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

5
votes
3answers
98 views

Help going from iterative to functional

The following code segment shows what I'd like to do. I'm a procedural programmer trying to learn the Mathematica functional style. Any help on this would be appreciated. ...
5
votes
1answer
107 views

Functional-programming virus infection

Update: The question may seem too broad, but the answer provided by belisarius responds perfectly to the question, as the use of $ListConvolve$ and $NestList$ meets the desired criteria in in addition ...
1
vote
1answer
42 views

Let's do this list-rearrangement prettier [duplicate]

Suppose that i have a list in this format= $list=\{ \{a,obj1 \} ,\{c,obj2 \}, \{a,obj3 \}, \{b,obj4 \} \dots\}$ I want to construct a new list in this way: $ newlist= \{ \{ \{a,obj1\} , \{a,obj3\} ...
1
vote
1answer
32 views

Function taking arbitrary number of arguments

I have a very similar function to that which a solution was provided by kguler, but am unsure as to how to adapt the solution that was given there. That post can be seen here. The adaptation is only ...
4
votes
4answers
184 views

Iterating over a list, in a functional way

I have learned a lot about functional programming just from messing around in Mathematica, but I've come across a problem that I don't know how to solve in a "functional" way. Any help would be ...
3
votes
1answer
72 views

Combining MapAt and MapIndexed

The very last example in the documentation for MapAt is: MapAt applies f repeatedly if a part is mentioned repeatedly: ...
0
votes
2answers
51 views

Supply a function as an argument to another, and find its minimum

I would like to minimize a function, which is supplied as an argument to another function, and report back the estimates of the values of the variables that result in its minimum. In specific, I would ...
1
vote
1answer
129 views

General function taking general number of arguments

The following is an edit of this post, for which a working solution was provided by John McGee. I have a different function and am not sure how to adapt the solution for it: I want to construct a ...
6
votes
3answers
317 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 ...
0
votes
1answer
75 views

How to improve this function that selects parameters from arbitrary distribution using Recursion?

Below, I have defined a function using Which to select model parameters based upon various conditions. My questions are: Is there any danger in writing this function using Recursion? Is there a more ...
3
votes
1answer
119 views

Functional programming approach to avoid traditional loops

I'm currently learning from the wonderful post: Where can I find examples of good Mathematica programming practice? And i'm correcting my habits using Nest/Map/Thread instead of loops. The problem ...
3
votes
3answers
245 views

fastest way to perform the following summation

I have a vector $A$ with components $A_{i}$, and two matrices $X$ and $Y$ with components $X_{ij}$, and $Y_{ij}$ respectively. What is the fastest way of performing the following summation ...
0
votes
2answers
48 views

How to continuous apply a function to an argument? [duplicate]

In order to calculate x = sqrt(1 + x) for a given number x, 40 times, I tried this: ...
4
votes
3answers
154 views

Selective threading of the Rule

How can I change form1 to form2 form1 {10000, 10004} -> {2, 2, 637} form2 ...
11
votes
2answers
245 views

Choose between `Apply` and `Map`

Even though this might be too general question(or not answerable), I want to get some advice here. I apologize in advance if it is not a relevant question. I frequently have to process large list of ...
5
votes
3answers
257 views

Multiplying block matrices

I have a 2*8 matrix A, and a 2*8*2 matrix B. So B[[1]] and B[[2]] are both 8*2 matrices. I need a neat way to multiply A by B so that the first list in the result is A.B[[1]] and the second list ...
1
vote
1answer
84 views

The problem (time) caused by ?NumericQ

In here, I asked a related (similar) question. Using ?NumericQ seems have slowed down the entire calculation. But I now have a more serious problem: ...
1
vote
0answers
67 views

What are the differences between these functions when used for NMaximize?

