Questions tagged [function-construction]
For questions on writing functions (pure or using Set/SetDelayed) for any purpose, including the features that may be incorporated in those functions, such as options, patterns and conditions.
2,414
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Functions with Options
Suppose you want to create a function which has optional arguments. Maeder's book Programming in Mathematica covers the topic extensively up to version 3, but some things have changed/evolved since ...
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Functions vs. patterns
Every time I define a new function, I wonder which construct I should use: true functions obtained by using Function, or rule-based syntax. For example, these are ...
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How to avoid collision between optional arguments and options?
Is it possible to create a function with optional arguments that also takes options?
Here is a simple example. I have a function f with option "g". It also has ...
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10
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Generating a Sierpinski carpet
I am trying to draw a Sierpinski_carpet. I have code that works, but I think there is a more elegant way to do than my way. Maybe I couls use Tuples or ...
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Enforcing correct variable bindings and avoiding renamings for conflicting variables in nested scoping constructs
Using global variables the following turns an "expression" into a Function:
expr = 2 x;
Function[x, Evaluate[expr]]
Of course ...
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Can I make a default for an optional argument the value of another argument?
I'd like to define a function with several optional arguments, some of which default to the value supplied for other arguments. For example, I'd like to be able to write something like
...
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47
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2
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Is there any algorithm that runs faster in Mathematica than in C or Fortran?
I'm just curious. My friend just told me that Mathematica is mostly for symbolic calculation and not efficient for Numerical computations. He told me that's the reason most of the people don't use ...
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Function in Table
I need a table with the elements made of pure functions and list elements. This is a simplified example:
I need a list as:
...
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Can a function be made to accept a variable amount of inputs?
I have a function that takes two inputs and processes them for a single output. What I need is one that can take a varying number of inputs. and process them to a single output. Is this possible in ...
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5
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Why is there no PositionFunction in Mathematica?
Too often I have seen the programs of inexperienced users greatly slowed by using Position in an iterative fashion, when far faster would have been to compute a ...
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2
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How can I make threading more flexible?
Threading automatically with Listable functions requires the argument expressions to have the same length (or for one of them to be atomic). For nested lists the ...
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2
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How can I export my learned ClassiferFunction[] and PredictorFunction[]s?
Mathematica 10 provides beautiful high-level machine learning functionality. Sadly, the learned functions once created are rather opaque objects. I need to use them in other projects, so here is my ...
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Variable naming changes everything
Bug fixed in 10.0.0
I am having a rather unusual problem I do not understand with Mathematica where renaming one of the variables of my function causes the function to stop "working". Here is the ...
- 503
39
votes
3
answers
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Tiling a square
I wondered if there was a way to automate the process of finding a way to tile a tile into a square.
The idea is to represent the tile with a matrix of $0$s for blank space and $1$s for filled spaces ...
- 715
37
votes
3
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Is there a comprehensive list of functions with operator forms?
As of version 10, Mathematica sports operator forms for many functions like Map, SortBy, ...
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37
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3
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Can we intelligently control evaluation in Thread?
This is a bid at creating a canonical Q&A.
Many questions have been asked that come down to the fact that Thread evaluates its first argument before threading ...
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37
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2
answers
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Best practice of passing a large number of parameters to functions
I have a number of functions that all take a large number of parameters. I am wondering what is the best practice of passing these parameters to those functions. I could, of course, simply specify ...
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How to Combine Pattern Constraints and Default Values for Function Arguments?
EDIT: As several respondents have noted in the answers and comments below, the original example had a default value that would never be used because of the way patterns and default values are ...
- 1,511
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2
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Define parameterized function
I would like to be able to define the gain function of a system from its parameters. Specifically, I'd like to define a function that accepts two inputs, call them $b$ and $w$, and returns a function ...
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How to make MapAt work with Span?
Span (;;) is very useful, but doesn't work with a lot of functions. Given the following input
...
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34
votes
3
answers
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Is there any way to define pure functions with optional arguments?
For example consider the following function:
Function[{u,v},u^2+v^4]
Is there anyway to define default values for the variables ...
- 1,461
34
votes
1
answer
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which is better, using Assert[] or manual checks on arguments and other computations?
I never used Asserts in Mathematica, but trying to see what advantage they have over just argument check and additional definitions of the function to capture unwanted input.
For example, which one ...
- 137k
34
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2
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Custom atomic expressions - modern tutorial
Atomic but sophisticated expressions are all around for a long time: Graph SparseArray.
More are coming with each new release, ...
Kuba♦
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votes
3
answers
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Function that counts the number of arguments of other functions
I have a newbie question: is it possible to write a function that counts the arguments (total and optionals) of a given function? Possibly it should be able to work with built-in and custom functions ...
