Questions tagged [algorithms]
A description of the specific steps needed to solve a particular problem in an unambiguous way, expressed in an abstract form.
528
questions
6
votes
1answer
132 views
General approach to infinite sums
My question is specific to algorithms and models of computation.
I would like to write code to evaluate the following expression quickly and accurately:
$$\log \left( \sum_{i=1}^{\infty}{I_{\nu+i}(2\...
1
vote
0answers
79 views
Fast evaluation of trigonometric polynomials
Suppose you have a trigonometric polynomial of the form
\begin{equation*}
x(t) = \sum_{k = 0}^N a_k \cos(2 \pi k f_0 t).
\end{equation*}
Using Clenshaw algorithm, one can evaluate this polynomial in $...
2
votes
0answers
57 views
Multigrid method: linear solver and modified residual
I am trying to better understand the FAS multigrid algorithm for Euler equation in FV discretization. The usage of the modified residual (the residual with forcing) inside the different cases:
...
1
vote
1answer
50 views
Resampling an array of objects
Context
I have an array of objects (or a list of dictionaries), sorted in order based on a property of each object, say, time. In JSON, it would look something ...
3
votes
0answers
46 views
Help with restart functionnality in sef-made GMRES solver in python
I am new to this forum and to computational science in general.
I started to learn numerical liner algebra on my own and would like to code a GMRES solver in python (no preconditioner for the time ...
2
votes
1answer
36 views
Simulate circular mold spread using cellular automata - square emerges instead
I am trying to simulate the spread of mold in a petri dish using a cellular automata based approach. Thanks to the answer in my other question Stochastic cellular automata - algorithm limited by 1 ...
2
votes
0answers
24 views
Scheduling Algorithm Goal is to Fix Max Number of Appointments
First post. Hi everyone.
I’m trying to develop an algorithm to later code that schedules appointments in a way such that the number of hours occupied by the appointments in a given day is maximized.
...
1
vote
0answers
81 views
What is the limit involving `Sum`, `Subsets`, and `RankedMax` as `t` approaches infinity?
Motivation
Suppose we have a countably infinite $A$ with order and group structures and suppose $F_1,F_2,\cdot\cdot\cdot$ are an infinite sequence of finite sets (denoted $\left\{F_n\right\}_{n=1}^{\...
8
votes
1answer
206 views
Is there a way we can compute my sum involving `subsets` more efficiently?
Suppose we have a countably infinite $A$ and $F_1,F_2,\cdot\cdot\cdot$ are an infinite sequence of finite sets (denoted $\left\{F_n\right\}_{n=1}^{\infty}$) such that $\bigcup\limits_{n=1}^{\infty}F_n=...
4
votes
1answer
65 views
Stochastic cellular automata - algorithm limited by 1 cell per timestep
Context
Let's say I am trying to model the spread of mold in a petri dish, using a stochastic cellular automata approach. The petri dish can be thought of as a grid of 1mm x 1mm squares, each called ...
2
votes
1answer
70 views
Dividing a continuous domain into small squares; how to perform storage and querying?
I recently had a software engineering interview and was asked a series of questions that was a bit outside of knowledge realm, and I feel like there's some scientific computing principles here (I took ...
0
votes
1answer
66 views
Looking for Partinioning Algorithms allowing for Constraints
What algorithms exist that partition the domain according to a black box evaluation function (possibly subject to some assumptions)?
Examples
Simple Example
To better exaplain we consider as our ...
0
votes
1answer
78 views
In Lanczos algorithm, can we choose the staring vector to be the first eigenvector of the input matrix A?
In Lanczos algorithm, can we choose the staring vector $v$ to be the first eigenvector of the input matrix $A$? How can we select it? and why $v$ need to have norm 1?
0
votes
0answers
19 views
Do the class of Construction Heuristic that does or does not change previous decisions have a name?
I'm writing a paper where I am discussing different types of construction heuristics.
One type does not change previous decisions when adding new elements to the solution. I'd call them "...
1
vote
0answers
41 views
Ising model in Python (Magnetization Scaling)
I am trying to implement the Ising Model in Python for Gibbs Distribution:
$$\pi(x) = \frac{1}{Z(\beta)} e^{-\beta H(x)}$$
\begin{align*}
p(x,y)&=r(x,y) \cdot \min \left( \frac{\pi(y)}{\pi(x)},1 \...
4
votes
3answers
169 views
Algorithms to generate spherical codes
A spherical code, specified by the parameters $(n,N,t)$, is a set of $N$ coordinates on the $n$-dimensional unit hypersphere such that the set of dot products between any two unit vectors from the ...
