# Questions tagged [functional-style]

Questions about Mathematica's functional programming style, including the use of pure functions (Function[], #, &) and functions such as Map, Apply, Nest, and Through.

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### Seeking for a general method to turn the term(s) in a formula into a list [closed]

If we want to make arbitary formula into a List, for example, input (1+a^3) and we want the output data to be {1,a^3}, we can use List@@(expr). However when input data becomes a^3, we need to change ...
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### Finding the integer values of $p$ and $l$ for which a function $b(p, l)$ is divisible by $n$

I wrote the code in the attached image to find the integer values of $p$ and $l$ for which a function $b(p, l)$ is divisible by 3. Does anyone know of a nicer way to achieve the same result? Perhaps ...
68 views

### Considerations for Compiling and Parallelizing Code Outside or Inside Map[]

Assume f as well as Map[f,list] are parallelizable and compilable, such that parallelization and compilation give significant ...
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### How to create and store a plot for each iteration of a Do loop

I have created the following code below. Its purpose is for me to divide the plot into grids and for each grid I reterive the center point's co-ordinates. ...
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### Defnining a function with a parameter which is not a slot but a constant [closed]

One convenient way to define a function is f[S,x_]:= 3 f[G,x_]:= 7 where the first parameter is not a slot but a constant. This way of constructing functions is ...
63 views

### Apply function modification to curried function

This is based on A function that modifies functions - well-defined operation?, a previous question of mine. Lukas Lang's answer of course works very well, but now I encountered the following edge case:...
28 views

### Create a function which takes a (or several) time-dependent plot(s) as input and produces a sequence of images

I want to use Wolfram Script to create a sequence of PNG images depending on some parameter (which I then turn into a movie). Currently I do this with a for loop. I would like to avoid having to write ...
31 views

### Use result of function without repeatedly evaluating [closed]

I have a function which takes the determinant of a matrix whose values depend on two parameters: f[x_,y_]:= Det[M[x,y]]; where M is a predetermined matrix which is ...
435 views

### Pure functions instead of For loop

How to get following loop output using pure functions such as NestList? For[i = 0; v = 0, i < 4 && v < 4, i++; v++, Print[x^i + b^v]] and the ...
507 views

### Writing Fold in terms of Map or MapThread?

Consider Fold[f,z,{a,b,c}] ==> f[f[f[z,a],b,c]] I'm looking for a way to write this (in general) using Map or ...
435 views

### Defining a sequence slot programmatically

This question is related to: Composition of functions using slots Slot (#) interfering with evaluation Consider a toy example: ...
51 views

### Folow-up on combining pure functions [duplicate]

This is a follow-up to this question. Consider: f = #^2& g = #^3& Compose[f, g] (#1^3 &)^2 Am I the only one to think this is a bug?
170 views

### Performance of pure function - Best way to define a function?

In general, to define a function, we often use f[x_]. Another way is to use pure function (full form and shorthand). I want to test the performance of these ...
151 views

### Robust PCA (better Mathematica style)

I've parsed (almost verbatim) Python RPCA implementation to WM. Can it be rewritten using a better WM style? In particular, I'm not happy with ...
49 views

### Functional iteration of list of functions

I'm getting completely stumped on writing a function makeIterate that constructs an iterated structure out of a list of functions e.g. ...
5k views

### Functional style using lazy lists?

Let's say I want to answer the question "what are the first 400 palindromic prime numbers?" The first approach that comes to my mind from the set of languages that I know is to use some sort ...
81 views

### How do I correctly iterate using Outer when an argument / slot is a nested list?

I have the following complex nested iteration situation. I begin with a list, data, that comprises 16 TemporalData objects Each TemporalData object contains 2 ...
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### Idiomatic pattern for subtracting a function from a list

I would like to know a more idiomatic way to subtract a function from a list of pairs than this: Table[point-{0,fitFunction[point[]]}, {point,data}] I use this ...
411 views

### About auto-compiling and performance between Do and Fold

I was investigating how Fold could improve performance vs Do. I tested the code ...
113 views

### Best way to write a system of conditions

Quite simply, I am wondering if there is a cleaner (and more easily altered) way to write a system of conditions for an evaluation. For instance, suppose I have something like (I don't think a real ...
137 views

### Functional realisation of do-loop

I'm currently optimising my code and I'm using a lot of loops, so I was wondering if there is a smarter or faster way to do things like: ...
810 views

### FoldWhile and FoldWhileList

Mathematica has had NestWhile and NestWhileList for some time. But, to date, it has not implemented a built-in ...
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### How do I integrate a For loop to generate iterations of the Sierpinski's Triangle?

