Questions on the manipulation of List objects in Mathematica, and the functions used for these manipulations.

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18
votes
6answers
1k views

On generalizing Partition[] (with offsets) to sublists of unequal length

The usual Partition[] function is a very handy little thing: ...
17
votes
12answers
2k views

Pick elements of largest absolute value

For example, given list = {{1, -3, -5}, {2, 1, 6}, {0, 2, 4}, {-9, 2, 6}} should return: {-5, 6, 4, -9} Updated I found ...
17
votes
7answers
2k views

How do I check if any element in a list is positive?

As a simple example of what I would like to do, suppose I have a list a of all real numbers. I would like to perform a simple check to see if some element of ...
17
votes
6answers
800 views

Apply multiple functions to same list

I'd like to get the Min, Max, Median, Mean, etc. for the same list. For now I'm doing the following: ...
17
votes
5answers
1k views

Picking random items out of a list only once

I'm trying to create a function that randomly returns a value from a list but remembers the values that have been given before. At the end when the list is empty it should return an empty list. ...
17
votes
6answers
722 views

How do I replace a missing value in a column with the value immediately above throughout a table?

I have a large table (7000 rows × 17 columns) of terse textual data. In many of the columns, empty entries have been replaced with "." as a marker. Working from the top of the columns downward, I want ...
17
votes
3answers
1k views

Fastest way to check for List membership

I have a set of say 100 numbers {1,3,7,11,19,...3971}. All elements are previously determined. I want to check whether ...
17
votes
4answers
510 views

Splitting a list

Please consider the following list: data={1, 0, 0, 0, 2, 5, 2, 3, 0, 0, 3}; Now I would like to split the list into 0-sequences and Not-0-sequences as following: ...
17
votes
4answers
2k views

Constructing a list that includes a leading zero (01,02,03 … 55, 56, etc.)

I am constructing a list for use in file operations. Say I want to create list which contains values from 01 to 87. The kicker is that the first nine integers need ...
17
votes
2answers
1k views

How to monitor the progress of Map?

I have a function doSomethingComplicated[...] that takes about 10s on average to evaluate. My list, listOfArgs has about 10000 ...
17
votes
4answers
321 views

Setting parts of a list

Suppose I have list a = Range[10] {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} in which I want to set some elements to be a list <...
17
votes
1answer
242 views

Why changing list's head takes time?

Consider AbsoluteTiming[Range[10^7];][[1]] 0.035000 and AbsoluteTiming[HoldComplete @@ Range[10^7];][[1]] 0....
17
votes
2answers
423 views

Count number of sublists with a total not greater than a given max

Suppose I have a list of positive integers: data={1, 1, 2, 3, 3, 3, 5, 5, 5, 7, 7, 8, 8, 9, 10, 10, 12, 16, 23} I want to count the number of subsets up to ...
16
votes
16answers
2k views

Generating a list of numbers that are not multiples of 4

I want to write simple code that will list all numbers from $1$ to $n$ that are not multiples of $4$. And in this case I consider that ...
16
votes
10answers
740 views

Count the sequences in an array

Is there a short and easier way to count number of sequences in a list? Let's say I have three lists: list1 = {0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0} ...
16
votes
8answers
739 views

UnFlatten an array into a ragged matrix

Trying to unflatten an array that was part of ragged array of sub matrices. As input we have flattened array: ...
16
votes
5answers
639 views

Add a vector to a list of vectors

What is the syntax to add v1 to each vector in v2? I know it has to be simple, but I really have searched and not found it. <...
16
votes
7answers
912 views
16
votes
8answers
3k views

extract values from replacement list

Solve returns a list of replacement rules In: Solve[x + y == 3 && x - y == 6, {x, y}] Out: {{x -> 9/2, y -> -(3/2)}} I am only interested in the ...
16
votes
6answers
2k views

Max of a table/list with indeterminate values

Suppose I have a Table: tab = {1., 2., 3., Indeterminate} When I type Max[tab] I get ...
16
votes
6answers
501 views

Splitting a list by specifying section headers

I have a list of strings called mylist: mylist = {"[a]", "a", "a", "[b]", "b", "b", "[ c ]", "c", "c"}; I would like to split ...
16
votes
5answers
629 views

Easiest/most efficient way to delete duplicates from one list at the positions of another?

This question is somewhat related to How to efficiently find positions of duplicates? , although I'm interested in something a little bit simpler since I'm not really interested in a list of all the ...
16
votes
3answers
4k views

How do I use Map for a function with two arguments?

I'm a newbie who tries to be a good boy, and use Map instead of writing out a list of functions. I have a table I want to Map ...
16
votes
4answers
486 views

How to enumerate all possible binary associations?

Suppose I have a list of symbols like: {a,b,c,d} I would like to enumerate all possible binary associations (combining symbols and/or sublists pairwise): ...
16
votes
3answers
458 views

How to group and join points

It seems there are many similar questions on Mathematica.SE, but none addresses (to the best of google) exactly my problem. I have the following data: ...
16
votes
4answers
628 views

How to remove duplicates from set of machine precision 2D points?

I have a set of 2D points with machine precision coordinates. I need to remove all duplicates. Performance is important. This is the most obvious fast solution: ...
16
votes
4answers
2k views

What is the right way to rotate an array?

