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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0
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1answer
35 views

Define inverse Laplace operator as map from functions to functions

I am trying to implement the inverse Laplace operator through P[g_] := h /.NDSolve[{h''[x] == g[x], h[0] == 0, h[1] == 0}, h, {x, 0, 1}][[1]] If I now define ...
1
vote
0answers
35 views

Which the functions of parameters can use Span [closed]

As I know,ImageValue,PixelValue,ReplaceImageValue,...
1
vote
2answers
40 views

How to round all the numbers in a function?

I have a complicated function that is a combination of floating-point numbers and variables. I want all the numbers rounded off, but I have no clue how to do this. For example I would want ...
9
votes
1answer
160 views

How to construct the RHS of Wick's theorem

I've been trying this for a few days now, but I just can't seem to find an efficient (speed-wise) functional way to code the following task. Context: I would like to construct an expressions that is ...
10
votes
1answer
171 views

Core functions or operations that every aspiring Mathematica programmer should know? [duplicate]

I am aware that there are common yet very powerful operations like Map, Thread, Apply, ...
11
votes
0answers
301 views

Is there research about the Mathematica programming paradigm?

There seem to be lots of papers discussing the functional programming paradigm terminology for Haskell, such as monad, category theory, lambda calculus, *morphism, etc. People study concepts and ...
1
vote
0answers
48 views

Different ways to program a recursive algorithm

Construct f (a numeric function) which takes multiple arguments with the following property: The single argument case $f(x_1)$ is meaningless, and the two-argument ...
1
vote
2answers
83 views

Partial Function Evaluation [closed]

How can I evaluate only part of a stack of function calls? In particular, given f[x_,y_,z_]=x+y+z;, say, I'd like to define a function ...
0
votes
0answers
55 views

Strange sharp spikes causing overflow while doing gradient descent

I am trying to find a function h(r) that minimises a functional H(h) by gradient descent. The result of H(h) is a single number. (Basically, I have a field configuration in space and I am trying to ...
4
votes
1answer
64 views

How to use currying to write a tail recursive function for summing factorials given a certain bound

I am very confused about how can i use currying to write a tail recursive function for summing factorials within a certain bound or summing the bounds i.e. given [1,5] i should be getting ...
89
votes
8answers
5k views

General strategies to write big code in Mathematica?

I think after six months of exposure to Mathematica and the Wolfram Language I am fairly OK with writing short codes and snippets. However, what are some general strategies to use in order to write ...
2
votes
1answer
60 views

Pairing values with their indexes for MapThread

Several operations require you to map over a list of values and to know the index of each value as you process it. To accomplish this, my current somewhat ugly solution uses MapThread: ...
3
votes
3answers
99 views

Counting runs in bits, along with their starts and lengths, in functional style

Here is some code to visualize Project Euler Problem 502. The code scans for runs of bits in the binary representation of an integer, and outputs the beginning position of each run and the length of ...
4
votes
0answers
68 views

RealDigits and functional style

So while thinking about Replacing numbers of which you only know certain digits I have faced, again, a problem that I find hard to extract from RealDigits' output ...
2
votes
1answer
49 views

Recognition Power Head for numeric value

We know: Map[Head, {a, a^2, a^3}] (* {Symbol, Power, Power} *) and Map[Head, {2, 2^2, 2^3}] all of them will be known as ...
1
vote
0answers
122 views

Variable naming conventions for nested pure functions [closed]

My understanding is that for nesting pure functions, one should use the explicit version of pure functions. I would like to know the best way of making it readable for people. I currently have ...
3
votes
3answers
116 views

how to map a function on a variable list

The following is just an example that captures what I want to do (more on it at the bottom). I'm trying to do something that can be paraphrased as follows: I have a global list, say ...
10
votes
0answers
159 views

How best to simulate n-body systems in a functional way

I want to simulate a N-body system in the most functional way possible. The system I'm modeling are metallic colloidal particles in a solution of peroxide water, as here ...
3
votes
1answer
118 views

The basic primitive recursive functions

How can the basic primitive recursive functions be expressed in the Wolfram Language? Apparently here's an example for primitive recursion: ...
3
votes
0answers
86 views

Delimited Continuations: Easy? or Fundamentally Difficult?

Apologies in advance for the length of this question, but this is as short as I have been able to make it. The Prescription I'm looking at the following tutorial on delimited (or composable) ...
6
votes
4answers
925 views

How can I avoid using a For-loop in my code?

