# Tagged Questions

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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### Applying a function to a Dataset column conditional on another slot's value

How to apply a function to a column conditional on another slot's value? The Dataset documentation show only how to apply a function to named slots independently. The ...
304 views

### have a function redefine itself as it maps through a list

I have a list which contains sublists, e.g. list = {{a,b}, {a,b,c}, {a,b,a,a}, {b,c}, ...} I then map a function through each sublist. This function should ...
184 views

### Listable on first level [duplicate]

I have some function which take List as input. f[l_List]:=someActions[l] I need apply this function to a list of lists. Now I ...
255 views

### How to replace While construct to NestWhile(functional-style) correctly?

Recently,I find the program of @J.M. about Get a "step by step" evaluation in Mathematica is a very useful example for learning Mathematica programming. In the function ...
189 views

### Local variables whose definitions depend on each other [duplicate]

Consider the following (pseudo-)function definition: f[l_] := Let[{ a = Length[l], b = First[l], c = b/a, }, c*10] So for ...
431 views

### Make MapIndexed listable

My goal is to apply MapIndexed to every element of a nested list without destroying the arithmetic operations within the elements. For example, let's start with ...
198 views

### Can $\it{every}$ usage of While be changed into NestWhile?

Ok, I think this problem is more close to philosophy. :P I've some idea now. But I'm not sure whether it's correct. For the purpose of convenience, I will use some C-like code instead of MMA's. A <...
192 views

### Improving the speed of evaluating Table with nested functions

I am a Mathematica novice working with a stack of 1024 x 1024 WatershedComponents (or MorphologicalComponents) label matrices ...
350 views

### AssociationMap to query Dataset across levels?

Is there a way to operate on Dataset across levels to apply a function f to a key -> value pair in an Association as follows: ...
62 views

### Mapping with Trace[] [duplicate]

As part of some data anaylsis, I am using the function Trace to give me the name of an array of data, which I then use to label my plots. eg. my data array is called r1 so I run: ...
33 views

### Expressions to functions, and evaluation [duplicate]

When calculating derivatives a expression is the result: in:= f[x_,y_]:= 1 + 2 x + 3 x^2 y + 4 x y^2 in:= D[f[x,y],x] out= 2 + 6 x y + 4 y^2 how do i make this ...
252 views

### Defining a sequence slot programmatically

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

### Shorter syntax for Fold and FoldList?

I find it tedious to write out the following: a = {1, 2, 3, 4}; Fold[f, First @ a, Rest @ a] f[f[f[1, 2], 3], 4] It ...
269 views

### MapAt and generic Functions on Associations and Datasets

These are distinct but related questions about mapping functions to Associations and Datasets. Given: assoc = <| a -> 1, b -> 2, c -> 3|> And <...
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### How can I use NestWhileList instead of While in this case?

OK, the problem occurred when I challenged with Project Euler No. 10 The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below two million. My code is: ...
468 views

### 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: $L(u(x))=\int_0^1 \frac{1}{2} (u'(x))^2 dx$ ...
946 views

### Find the smallest positive integer that satisfies a certain condition

I know Mathematica is really powerful when it comes to functional operations like applying a list of tasks to a list of variables. Sometimes I feel like it isn't the most powerful tool when it comes ...
107 views

### Nest Replace Function with different rules

I have a table of data that I want to filter. Any value of zero in the table means that value was not calculated, so it should get populated with the tag "NC". Next the table is filtered for all ...
63 views

### Resolving Error: Mathematica evaluation order on Lists

I have a table that is 27 x 27, each entry corresponds to an element from the periodic table. I use the replacement rules in element list to allow me to convert a list of elements into a list of ...
136 views

### Finding Values of All Nine Constants in q-hypergeometric Equation

I suspect that an identity of the form $$\sum_{j=-n}^{j=n}(-1)^jq^{j(5j+1)/2}=\sum_{r=0}^{n}f_{ar+bn+c}(-1)^{n-r}q^{(n-r)(dr+en+f)/2}\frac{(q;q)_{gr+hn+j}}{(q;q)_{n-r}}$$ for $a, \dots , j$ integer ...
172 views

### Dealing with nested lists

This question is strongly related to: Map and Apply a function on a nested list I am in a bit of a rut in terms of my MMA skills and looking to improve my coding. I've realized that rather than ...
106 views

### Is it possible to change to a functional approach in this game-based procedural algorithm?

First of all, I'm aware that Mathematica StackExchange prefer specific questions, not discussions, but I need some enlightenment with this issue for I have nowhere else to ask :) The thing is, our ...
309 views

### Conditional search along the columns of a matrix

I want to implement the following algorithm in Mathematica. Get element along main diagonal of a matrix. If the element along the main diagonal is positive, then return the positions of the elements ...
2k views

