Questions tagged [algorithm]
Questions about algorithms used or which might be used to implement a procedure known by name or loosely but not in detail. The subject of the question may be a procedure mentioned in the literature or a Mathematica built-in function
384
questions
4
votes
1
answer
183
views
Slicing Graph by path
I have a Graph (generally not planar and without particular layout), and a simple path that connects two points of its boundary, as in the example shown below.
How to ...
- 609
0
votes
1
answer
55
views
Apply an equation based on two sets with different indexes
Apply an equation based on two sets with different indexes
Simple example
If I have the following elements in the form of two sets with different indexes:
$m=\{m_1,m_2,m_3,m_4,m_5\}=\{1,2,2,2,1\}$
$p=\...
- 1,014
2
votes
1
answer
233
views
Why does FindInstance[x>0,x] give 27? [closed]
Why does FindInstance[x>0,x] give 27? I would think it would give 1… maybe 2 or some small positive decimal.
- 1,627
9
votes
8
answers
757
views
Numerical approximation of the integral by using data
I want to use the numerical approximation of the integral of a function given a list of data:
$$\int_a^bf(x)dx\approx\sum_{k=1}^N\frac{f(x_{k})+f(x_{k-1})}{2}(x_{k}-x_{k-1}),$$
where $f(x_0)=f(a)$ and ...
- 685
7
votes
1
answer
113
views
How is the Mathematica command FindGeometricTransformation related to the Kabsch agorithm?
I searched the internet for a Mathematica version of the Kabsch algorithm, using the search terms "Mathematica and Kabsch" nothing came up in. Looking through Mathematica documentation, I ...
- 333
3
votes
2
answers
677
views
Recycle buying soda problem
there is a question：
"
If a bottle of soda costs \$1 and you can exchange two empty bottles for one soda, how many sodas can you drink with \$20
"
...
- 1,572
1
vote
1
answer
187
views
Counting the numbers that yield a constant when summed
I was initially trying to code an algo that can rapidly count k numbers that yield s when summed. These numbers must lie in the interval from 0 to d. For instance, taking d=2, k=2 and s=3, the ...
- 11
1
vote
0
answers
74
views
Sum of disjoint product of sets [closed]
If we have the following sets and we need to apply the Sum of disjoint product property to them, as in the following example:
Take: $$P_1=\{x_1 x_4\}$$
$$P_2=\{x_2 x_5\}$$
$$P_3=\{x_1 x_3 x_5\}$$
<...
- 1,014
0
votes
0
answers
69
views
Missing "StructuredAlgorithms"in the installation
I typed the following
array = SymmetrizedArray[{{1, 3} -> a, {2, 2} -> b}, {3, 3},
Symmetric[All]]
array["StructuredAlgorithms"]
which should ...
- 669
1
vote
1
answer
46
views
Performing logical reasoning to find minimum function between two functions
Consider the following two expressions:
f[x_,y_] := (1+x)
g[x_,y_] := (1+x*y^2)
x,y are bounded in a unit hypercube. (Ignore ...
- 1,897
0
votes
0
answers
65
views
How can a program be configured for these steps?
Is it possible to create a program that implements sequential mathematical steps... in order to be circulated to more than one selected set?
Step 1: For the following sets:
$$S_1=\{x_1,x_2,x_3\},S_2=\{...
- 1,014
10
votes
5
answers
1k
views
How can I get samples of f(x) that are roughly evenly spaced?
I am looking for an efficient way of getting 60 to 80 samples of an arbitrary f(x) such that the distance between adjacent samples are approximately equal. My first attempt is based on a first order ...
- 7,144
2
votes
3
answers
167
views
Simplifying 'symbol-linear combinations' of nested monomials
I'm working with a custom binary 'operation' $F$ which takes $x, y$ and produces $F[x, y]$, where the possible arguments are already given by some list $\{ \text{one}, a, b, c, d, x, y, e, f\}$ where $...
- 23
2
votes
1
answer
116
views
Efficiently Finding Weighted Integer Partitions
Suppose we have some list of natural numbers $\{ 1, 2, \dots, N \}$ and each natural number $i$ has a 'weight' $w_i$. I would like to generate the all the integer partitions which satisfy the ...
3
votes
2
answers
162
views
Taylor approximation of integrals
I have BVP as in the picture and I want to solve it numerically by method given as follow. In the original paper, it is motioned that first iteration is computed and other are computed with Taylor ...