0
votes
1answer
114 views
Trouble Implementing 1d Wave Equation Finite Difference Solver
Im trying to solve the 1d Wave Equation on $x \in \mathbb{R}, t > 0$: $$u_{tt} = c^2u_{xx}, \hspace{5mm} u(x,0) = \cos(4 \pi x), \hspace{5mm} u_t(x,0) = 0$$ with $c = 1$ and a periodic boundary ...
3
votes
1answer
77 views
Maintain unitary time evolution for a nonlinear ODE
I want to solve a nonlinear ODE of matrix $A(t)$
$$\mathrm{i}\dot A = A(t)M(t),\:\mathrm{with}\: M(t)=A^\dagger(t)H(t)A(t)$$ where $H(t)$ and hence $M(t)$ are Hermitian. Therefore, I presume the time ...
0
votes
2answers
49 views
Technique or Pattern to calculate conditional statement
I am attempting to create a conditional statement that compares four (4) true/false conditions. Depending on the state of these four conditions (either true or false) the conditional statement will ...
4
votes
1answer
88 views
Algorithm to merge two polygons (using connectivities)?
I am struggling with implementing an algorithm that does one simple thing:
Consider two polygons (one can just draw any two polygons and number their vertices), whose connectivities in a node list are:...
5
votes
2answers
129 views
Exponent log to compute reciprocal power?
A MATLAB library seems to overcomplicate a computation:
exp( (log(a) - log(b))/b )
which is mathematically equivalent (assuming real & positive ...
3
votes
1answer
183 views
Understand the need for Welford's online algorithm
I am puzzled by the Wikipedia entry discussing many online algorithms for computing the sample variance, including the Welford's online algorithm.
In particular, the sample variance $s_n^2$ can be ...
1
vote
0answers
36 views
Largest triangle that contains a point
Given the location of $n$ points on a 2D plane ($P_1, P_2, \ldots, P_n$); and the location of a special point $X$.
Find three points $P_i,P_j,P_k$ ($i \neq j \neq k$) such that point $X$ is inside the ...
0
votes
0answers
35 views
Parameter sampling from a 3D isosurface in R
Before we start, a small disclaimer: I am not a computer scientist, and the field of isosurfaces is new to me, so hopefully, the question is phrased clearly:) Otherwise, let me know, and I will (try ...
1
vote
1answer
80 views
Transition from 2D to 3D finite element code, what are the inevitable modifications to be implemented?
Imagine we have a simple 2D FEM solver (we are dealing with solid mechanics) and we would like to develop it to a 3D FEM solver (let's say for the same solid mechanics problem) in this case what are ...
0
votes
0answers
45 views
Storing and retrieving two-dimensional and three-dimensional data
I work on computational geometry.
A huge number of two-dimensional and three-dimensional data are found in my project. Coordinates of polygon and polyhedrons vertices consisted of two-dimensional and ...
3
votes
3answers
271 views
How to determine if 2 rays intersect?
We are given the 2D coordinates of 2 points: the first point is where the ray starts and it goes through the second point. We are given another ray in the same way. How do we determine if they have a ...
0
votes
0answers
50 views
Finding block structure of a tensor
Are there any well-known algorithms for partitioning a dense tensor into block-sparse form?
In other words, I need to find a set of non-overlapping blocks that contain all non-zero entries of the ...
3
votes
2answers
541 views
Time Reversibility of Velocity Verlet Algorithm
I'm very new to computational Physics and am finding conflicting statements on whether the velocity Verlet algorithm, defined as:
$\begin{align}
x_{n+1} &= x_n + v_n \Delta t + \frac{1}{2} a_n \...
1
vote
1answer
82 views
Asymptotic complexity of fixed-rank SVD
According to the Wikipedia article on Singular Value Decomposition, the asymptotic complexity of computing the SVD of an arbitrary m×n matrix M with m>n by the popular Householder QR methods is O(...
2
votes
1answer
192 views
How to select initial time step in adaptive time step ODE solver (TR-BDF2)
The Problem
I am currently reconstructing a TR-BDF2 scheme which contains the following two stages:
\begin{align}
y_{n+\gamma} & = y_n + \gamma \frac{h}{2}\left( f_n + f_{n+\gamma} \right) \...
4
votes
2answers
119 views
Which algorithms(paper) should be reproduced by a student to enter the field of computational fluid-structure interaction?
We'd better not to reinvent the wheel. But without some programming, one can hardly understand computational fluid-structure interaction. And I would like to know which papers or algorithms should a ...
1
vote
0answers
29 views
Bipartite Euclidean Matching simple to implement approximate algorithm
I am looking for a simple to implement algorithm for the bipartite euclidean matching problem (or an implementation of any practical algorithm). I am aware of Agarwal's paper, but I would like to ...
