Related
I've got some symbols which should are non-commutative, but I don't want to have to remember which expressions have this behaviour whilst constructing equations.
I've had the thought to use MakeExpression to act on the raw boxes, and automatically uplift multiply to non-commutative multiply when appropriate (for instance when some of the symbols are non-commutative objects).
I was wondering whether anyone had any experience with this kind of configuration.
Here's what I've got so far:
(* Detect whether a set of row boxes represents a multiplication *)
Clear[isRowBoxMultiply];
isRowBoxMultiply[x_RowBox] := (Print["rowbox: ", x];
Head[ToExpression[x]] === Times)
isRowBoxMultiply[x___] := (Print["non-rowbox: ", x]; False)
(* Hook into the expression maker, so that we can capture any \
expression of the form F[x___], to see how it is composed of boxes, \
and return true or false on that basis *)
MakeExpression[
RowBox[List["F", "[", x___, "]"]], _] := (HoldComplete[
isRowBoxMultiply[x]])
(* Test a number of expressions to see whether they are automatically \
detected as multiplies or not. *)
F[a]
F[a b]
F[a*b]
F[a - b]
F[3 x]
F[x^2]
F[e f*g ** h*i j]
Clear[MakeExpression]
This appears to correctly identify expressions that are multiplication statements:
During evaluation of In[561]:= non-rowbox: a
Out[565]= False
During evaluation of In[561]:= rowbox: RowBox[{a,b}]
Out[566]= True
During evaluation of In[561]:= rowbox: RowBox[{a,*,b}]
Out[567]= True
During evaluation of In[561]:= rowbox: RowBox[{a,-,b}]
Out[568]= False
During evaluation of In[561]:= rowbox: RowBox[{3,x}]
Out[569]= True
During evaluation of In[561]:= non-rowbox: SuperscriptBox[x,2]
Out[570]= False
During evaluation of In[561]:= rowbox: RowBox[{e,f,*,RowBox[{g,**,h}],*,i,j}]
Out[571]= True
So, it looks like it's not out of the questions that I might be able to conditionally rewrite the boxes of the underlying expression; but how to do this reliably?
Take the expression RowBox[{"e","f","*",RowBox[{"g","**","h"}],"*","i","j"}], this would need to be rewritten as RowBox[{"e","**","f","**",RowBox[{"g","**","h"}],"**","i","**","j"}] which seems like a non trivial operation to do with the pattern matcher and a rule set.
I'd be grateful for any suggestions from those more experienced with me.
I'm trying to find a way of doing this without altering the default behaviour and ordering of multiply.
Thanks! :)
Joe
This is not a most direct answer to your question, but for many purposes working as low-level as directly with the boxes might be an overkill. Here is an alternative: let the Mathematica parser parse your code, and make a change then. Here is a possibility:
ClearAll[withNoncommutativeMultiply];
SetAttributes[withNoncommutativeMultiply, HoldAll];
withNoncommutativeMultiply[code_] :=
Internal`InheritedBlock[{Times},
Unprotect[Times];
Times = NonCommutativeMultiply;
Protect[Times];
code];
This replaces Times dynamically with NonCommutativeMultiply, and avoids the intricacies you mentioned. By using Internal`InheritedBlock, I make modifications to Times local to the code executed inside withNoncommutativeMultiply.
You now can automate the application of this function with $Pre:
$Pre = withNoncommutativeMultiply;
Now, for example:
In[36]:=
F[a]
F[a b]
F[a*b]
F[a-b]
F[3 x]
F[x^2]
F[e f*g**h*i j]
Out[36]= F[a]
Out[37]= F[a**b]
Out[38]= F[a**b]
Out[39]= F[a+(-1)**b]
Out[40]= F[3**x]
Out[41]= F[x^2]
Out[42]= F[e**f**g**h**i**j]
Surely, using $Pre in such manner is hardly appropriate, since in all your code multiplication will be replaced with noncommutative multiplication - I used this as an illustration. You could make a more complicated redefinition of Times, so that this would only work for certain symbols.
Here is a safer alternative based on lexical, rather than dynamic, scoping:
ClearAll[withNoncommutativeMultiplyLex];
SetAttributes[withNoncommutativeMultiplyLex, HoldAll];
withNoncommutativeMultiplyLex[code_] :=
With ## Append[
Hold[{Times = NonCommutativeMultiply}],
Unevaluated[code]]
you can use this in the same way, but only those instances of Times which are explicitly present in the code would be replaced. Again, this is just an illustration of the principles, one can extend or specialize this as needed. Instead of With, which is rather limited in its ability to specialize / add special cases, one can use replacement rules which have similar semantics.