- 83
5
votes
2
answers
196
views
Minimum/optimal number of tiles to cover all boxes
I have been struggling with the following problem.
Given:
the coordinates of a bunch of boxes/rectangles (in the form {xmin,ymin,xmax,ymax}) aligned with the x-y ...
- 6,107
1
vote
3
answers
228
views
0
votes
0
answers
79
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Which algorithms are implemented in community detection based on AdjacencyGraph[.] and WeightedAdjacencyGraph[.]?
The following code generates two distinct community structures: one uses a simple adjacency matrix (with 1 and 0), another uses a weighted adjacency graph (with positive real numbers). I like to know ...
- 6,263
5
votes
4
answers
411
views
An accumulated moving average
1. Problem statement
In accordance with the standard definitions the inbuilt MovingAverage
...
- 82.4k
4
votes
2
answers
931
views
How to calculate equivalent resistance for a network of same-value resistors?
Let's assume I have n identical resistors. I can connect them either in series or in parallel (let's disregard bridge connections for now). Now, I want to list all ...
- 2,111
5
votes
2
answers
198
views
Fill a sequence containing missing values
Example data
list = {Missing[], Missing[], 100., 200., Missing[], Missing[], 250., 210., Missing[]};
With downloaded data I often have the situation that there are ...
- 82.4k
6
votes
2
answers
249
views
Split a sequence with conditions
I need a function which splits a sequence of arbitrary length
at x random points and which guarantees that each partition (bin) contains a minimum of ...
- 82.4k
5
votes
5
answers
604
views
Analyzing football games (pairing matrix)
I want to cross-tabulate football games over several years.
Setting up example pairings:
Please note that there can be up to 20 clubs and a couple of thousand matches!
...
- 82.4k
8
votes
6
answers
450
views
Accumulate up and down
I want to accumulate positive and negative values separately.
dt = RandomSample[Range[-10, 10]]
{3, -5, 2, -9, 1, -1, 0, 8, 10, 4, -7, 7, -8, -3, 6, -4, -2, 5, -10,...
- 82.4k
9
votes
9
answers
675
views
Partition a random sequence composed of three numbers
I want to partition an array composed of 1s, 2s and 3s in such a way that,
going from left ...
- 82.4k
9
votes
4
answers
709
views
Smooth a list of integer values
I want to smooth a list of Integers so that outlying values
become less spiky. The result vector must again contain Integer ...
- 82.4k
7
votes
6
answers
378
views
Replace duplicate list values with unique elements
My request is a follow-up on this question:
Replacing duplicates instead of deleting them
What if we want to replace duplicated values not with a single value but with newly created values distinct ...
- 82.4k
3
votes
0
answers
78
views
How to ask Mathematica to give me possible closed forms from a given numerical approximation
Imagine I am solving a some Infinite Series and I cannot directly compute the value using Mathematica.
The value of this series approximates $ 0.785398....$ (Actually is $\frac{\pi}{4}$). I want to be ...
- 141
4
votes
2
answers
156
views
Extract terms containing symbols
I would like to be able to extract terms that contain a symbol expression and leave the special function alone.
I have a list:
...
- 14.9k
5
votes
3
answers
318
views
1
vote
0
answers
101
views
Solving system of linear equations in specific order
I know how to solve set of linear equations using Solve, or by hand of course. However, my current problem requires me to solve the equations in a specific order, ...
- 545
2
votes
1
answer
242
views
Finding induced subgraphs that are also trees
Given a graph $G$ with $n$ vertices, I need to find a subgraph consisting of $m$ vertices $\{v_1,\ldots,v_m\}$, and the induced subgraph of this subgraph should also be a tree.
For example, suppose $G$...
- 496
1
vote
1
answer
36
views
Unable to apply Reduce to a variable number of inequalities (obtained by InputFields)
I'm new to Mathematica and I'm stuck on this piece of code.
The code is supposed to let the user choose how many inequalities (in a number between 1 and 5) they want to be evaluated.
...
- 11
5
votes
4
answers
302
views
Efficient generation of n-bit base-m Gray code with adjacent bit changes
How can I generate n-bit base-m Gray code in Mathematica, where only 1 bit changes at a time and all possibilities are covered? I have been hitting my head against a metaphorical wall for a few hours ...
- 63
3
votes
1
answer
193
views
On the solution of systems equations with exact coefficients
It all starts with the following system of equations that I can't solve by hand:
...
