x,_Real,0},{a,_Real,1}},D[Product[x-a[[i]],{i,3}],x]]],
{D,Product,Derivative,Plus}
]
Out[80]=
Hold[Compile[{{x,_Real,0},{a,_Real,1}},
(x-a[[1]]) (x-a[[2]])+(x-a[[1]]) (x-a[[3]])+(x-a[[2]]) (x-a[[3]])]]
In[102]:=
FrozenCodeEval[
Hold[f[x_, y_, z_] :=
With[Thread[{a, b, c} = Map[Sqrt, {x, y, z}]],
a + b + c]],
{Thread, Map}]
Out[102]=
Hold[
f[x_, y_, z_] :=
With[{a = Sqrt[x], b = Sqrt[y], c = Sqrt[z]}, a + b + c]]
newtonC = Function[{degree, f, df, colors},
Compile[{{x0, _Complex, 0}, {a, _Complex, 1}},
Block[{x = x0, xn = 0.0 + 0.0 I, i = 0, maxiter = 256,
...
RuntimeOptions -> "Speed", Parallelization -> True]]@@
(Quiet@Block[{degree = 3, polynomial, a, x},
polynomial = HornerForm[Product[x - a[[i]], {i, degree}]];
...
newtonC = Function[{degree, f, df, colors},
Compile[{{x0, _Complex, 0}, {a, _Complex, 1}},
Block[{x = x0, xn = 0.0 + 0.0 I, i = 0, maxiter = 256,
...
RuntimeOptions -> "Speed", Parallelization -> True],HoldAllComplete]@@
( (( (HoldComplete@@#)/.a[i_]:>a[[i]] )&)@Block[{degree = 3, polynomial, a, x},
polynomial = HornerForm[Product[x - a[i], {i, degree}]];
...