In short, the question is how to construct the function you want to optimize? ...
5
votes
1answer
313 views

Simple while loop alternative in Mathematica

I have noticed that there are a few examples that go into some detail regarding While loop alternatives. (See here for example: Alternatives to While Loops?) However, I wanted to provide a simpler ...
1
vote
0answers
66 views

Updating procedural fitting algorithm to more efficient style?

For some time now, I have used this procedural programming approach to fit data in my research that is too cumbersome for the built in Mathematica functions. (Although this simple example works fine ...
1
vote
3answers
84 views

How to distribute but skipping one level

I would like to write a Rule that mimics built-in Distribute[], but one that distributes ...
0
votes
2answers
71 views

How do I tell pattern searcher the order in which to search for patterns given in general form?

I have a really long sequence of Symbols inside a function, say nonCommute[a,b,c,e,e,f,g,b,i,j], and I am implementing a ...
2
votes
1answer
54 views

Searching for symbol except within subexpressions with a particular Head

I would like to write a searcher like FreeQ that looks for a Symbol (or Head) in an ...
1
vote
1answer
194 views

How can I call the R-programming packages in my Mathematica?

I am trying to call the R-programming package called highfrequency in my Mathematica so that I can use its function rCov. I ...
3
votes
1answer
43 views

Mapping also for one element (or telling it how to do so if head got changed)

Some code generates a polynomial, and has the form: expr = Plus[a[i],b[i],c[i],d[i]] I need to apply f to each term. To do ...
6
votes
3answers
187 views

How to get “Signature” of each element of “Permutation” output

I need to sum over all possible permutations, multiplied by the Signature of each permutation of a given list of symbols. But, I don't know how to determine the ...
4
votes
2answers
125 views

Can't figure out how to apply these functions repeatedly

I have the following problem, and even though I've tried Fold & Inner, Sow & Reap, et al. I can't figure out the clean way to do this. Here's the problem. I have a list that starts as ...
3
votes
2answers
62 views

Fast functional method for multiplying duplication numbers in a large list

Consider a list of symbols: mySet = {a, b, b, c, a, b, c, d}; I would like to form the product of duplication numbers. In the example above, I have 2 ...
3
votes
1answer
122 views

How to remove recursion, and write it functional and efficient way?

I wish to implement the following recursion efficiently. ...
-1
votes
4answers
277 views

Mathematica's equivalent to the Python's Zip command in List-comprehension? [closed]

What is Mathematica's equivalent to Python's ZIP command? Is this called nesting? It means iterating over sub-sets of values like the below example. How can I do it in Mathematica? Example in Python ...
3
votes
3answers
128 views

Working with calculations that depend on the previous value in a list

I'm trying to make calculations on a list that depend on the previous value. In my case I'm doing event detection - detecting the point where a value rises above some threshold for the first time ...
11
votes
5answers
287 views

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 ...
4
votes
3answers
287 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 ...
3
votes
1answer
89 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 ...
3
votes
1answer
171 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 ...
2
votes
2answers
117 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 ...
4
votes
1answer
139 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 ...
0
votes
0answers
124 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 ...
7
votes
3answers
269 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: ...
0
votes
1answer
49 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: ...
0
votes
0answers
31 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 ...
2
votes
2answers
210 views

Defining a sequence slot programmatically

This question is related to: Composition of functions using slots `Slot` (#) interfering with evaluation Consider a toy example: ...
18
votes
1answer
393 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 ...
5
votes
1answer
182 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 ...
2
votes
3answers
172 views

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: ...
3
votes
1answer
252 views

Gateaux (directional) derivatives and higher order differentials of a functional

I would like to calculate the Gateaux derivative of a functional (i.e. a function depending on functions). A simple example for the Dirichlet functional: $L(u(x))=\int_0^1 \frac{1}{2} (u'(x))^2 dx$ ...
6
votes
9answers
873 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 ...
1
vote
1answer
90 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 ...
0
votes
1answer
45 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 ...
1
vote
0answers
122 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 ...