- 4,452
0
votes
0
answers
63
views
How to use quasi-Newton methods to solve a non-linear system?
Consider the following function, for $\mathbf{x}=\{x_1,...,x_n\}$
$$
F(\mathbf{x})=\sum_{k=0}^n \frac{e^{A_k\mathbf{x}}-e^{B_k\mathbf{x}}}{C_k\mathbf{x}}-\mathbf{b}
$$
where $\{A_k\}$, $\{B_k\}$ and $\...
- 4,933
5
votes
1
answer
97
views
How to Find a Weighing Matrix of Size n?
Weighting matrices appear in the statistical design of experiments (Weighting Matrices and Statistical Design of Experiments.
A weighting matrix is a generalization of Hadamard matrices, e.g.,
...
- 4,675
1
vote
0
answers
113
views
Solving the Unbalanced Assignment Problem with FindMinimumCostFlow?
I want to adapt this code from this answer to work with unbalanced bipartite graphs:
...
- 185
2
votes
2
answers
153
views
How can I calculate complicated infinite sums with FindIntegerNullVector (or related methods)?
I've recently been very interested in the wonderfully complex world of Euler sums, i.e. (convergent) infinite sums that, roughly speaking, consist of some rational polynomial combination of ...
- 215
0
votes
0
answers
63
views
What strategy would you adopt for this deep search on a function?
Ok, so I have a problem where I have a function that depends on 9 parameters and a bound condition
$$f(x,y,z,w,t,u,v,r,s)<K$$
Now all these variables take discrete values such as:
$$x \in \{x_1, ...
2
votes
3
answers
134
views
Iterative method for fixed point of a mapping with domain and range contained in $\mathbb{R}^{2}$
Let $X$ be a metric space and $T:X\rightarrow X$ be a function. A point $x\in X$ is called a fixed point of $T$ if $x=Tx$. For example, if $X=[0,1]$ and $Tx=\frac{x}{2}$ then $T$ has a unique fixed ...
- 83
21
votes
4
answers
1k
views
What's wrong with this FFT-based Von Kármán vortex street simulation?
About 9 years ago, I came across this interesting website, and found the following paragraph with a broken Mathematica code sample:
When fluid passes an object, it can leave a trail of vortices ...
- 67.6k
4
votes
3
answers
345
views
Find all sets whose index is divisible by the elements
Suppose I have such a set $S=\{3,4,5,...n+2\}, n\in \mathbb{Z}_{>\, 0} $, $a_n$ is any permutation of $S$ such that $n|a_n$, I want to know how many such $a_n$. The easy but inefficient way to do ...
- 5,672
2
votes
1
answer
108
views
Do loop not running the If clause [closed]
My full code is a bit more complicated but I hope that this works as a minimal example.
...
- 335
2
votes
0
answers
53
views
Memorization for Rule + ReplaceRepeated?
Question
When build packages of noncummutative algebras I met the choice:
Rule + ReplaceRepeated
...
- 2,557
0
votes
0
answers
65
views
Algorithm: Permutations & Signature
Theoretical side
Simple example: If I have two sets $A_1=\{1,3\} ,A_2=\{2,3\}$
and Permutations[{1, 2, 3}]= $\left(
\begin{array}{ccc}
1 & 2 & 3 \\
1 &...
- 1,014
0
votes
0
answers
56
views
Algorithm consisting of modules returning multiple errors
I'm trying to write a genetic algorithm that will take a list of lists of reals in interval [0,1], my "starting population", "score" them according to a fitness function, append ...
- 115
0
votes
1
answer
115
views
Visualization of an iteration scheme in Mathematica
I have a mapping T as attached (here. Now for $x_{0}\in C$ the Mann iteration process read as $x_{n+1}=(1-\alpha_{n})x_{n}+\alpha_{n}Tx_{n}$ n=0,1,2,3,... Now I want to obtain a visualization of the ...
- 161
2
votes
0
answers
135
views
Implement of faster(maybe paralleled) K-Means clustering
I am writing an algorithm that needs to add noise to the centroid of each iteration on top of KMeans. Therefore, I need to implement a custom KMeans function. I checked out the methods in Mathematica ...
- 534
0
votes
1
answer
614
views
Algorithm to convert real numbers decimal to binary
Currently trying to write code that converts decimal floats to binary base form (I know BaseForm exists).
Currently I'm working with an example that takes 3.3 and converts it:
...