I am trying to avoid using For because I heard that For is not cool in functional programming. Below is a problem that the first ...
7
votes
3answers
90 views

How to organize expression by symbols (like Collect), but apply different functions to each coefficient

I want to mimic the functionality of Collect[expr, {vars}, func], but with the following modification: The function f that is ...
3
votes
1answer
74 views

Defining a list of functions

I'm using polynomial mappings such as s[{x_,y_}] := {x + y^2, y -x} and playing with compositions of such mapping, e.g. ...
2
votes
2answers
100 views

Repeatedly apply a bivariate function with one argument running over a list

I'd like to know how, given symbols f and g, and a list {a,b,c,...}, to produce the ...
2
votes
2answers
46 views

Deciding whether the return value of a function is defined based on its input [duplicate]

I have been met with the following problem: I have defined the following: myFunc[e_Integer]; That means, if I call: ...
1
vote
1answer
96 views

Iterations in Mathematica [closed]

this is probably a very easy question for all of you. I have a stochastic Mathematica code (not important what it's exactly) which gives me a number at the end. Now I want Mathematica to run this ...
7
votes
1answer
204 views

How to terminate early a functional computation

Problem description: Given a list $A=\{1,2,0,7,0,-1,2,6,\ldots\}$ and a list $B=\{0,7,0\}$ write a program that determines whether $B$ appears in $A$ or not. Note: the order of $B$'s items does ...
6
votes
1answer
496 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). ...
1
vote
2answers
114 views

A better way than using nested For-loops to make a search list

I'm generating a List that can be up to 26 values long, a simplified example is below. Is there a better way than nested loops? ...
4
votes
1answer
72 views

How can I get all pairs of values from an association with elements key->list

I have an association of the form ds=<|key1 -> list1, key2 -> list2,... ,keyn -> listn|> I would like a simple way to map a function to all pairs ...
4
votes
3answers
139 views

List of functions to list of parameters

I am working in a Dataset and I need to create a function for a ChartStyle option of a ...
7
votes
1answer
127 views

Writing code which generates a function to append many columns to a dataset

I love datasets in Mathematica. Say I have one that looks like this: ...
7
votes
3answers
194 views

Through does not work with Subtract

Through[(Max - Min)[#]] & @ {1, 2, 3, 4, 5} gives 5 + (-Min)[{1, 2, 3, 4, 5}] Of course I can work around by ...
11
votes
1answer
159 views

The equivalent of dplyr mutate with Dataset

In R, there is a package "dplyr" that works on data.frame objects, which is one of the origins of the Mathematica Dataset construct. One of the things dplyr can do is "mutate" the columns of a ...
6
votes
1answer
129 views

functional way to identify & summarize repeated elements in List?

I have a List, for example (assume it's always ordered like this one): myList = {6, 6, 8, 10, 14} I would like to get a result like this: ...
3
votes
1answer
99 views

Using Map multiple times in one command

Is there a way to reproduce the effect of Table[i ** j, {i, list1}, {j, list2}] using Map instead of Table? Specifically, I want to write something along the ...
1
vote
2answers
87 views
2
votes
3answers
165 views

Given a list of triangle vertices, how to find the neighbors for each vertex?

A triangle is represented by {a,b,c}, indicting that its vertex IDs are a, b, and ...
7
votes
1answer
130 views

Unevaluated @ {args} versus Unevaluated /@ {args}

Working my way through Robby Villegas's lovely notes on withholding evaluation, I almost got Polish Notation on my first try. Here is my final solution, which seems to work well enough: ...
2
votes
1answer
134 views

Use Map with multiple arguments over a nested list

I noticed there are a few similar questions to mine on here, but I couldn't figure out how to accomplish this mapping. I have sets of data I want to plot, which represent intensity and frames, and I ...
2
votes
2answers
228 views

Multiply pure function with scalar

Somtimes I still get lost in the Hold, HoldAll etc. functions of Mathematica. I want to scale a simple PDF function with a previously calculated variable e.g. ...
0
votes
1answer
56 views

Mapping Linear Model Fit Over An Arbitrary Number of sets

I have multiple sets of data, and I want to apply Linear Model Fit sequentially to each set of data. For example, below tstlst contains 3 data sets. Right now I ...
7
votes
5answers
620 views
4
votes
1answer
61 views

How to define a function to save a list to a same-name file

I want a convenient way to save lots of intermediate data lists into files, so that next time the files can be imported automatically to homonym list variables in the notebook, without having to ...
2
votes
2answers
100 views

Better to use loop or function when populated list?

In the past I have pretty much stuck to expression building when using Mathematica, but recently I have been writing a procedure to populate an array, which I guess are called "lists" in Mathematica. ...
14
votes
3answers
332 views

Mimic a procedural, recursive clustering algorithm for site percolation using functional programming

Sorry in advance for my logorrhea: I just want to make sure all of the information is here. Context and Question I am investigating site percolation on a square lattice. I have a working, ...
1
vote
1answer
105 views

Compute Mean and Variance for Random Choice

I have data ...
3
votes
3answers
107 views

How to force evaluation on the right of an @ operator?

Is there a way to force evaluation on the right before the Prefix operator (@) without using parentheses? I came across this question when I was working with the ...
0
votes
0answers
119 views

Loop in a loop, or how to evaluate complex expressions

I need to find $h_{0j}$ for every $1\leq j\leq300$, where \begin{multline*} h_{0j} = \sum_{q=1}^{Q}g_qe^{-\lambda_q j\Delta}\frac{e^{\lambda_q\Delta}-1}{\lambda_q} + \sum_{p=1}^{P}\frac{e^{-\alpha_p ...
10
votes
4answers
284 views

Handy / flexible directory tree operations

Is there any shorter / more handy / more flexible way to get directory tree as a nested Rules/Associations list? I tried to incorporate ...