If I understand correctly, you want to input
a b and a*b
and have MMA understand automatically that Times is really a non commutative operator (which has its own -separate - commutation rules).
Well, my suggestion is that you use the Notation package.
It is very powerful and (relatively) easy to use (especially for a sophisticated user like you seem to be).
It can be used programmatically and it can reinterpret predefined symbols like Times.
Basically it can intercept Times and change it to MyTimes. You then write code for MyTimes deciding for example which symbols are non commuting and then the output can be pretty formatted again as times or whatever else you wish.
The input and output processing are 2 lines of code. That’s it!
You have to read the documentation carefully and do some experimentation, if what you want is not more or less “standard hacking” of the input-output jobs.
Your case seems to me pretty much standard (again: If I understood well what you want to achieve) and you should find useful to read the “advanced” pages of the Notation package.
To give you an idea of how powerful and flexible the package is, I am using it to write the input-output formatting of a sizable package of Category Theory where noncommutative operations abound. But wait! I am not just defining ONE noncommutative operation, I am defining an unlimited number of noncommutative operations.
Another thing I did was to reinterpret Power when the arguments are categories, without overloading Power. This allows me to treat functorial categories using standard mathematics notation.
Now my “infinite” operations and "super Power" have the same look and feel of standard MMA symbols, including copy-paste functionality.
So, this doesn't directly answer the question, but it's does provide the sort of implementation that I was thinking about.
So, after a bit of investigation and taking on board some of #LeonidShifrin's suggestions, I've managed to implement most of what I was thinking of. The idea is that it's possible to define patterns that should be considered to be non-commuting quantities, using commutingQ[form] := False. Then any multiplicative expression (actually any expression) can be wrapped with withCommutativeSensitivity[expr] and the expression will be manipulated to separate the quantities into Times[] and NonCommutativeMultiply[] sub-expressions as appropriate,
In[1]:= commutingQ[b] ^:= False;
In[2]:= withCommutativeSensitivity[ a (a + b + 4) b (3 + a) b ]
Out[1]:= a (3 + a) (a + b + 4) ** b ** b
Of course it's possible to use $Pre = withCommutativeSensitivity to have this behaviour become default (come on Wolfram! Make it default already ;) ). It would, however, be nice to have it a more fundamental behaviour though. I'd really like to make a module and Needs[NonCommutativeQuantities] at the beginning of any note book that is needs it, and not have all the facilities that use $Pre break on me (doesn't tracing use it?).
Intuitively I feel that there must be a natural way to hook this functionality into Mathematica on at the level of box parsing and wire it up using MakeExpression[]. Am I over extending here? I'd appreciate any thoughts as to whether I'm chasing up a blind alley. (I've had a few experiments in this direction, but always get caught in a recursive definition that I can't work out how to break).
Any thoughts would be gladly received,
Joe.
Code
Unprotect[NonCommutativeMultiply];
ClearAll[NonCommutativeMultiply]
NonCommutativeMultiply[a_] := a
Protect[NonCommutativeMultiply];
ClearAll[commutingQ]
commutingQ::usage = "commutingQ[\!\(\*
StyleBox[\"expr\", \"InlineFormula\",\nFontSlant->\"Italic\"]\)] \
returns True if expr doesn't contain any constituent parts that fail \
the commutingQ test. By default all objects return True to \
commutingQ.";
commutingQ[x_] := If[Length[x] == 0, True, And ## (commutingQ /# List ## x)]
ClearAll[times2, withCommutativeSensitivity]
SetAttributes[times2, {Flat, OneIdentity, HoldAll}]
SetAttributes[withCommutativeSensitivity, HoldAll];
gatherByCriteria[list_List, crit_] :=
With[{gathered =
Gather[{#, crit[#1]} & /# list, #1[[2]] == #2[[2]] &]},
(Identity ## Union[#[[2]]] -> #[[1]] &)[Transpose[#]] & /# gathered]
times2[x__] := Module[{a, b, y = List[x]},
Times ## (gatherByCriteria[y, commutingQ] //.
