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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4
votes
2answers
329 views

Define product derivative

How do I define the $n$th product derivative of a function in Mathematica? The first product derivative $f^\ast$ of a function $f$ is $$ f^\ast(x)=\exp\left(\frac{f^\prime(x)}{f(x)}\right) $$ The ...
6
votes
4answers
1k views

Alternatives to While Loops?

I am using Mathematica to run a probabilistic simulation. Essentially, I have a list of members of a population (they only have one, numerical, attribute, so it's just implemented as a list of ...
11
votes
2answers
281 views

From iterative to functional

How to write this small piece in a functional way (ie. without state variables)?: ...
4
votes
1answer
227 views

Timing differences between multiple executions of identical code

I have a list of pairs of numbers and I'd like to change the sign of the second element in each pair i.e. $(a,b)\rightarrow (a,-b)$. I'm sure there are many ...
1
vote
2answers
277 views

How to create a list of variable names to some function of that variable

For example, for a single variable I can write Print[Unevaluated[a], "=", f[a]] But if I try the next thing I'd think of doing, assuming I want a list, it ...
3
votes
2answers
261 views

How do I convert an argument list to a list of arguments? [closed]

I think this is a basic question, but I am having difficulty finding the answer in the documentation. Thread is not what I am looking for, I think. Suppose that I ...
1
vote
2answers
137 views

How can define a set of nested parameters

I would like to know how I to define a function with a nested set of parameters (or whatever you would like to call it). For example, how would I get the following function ...
11
votes
4answers
295 views

Thread a function over a list and with a non-atomic 2nd parameter?

From the documentation, Thread's behavior on functions where the first parameter is a List and the second is an atomic expression, is this: ...
27
votes
12answers
1k views

Map a function across a list conditionally

It seems that this is a really basic question, and I feel that the answer should be obvious to me. However, I am not seeing. Can you please help me? Thanks. Suppose I have a list of data ...
0
votes
2answers
126 views

About minimizing calculations when using ComposeList

I have a lot of functions to use in a iterative way, and I need some of the calculation results. For example: ...
6
votes
5answers
259 views

How to nest my own “times” function to get powers

I have a "times" function. I'd like to create a power function using it. It should look like this for an 6th power: ...
6
votes
0answers
114 views

What are some general strategies to avoid using For loops? [duplicate]

Possible Duplicate: Iterating over lists in Mathematica While there are some cases where a For loop might be reasonable, it's a general mantra – one I ...
17
votes
3answers
833 views

Using pure functions 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: ...
-1
votes
1answer
184 views

GatherBy Option to group results?

How can GatherBy be programmed to take an option to group results as follows: ...
2
votes
3answers
167 views

Using Nest inside NestList

I need results like this: {Cos[Cos[x]], Sin[Cos[Cos[x]]],Cos[Cos[Sin[Cos[Cos[x]]]]], Sin[Cos[Cos[Sin[Cos[Cos[x]]]]]], ... } I've tried to use ...
13
votes
3answers
287 views

How to keep some of the results of the NestList

I'm using some iterative arithmetics to calculate wave propagation with the help of NestList. I have to use a small step size for iteration to guarantee the accuracy, which lead to too much data (e.g, ...
2
votes
3answers
205 views

Ways to change an explicit function into a pure function

I'm trying to use FixedPoint to solve a transcendental equations, but the first argument of the FixedPoint should be a pure ...
11
votes
2answers
534 views

What's the most “functional” way to do Cholesky decomposition?

I can do Cholesky in a procedural style, such as: ...
14
votes
0answers
401 views

How can I trace a functional expression's evaluation visually?

Ok, so the goal is to visualize the execution of this expression foo /@ {3 + 1, bar /@ {1 + 2, {4 + 7}}} in the following fashion using nested rectangles with ...
22
votes
1answer
533 views

Prefix operator with low precedence

The question is simple, but I will elaborate on the background as well for those interested in the idea: How to define a new operator with specified precedence value? Background Mathematica was ...
14
votes
2answers
514 views

Reproducing nested loops using Map?

I keep producing bits of code like the following: ...
5
votes
1answer
189 views

Composite graphics with Row, Column, data aggregation and layout control

This chromogram shown here represents data (mouse activity patterns during visits) for ~20 physicians in a study, each of which may have a variable number of visits in the study (physicians are color ...
4
votes
1answer
230 views
8
votes
2answers
235 views

Cases[data,Colon[key,_]] vs. Cases[data,key:_] toward XPath, XQuery

Exploring methods to index and search tree-structured key:value pairs via named-entity index (key paths) as opposed to Position-based indexing. Using Rule as ...
8
votes
3answers
349 views

Can this code be written in a more functional style

Referencing this question, I wonder if the following code can be written more concisely using a functional style, i.e. without For loops or ...
18
votes
3answers
1k views

Does every Symbol in Mathematica induce a monad?

From my question about types in Mathematica, I assume that every Symbol in Mathematica is a type if it appears as a Head of some ...
17
votes
2answers
777 views

Using a list of tuples in a pure function

I want to use a list of tuples within a function to make assignments. Say I want to make assignments of the form value[i,j] = val What I have is a list of ...
3
votes
1answer
331 views

Explanation on why Compile statement works only if input and output sizes work

I found the following code: Compile[{{m, _Real, 2}}, Fourier[m]][Table[N[i - j], {i, 4}, {j, 4}]] which doesn't work correctly. But the following was posted as a ...
16
votes
1answer
327 views

Are there advantages to using additional arguments of common functions rather than alternative ways of calculating with lists?

(Apologies for the long question title.) One of the interesting, if sometimes confusing, things about Mathematica is that there is always more than one way to do things. Even intermediate users can ...
21
votes
6answers
1k views

Can this be written well, without loops?

Inspired by this question I would like to know if the following code can be written without explicit loops (For, While, etc.) in a clean, efficient and non-contrived way. I have been unable to do so. ...
13
votes
4answers
685 views

Is there a more elegant and efficient way to write brainf*** style loops in Mathematica?

I'm having some fun writing a brainf*** interpreter in Mathematica. See this wiki article for more info. It works nicely but I'd like to find an elegant, preferably functional, way to handle the ...
15
votes
3answers
632 views

Can someone explain this snippet: (#[#] &)[#[#][#] &]

A friend showed me this snippet of code today: (#[#] &)[#[#][#] &] I can sort of see that we're constructing an anonymous function that takes a function ...
6
votes
1answer
465 views

How to solve this iteration in the functional programming way?

I am trying to come up with a functional programming method to calculate a list of replacements, that depend on previous replacements. Since there is always a finite number of steps, I would like to ...
55
votes
7answers
2k 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 of lazy ...