1
vote
1answer
67 views
An efficient algorithm to find Nearest Neighbours
So imagine I have a $m$ vectors each of dimension $d$. Lets call them, $\vec x_{i}$, with $i = 1, 2, 3, 4, 5, \dots, m$. Now the idea is to find the neighbours of $\vec x_{i}$ (calling them $\vec x_{j}...
2
votes
3answers
386 views
On the reordering of sparse matrices
I have been reading on different techniques used to reorder sparse matrices to achieve better performance, the most popular being the Cuthill-McKee or Reverse Cuthill-McKee algorithm. Most of those ...
2
votes
0answers
127 views
Computing Singular Value Decomposition of small ($4\times 4$) matrices
I need to compute the Singular Value Decomposition (SVD) of many $4 \times 4$ matrices. I'm looking for SVD algorithms specialized for small matrices. I've read that the ...
6
votes
1answer
773 views
Cheap recalculation of eigenvalues and eigenvectors for a low-rank update of the matrix
Suppose I have a correlation matrix, $A$, and I already have the eigenvalues and eigenvectors of this matrix.
For a given vector, $\mathbf{\mathit{v}}$, I want to calculate the eigenvalues and ...
0
votes
0answers
47 views
Producing Voronoi diagram in three dimensional
A Voronoi diagram is a kind of tesselation that divided the medium into polygons in 2D and polyhedrons in 3D.
Although there are many algorithms to construct a Voronoi diagram, some of them are faster ...
3
votes
3answers
232 views
What are some algorithms to calculate the width of an arbitrary polygon when a bounding box approximation is inaccurate
What are some alternative algorithms to creating a bounding box for finding the max width of a concave, simple winding polygon, like the one in the below image? I prefer solutions that are more ...
0
votes
0answers
74 views
Derivative-free ill-conditioned non-linear least squares
I am looking for a package which can solve (non-linear) least squares problems without the use of derivatives (because of an expensive model), but which also deals with ill-conditioning well (such as ...
0
votes
0answers
112 views
Explanation of Givens rotation in Jacobi Rotation SVD
I'm trying to implement Singular Value Decomposition (homework of sorts) via the Jacobi Rotation method (more info here, pages 11 and 12).
I am stuck at the bullet saying (sorry for the picture, but I'...
2
votes
1answer
42 views
How do you construct a self-similar binary structured-tree?
Please excuse me if this question somehow looks trivial or not really interesting, but I recently have a hard time to convince someone else that my algorithm for constructing a self-similar binary ...
0
votes
0answers
62 views
Surface mesh from labeled 3D points
I'm trying to figure out how to create a surface mesh from a set of labeled 3D points. The 3D object could be something like part of a cave system or asteroid where there would be parts of the surface ...
1
vote
0answers
24 views
Combining many probabilities, modifying, seeking general formula
CONTEXT
I need to combine the probability of occurrence of many thousands of events for millions of individuals (trees) in an agent-based/individual-based simulation model developed in NetLogo (agent-...
2
votes
1answer
76 views
Question regarding the energy computation of the Ising-Spin Model
In most of the Monte-Carlo-Algorithms I studied, I found, at the place where they compute the energy, always a line of code, where they divided by four.
For example, this code-snippet is taken from ...
2
votes
1answer
119 views
Machine Learning for Optimization
I have a function which takes 100+ coefficients and outputs $x$. I wish to optimise $x$.
Running the simulation 50 000 times will take around 15 minutes, however, this happens in parallel - and the ...
1
vote
0answers
52 views
Assume $AX = C$. How to determine which entry of $BX - D$ is non-negative?
Let $A,B$ be $n \times n$ matrices and $C,D$ be $n \times 1$ matrices. Moreover, all entries of $A,B,C,D$ are non-negative. Assume that there is a unique matrix $X$ that solves $AX = C$.
My goal is ...
0
votes
2answers
137 views
Best way to find biggest & smallest number in a random list?
Given a list of some length, containing random numbers.
What method would need the least amount of checks to find the largest & smallest number in the list?
My best guess is: (list_length)/2 ...
-1
votes
1answer
31 views
An almost surly fine-time game of coin toss where you win with probability $p$
Given a fair coin and a number $p\in(0,1)$. How do you design a game that finishes in a finite number of tosses with a probability of $1$? And further, with the probability $p$ you win the game.
I ...
1
vote
1answer
68 views
Newman algorithm yielding different result to what is given in his paper
Summary
I am trying to implement Newman's algorithm for community detection, outlined in this paper. I am testing my implementation against one of the datasets used in that paper to benchmark the ...