{True -> Times, False -> NonCommutativeMultiply,
HoldPattern[a_ -> b_] :> a ## b})]
withCommutativeSensitivity[code_] := With ## Append[
Hold[{Times = times2, NonCommutativeMultiply = times2}],
Unevaluated[code]]
This answer does not address your question but rather the problem that leads you to ask that question. Mathematica is pretty useless when dealing with non-commuting objects but since such objects abound in, e.g., particle physics, there are some usefull packages around to deal with the situation.
Look at the grassmanOps package. They have a method to define symbols as either commuting or anti-commuting and overload the standard NonCommutativeMultiply to handle, i.e. pass through, commuting symbols. They also define several other operators, such as Derivative, to handle anti-commuting symbols. It is probably easily adapted to cover arbitrary commutation rules and it should at the very least give you an insigt into what things need to be changed if you want to roll your own.
I'm in love with Ruby. In this language all core functions are actually methods. That's why I prefer postfix notation – when the data, which I want to process is placed left from the body of anonymous processing function, for example: array.map{...}. I believe, that it has advantages in how easy is this code to read.
But Mathetica, being functional (yeah, it can be procedural if you want) dictates a style, where Function name is placed left from the data. As we can see in its manuals, // is used only when it's some simple Function, without arguments, like list // MatrixForm. When Function needs a lot of arguments, people who wrote manuals, use syntax F[data].
It would be okay, but my problem is the case F[f,data], for example Do[function, {x, a, b}]. Most of Mathematica functions (if not all) have arguments in exactly this order – [function, data], not [data, function]. As I prefer to use pure functions to keep namespace clean instead of creating a lot of named functions in my notebook, the argument function can be too big – so big, that argument data would be placed on the 5-20th line of code after the line with Function call.
This is why sometimes, when evil Ruby nature takes me under control, I rewrite such functions in postfix way:
Because it's important for me, that pure function (potentially big code) is placed right from processing data. Yeah I do it and I'm happy. But there are two things:
this causes Mathematica's highlighting parser problem: the x in postfix notation is highlighted with blue color, not turquoise;
everytime when I look into Mathematica manuals, I see examples like this one: Do[x[[i]] = (v[[i]] - U[[i, i + 1 ;; n]].x[[i + 1 ;; n]])/ U[[i, i]], {i, n, 1, -1}];, which means... hell, they think it's easy to read/support/etc.?!
So these two things made me ask this question here: am I so bad boy, that use my Ruby-style, and should I write code like these guys do, or is it OK, and I don't have to worry, and should write as I like to?
The style you propose is frequently possible, but is inadvisable in the case of Do. The problem is that Do has the attribute HoldAll. This is important because the loop variable (x in the example) must remain unevaluated and be treated as a local variable. To see this, try evaluating these expressions:
x = 123;
Do[Print[x], {x, 1, 2}]
(* prints 1 and 2 *)
{x, 1, 2} // Do[Print[x], #]&
(* error: Do::itraw: Raw object 123 cannot be used as an iterator.
Do[Print[x], {123, 1, 2}]
*)
The error occurs because the pure function Do[Print[x], #]& lacks the HoldAll attribute, causing {x, 1, 2} to be evaluated. You could solve the problem by explicitly defining a pure function with the HoldAll attribute, thus:
{x, 1, 2} // Function[Null, Do[Print[x], #], HoldAll]
... but I suspect that the cure is worse than the disease :)
Thus, when one is using "binding" expressions like Do, Table, Module and so on, it is safest to conform with the herd.
I think you need to learn to use the styles that Mathematica most naturally supports. Certainly there is more than one way, and my code does not look like everyone else's. Nevertheless, if you continue to try to beat Mathematica syntax into your own preconceived style, based on a different language, I foresee nothing but continued frustration for you.
Whitespace is not evil, and you can easily add line breaks to separate long arguments:
Do[
x[[i]] = (v[[i]] - U[[i, i + 1 ;; n]].x[[i + 1 ;; n]]) / U[[i, i]]
, {i, n, 1, -1}
];
This said, I like to write using more prefix (f # x) and infix (x ~ f ~ y) notation that I usually see, and I find this valuable because it is easy to determine that such functions are receiving one and two arguments respectively. This is somewhat nonstandard, but I do not think it is kicking over the traces of Mathematica syntax. Rather, I see it as using the syntax to advantage. Sometimes this causes syntax highlighting to fail, but I can live with that:
f[x] ~Do~ {x, 2, 5}
When using anything besides the standard form of f[x, y, z] (with line breaks as needed), you must be more careful of evaluation order, and IMHO, readability can suffer. Consider this contrived example:
{x, y} // # + 1 & ## # &
I do not find this intuitive. Yes, for someone intimate with Mathematica's order of operations, it is readable, but I believe it does not improve clarity. I tend to reserve // postfix for named functions where reading is natural:
Do[f[x], {x, 10000}] //Timing //First
I'd say it is one of the biggest mistakes to try program in a language B in ways idiomatic for a language A, only because you happen to know the latter well and like it. There is nothing wrong in borrowing idioms, but you have to make sure to understand the second language well enough so that you know why other people use it the way they do.
