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

learn more… | top users | synonyms

12
votes
5answers
637 views

What's the cleanest functional-programming style way to perform this list operation?

I am looking for the correct method for accomplishing the unknown piece in the following code snippet: rolls = Tuples[Range[1, 4], {2}] ...
4
votes
4answers
440 views

Replace For-loop with functional code

I am very new to Mathematica. I have code written using for loops. I want to rewrite it using Map/Thread but I am not sure how ...
10
votes
5answers
487 views

How to find first list element that differs from average of N previous elements by more than a given amount?

Given a list of real numbers, I need to write a function that returns the value of the first element in the list that differs from the mean of the previous $N$ elements by greater than $P$ standard ...
3
votes
1answer
234 views

NestList with a list inside?

I'm new to Mathematica, and was looking for more efficient ways to implement the Do loop below. a, ...
5
votes
2answers
224 views

Overlapping pure functions

Let say I need and option for Plot: RegionFunction -> (-6 < #2 < 6 &) But I also want those ...
2
votes
0answers
127 views

DownValues for Built-in Functions

N.B. I have bitten the bullet, and I am going through Leonid Shifrin's "Mathematica Programming: An Advanced Introduction." (Which needs no introduction in this forum) One question I have: could one ...
0
votes
1answer
254 views

How to nest the output of FindRoot in a table of Derivative evaluations?

I am using ParametericNDSolveValue to numerically solve an ODE system, which I then use to find the definite integral of one of the variables in the solution for different values of a parameter. Here ...
11
votes
3answers
190 views

Using Through to evaluate complex expressions

Suppose we're given the expression f*g+h, where f,g,h are all pure functions. How can we evaluate this expression on some ...
6
votes
2answers
274 views

Why are we so sure about Map results?

I do abuse it often but when I have faced this feature first time I was really suprised: i = 0; (i++; # - i) & /@ Range[5] {0, 0, 0, 0, 0} What am I ...
2
votes
1answer
115 views

Composition with Apply

Composition is sometimes useful for clarity of a code. For the same purpose I try to Apply(@@) functions as often as it is ...
1
vote
0answers
92 views

Optimized subset algorithm implementation

I was reading a paper from Mathematica Journal.It mentions a code for calculating subsets. ...
1
vote
2answers
123 views

Scripting a visual comparison between the derivative and some finite scheme

I want to make an application where I can specify a function $f:\mathbb R\to \mathbb R$ and a dynamic value $n$ and get the function $\frac{f(x+\frac{1}{n})-f(x)}{\frac{1}{n}}$. I moreover want to ...
3
votes
3answers
102 views

Applying a function of several arguments to the rows of a matrix

I have a user-defined function which takes three vectors as input. Suppose that is like this: f[a_, b_, u_] := Total[a*Total[u]^b] Usually I have vectors for ...
1
vote
0answers
45 views

Using anonymous functions instead of module or block. Bad idea? [duplicate]

Here is an example function which returns True if a point p is on an (open) line segment (A, B) assuming that Orientation[A, p, B] returns 0 if the three points are collinear: ...
4
votes
1answer
137 views

Why is this code in functional style is slower than procedural style?

I know that in Mathematica a functional programming style is often more efficient than procedural style programming using For loops. But the code shown below seems ...
17
votes
2answers
791 views

Going full functional (Haskell style)

I'm trying to define some notation so that Mathematica code would be more functional, similar to Haskell (just for fun): currying, lambdas, infix operator to function conversion, etc.. And I have some ...
1
vote
1answer
265 views

Arbitrary depth patterns/rules

Temporary message: I am now really confused. I am not sure how using Power and Unevaluated together works in the examples below. While answering this question, I stumbled upon the following. We ...
1
vote
2answers
221 views

Computing distance matrix for a list

Using functional programming in Mathematica, how can I compute a distance matrix for every element in a list of matrices... The distance would be computed between the item in the list and a "target ...
1
vote
1answer
100 views

given n lists, get list of applications of function to n-tuples

Is there a built in function or an easy rule to do the following transformation? H[{A[0], A[1], ...},{B[0], B[1], ...},...] into ...
10
votes
5answers
332 views

Transform a list of functions to a composition

How do I apply a list of functions in a nested way? Example: functionList = {f1,f2,f3} RequiredCommand[functionList,Pi] such that the required command returns ...
18
votes
3answers
1k views

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: ...
5
votes
2answers
211 views

Update a function avoiding infinite recursion

I am quite new to Mathematica and not completely familiar with functional programming. I am currently working with a function (call it foo) and wish to change its behaviour, for example, by adding 1 ...
2
votes
3answers
214 views

Defining a function to determine when convergence is guaranteed

I'm investigating how many iterations are needed for a particular orbit to reach a fixed point of a function. Since I have many functions to test, I want to define a function in Mathematica that will ...
3
votes
1answer
176 views

Issue with ListConvolve

I am a new Mathematica user, learning the intricacies of functional programming. I have issues withe applying a function over a moving list. My function seems to work and give correct results but it ...
4
votes
4answers
372 views

How to transform Do loop to more efficient codes?

