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
372
questions
2
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1
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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 ...
- 73
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votes
2
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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})
the overall image size ...
- 5,997
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3
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189
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0
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0
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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 ...
- 5,470
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4
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390
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An accumulated moving average
1. Problem statement
In accordance with the standard definitions the inbuilt MovingAverage
...
- 47.8k
4
votes
2
answers
595
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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 ...
- 2,411
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2
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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 ...
- 47.8k
6
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2
answers
233
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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 ...
- 47.8k
5
votes
5
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588
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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!
...
- 47.8k
8
votes
6
answers
437
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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,...
- 47.8k
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9
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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 ...
- 47.8k
9
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4
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645
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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 ...
- 47.8k
7
votes
6
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357
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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 ...
- 47.8k
3
votes
0
answers
61
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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
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votes
2
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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:
...
- 13.5k
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3
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295
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1
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0
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84
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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, ...
- 513
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votes
1
answer
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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 $G$...
- 414
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1
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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
4
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4
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272
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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 ...
- 53
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1
answer
174
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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:
...
- 4,422
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0
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52
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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 $\...
- 4,167
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1
answer
85
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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.,
...
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0
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92
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Solving the Unbalanced Assignment Problem with FindMinimumCostFlow?
I want to adapt this code from this answer to work with unbalanced bipartite graphs:
...
- 185
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votes
2
answers
119
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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
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0
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103
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Implement of Euler Method of Parabolic PDE
I'm experimenting with different schemes for numerically solving PDEs in Mathematica. I use NestList to implement the Euler Method for 1-D PDE, the code is concise:
...
- 524
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0
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61
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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
112
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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 ...
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4
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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 ...
- 63.5k
4
votes
3
answers
313
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 ...
- 5,562
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1
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108
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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
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0
answers
50
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Memorization for Rule + ReplaceRepeated?
Question
When build packages of noncummutative algebras I met the choice:
Rule + ReplaceRepeated
...
- 2,208
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0
answers
62
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 &...
- 732
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56
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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 ...
- 65
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votes
1
answer
103
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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
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0
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127
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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 ...
- 524
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votes
1
answer
500
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:
...
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1
answer
119
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0
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0
answers
225
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Particle Swarm Optimization implementation in mathematica
Hi I am new to mathematica, I want to use it to implement PSO instead of using matlab. Could anyone suggest me how to find some implementation examples with code or its general implementation for ...
1
vote
1
answer
143
views
A method for endpoints in mathemtica [closed]
If $(\mathbb{R},|.|)$ is a real line, $C$ a subset of $\mathbb{R}$ and $K(C)$ denote set of a compact subset of $C$. Define a multivalued mapping $T:C\rightarrow K(C)$. We know that a point $p\in C$ ...
- 161
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3
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301
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How to compute higher iterations in mathemtica
I have the equation $u^{\prime\prime}(t)+u^{2}(t)-t^{4}-2=0$ such that $0\leq t\leq 1$and also I have $u(0)=0$ as well as $u(1)=1$. Noe the exact solution of the equation is $u(t)=t^{2}$. Now I ...
- 161
0
votes
1
answer
291
views
How to obtain the convolution of these functions?
I am starting to use Mathematica. I wanted to compute
$$\nabla F*\phi(x),\;x\in\mathbb{R^2}$$
where $F(x)=\ln\|x\|$ and $\phi(x)=\chi_{B(0,2)}(x)$.
I am a new user of this software, so I don't know ...
- 101
2
votes
2
answers
751
views
Solution of differential equation by by an iterative method
Let $y^{\prime\prime}(t)+y^{2}(t)-t^{4}-2=0$, where $0\leq t\leq 1$. The boundary conditions are $y(0)=0$ and $y(1)=1$ and so its exact solution is $y(t)=t^{2}$. Now I want to compute the solution by ...
- 161
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0
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135
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On the numerical computation of polynomial roots
In the guide on the NRoots[] function I read:
...
- 291
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votes
1
answer
55
views
How many nearest neighbours in a classifier by default?
I've been running a classifier on my data with the 'NearestNeighbors' method. I've learned that I can specify the number of neighbours used with the following command:
...
- 189
1
vote
0
answers
89
views
Shortest paths Knights Tour
I am trying to print the minimum steps needed to traverse a chessboard as a knight from one diagonal position to the other. I have the following code:
Building the chessboard
I started with creating ...
2
votes
3
answers
160
views
Path finding in Complete Graph [closed]
I have the following Complete Graph with random labels on its edges
...
- 167
1
vote
0
answers
76
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“Largest” symbolic common factor of an integer sequence (not simply GCD)
Suppose, I have a finite fragment of a quickly increasing sequence of integers $\{a_n\}$ that is too complex, unusual, or irregular for FindSequenceFunction to find ...
- 7,163
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vote
0
answers
94
views
How to optimize Code for Wolfram Challenges? [closed]
I am wondering if anyone who has knowledge of optimizing programs in the Wolfram language has any advice on how to optimize the following quantities of programs written to solve Wolfram Challenges.
I ...
- 1,663
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votes
0
answers
50
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Numerical minimization of function
So I have the following equation:
3 Sqrt[9.15753*10^-6 + 25.1556 TolC^2 + 25.1556 TolL^2]==1;
Now TolC and TolL can take respectively the values of these lists:
<...