In the particular case of your example, and generally, I want to draw attention to a few things others did not mention. First, Do is a scoping construct which uses dynamic scoping to localize its iterator symbols. Therefore, you have:
In[4]:=
x=1;
{x,1,5}//Do[f[x],#]&
During evaluation of In[4]:= Do::itraw: Raw object
1 cannot be used as an iterator. >>
Out[5]= Do[f[x],{1,1,5}]
What a surprise, isn't it. This won't happen when you use Do in a standard fashion.
Second, note that, while this fact is largely ignored, f[#]&[arg] is NOT always the same as f[arg]. Example:
ClearAll[f];
SetAttributes[f, HoldAll];
f[x_] := Print[Unevaluated[x]]
f[5^2]
5^2
f[#] &[5^2]
25
This does not affect your example, but your usage is close enough to those cases affected by this, since you manipulate the scopes.
Mathematica supports 4 ways of applying a function to its arguments:
standard function form: f[x]
prefix: f#x or g##{x,y}
postfix: x // f, and
infix: x~g~y which is equivalent to g[x,y].
What form you choose to use is up to you, and is often an aesthetic choice, more than anything else. Internally, f#x is interpreted as f[x]. Personally, I primarily use postfix, like you, because I view each function in the chain as a transformation, and it is easier to string multiple transformations together like that. That said, my code will be littered with both the standard form and prefix form mostly depending on whim, but I tend to use standard form more as it evokes a feeling of containment with regards to the functions parameters.
I took a little liberty with the prefix form, as I included the shorthand form of Apply (##) alongside Prefix (#). Of the built in commands, only the standard form, infix form, and Apply allow you easily pass more than one variable to your function without additional work. Apply (e.g. g ## {x,y}) works by replacing the Head of the expression ({x,y}) with the function, in effect evaluating the function with multiple variables (g##{x,y} == g[x,y]).
The method I use to pass multiple variables to my functions using the postfix form is via lists. This necessitates a little more work as I have to write
{x,y} // f[ #[[1]], #[[2]] ]&
to specify which element of the List corresponds to the appropriate parameter. I tend to do this, but you could combine this with Apply like
{x,y} // f ## #&
which involves less typing, but could be more difficult to interpret when you read it later.
Edit: I should point out that f and g above are just placeholders, they can, and often are, replaced with pure functions, e.g. #+1& # x is mostly equivalent to #+1&[x], see Leonid's answer.
To clarify, per Leonid's answer, the equivalence between f#expr and f[expr] is true if f does not posses an attribute that would prevent the expression, expr, from being evaluated before being passed to f. For instance, one of the Attributes of Do is HoldAll which allows it to act as a scoping construct which allows its parameters to be evaluated internally without undo outside influence. The point is expr will be evaluated prior to it being passed to f, so if you need it to remain unevaluated, extra care must be taken, like creating a pure function with a Hold style attribute.
You can certainly do it, as you evidently know. Personally, I would not worry about how the manuals write code, and just write it the way I find natural and memorable.
However, I have noticed that I usually fall into definite patterns. For instance, if I produce a list after some computation and incidentally plot it to make sure it's what I expected, I usually do
prodListAfterLongComputation[
args,
]//ListPlot[#,PlotRange->Full]&
If I have a list, say lst, and I am now focusing on producing a complicated plot, I'll do
ListPlot[
lst,
Option1->Setting1,
Option2->Setting2
]
So basically, anything that is incidental and perhaps not important to be readable (I don't need to be able to instantaneously parse the first ListPlot as it's not the point of that bit of code) ends up being postfix, to avoid disrupting the already-written complicated code it is applied to. Conversely, complicated code I tend to write in the way I find easiest to parse later, which, in my case, is something like
f[
g[
a,
b,
c
]
]
even though it takes more typing and, if one does not use the Workbench/Eclipse plugin, makes it more work to reorganize code.
