# Questions tagged [algorithms]

A description of the specific steps needed to solve a particular problem in an unambiguous way, expressed in an abstract form.

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### 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 ...
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:...
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 ...
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 ...
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 ...
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### 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 ...
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 ...
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 ...
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 ...
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 ...
541 views

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 ...
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### 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 ...
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 ...
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### 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 ...
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 ...
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 ...
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'...
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 ...
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 ...
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-...
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### 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 ...
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 ...
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 ...
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 ...
### 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 ...