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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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4
votes
5answers
217 views

Using Through with SlotSequence

I have an expression consisting of a few pure functions added together like so: f+g+h I want to add the bodies of these functions together and make that a pure ...
2
votes
1answer
411 views

Use Map with multiple arguments over a nested list

I noticed there are a few similar questions to mine on here, but I couldn't figure out how to accomplish this mapping. I have sets of data I want to plot, which represent intensity and frames, and I ...
7
votes
5answers
654 views

How to write an operator that acts on pure function (to give another pure function)

I would like to write an operator oper that acts on a pure function f with an undetermined number of arguments, with the syntax <...
1
vote
1answer
162 views

Sum of Integers with a Pure Function

How would I find the sum of an argument, with the constraint that they are all integers (so if the argument contains a non-integer value, the function will not evaluate). I came up with these two: ...
0
votes
1answer
136 views

Pure Function that adds all arguments

the question asks to create a pure function that adds any number of arguments. Is the following acceptable? sum := Plus[##] & It does work, but can it be considered a pure function? I felt like ...
7
votes
5answers
2k views

How to elegantly map multiple functions over a matrix?

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1
vote
1answer
79 views

How-to implement iteration over a result of an iteration in a functional way

I have a pure function f:= #1 * #2 * #3 &; Which I can invoke in a following way: f[#,2,3]& /@ {1,2,3} Which ...
47
votes
2answers
3k views

Memoization with pure functions?

Is this possible? If I have a simple function, say: f=If[#>0,1,2]& then for each value of # this will re-evaluate f right? Is it possible to define a ...
0
votes
0answers
60 views

What makes items with head `Function` different?

I apologize beforehand for the muddleheadedness of this question. It reflects the fact that I'm trying to interpret outward "behaviors" of Mathematica expressions without having any understanding of ...
0
votes
1answer
101 views

Interpreting Mathematica output or producing cleaner output [closed]

Could someone please explain what the following would look like in standard math notation (or explain to me what this means): ...
2
votes
1answer
141 views

Expressing a definite integral as pure function with the upper-bound as it argument

Suppose i have an integral which has a closed form, $\quad \quad \int_{a}^{b} f(x) dx=F(a,b)$ I want to use output function $F$ as a pure function, like ...
4
votes
0answers
74 views

Wrong autogenerated package from notebook containing #key and Part as subscript

Bug introduced in 10.0.0 and persisting through 10.1.0 or later Mathematica v10.1.0, under Windows 8.1 x64 Mathematica v10.0.2, under Windows 1) Define a function in an initialization cell: ...
3
votes
1answer
141 views

Use of parenthesis and pure function

I had read that when using a pure-function it was a good general practice to enclose the function and the associated ampersand in parenthesis. (#^2 &)[a] I ...
31
votes
2answers
2k views

What are the cool kids talking about when they use ##&[]? [duplicate]

All the cool kids are apparently using ##&[] for Unevaluated @ Sequence[] but I have no idea what either means. ...
5
votes
2answers
196 views

Conflict with variables in pure functions

Consider the following snippet of code. Clear[f, g] f[x_] := Function[{i}, x]; g[h_] := Module[{Z}, Z[i_] := Print[h]; Print[h]; Z[1]; ]; When ...
10
votes
2answers
999 views

How to programmatically covert a function-like rule to a pure function?

Is there a programmatic way to convert a Mathematica rule that acts like a typical mathematical function of one variable into the equivalent pure function? For example, the code should convert ...
1
vote
0answers
112 views

Using Solve without introducing extra variables

First post here. I've tried searching for an answer for this for a few days now, but it seems the search terms (solve, slot, etc) are too generic to be helpful. I'm struggling with understanding how ...
2
votes
1answer
198 views

Patterns for destructuring “Function” function arguments

I want to define a function for finding a Jacobian matrix of pure vector function of vector argument. I try ...
9
votes
3answers
547 views

Functional equivalent of a For loop referring to consecutive elements in a list

I have implemented this function which smooths the values in a list by, if it encounters a zero, replacing this entry by the average of its two neighbours (apart from the first and last values of the ...
3
votes
3answers
421 views

How to make a symbolic vector into a pure function?

As part of a set of functions to implement a steepest descent algorithm I created my own n dimensional gradient function. It is defined as follows: ...
2
votes
4answers
462 views

Pure function, one slot refers to List-position

I used all my google-fu trying to find how to make this work; read the docs as well. What have I missed? I feel sure this can't be a new question, but I can't find anything Here is is: ...
1
vote
0answers
102 views

How to Fold (FoldList) this in a more compact (efficient) way?

Example code: x = Table[something[i], {i, 5}] Table[Fold[f1[#1, f2[#2, a], a] &, x[[i]], {c1, c2, c3}], {i, Length[x]}] This above is just an example. I ...
17
votes
2answers
1k views

What happens when you divide by ##?

I've been playing around with sequences a bit. In particular with using ## with unary and binary operators. Let's start simple, the following all make some kind of ...
0
votes
2answers
190 views

How to make a density plot with composed functions [closed]

I want to create a monochromatic density plot of the E-field around an optical vortex. To do this I've written ...
0
votes
1answer
232 views

What does the expression “Total[funca[a,#] & /@ #] & /@ {x,y}” possibly mean?