So I suppose I'd answer your question with "do whatever is most convenient after taking into account the possible need for readability and the possible loss of convenience such as code highlighting, extra work to refactor code etc".
Of course all this applies if you're the only one working with some piece of code; if there are others, it is a different question alltogether.
But this is just an opinion. I doubt it's possible for anybody to offer more than this.
For one-argument functions (f#(arg)), ((arg)//f) and f[arg] are completely equivalent even in the sense of applying of attributes of f. In the case of multi-argument functions one may write f#Sequence[args] or Sequence[args]//f with the same effect:
In[1]:= SetAttributes[f,HoldAll];
In[2]:= arg1:=Print[];
In[3]:= f#arg1
Out[3]= f[arg1]
In[4]:= f#Sequence[arg1,arg1]
Out[4]= f[arg1,arg1]
So it seems that the solution for anyone who likes postfix notation is to use Sequence:
x=123;
Sequence[Print[x],{x,1,2}]//Do
(* prints 1 and 2 *)
Some difficulties can potentially appear with functions having attribute SequenceHold or HoldAllComplete:
In[18]:= Select[{#, ToExpression[#, InputForm, Attributes]} & /#
Names["System`*"],
MemberQ[#[[2]], SequenceHold | HoldAllComplete] &][[All, 1]]
Out[18]= {"AbsoluteTiming", "DebugTag", "EvaluationObject", \
"HoldComplete", "InterpretationBox", "MakeBoxes", "ParallelEvaluate", \
"ParallelSubmit", "Parenthesize", "PreemptProtect", "Rule", \
"RuleDelayed", "Set", "SetDelayed", "SystemException", "TagSet", \
"TagSetDelayed", "Timing", "Unevaluated", "UpSet", "UpSetDelayed"}
My code relies on version of Element which works like MemberQ, but when I load Combinatorica, Element gets redefined to work like Part. What is the easiest way to fix this conflict? Specifically, what is the syntax to remove Combinatorica's definition from DownValues? Here's what I get for DownValues[Element]
{HoldPattern[
Combinatorica`Private`a_List \[Element] \
{Combinatorica`Private`index___}] :>
Combinatorica`Private`a[[Combinatorica`Private`index]],
HoldPattern[Private`x_ \[Element] Private`list_List] :>
MemberQ[Private`list, Private`x]}
If your goal is to prevent Combinatorica from installing the definition in the first place, you can achieve this result by loading the package for the first time thus:
Block[{Element}, Needs["Combinatorica`"]]
However, this will almost certainly make any Combinatorica features that depend upon the definition fail (which may or may not be of concern in your particular application).
You can do several things. Let us introduce a convenience function
ClearAll[redef];
SetAttributes[redef, HoldRest];
redef[f_, code_] := (Unprotect[f]; code; Protect[f])
If you are sure about the order of definitions, you can do something like
redef[Element, DownValues[Element] = Rest[DownValues[Element]]]
If you want to delete definitions based on the context, you can do something like this:
redef[Element, DownValues[Element] =
DeleteCases[DownValues[Element],
rule_ /; Cases[rule, x_Symbol /; (StringSplit[Context[x], "`"][[1]] ===
"Combinatorica"), Infinity, Heads -> True] =!= {}]]
You can also use a softer way - reorder definitions rather than delete:
redef[Element, DownValues[Element] = RotateRight[DownValues[Element]]]
There are many other ways of dealing with this problem. Another one (which I already recommended) is to use UpValues, if this is suitable. The last one I want to mention here is to make a kind of custom dynamic scoping construct based on Block, and wrap it around your code. I personally find it the safest variant, in case if you want strictly your definition to apply (because it does not care about the order in which various definitions could have been created - it removes all of them and adds just yours). It is also safer in that outside those places where you want your definitions to apply (by "places" I mean parts of the evaluation stack), other definitions will still apply, so this seems to be the least intrusive way. Here is how it may look:
elementDef[] := Element[x_, list_List] := MemberQ[list, x];
ClearAll[elemExec];
SetAttributes[elemExec, HoldAll];
elemExec[code_] := Block[{Element}, elementDef[]; code];
Example of use:
In[10]:= elemExec[Element[1,{1,2,3}]]
Out[10]= True
Edit:
If you need to automate the use of Block, here is an example package to show one way how this can be done:
BeginPackage["Test`"]
var;
f1;
f2;
Begin["`Private`"];
(* Implementations of your functions *)
var = 1;
f1[x_, y_List] := If[Element[x, y], x^2];
f2[x_, y_List] := If[Element[x, y], x^3];
elementDef[] := Element[x_, list_List] := MemberQ[list, x];
(* The following part of the package is defined at the start and you don't
touch it any more, when adding new functions to the package *)
mainContext = StringReplace[Context[], x__ ~~ "Private`" :> x];
SetAttributes[elemExec, HoldAll];
elemExec[code_] := Block[{Element}, elementDef[]; code];
postprocessDefs[context_String] :=
Map[
ToExpression[#, StandardForm,
Function[sym,DownValues[sym] =
DownValues[sym] /.
