Questions tagged [pure-function]

Questions about implementing or applying functions which: (1) always yield the same result for the same input, (2) are independent of outside information, and (3) produce no side effects.

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8 votes
4 answers
560 views

Pure function on pure function

Given t1 = {2, 4, 8, 16}; t2 = {1, 5, 9}; First[Select[t1, # > 1 &]] First[Select[t1, # > 5 &]] First[Select[t1, # > 9 &]] can somehow be ...
4 votes
2 answers
116 views

How to call a list of pure functions/pure vector function? [closed]

In one dimension, pure functions work as usual: f = Function[{x}, 2 x] f[a] However, with a list of pure functions / a vector pure function this does not work with ...
1 vote
1 answer
106 views

A way to generalize my code for this non linear ODE problem

I am trying to solve the differential equation $y''(x) = y(x)+\sin[y'(x)]$ using "Fixed Point Iteration" over the interval $[0,1].$ Now using central difference method I arrived at the ...
4 votes
4 answers
227 views

Using MapThread with pure function and variable number of elements

I have a variable size array of lists and would like to set up a MapThread of the lists with a variable pure function $\{\#1,\#2,...,\#n\}\&$ with $n$ being the number of rows in the array and am ...
7 votes
5 answers
218 views

How to apply the multiple composite functions to a list?

A minimum example is this: ls = {1 + I, 2 - I}; Max@Re[ls] Min@Im[ls] #[ls] & /@ {Max@Re, Min@Im} (*want {2, -1}*) The result is: ...
5 votes
3 answers
208 views

AppendTo in combination with pure function

spA = {}; spB = {}; spC = {}; AppendTo[#, {"Up", "Down"}] & /@ {spA, spB, spC} doesn't work in Mathematica 11.1.1. Why? What is an alternative?
0 votes
1 answer
76 views

How Can I Use an Element of a Tuple as an Argument for a Pure Function?

(If I should elaborate on the circumstances, tell me.) I want to do the following: Suppose I have a tuple tuple={x,4,something,...} and I want to define a pure ...
0 votes
2 answers
81 views

Same code behaves differently as a pure function and a function, and insider another function

I have a rule-transformer that takes a list of rules (and a list generator = {σ[z], σ[-1], σ[1]}) ...
0 votes
2 answers
58 views

How to interpret the solution and how to work with it further?

Please help me understand the solution to the following problem: ...
2 votes
3 answers
172 views

Define equations as a pure function with list as argument

I have these set of equations. The number of equations depends on $n,$ which I want to keep control of. The code that I have generates it using Table and equations generated by this does not take an ...
0 votes
3 answers
112 views

Generalize the code to more variables

I have this code it runs and gives me the solution. How can I make it more compact and If I want it to extend(generalize) it to more variables how can I do it. I had asked a similar question here (...
1 vote
0 answers
72 views

Mapping two pure functions over different lists

Say if I have two lists of vectors of the same length, for example: u = {{1,0,0},{0,1,0},{0,0,1}} v = {{1,0,1},{1,1,0},{1,1,1}} I want to add (modulo 2) ...
1 vote
0 answers
72 views

Why must the "&" symbol be placed inside function instead of outside? [closed]

The following code is taken from Wolfram Community "Quantum Error Correction: bit flip". ...
2 votes
0 answers
75 views

Memory leak with pure function and in the listable option of compiled function?

I'm using 13.0.0 for Microsoft Windows (64-bit) (December 3, 2021) When I repeatedly run the command ...
2 votes
0 answers
35 views

Use FoldList to successively ImageAdd regular polygons with between 3 and 8 sides, and with opacity 0.2 [closed]

This question is from Section 29 of "An Elementary Introduction to the Wolfram Language". The objective is to successively add regular polygons with between 3 and 8 sides, and with opacity 0....
5 votes
1 answer
245 views

Pure functions: currying for & notation

I looked up currying in Shifrin's book. He points out that currying can be used for pure functions using nested functions as in the following example: ...
5 votes
1 answer
115 views

Condition inside pure function

Why condition /; not work inside pure function? Suppose we have: ...
1 vote
2 answers
217 views

Pattern matching tuples as inputs to pure function

I've been having an issue with functions which are supposed to receive as input a list of tuples. My troubles are two-fold: The function doesn't properly identify the pattern test I laid out in the ...
3 votes
1 answer
77 views

Pure function with pattern test

Is it possible to achieve pattern test inside a pure function? I have tried f = Function[{x_?NumericQ}, x ] but the error Function::flpar occured.
10 votes
5 answers
1k views

Pure function of lists

I need to create a function with two arguments f(s, l): s is a list of three integer like: s={1,-3,+5} and l is a list of lists of naturals of same length: ...
3 votes
1 answer
191 views

Pure functions failing in algebra

f[equation_] := Module[{}, ContourPlot[equation[x, y] == 1, {x, -2, 2}, {y, -2, 2}] ] equation = (#1^2 + #2^2) &; f[equation] The above code draws a circle....
3 votes
1 answer
82 views

How to define pure functions in matrix form?