Can the expression be simplified as "Total[funca[a,#]] & /@ {x,y}"? What does the double of "& /@" mean? Where can I find some reference? Updated According to Mr.Wizard's answer, I now know ...
11
votes
1answer
565 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): ...
0
votes
1answer
155 views

Why is `B /. h -> #2 &` not a pure function?

I am trying to plot the energy surface of the mean field Ising model, but I am running into a problem with setting the MeshFunctions for the plot. ...
10
votes
3answers
469 views

Operate over list of pure functions

I have list of pure functions (All functions are InterpolatingFunction) i.e {{a, b}, {c, d}, {e, f}, ...} and I would like ...
0
votes
0answers
46 views

How can I mix // with a function of two arguments? [duplicate]

I often find myself using // when playing around with expressions, but it is always cumbersome to have to switch to the full notation just to apply a function of ...
5
votes
4answers
369 views

Syntax for Table with a pure function

I have: g = #1^2 + a #2^3 / #1 & Now I wish to make a Table evaluating this from 1 ...
3
votes
5answers
318 views

Algebraic expressions on pure functions

I would like to know how to perform algebraic operations with pure functions. Simple version: Here's a silly toy model: I want to transform the algebraic expression Sin*Cos into the function ...
5
votes
1answer
245 views

How can I make a “self-referential” replacement operation self-contained?

Fairly often I find use for replacement rules that call themselves on the right-hand side of the rule, e.g.: ...
2
votes
1answer
965 views

Why is either Listable or HoldFirst not working?

Starting with a fresh kernel, I evaluate the following: ...
8
votes
1answer
336 views

Mma10 mystery: Failure of pure function substitution with Interpretation?

Bug introduced in 10.0.0 and fixed in 10.0.1 I had code to display with subscripts from Displaying index as subscript on output: e.g. C[i] -> C_i with Notation[...] or Interpretation[..]? which is ...
1
vote
1answer
81 views

How can I change the scoping of a pure function returned by a function in a package?

I have written a small Mathematica package that contains a module that solves some differential equation with initial conditions. Suppose that the solution to this differential equation defines some ...
6
votes
3answers
607 views

How to use multiple pure functions correctly?

I have used Mathematica for two years.And usually,I can use single pure function(#&) rightly.However,for the use of multiple pure function,I always make all ...
5
votes
4answers
1k views

How to find all symbols in an expression and perform an operation on them?

========== motivation =========== Suppose, for example, I have an incoming expression like m = (3-I)x + 4(x y)/(Cos[y]) I want to find all the symbols in ...
3
votes
4answers
220 views

Correct slot assignment when mapping from different lists using pure function

Given expr = u == a1 + a2 x + a3 y; and uRep = {u1, u2, u3}; xyRep = {{x1, y1}, {x2, y2}, {x3, y3}}; I'd like to generate ...
2
votes
1answer
170 views

Why is Chop ignored in Plot?

I want to plot multiple functions with the same settings side-by-side, so I use the pure function construct (for clarity, I only use one function in this example) ...
2
votes
1answer
384 views

Requiring NumericQ in Pure Function

Potential duplicate, but doesn't seem to solve my problem: Using patterns in pure functions I have a function that returns an InterpolatingFunction, and it works ...
5
votes
0answers
149 views

Third syntax version of LogitModelFit: unexpected result of “BestFit”

The third listed syntax version of LogitModelFit allows one to specify input in a simple way: Only a design matrix (with a row of values of the explanatory input ...
0
votes
1answer
134 views

Define a function that returns a function with a variable number of arguments

Previously, I've defined a function with a variable number of arguments with the following method. ...
3
votes
3answers
473 views

How to exchange two arguments?

Recently, I have being using Mathematica to write my undergraduate paper. I want to use two pattern lists such as { A -> a, B -> b, c -> C, ....} and ...
3
votes
1answer
139 views

What is happening in Map[Function[x, x^2], a + b + c] from the Pure Function tutorial

The Pure Function tutorial gives an example: Map[Function[x, x^2], a + b + c]. I would expect the output to be (a + b + c)^2, ...
1
vote
2answers
214 views

`Slot` (#) interfering with evaluation

In the following I am using one function makeFunc to assemble two functions a[t] and b[t] to ...
1
vote
1answer
146 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: ...
0
votes
1answer
174 views

Replacement rules in combination with pure functions to make a change of variables

I have defined my function in this way w = f[r,Θ] ; After some calculations i obtained my results with respect to the previous function. For instance: ...
3
votes
1answer
128 views

Recursion when randomizing elements in a list

I want to randomize certain elements of a list; Since the code list = {a, b, c, d, e, f, g}; list[[{1, 3, 5}]] = RandomSample@list[[{1, 3, 5}]]; list works fine, ...
2
votes
1answer
89 views

Need to run evaluation 2 times

Why does this only work after running the evaluation 2 times? ...
0
votes
1answer
196 views

Pure function in Nest

I can't figure out what I'm doing wrong here: Table[Nest[# + 0.1 * -i * #^2 &, 2, 1] , {i, 0, 0.5, 0.1}] (* {2., 1.96, 1.92, 1.88, 1.84, 1.8} *) The problem ...