Verbatim[RuleDelayed][lhs_,rhs_] :> (lhs :> elemExec[rhs])]] &,
Select[Names[context <> "*"], ToExpression[#, StandardForm, DownValues] =!= {} &]];
postprocessDefs[mainContext];
End[]
EndPackage[]
You can load the package and look at the DownValues for f1 and f2, for example:
In[17]:= DownValues[f1]
Out[17]= {HoldPattern[f1[Test`Private`x_,Test`Private`y_List]]:>
Test`Private`elemExec[If[Test`Private`x\[Element]Test`Private`y,Test`Private`x^2]]}
The same scheme will also work for functions not in the same package. In fact, you could separate
the bottom part (code-processing package) to be a package on its own, import it into any other
package where you want to inject Block into your functions' definitions, and then just call something like postprocessDefs[mainContext], as above. You could make the function which makes definitions inside Block (elementDef here) to be an extra parameter to a generalized version of elemExec, which would make this approach more modular and reusable.
If you want to be more selective about the functions where you want to inject Block, this can also be done in various ways. In fact, the whole Block-injection scheme can be made cleaner then, but it will require slightly more care when implementing each function, while the above approach is completely automatic. I can post the code which will illustrate this, if needed.
One more thing: for the less intrusive nature of this method you pay a price - dynamic scope (Block) is usually harder to control than lexically-scoped constructs. So, you must know exactly the parts of evaluation stack where you want that to apply. For example, I would hesitate to inject Block into a definition of a higher order function, which takes some functions as parameters, since those functions may come from code that assumes other definitions (like for example Combinatorica` functions relying on overloaded Element). This is not a big problem, just requires care.
The bottom line of this seems to be: try to avoid overloading built-ins if at all possible. In this case you faced this definitions clash yourself, but it would be even worse if the one who faces this problem is a user of your package (may be yourself a few months later), who wants to combine your package with another one (which happens to overload same system functions as yours). Of course, it also depends on who will be the users of your package - only yourself or potentially others as well. But in terms of design, and in the long term, you may be better off assuming the latter scenario from the start.
To remove Combinatorica's definition, use Unset or the equivalent form =.. The pattern to unset you can grab from the Information output you show in the question:
Unprotect[Element];
Element[a_List, {index___}] =.
Protect[Element];
The worry would be, of course, that Combinatorica depends internally on this ill-conceived redefinition, but you have reason to believe this to not be the case as the Information output from the redefined Element says:
The use of the function
Element in Combinatorica is now
obsolete, though the function call
Element[a, p] still gives the pth
element of nested list a, where p is a
list of indices.
HTH
I propose an entirely different approach than removing Element from DownValues. Simply use the full name of the Element function.
So, if the original is
System`Element[]
the default is now
Combinatorica`Element[]
because of loading the Combinatorica Package.
Just explicitly use
System`Element[]
wherever you need it. Of course check that System is the correct Context using the Context function:
Context[Element]
This approach ensures several things:
The Combinatorica Package will still work in your notebook, even if the Combinatorica Package is updated in the future
You wont have to redefine the Element function, as some have suggested
You can use the Combinatorica`Element function when needed
The only downside is having to explicitly write it every time.
I don't know why Wikipedia lists Mathematica as a programming language with printf. I just couldn't find the equivalent in Mathematica.
My specific task is to process a list of data files with padded numbers, which I used to do it in bash with
fn=$(printf "filename_%05d" $n)
The closest function I found in Mathematica is PaddedForm. And after some trial and error, I got it with
"filename_" <> PaddedForm[ Round##, 4, NumberPadding -> {"0", ""} ]&
It is very odd that I have to use the number 4 to get the result similar to what I get from "%05d". I don't understand this behavior at all. Can someone explain it to me?
