I wanted to know, how to evaluate multiple statements in a function in Mathematica.
E.g.
f[x_]:=x=x+5 and then return x^2
I know this much can be modified as (x+5)^2 but originally I wanted to read data from the file in the function and print the result after doing some data manipulation.
If you want to group several commands and output the last use the semicolon (;) between them, like
f[y_]:=(x=y+5;x^2)
Just don't use a ; for the last statement.
If your set of commands grows bigger you might want to use scoping structures like Module or Block.
You are looking for CompoundExpression (short form ;):
f[x_]:= (thing = x+5 ; thing^2)
The parentheses are necessary due to the very low precedence of ;.
As Szabolcs called me on, you cannot write:
f[x_]:= (x = x+5 ; x^2)
See this answer for an explanation and alternatives.
Leonid, who you should listen to, says that thing should be localized. I didn't do this above because I wanted to emphasize CompoundExpression as a specific fit for your "and then" construct. As it is written, this will affect the global value of thing which may or may not be what you actually want to do. If it is not, see both the answer linked above, and also:
Mathematica Module versus With or Block - Guideline, rule of thumb for usage?
Several people have mentioned already that you can use CompoundExpression:
f[x_] := (y=x+5; y^2)
However, if you use the same variable x in the expression as in the argument,
f[x_] := (x=x+5; x^2)
then you'll get errors when evaluating the function with a number. This is because := essentially defines a replacement of the pattern variables from the lhs, i.e. f[1] evaluates to the (incorrect) (1 = 1+5; 1^2).
So, as Sjoerd said, use Module (or Block sometimes, but this one has caveats!) to localize a function-variable:
f[x_] := Module[{y}, y=x+5; y^2]
Finally, if you need a function that modified its arguments, then you can set the attribute HoldAll:
Clear[addFive]
SetAttributes[addFive, HoldAll]
addFive[x_] := (x=x+5)
Then use it as
a = 3;
addFive[a]
a
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"}
Before jumping into python, I had started with some Objective-C / Cocoa books. As I recall, most functions required keyword arguments to be explicitly stated. Until recently I forgot all about this, and just used positional arguments in Python. But lately, I've ran into a few bugs which resulted from improper positions - sneaky little things they were.
Got me thinking - generally speaking, unless there is a circumstance that specifically requires non-keyword arguments - is there any good reason NOT to use keyword arguments? Is it considered bad style to always use them, even for simple functions?
I feel like as most of my 50-line programs have been scaling to 500 or more lines regularly, if I just get accustomed to always using keyword arguments, the code will be more easily readable and maintainable as it grows. Any reason this might not be so?
UPDATE:
The general impression I am getting is that its a style preference, with many good arguments that they should generally not be used for very simple arguments, but are otherwise consistent with good style. Before accepting I just want to clarify though - is there any specific non-style problems that arise from this method - for instance, significant performance hits?
There isn't any reason not to use keyword arguments apart from the clarity and readability of the code. The choice of whether to use keywords should be based on whether the keyword adds additional useful information when reading the code or not.
I follow the following general rule:
If it is hard to infer the function (name) of the argument from the function name – pass it by keyword (e.g. I wouldn't want to have text.splitlines(True) in my code).
If it is hard to infer the order of the arguments, for example if you have too many arguments, or when you have independent optional arguments – pass it by keyword (e.g. funkyplot(x, y, None, None, None, None, None, None, 'red') doesn't look particularly nice).
Never pass the first few arguments by keyword if the purpose of the argument is obvious. You see, sin(2*pi) is better than sin(value=2*pi), the same is true for plot(x, y, z).
In most cases, stable mandatory arguments would be positional, and optional arguments would be keyword.
There's also a possible difference in performance, because in every implementation the keyword arguments would be slightly slower, but considering this would be generally a premature optimisation and the results from it wouldn't be significant, I don't think it's crucial for the decision.
UPDATE: Non-stylistical concerns
Keyword arguments can do everything that positional arguments can, and if you're defining a new API there are no technical disadvantages apart from possible performance issues. However, you might have little issues if you're combining your code with existing elements.
Consider the following:
If you make your function take keyword arguments, that becomes part of your interface.
You can't replace your function with another that has a similar signature but a different keyword for the same argument.
You might want to use a decorator or another utility on your function that assumes that your function takes a positional argument. Unbound methods are an example of such utility because they always pass the first argument as positional after reading it as positional, so cls.method(self=cls_instance) doesn't work even if there is an argument self in the definition.
