I'm trying to run a cobweb code in Mathematica and I need the following script:
ClearAll[CobwebPlot]
Options[CobwebPlot]=Join[{CobStyle->Automatic},Options[Graphics]];
CobwebPlot[f_,start_?NumericQ,n_,xrange:{xmin_,xmax_},opts:OptionsPattern[]]:=Module[{cob,x,g1,coor},
cob=NestList[f,N[start],n];
coor = Partition[Riffle[cob,cob],2,1];
coor[[1,2]]=0;
cobstyle=OptionValue[CobwebPlot,CobStyle];
cobstyle=If[cobstyle===Automatic,Red,cobstyle];
g1=Graphics[{cobstyle,Line[coor]}];
Show[{Plot[{x,f[x]},{x,xmin,xmax},PlotStyle->{{Thick,Black},Black}],g1},FilterRules[{opts},Options[Graphics]]]
]
Manipulate[CobwebPlot[Sqrt[3#-1]&,\[Alpha],40,{0,5},PlotRange->{{0,4.5},{0,3.65}},Frame->True,Axes->False,CobStyle->Directive[Dashed,Red],PlotRangePadding->None],{\[Alpha],0.5,4.375}]
I found the script online but I don't understand some features, such as what is the purpose of the following characters, # and &, in the Manipulate[] segment of the code:
Manipulate[CobwebPlot[Sqrt[3#-1]&,\[Alpha],40,{0,5},PlotRange->{{0,4.5},{0,3.65}},Frame->True,Axes->False,CobStyle->Directive[Dashed,Red],PlotRangePadding->None],{\[Alpha],0.5,4.375}]
Can you help me?
See this Mathematica documentation page on pure functions, or what other languages call anonymous functions, or lambda functions.
To give a cute example, suppose you have the function
doItTwice[x_,f_] := f[f[x]];
Now say you want to use this function to square the number seven twice. One way to do this would be to define a square function like this:
square[x_] := x^2;
doItTwice[7, square]
Well, there is a cleaner way to do this by simply writing the square function as a pure function, which would look like (#^2)&. The # is the parameter to the pure function, and the & is just there to indicate that it's a pure function. Really the parenthesis aren't even necessary, so you could write #^2&. Anyways, the following code is now a cleaner way to square seven twice:
doItTwice[7, (#^2)&]
Related
I am refactoring some business rule functions to provide a more generic version of the function.
The functions I am refactoring are:
DetermineWindowWidth
DetermineWindowHeight
DetermineWindowPositionX
DetermineWindowPositionY
All of them do string parsing, as it is a string parsing business rules engine.
My question is what would be a good name for the newly refactored function?
Obviously I want to shy away from a function name like:
DetermineWindowWidthHeightPositionXPositionY
I mean that would work, but it seems unnecessarily long when it could be something like:
DetermineWindowMoniker or something to that effect.
Function objective: Parse an input string like 1280x1024 or 200,100 and return either the first or second number. The use case is for data-driving test automation of a web browser window, but this should be irrelevant to the answer.
Question objective: I have the code to do this, so my question is not about code, but just the function name. Any ideas?
There are too little details, you should have specified at least the parameters and returns of the functions.
Have I understood correctly that you use strings of the format NxN for sizes and N,N for positions?
And that this generic function will have to parse both (and nothing else), and will return either the first or second part depending on a parameter of the function?
And that you'll then keep the various DetermineWindow* functions but make them all call this generic function?
If so:
Without knowing what parameters the generic function has it's even harder to help, but it's most likely impossible to give it a simple name.
Not all batches of code can be described by a simple name.
You'll most likely need to use a different construction if you want to have clear names. Here's an idea, in pseudo code:
ParseSize(string, outWidth, outHeight) {
ParsePair(string, "x", outWidht, outHeight)
}
ParsePosition(string, outX, outY) {
ParsePair(string, ",", outX, outY)
}
ParsePair(string, separator, outFirstItem, outSecondItem) {
...
}
And the various DetermineWindow would call ParseSize or ParsePosition.
You could also use just ParsePair, directly, but I thinks it's cleaner to have the two other functions in the middle.
Objects
Note that you'd probably get cleaner code by using objects rather than strings (a Size and a Position one, and probably a Pair one too).
The ParsePair code (adapted appropriately) would be included in a constructor or factory method that gives you a Pair out of a string.
---
Of course you can give other names to the various functions, objects and parameters, here I used the first that came to my mind.
It seems this question-answer provides a good starting point to answer this question:
Appropriate name for container of position, size, angle
A search on www.thesaurus.com for "Property" gives some interesting possible answers that provide enough meaningful context to the usage:
Aspect
Character
Characteristic
Trait
Virtue
Property
Quality
Attribute
Differentia
Frame
Constituent
I think ConstituentProperty is probably the most apt.
I'm trying to optimize a given object oriented code in matlab. It is an economical model and consists of a Market and Agents. The time consuming part is to update certain attributes of all Agents during each timestep which is implemented in a for loop.