And is it the best way to achieve what I used to in bash?
I wouldn't use PaddedForm for this. In fact, I'm not sure that PaddedForm is good for much of anything. Instead, I'd use good old ToString, Characters and PadLeft, like so:
toFixedWidth[n_Integer, width_Integer] :=
StringJoin[PadLeft[Characters[ToString[n]], width, "0"]]
Then you can use StringForm and ToString to make your file name:
toNumberedFileName[n_Integer] :=
ToString#StringForm["filename_``", toFixedWidth[n, 5]]
Mathematica is not well-suited to this kind of string munging.
EDIT to add: Mathematica proper doesn't have the required functionality, but the java.lang.String class has the static method format() which takes printf-style arguments. You can call out to it using Mathematica's JLink functionality pretty easily. The performance won't be very good, but for many use cases you just won't care that much:
Needs["JLink`"];
LoadJavaClass["java.lang.String"];
LoadJavaClass["java.util.Locale"];
sprintf[fmt_, args___] :=
String`format[Locale`ENGLISH,fmt,
MakeJavaObject /#
Replace[{args},
{x_?NumericQ :> N#x,
x : (_Real | _Integer | True |
False | _String | _?JavaObjectQ) :> x,
x_ :> MakeJavaExpr[x]},
{1}]]
You need to do a little more work, because JLink is a bit dumb about Java functions with a variable number of arguments. The format() method takes a format string and an array of Java Objects, and Mathematica won't do the conversion automatically, which is what the MakeJavaObject is there for.
I've run into the same problem quite a bit, and decided to code my own function. I didn't do it in Java but instead just used string operations in Mathematica. It turned out quite lengthy, since I actually also needed %f functionality, but it works, and now I have it as a package that I can use at any time. Here's a link to the GitHub project:
https://github.com/vlsd/MathPrintF
It comes with installation instructions (really just copying the directory somewhere in the $Path).
Hope this will be helpful to at least some.
You could also define a function which passes all arguments to StringForm[] and use IntegerString or the padding functions as previously mentioned:
Sprintf[args__] := StringForm[args__] // ToString;
file = Sprintf["filename_``", IntegerString[n, 10, 5]];
IntegerString does exactly what you need. In this case it would be
IntegerString[x,10,5]
I agree with Pillsy.
Here's how I would do it.
Note the handy cat function, which I think of as kind of like sprintf (minus the placeholders like StringForm provides) in that it works like Print (you can print any concatenation of expressions without converting to String) but generates a string instead of sending to stdout.
cat = StringJoin##(ToString/#{##})&;
pad[x_, n_] := If[StringLength#cat[x]>=n, cat[x],
cat##PadLeft[Characters#cat[x],n,"0"]]
cat["filename_", pad[#, 5]]&
This is very much like Pillsy's answer but I think cat makes it a little cleaner.
Also, I think it's safer to have that conditional in the pad function -- better to have the padding wrong than the number wrong.
I came across lot of flags while reading someone else code,
if (condition1)
var1 = true
else
var1 = false
then later,
if (var1 == true)
// do something.
There are lot of flags like this. I eager to know, is using flags very often in code advisable?
This:
if (condition1)
var1= true;
else
var1 = false;
Is a classic badly written code.
Instead you should write:
var1 = condition1;
And yes, flags are very useful for making the code be more readable and possibly, faster.
It's advisable if condition1 is something quite complicated - like if (A && (B || C) && !D) or contains a lot of overhead (if (somethingTimeConsumingThatWontChange())) then it makes sense to store that result instead of copy-pasting the code.
If condition1 is just a simple comparison then no, I wouldn't use a flag.
This is pretty subjective, and depends on the rest of the code. "Flags" as you call them have their place.
First of all, this code should read like this:
var1 = condition1;
if( var1 )
// No need to compare *true* to *true* when you're looking for *true*
As for the number of flags, there are more elegant ways of branching your code. For instance , when using javascript you can do stuff like this:
var methodName = someFunctionThatReturnsAString();
// assuming you name the method according to what's returned
myObject[ methodName ]();
instead of
if( someFunctionThatReturnsAString === 'myPreferedMethod' ){
myObject.myPreferedMethod();
}else{
myObject.theOtherMethod();
}
If you're using a strongly typed language, polymorphism is your friend. I think the technique is refered to as polymorphic dispatch
I remember this Replace Temp var with Query method from the refactoring book.