### Scan vs. Map vs. Apply

I cannot understand the difference between Apply, Scan, and Map. I have tried to play with ...
322 views

### Transform elements in list from form {x_} to form {x_, 0}

I have the following list ...
1k views

### What is the most efficient way to map a linked list?

In order to work with lists effectively using common recursive patterns from functional programming, it's often most convenient to worked with the "linked list" representation, that looks like this: <...
181 views

### Using Mathematica to derive the PDF of the normal distribution

I am trying to use Mathematica, in this case in a well known and rather simple list of equations, but I get stuck whit Mathematica. Since I am just starting to use Mathematica for mathematical ...
113 views

### How to input pure function to package?

I would like to input a pure function into a custom written package, but am running into a variety of errors. The package I have created is as follows: ...
350 views

### Summing Over a Variable Number of Indices

I am trying to figure out the best way to include a variable number of indexes of summation in a program. For example: Suppose I want to define a function $g[n,s]$ that returns the sum \sum_{a_1+.....
257 views

### How to set up and minimize a large system of equations to resolve the individual components

I am trying to set up a system of 400*N equations to deconvolute spectral data for four different compounds. I monitored 400 different wavelengths in N solvents (3 solvents in this case). In order ...
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### How to write series of Do[ ]'s with a single Table[ ]?

Edited to provide more information (sorry I don't know how to format matrices here) I would like to replace: m = 4; ...
257 views

### Evaluation in lambda function

If I have a function, that returns a function, for example: f[a_] := a^2 * # & then f[3] == 3^2 # & Is there a way ...
209 views

### Optimizing my code to generate symmetric tensors

I have written code that does carries out the following task: Construct a fully symmetric rank-$P$ "tensor" out of a collection of user-input rank-1 vectors, and a rank-2 symmetric tensor $h$. The ...
312 views

### What is the most elegant way to specifiy a start case for recursion?

When writing recursive code that computes the least value at which a condition is true and various other scenarios it is often necessary to specify a base case. What I have done to supply this is ...
564 views

### Mapping functions over multiple lists

I am not sure if this is a duplicate. Spent some time looking over list-manip questions. I’d like to know the Quickest Way to achieve the following Mapping of a function over multiple lists. ...
256 views

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

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

### Defining a formal Primitive Recursion

I'm searching for a way to define the function this wikipedia article call Primitive Recursion. It should have two functions as argument and it should return a function. I need this as helping in ...
217 views

### How should I go about writing more functional and list based code? [duplicate]

I've heard that Mathematica is usually faster when the code is list-based and/or uses a functional paradigm. I'm still working on getting the hang of this; there are a lot of ...
463 views

### How can I iterate my code a 1000 times?

this is my solution to Exercise 5 of http://work.caltech.edu/homework/hw2.pdf Please help me make this more elegant. The exercise is about classifying random Points by a (randomly generated) target ...
94 views

### Behavior of ValueQ inside a function

The following code Cases[Function[{x}, x + 1], a_?ValueQ :> Hold[a], ∞, Heads -> True] unexpectedly returns {Hold[x + 1]} According to the manual, "...
134 views

### Where are the functional programming constructs: every and some? [duplicate]

Coming from other functional programming environments (e.g., Clojure) I've become accustomed to some functions that I haven't found equivalents for in Mathematica yet. The two I reached for last ...
306 views

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### Q-Function representation in Mathematica

I observed that there is no Q-function representation in Mathematica. The definition of Q-Function is: \begin{align} Q(x) &= \frac{1}{\sqrt{2\pi}} \int_x^\infty e^{-\frac{u^2}{2}}du \\ &...
163 views

### How to “explode” a list inside a function call argument list? [duplicate]

I'm trying to do something like below, but it doesn't work, since StringForm requires each item from parts to be given ...
199 views

### Using functions to make loops

I'm trying to make a simulation of an electron that goes through a magnetic and electric field perpendicular to each other and to the velocity of the electron but I'm running in some troubles with the ...
119 views

### How do I operate on this list elegantly? [duplicate]

calibData = { {200, 10}, {100, 20} } MapAt[N, MapAt[Log10, calibData, {;; , 1}], {;; , 1}] I want to apply a base 10 Log to the first element of each tuple. ...
1k views

### Better code to find Narcissistic number

My code finding Narcissistic numbers is not that slow, but it's not in functional style and lacks flexibility: if $n \neq 7$, I have to rewrite my code. Could you give some good advice? ...
96 views

### Evaluate outer function first

I'm new in Mathematica so this is maybe super easy to do, but I can't figure out how. I've got a function plus[a,b] that sums two numbers and I need to implement a ...