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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2
votes
3answers
187 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 ...
2
votes
1answer
153 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
313 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
310 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
278 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 ...
7
votes
2answers
378 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
183 views

Can my permutations function be defined using iteration?

I have two functions, tuples and perm. They are similar. ...
24
votes
3answers
381 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
77 views
6
votes
3answers
329 views

How can I rewrite this with NestList or FoldList?

The original code used For: ...
11
votes
4answers
524 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
239 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
269 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
123 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
527 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
163 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
175 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
197 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
170 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
216 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
134 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
315 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
171 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
412 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
663 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
337 views

Generate a Combination of letters by a number

I'm trying to write a function f. example: ...
4
votes
2answers
279 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
811 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
248 views

From iterative to functional

How to write this small piece in a functional way (ie. without state variables)?: ...
4
votes
1answer
214 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
215 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
174 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
127 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
272 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
121 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
247 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 ...
16
votes
3answers
618 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
168 views

GatherBy Option to group results?

How can GatherBy be programmed to take an option to group results as follows: ...
2
votes
3answers
157 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
260 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
188 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 ...
10
votes
2answers
446 views

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

I can do Cholesky in a procedural style, such as: ...
13
votes
0answers
339 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 ...
20
votes
1answer
464 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 ...
12
votes
2answers
464 views

Reproducing nested loops using Map?

I keep producing bits of code like the following: ...
5
votes
1answer
185 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
216 views
8
votes
2answers
216 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 ...