I think this refactoring will make the code more readable, but, I agree that it might affect performance when the query method is expensive ... (But, maybe the query method can be put in its own class, and the result can be cached into that class).
This is question is a bit generic. The answer depends on what you want to do and with which language you want it to do. Assuming an OO context than there could be better approaches.
If the condition is the result of some object state than the "flag" should propably be a property of the object itself. If it is a condition of the running application and you have a lot of these things it might could be that you should think about a state pattern/state machine.
Flags are very useful - but give them sensible names, e.g. using "Is" or similar in their names.
For example, compare:
if(Direction) {/* do something */}
if(PowerSetting) {/* do something else */}
with:
if(DirectionIsUp) {/* do something */}
if(PowerIsOn) {/* do something else */}
If it is readable and does the job then there's nothing wrong with it. Just make use of "has" and "is" prefix to make it more readable:
var $isNewRecord;
var $hasUpdated;
if ($isNewRecord)
{
}
if ($hasUpdated)
{
}
Bearing in mind that that code could be more readably written as
var1 = condition1
, this assignment has some useful properties if used well. One use case is to name a complicated calculation without breaking it out into a function:
user_is_on_fire = condition_that_holds_when_user_is_on_fire
That allows one to explain what one is using the condition to mean, which is often not obvious from the bare condition.
If evaluating the condition is expensive (or has side effects), it might also be desirable to store the result locally rather than reevaluate the condition.
Some caveats: Badly named flags will tend to make the code less readable. So will flags that are set far from the place where they are used. Also, the fact that one wants to use flags is a code smell suggesting that one should consider breaking the condition out into a function.
D'A
Call it flags when you work in a pre-OO language. They are useful to parameterize the behaviour of a piece of code.
You'll find the code hard to follow, soon, however. It would be easier reading/changing/maintaining when you abstract away the differences by e.g. providing a reference to the changeable functionality.
In languages where functions are first-class citisens (e.g. Javascript, Haskell, Lisp, ...), this is a breeze.
In OO languages, you can implement some design patterns like Abstract Factory, Strategy/Policy, ...
Too many switches I personally regard as code smell.
That depends on the condition and how many times it's used. Anyway, refactoring into function (preferably caching the result if condition is slow to calculate) might give you a lot more readable code.
Consider for example this:
def checkCondition():
import __builtin__ as cached
try:
return cached.conditionValue
except NameError:
cached.conditionValue = someSlowFunction()
return cached.conditionValue
As for coding style:
if (condition1)
var1= true
else
var1 = false
I hate that kind of code. It should be either simply:
var1 = condition1
or if you want to assure that's result is boolean:
var1 = bool(condition1)
if (var1 == true)
Again. Bad coding style. It's:
if (var1)
What i dont like about flags, is when they are called flags, with no comment whatsoever.
e.g
void foo(...){
bool flag;
//begin some weird looking code
if (something)
[...]
flag = true;
}
They attempt against code redeability. And the poor guy who has to read it months/years after the original programmer is gone, is going to have some hard time trying to understand what the purposse of it originally was.
However, if the flag variable has a representative name, then i think they are ok, as long as used wisely (see other responses).
Yes, that is just silly nonsensical code.
You can simplify all that down to:
if (condition1)
{
// do something
}
Here's my take.
Code using flags:
...
if (dogIsBarking && smellsBad) {
cleanupNeeded = true;
}
doOtherStuff();
... many lines later
if (cleanupNeeded) {
startCleanup();
}
...
Very unclean. The programmer simply happens to code in whatever order his mind tells him to. He just added code at a random place to remind himself that cleanup is needed later on... Why didn't he do this:
...
doOtherStuff();
... many lines later
if (dogIsBarking && smellsBad) {
startCleanup();
}
...
And, following advise from Robert Martin (Clean Code), can refactor logic into more meaningful method:
...
doSomeStuff();
... many lines later
if (dogTookADump()) {
startCleanup();
}
...
boolean dogTookADump() {
return (dogIsBarking && smellsBad);
}
So, I have seen lots and lots of code where simple rules like above could be followed, yet people keep adding complications and flags for no reason! Now, there are legit cases where flags might be needed, but for most cases they are one style that programmers are carrying over from the past.