Suppose I have an array, not necessarily square: a = $\left( \begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array} \right)$ I want to rotate it like one ...
16
votes
7answers
714 views

Enumerating tuples from a larger space such that all pairs of values are present at least once

I am trying to write a function that will accept a list of N lists and returns a list of N-tuples that represent all pairs of values from the original N lists at least once. To illustrate with an ...
16
votes
1answer
409 views

Are there advantages to using additional arguments of common functions rather than alternative ways of calculating with lists?

(Apologies for the long question title.) One of the interesting, if sometimes confusing, things about Mathematica is that there is always more than one way to do things. Even intermediate users can ...
15
votes
10answers
2k views

Pretty way to group elements at odd and even positions

How to make a function that splits list elements by odd and even positions? Shortest implementation wins. I myself came up with: ...
15
votes
9answers
622 views

Any built-in function to generate successive sublists from a list?

Given lst = {a, b, c, d} I'd like to generate {{a}, {a, b}, {a, b, c}, {a, b, c, d}} but using built-in functions only, ...
15
votes
8answers
1k views

How to Map a subset of list elements to a function?

How would you, given a list {1, 2, 3, 4}, apply a function f to 1 and ...
15
votes
6answers
516 views

How can I remove B -> A from a list if A -> B is in the list?

I have a list of transformations like this: list = {"A" -> "B", "B" -> "A", "C" -> "D"} As this is used to plot an undirected graph with ...
15
votes
7answers
1k views

How do I delete all items that occur more than once?

DeleteDuplicates works fine but leaves a single copy of the duplicated item. I need to remove all items that occur more than once i.e. {{1,2},{1,2},{3,4}} -> ...
15
votes
3answers
1k views

What is Mathematica's equivalent to MATLAB's filter function?

The MATLAB code filter(0.5,[1, -0.5], [1:10]) is equivalent to Rest@FoldList[(#1 + #2)/2. &, 0, Range[10]] I don't ...
15
votes
5answers
461 views

Partitioning a list of numbers the Mathematica way

I have two sorted lists, one list will be called the "fences" and the other the "values" Fences could be: $\{1, 5, 9, 14\}$ Values could be $\{-1, 1, 3, 4, 6, 9, 10, 13, 14, 15\}$ I want to ...
15
votes
4answers
3k views

Semi prime numbers

The high school textbook I am using has the example of semi-prime numbers. They wanted students to find (by "perspiration") all the semi-prime numbers less than $50$ (for a question on set theory). ...
15
votes
6answers
818 views

Matrix Rotation

If I have a matrix of any size, say $\begin{pmatrix} 72 & 32 & 64 \\ 18 & 8 & 16 \\ 63 & 28 & 56 \\ \end{pmatrix}$ $\begin{pmatrix} 72 & 32 \\ 18 & 8 \\ 63 &...
15
votes
5answers
551 views

A quicker than outer

I need to get a matrix $\{a(x_i-x_j)\}$, where $x_i$ form a partition of an interval, $a(x)$ is a given function. I use ...
15
votes
6answers
1k views

Finding the period of an array of integers

A simple array of integers is given. The problem is to detect if a pattern is repeatedly occurring in the array, and find the length of that pattern. For example, for ...
15
votes
4answers
866 views

Exclude data from a list

Let's create some random sample data data = Table[{RandomReal[{-10, 10}], RandomReal[{-10, 10}]}, {i, 1, 300}]; Then we plot them using ...
15
votes
4answers
520 views

Reproducing a ranking function that behaves like Excel's RANK

I tried to find a function or expression in Mathematica that produces the same output as the RANK function in Excel (see its description here), but unfortunately I ...
15
votes
3answers
348 views

Find duplicates in list of InfiniteLine

MMA 10 introduced a new function, which can be very convenient: InfiniteLine. Of course, two infinite lines can be described by different arguments: for example <...
15
votes
6answers
1k views

Generating an Ulam spiral

An Ulam Spiral is quite an interesting construction, revealing unexpected features in the distribution of primes. Here is a related topic with one answer by Pinguin Dirk, who has provided one ...
15
votes
8answers
531 views

Splitting a list into increasing sublists

I have a list of numbers (say, for example, {1,2,3,4,3,2,1,2,3,4,3,2}), and I want to split it into sublists so that each sublist is the (smallest) sublist whose ...
15
votes
4answers
408 views

MapThread with non-rectangular lists

MapThread works fine and dandy with rectangular list structures: MapThread[f, {{{a, b}, {c, d}}, {{1, 2}, {3, 4}}}, 2] <...
15
votes
3answers
485 views

Generating Tuples with restrictions

I am interested in a certain subset of all tuples. Generating all with Tuples and then filtering is wasteful, and will "blow up" very quickly. For a concrete ...
15
votes
6answers
576 views

Elegantly pairing up mismatched lists

HistogramList returns a list of bin boundaries and a list of counts. There is one more boundary than counts, and I'd like to pair them up so I can feed it into <...
15
votes
1answer
1k views

Solving and Animating Three Body Problem

I am attempting to solve a three-body problem using the Lagrange formalism, with a 1/r potential. I started off by defining T and U (kinetic and potential energy) as follows: ...
15
votes
4answers
1k views

List comprehension in Mathematica

Python supports a concept called "list comprehensions". Following is sample example ...