I'm new to Mathematica. Here is my original program: How to rewrite the Do part? ...
5
votes
2answers
329 views

Variant of the cutting-stock problem in Mathematica

I'm pretty new to Mathematica and am trying to learn to solve problems in a functional way. The problem I was solving was to list the ways in which I could sum elements from a list (with repetitions), ...
4
votes
4answers
299 views

Differentiating space curves

I'm trying to do some very basic differential geometry of space curves. For example, a space curve $\gamma:\mathbb R\to\mathbb R^3$ has unit tangent and normal vectors given by ...
8
votes
2answers
426 views

Feedback on Functional Programming: Propagation of uncertainty

Lately I've been trying to use functional prgramming and tried to implement the gaussian propagation of uncertainty (without correlation) in an elegant way, here is the outcome: ...
2
votes
1answer
200 views

Can my permutations function be defined using iteration?

I have two functions, tuples and perm. They are similar. ...
24
votes
3answers
409 views

FoldWhile and FoldWhileList

Mathematica has had NestWhile and NestWhileList for some time. But, to date, it has not implemented a built-in ...
2
votes
0answers
80 views
6
votes
3answers
380 views

How can I rewrite this with NestList or FoldList?

The original code used For: ...
11
votes
4answers
545 views

How to write this without For loop

Suppose I have a few lists of numbers and want to exponentiate element-wise, then sum up everything into a polynomial. For example, if I have ...
0
votes
1answer
253 views

How can I improve my code with efficient mathematica built-in functions?

I have written a module for my assignment like below. V[n + 1] = rk[x[n], y[n] ,z[n], V[n]]; vs = V[n].V[n+1]; V[n + 1] = I want to modify it with efficient ...
8
votes
3answers
313 views

Map over list of functions

I would like to convert a list of $n$ complex equations to a list of $2n$ real ones. At the moment I am doing it like this: ...
4
votes
1answer
128 views

Functional Programming: modify EdgeList based on condition

I have a simple functional programming question: I have a simple EdgeList defined in Mathematica, I would like to modify the value of certain element of the list based on a condition. I see how to ...
14
votes
3answers
542 views

How can I improve my code for drawing a tree?

This code draws a tree, but it's not in the functional style. ...
5
votes
3answers
167 views

All values for a function with two arguments without Outer

Given two lists $l_a = \{a_1, a_2, a_3\}$, $l_b = \{b_1, b_2, b_3, b_4\}$ and some function $f$ accepting two arguments, how can I produce a list of all values $f(a, b)$ for $a\in l_a$ and $b \in l_b$ ...
4
votes
2answers
181 views

How can I improve this trial division procedure?

My background is procedural programming, so I find this construction quite natural. Is there a way to get rid of the While? ...
4
votes
6answers
207 views

Filter list with different list in it

I have a list like: {{{4, 14}, 1}, {{4, 15}, 1}, {{4, 16}, 1}, {{4, 17}, 1}, {{4, 18}, 1}, {{4, 14}, 3}, {4,15}, {{4, 16}, 2},{4,18}} Now I want to ...
0
votes
1answer
192 views

Iterative Function Mapping [duplicate]

Possible Duplicate: How to nest my own “times” function to get powers What I want to do is something like : Sin[...Sin[Sin[Sin[Sin[x]]]]] Basically, ...
3
votes
1answer
231 views

Evaluating a function on permutations of its arguments

Say I have a function "temp" of $n+1$ variables, $y,z1,z2,z3,...,zn$. I want to test if my function has certain symmetries like swapping $y$ with square of any $z$, swapping any two of the zs, ...
2
votes
1answer
144 views

#[[1]]//FullForm = 1?

I have a set of symbolic algebraic expressions that I'm trying to get some speed into. To illustrate the issue, I'll use a simple form like { k0 X, k1 Y, k1 Z}, ...
2
votes
1answer
442 views

Converting expressions into functions

I have defined an expression, such as a = x I would like to convert this into a function, such as f[x_]:=x However, in my ...
1
vote
4answers
183 views

Order of operations for the Table function [duplicate]

Possible Duplicate: Using pure functions in Table I have run into a situation that I do not understand when trying to generate a nested list of pure functions. I have the following code. ...
7
votes
3answers
453 views

Rewriting For loop to FoldList or similar

In CrossValidated, the answer to a question on prediction of number of viewers of Gangnam Style is given in R. I have mapped the answer directly to Mathematica: ...
12
votes
5answers
689 views

How to improve this code for solving the “Mr.S and Mr.P” puzzle?

Mr.S and Mr. P puzzle — "Formalization of two Puzzles Involving Knowledge", McCarthy, John (1987) We pick two numbers $a$ and $b$, such that $a\geq b$ and both numbers are within the range ...
4
votes
3answers
369 views

Generate a Combination of letters by a number

I'm trying to write a function f. example: ...
4
votes
2answers
321 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 ...