I want to define pure functions x(#1,#2) and y(#1,#2) like But they aren't proper pure functions in the current form. How to modify the code?
1 vote
2 answers
106 views

Nested pure function argument as table

I made a nested pure function Nest[(x^2)/ ((2x+1) + #)&, x,n] I would like that for each iteration the value of x increment of 1, to have something like $$\...
5 votes
2 answers
182 views

Slots inside nested pure functions

I'd like /@ instead of Table or Map. But let we have it inside pure function: ...
3 votes
3 answers
82 views

Sort a list using a scoring list with Switch [duplicate]

I have a minimal working example (MWE) list called listToSort that is a list of string triplets: ...
0 votes
1 answer
55 views

Sorting a list by increasing order algorythm [closed]

Im new to loops on mathematica,was wondering how could I create a function to loop through a list which finds the index of the smallest value of that list, makes a sublist from index 1 to that ...
1 vote
1 answer
116 views

Drawing lines between coordinates in a list

Variable "l" is a list of coordinates and I am trying to draw a line from each coordinate to the next. But how? Apparently the last line isn't working. ...
3 votes
1 answer
94 views

MapAt with pure functions

Consider expr = Hold[1 + a + x + b + c + y + z]; idxes = {{1, 3}, {1, 4}}; Q1. I don't understand why ...
9 votes
4 answers
470 views

Construct a pure function containing built-in 'Sequence'

I guessed the output for (Sequence[#, 7]&)[3] should be Sequence[3,7] But my guess was wrong. See the screenshot: And I ...
0 votes
2 answers
127 views

Spurious renaming in nested Function construct

From the documentation of Function, I take this example (slightly simplified). Renaming the dummy or bound variable (y->y$ in the inner ...
5 votes
3 answers
586 views

Can a pure function be constructed whose argument list is a matrix?

Can a pure function be constructed whose argument list is a matrix? Using Function, I know it's not possible, but I'd like to get something like: ...
5 votes
5 answers
1k views

How to simplify a pure function?

I am dealing with the vibration of a multi degree of freedom system with driving force, and I need to find the relation between the amplitude and the frequency of the driving force. I hope to get an ...
3 votes
1 answer
161 views

How to replace a multiple iterator Table to speed up computation

I need to create an array of data which resembles to something like this Table[{i, Sin[j^2*i]}, {j, 2000}, {i, 0., Pi, Pi/10000.}] where each "row" of ...
0 votes
0 answers
21 views

How to select from a sum the terms containing minus? [duplicate]

In a sum y = \[Beta] x v - \[Mu] y z - \[Gamma] y; I would like to extract the terms which contain a minus, i.e. - [Mu] y z and - [Gamma] y I can test when a term ...
2 votes
1 answer
142 views

Minimize Sum of Hamming Distances

Problem: Given an $n \times m$ matrix with binary values $(0,1)$, find a binary vector that minimizes the sum of Hamming Distances to the rows. Example: If the matrix is {{$1,1,1$},{$0,0,0$},{$1,0,1$}}...
24 votes
1 answer
842 views

Why does the documentation call functions "pure"?

Clearly, Functions in mathematica are not pure functions according to the definition on Wikipedia (no side effects - basically implementabe with table lookups) the ...
5 votes
3 answers
284 views

Generating a list of pure variables

I want to pass a list of pure variables to a function, in which the ordering of the variables matters. For instance, if I want a palindrome, my function might be: ...
28 votes
1 answer
942 views

When is ##@@@##& more appropriate than ##@@##&?

When assigning attachment operators, I often run into confusing statements like ##@@##&, ##@@@##&, or even ...
5 votes
3 answers
200 views

Function incorrectly renaming variables in Rule Pattern

Consider the simple pure Function containing a Rule with the named pattern q. ...
31 votes
9 answers
3k views

Using patterns in pure functions

Pure functions may be handy if you don't want to assign your function a name. For example I would calculate $x(x-1)$ for some numbers $x$ by ...
5 votes
1 answer
68 views

Splitting a list into sublists at provided markers

For a list of strings (or other elements): SeedRandom[3]; t1 = Table[RandomChoice[CharacterRange["A", "E"]], 20] ...
2 votes
2 answers
146 views

Evaluating a FittedModel over a list of values

Simplified version Using the simpler version suggested by @ulrich-neumann : ...
3 votes
1 answer
118 views

Why do these two calls to Apply return different results?

In the following example, why do these two calls to Apply return different results? ...
7 votes
5 answers
503 views

An anonymous function with constraints [duplicate]

I'm not very good at working with anonymous functions, a fact that has now come back to bite me. Suppose I have a function defined as follows: ...
6 votes
2 answers
601 views

How to condition arguments of a pure function?

I would like to exclude the point {x=0,y=0} in the function definition ...
0 votes
1 answer
51 views

MeshFunctions::invmeshf that resists other solutions

I'm trying to base mesh on the slope of the function. That's why there is a Cross of two partial derivatives. ...
4 votes
1 answer
102 views

Apply function modification to curried function

This is based on A function that modifies functions - well-defined operation?, a previous question of mine. Lukas Lang's answer of course works very well, but now I encountered the following edge case:...
8 votes
1 answer
314 views

How to supply argument to pure function when slot is already defined?

Here's an example of a pure function: 3^# > 100 & I can supply any value I please to the function, by placing that value after the prefix. E.g.: ...
0 votes
0 answers
47 views

Why does this function only work with exact numbers?

First, I tried calculating A^k with this and got an error. ...
0 votes
3 answers
145 views

How to use a pure function to write following sum?

How to use a pure function to write following sum? I have tried to use FoldList, but it is still not working.

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