None of these would be a real issue if you design your API well and document the use of keyword arguments, especially if you're not designing something that should be interchangeable with something that already exists.
If your consideration is to improve readability of function calls, why not simply declare functions as normal, e.g.
def test(x, y):
print "x:", x
print "y:", y
And simply call functions by declaring the names explicitly, like so:
test(y=4, x=1)
Which obviously gives you the output:
x: 1
y: 4
or this exercise would be pointless.
This avoids having arguments be optional and needing default values (unless you want them to be, in which case just go ahead with the keyword arguments! :) and gives you all the versatility and improved readability of named arguments that are not limited by order.
Well, there are a few reasons why I would not do that.
If all your arguments are keyword arguments, it increases noise in the code and it might remove clarity about which arguments are required and which ones are optionnal.
Also, if I have to use your code, I might want to kill you !! (Just kidding), but having to type the name of all the parameters everytime... not so fun.
Just to offer a different argument, I think there are some cases in which named parameters might improve readability. For example, imagine a function that creates a user in your system:
create_user("George", "Martin", "g.m#example.com", "payments#example.com", "1", "Radius Circle")
From that definition, it is not at all clear what these values might mean, even though they are all required, however with named parameters it is always obvious:
create_user(
first_name="George",
last_name="Martin",
contact_email="g.m#example.com",
billing_email="payments#example.com",
street_number="1",
street_name="Radius Circle")
I remember reading a very good explanation of "options" in UNIX programs: "Options are meant to be optional, a program should be able to run without any options at all".
The same principle could be applied to keyword arguments in Python.
These kind of arguments should allow a user to "customize" the function call, but a function should be able to be called without any implicit keyword-value argument pairs at all.
Sometimes, things should be simple because they are simple.
If you always enforce you to use keyword arguments on every function call, soon your code will be unreadable.
When Python's built-in compile() and __import__() functions gain keyword argument support, the same argument was made in favor of clarity. There appears to be no significant performance hit, if any.
Now, if you make your functions only accept keyword arguments (as opposed to passing the positional parameters using keywords when calling them, which is allowed), then yes, it'd be annoying.
I don't see the purpose of using keyword arguments when the meaning of the arguments is obvious
Keyword args are good when you have long parameter lists with no well defined order (that you can't easily come up with a clear scheme to remember); however there are many situations where using them is overkill or makes the program less clear.
First, sometimes is much easier to remember the order of keywords than the names of keyword arguments, and specifying the names of arguments could make it less clear. Take randint from scipy.random with the following docstring:
randint(low, high=None, size=None)
Return random integers x such that low <= x < high.
If high is None, then 0 <= x < low.
When wanting to generate a random int from [0,10) its clearer to write randint(10) than randint(low=10) in my view. If you need to generate an array with 100 numbers in [0,10) you can probably remember the argument order and write randint(0, 10, 100). However, you may not remember the variable names (e.g., is the first parameter low, lower, start, min, minimum) and once you have to look up the parameter names, you might as well not use them (as you just looked up the proper order).
Also consider variadic functions (ones with variable number of parameters that are anonymous themselves). E.g., you may want to write something like:
def square_sum(*params):
sq_sum = 0
for p in params:
sq_sum += p*p
return sq_sum
that can be applied a bunch of bare parameters (square_sum(1,2,3,4,5) # gives 55 ). Sure you could have written the function to take an named keyword iterable def square_sum(params): and called it like square_sum([1,2,3,4,5]) but that may be less intuitive, especially when there's no potential confusion about the argument name or its contents.
A mistake I often do is that I forget that positional arguments have to be specified before any keyword arguments, when calling a function. If testing is a function, then:
testing(arg = 20, 56)
gives a SyntaxError message; something like:
SyntaxError: non-keyword arg after keyword arg
It is easy to fix of course, it's just annoying. So in the case of few - lines programs as the ones you mention, I would probably just go with positional arguments after giving nice, descriptive names to the parameters of the function. I don't know if what I mention is that big of a problem though.
One downside I could see is that you'd have to think of a sensible default value for everything, and in many cases there might not be any sensible default value (including None). Then you would feel obliged to write a whole lot of error handling code for the cases where a kwarg that logically should be a positional arg was left unspecified.
Imagine writing stuff like this every time..
def logarithm(x=None):
if x is None:
raise TypeError("You can't do log(None), sorry!")