However, I fail to vectorize the object oriented code.
Here is an example (Note, the second thing that slows down the code so far is the fact, that new entries are attached to the end of the vector. I'm aware of that and will fix that also):
for i=1:length(obj.traders)
obj.traders(i).update(obj.Price,obj.Sentiment(end),obj.h);
end
Where update looks like
function obj=update(obj,price,s,h)
obj.pos(end+1)=obj.p;
obj.wealth(end+1)=obj.w(1,1,1);
obj.g(end+1)=s;
obj.price=price;
obj.Update_pos(sentiment,h);
if (obj.c)
obj.Switch_Pos;
end
...
My first idea was to try something like
obj.traders(:).update(obj.Price,obj.Sentiment(end),obj.h);
Which didn't work. If someone has any suggestions how to vectorize this code, while keeping the object oriented implementation, I would be very happy.
I cannot provide a complete solution as this depends on the details of your implementation, but here are some tips which you could use to improve your code:
Remembering that a MATLAB object generally behaves like a struct, assignment of a constant value to a field can be done using [obj.field] =​deal(val); e.g.:
[obj.trader.price] = deal(obj.Price);
This can also be extended to non-constant RHS, using cell, like so:
[aStruct.(fieldNamesCell{idx})] = deal(valueCell{:}); %// or deal(numericVector(:));
To improve the update function, I would suggest making several lines where you create the RHS vectors\cells followed by "simultaneous" assignment to all relevant fields of the objects in the array.
Other than that consider:
setfield: s = setfield(s,{sIndx1,...,sIndxM},'field',{fIndx1,...,fIndxN},value);
structfun:
s = structfun(#(x)x(1:3), s, 'UniformOutput', false, 'ErrorHandler', #errfn);
"A loop-based solution can be flexible and easily readable".
P.S.
On a side note, I'd suggest you name the obj in your functions according to the class name, which would make it more readable to others, i.e.:
function obj=update(obj,price,s,h) => function traderObj=update(traderObj,price,s,h)
It has been a while since I've used Mathematica, and I looked all throughout the help menu. I think one problem I'm having is that I do not know what exactly to look up. I have a block of code, with things like appending lists and doing basic math, that I want to define as a single variable.
My goal is to loop through a sequence and when needed I wanted to call a block of code that I will be using several times throughout the loop. I am guessing I should just put it all in a loop anyway, but I would like to be able to define it all as one function.
It seems like this should be an easy and straightforward procedure. Am I missing something simple?
This is the basic format for a function definition in Mathematica.
myFunc[par1_,par2_]:=Module[{localVar1,localVar2},
statement1; statement2; returnStatement ]
Your question is not entirely clear, but I interpret that you want something like this:
facRand[] :=
({b, x} = Last#FactorInteger[RandomInteger[1*^12]]; Print[b])
Now every time facRand[] is called a new random integer is factored, global variables b and x are assigned, and the value of b is printed. This could also be done with Function:
Clear[facRand]
facRand =
({b, x} = Last#FactorInteger[RandomInteger[1*^12]]; Print[b]) &
This is also called with facRand[]. This form is standard, and allows addressing or passing the symbol facRand without triggering evaluation.
I'm trying to make a conditinal expression which would initialize some functions, variables etc.. Something which would look like this in C:
#if option==1
int foo(int x){/*some code here*/}
int q=10;
#else
char foo(int x){/*some other code*/}
double q=3.141592;
#endif
use_q(q);
f(some_var);
In Mathematica I've tried using If, like this:
If[option==1,
foo[x_]=some_expression1;
q=10;
,
foo[x_]=some_expression2;
q=3.141592;
]
use_q[q];
f[some_var];
But the result is that functions' arguments are colored red, and nothing gets initialized or computed inside If.
So, how should I do instead to get conditional "compilation"?
Several things:
Do not use blanks (underscores) in variable names - in Mathematica these are reserved symbols, representing patterns.
In case you condition does not evaluate to True or False, If does not evaluate either.
Thus:
In[12]:= If[option==1,Print["1"],Print["Not 1"]]
Out[12]= If[option==1,Print[1],Print[Not 1]]
thus your result. Red colred arguments are not the issue in this particular case. You should either use === in place of ==, or TrueQ[option==1], to get what you want. Have a look here, for more information.
This sounds like something that would be better done as a function with an option, for example
Options[myfunction,{Compiled->False}]
myfunction[x_,opts:OptionsPattern[]]:=
With[{comp= TrueQ[OptionValue[Compiled]]},
If[comp, compiledFunction[x], notcompiledFunction[x] ]]
(The local constant comp within the With statement is not strictly necessary for this example but would be useful if your code is at all complex and you use this conditional more than once.)
I do not recommend defining different cases of a function inside an If[] statement. You would be better off using the built-in pattern-matching abilities in Mathematica. (See documentation here and especially here.)
Some useful documentation on options within functions can be found here, here and here.
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.