I'm sorry if this is a basic question—I don't know anything about programming. I know you can create a graphic of Sierpinski's Triangle with a single command, but I'd like to know how to create one ...
260 views

### How to select the fastest approach for large numerical data computations?

I really love the flexibility of Mathematica: there are several ways to perform one task. However, to get the performance of the intense numeric calculation, it can ...
120 views

### How to implement fast series multiplication

I need to generalize the SeriesData object for my own purposes. One of the things I need to do is to reimplement code to multiply product of series. I've made two ...
69 views

### How to change list type from CountryData to regular text? [closed]

When you access a list of countries from CountryData the outputs are boxed and is not normal text. How do I convert the type of items inside the list so I can modify the style? For example I have: <...
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### What is the most efficient way to implement NestPairWhileList[f,expr,test,g]

Question NestWhileList[f,x,test] lets you iterate a function until a condition is satisfied, outputting the list of iterated values ...
78 views

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### Breaking "Functional Loops" and Doing Lazy Evaluation In Mathematica

Alright, so this is a question about the functional way to break a for/while loop. Since we're on the Mathematica SE, I'm interested in the ways a Mathematica vet would handle this, however the ...
168 views

### Why Does Parallelization Not Speed Up these Seemingly Well-Parallelizable, Simple Functions?

Original Example Consider function f, a parallelized version fPar, and a coarsest-grained parallelized version ...
471 views

### Creating a list with Thread

I have a list like this one: aaah= {{11, 21, 31}, {12, 22, 32}, {13, 23, 33}} and I finally want to get a list which looks like this one: ...
71 views

### How do I correctly use OperatorApplied?

Starting with ClearAll[f, list] list = {"a", "the"} f[s_, n1_, n2_] := {s, n1, n2} Then f[list, 20, 10] ...
921 views

### How can I replace a set of Nested For Loops with a Functional Code Alternative?

Despite having looked over various posts concerning optimizing nested For loop expressions into a functional programming equivalent I still can not figure out how to actually to do this. Such ...
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### Style function not working inside Print Row functions

About Watch[...] is a helper function for watching a list of variables or other functions inside a Module[...] during ...
756 views

### Analogies to Help New Users

In many of the classes that I teach, I require students to learn the basics of Mathematica which we use throughout the semester to do computations and to submit homeworks (in notebook form). Some ...
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### Using Fold[ or Map[ Better?

I'm working through MMA Cookbook by Mangano, page 54. He shows Map is a compact form of Fold function. Is using ...
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### Gâteaux (directional) derivatives and higher order differentials of a functional

I would like to calculate the Gâteaux derivative of a functional (i.e. a function depending on functions). A simple example for the Dirichlet functional: $L(u(x))=\int_0^1 \frac{1}{2} (u'(x))^2 dx$ ...
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### Fold a list but alternate used functions

Is there a clean way to fold a list but alternate functions used? Say we call such function FoldAlternating. Then for example, The ...
24 views

### How to style a row of lists of lists created with a Table and return all lists?

I want to return a list of all lists with elements in a single first list styled if it meets a condition so that it stands out from other lists. My attempt at this only returns all data with no row ...
44 views

### Results of recursion grouped in list [closed]

I made a recursion where I should plot resulting points. When I do Print[point1], it just gives me result: ...
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### Programming a numerical method in the functional style

I am new to Mathematica and I would like to learn a bit more about functional programming. At the moment I have assignments like programming different numerical methods (for integration: ...
752 views

### Does Mathematica have a functional programming idiom to loop over a list till a condition is met? [duplicate]

The module below takes a list of integers and performs fadic addition on it (if a bit slowly). ...
58 views

### Implements the binary-searching style code in functional way

Given that I have a code snippet written in binary-searching way: ...
64 views

### Replace Solution arrow in list of list

I have solutions like ...
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### Plot is passing a bizarrely shifted x_min value to the user-specified Ticks function

The documentation for Mathematica's Ticks option says that you can specify the ticks for an axis by passing a function rather than a plain list description. The ...
426 views

### Operator currying: how to convert f[a,b][c,d] to {a+c,b+d}?

This question is related to this golfing question (but I'm not interested in golfing, only in functional operator composition): How can we convert f[a,b][c,d] to <...
293 views

### An efficient way to evaluate this expression with deeply nested Do loops

Is there an efficient way to evaluate something like this? ...
Suppose that I have a list of depth $k$, and I want to apply a function $f$ to all elements at level $n$ - e.g. \$f,\{\{\{a,b\},\{b,c\}\},\{\{c,d\}\}\},3\mapsto\{\{\{f(a),f(b)\},\{f(b),f(c)\}\},\{\{f(c)...