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How does Return work?
It is not completely clear to me how Return[] works.
The documentation says:
Return[expr] returns the value expr from a ...
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31
votes
3
answers
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Why does removing a function and defining it on the same line not work?
Why do the two pieces of code below yield rather different results? The only difference is that in the first one the function definition is in the same line as the ...
- 1,289
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9
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Using patterns in pure functions
Pure functions may be handy if you don't want to assign your function a name. For example I would calculate $x(x-1)$ for some numbers $x$ by
...
- 7,607
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5
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Second level depth pure function?
I have the following working construction:
Select[ln125, # == Nearest[ln125, 551.748][[1]] &]
Here, ln125 is a one ...
- 608
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votes
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Module with "local functions"
I am trying to use a Module having "local functions", i.e., those which I need to define only inside this module.
So I tried this:
...
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29
votes
6
answers
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Convert an expression to a Function
I need a function which can take an expression and return a pure function based on the symbols in the expression. The symbols might have values so must be protected from evaluation. It is probably ...
- 84.6k
28
votes
3
answers
1k
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Writing functions with "Method" options
I'd like to implement several behaviors for a particular function using a Method option added to the function definition:
...
- 4,301
27
votes
4
answers
17k
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Turn expression into function
I'm new to Mathematica and I spent the last hour trying to make the expression
...
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27
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4
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Sum over n variables
What is the most painless way to sum over n variables, for example, if the range of summation is $i_1 < i_2 < i_3 < \dots < i_n$, where $n$ is an argument of the function in question?
Is ...
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Is there a GraphicsPrimitiveQ (or a complete list of Heads of graphics primitives)?
For various reasons related to workflow associated with creating figures for journals, I am creating functions that will accept graphics primitives and a set of options and spit out a ...
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Constructing symbol definitions for With
I would like to be able to define two arrays, one containing symbol names and one containing the values of those symbols, for use in constructs such as With. For ...
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4
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Quick way to use conditioned patterns when defining multi-argument function?
I have a simple function that is supposed to only accept numeric values (i.e. complex/real numbers and constant symbols e.g. Pi, E).
$$f(a,b,c)=a+b+c$$
Edit: I should have chosen a less simple ...
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Modeling the spread of an infection in networked computers
I would like to show the iterative stages of infection for problem 2 in this link.
In case the link dies, I have copied the text for the problem below:
One hundred computers are connected in a ...
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How to program a F::argx message?
How useful is it to program a user-built function in a package to produce a red warning message F::argx if you give the wrong number of arguments to that function? ...
24
votes
3
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Why x = x doesn't cause an infinite loop, but f[x_] := f[x] does?
If I execute:
In[1] := x = x
Out[1] = x
and then I evaluate the symbol x:
...
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23
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Nested definition: How can I define a function with a passed-in expression?
Here's a simplified version of what I'm trying to do:
...
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3
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How to find the name of the current function?
I would like to know the name of the current function from within that function. For example, consider the following code
...
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votes
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SetAttributes[f,Flat]: Why the order dependence?
I'm experiencing a strange phenomenon. Here's a (quite artificial) test case:
The following definition work just fine:
...
- 19.1k
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votes
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answer
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Lazy lists of Tuples and Subsets
I'm trying to build a lazy list that evaluates the n'th m-tuple or subset of a given list using Mathematicas ordering without calculating all the Tuples. The purpose is to allow for example the ...
- 14.8k
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9
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How do you check if there are any equal arguments(even sublist) in a list?
I would like to set up a function which has to return True if at least two arguments of a given List are equal.
So if I give {1,4,6,2} to the function it has to ...
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votes
5
answers
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The difference between 0. and 0
I have a function for which 0 is a special case:
f[A___, 0, B___] := 0
But since I am doing numerics, sometimes in the course ...
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5
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Distributing function arguments with function compositions. How to compute $(f + g^2)(x) = f(x) + g(x)^2$?
Suppose I have two functions f and g. To compute $f + g$ evaluated at a point $x$, I know that one can use ...
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How to create custom Graphics primitive?
How to create custom Graphics primitive?
It should have the following properties, resembling properties of built-in geometric figures, like ...
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How to define a function that is Listable for some but not all arguments?
I want to define a function f[x,y] that is Listable for only the first argument, not the second. If we use ...
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Plotting a defined function gives different results from plotting the function directly
Consider the following piece of code:
function[t_]:=Exp[-9 t^2];
LogLogPlot[{function[t],Exp[-9 t^2]},{t,.01,100}]
I expect the two plots to exactly overlap each ...
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Skipping "middle" Optional Arguments
Is there a way to call a function where the "middle" arguments should use their default value while specifying values for the "right-most" arguments? For example, given this function:
...
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