# Questions tagged [vector]

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### Helmholtz decomposition of a vector field in Fourier space with Python

I have a 3D vector field and I want to extract its divergence-free part (also called transverse component), using the Helmholtz decomposition. In principle, this can be done in the Fourier space, as ...
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### Describing a vector field

I am currently making use of a 2D vector field that I would like to be able to describe and characterize. I thought of a few metrics that I could use, but they seem limited for both a qualitative and ...
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613 views

### FEM for vector valued problems: reference request

I'm a PhD working in a computational mechanics lab. I come from a Math department, and I have a good background for what concerns the basics of finite elements, like inf-sup conditions, DG, non-...
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### 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?
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1 vote
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### k nearest neighbors dictionary for vectors?

Does there exists a data structure with these properties Stores vectors in a dictionary When given a key that is also a vector, returns the k nearest vectors using a similarity metric (e.g. Euclidean,...
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### 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:...
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### In Eigen, can a sparse matrix contain vectors/objects instead of simple scalar values?

I need to have a sparse matrix whose elements are not simple numbers, but objects, e.g. a couple of floating point values and a bunch of integer indices. I am wondering if Eigen has something similar, ...
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147 views

### If dot product is commutative, why does MATLAB give different answers?

Why does the dot() function in MATLAB return different expressions based on the order in which I pass vectors?
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### Lexicographically order matrix into a vector

I am trying to implement the algorithm contained in this article here. It is about solving a 2 and 2.5D Fredholm integral, focused on bidimensional NMR experiments. I've made significant progress, ...
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375 views

### Computing excited states using itensor (with DMRG)

I am trying to compute first few excited states of some Hamiltonian (I am using itensor and its DMRG algorithm). To do so, I am ...
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1 vote
48 views

### How to integrate the contents of a vector using an adaptive quadrature routine [duplicate]

I have a function which requires the return type to be a container. The problem is that I need to integrate the contents of the container as efficiently as possible and was hoping to use adaptive ...
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### Vector characterization of cylinder displacements in a box

We have a cylinder of length $l$ (in units of its radius $d,$ as basic unit of length set to $d=1.$) in a box, and we consider an orthonormal Cartesian coordinate system with its origin placed at the ...
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### How to compute the Helmholtz decomposition of 2D and 3D vector fields?

I have a sample of 100 particles with their 3D positions and velocities. I want to decompose the velocity vector field to its curl free and divergence free components. Is it a feasible to do so for ...
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321 views

### Software/code to extract a solenoidal (a.k.a. divergence-free) field from a 2D vector field numerically

Can somebody point me to software/code to extract a solenoidal (a.k.a. divergence-free) field from a 2D vector field numerically? There are a plethora of papers and documents describing how to do ...
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### two level iterators C++ [closed]

I am trying to implement a two level iterator as I will now describe. Basically I have a "vector of vectors" and I want a single iterator that will loop over all the objects in the vector of vectors. ...
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### Regarding solution vector of the wave equation

I am simulating the wave equation using FEM. For a 2D wave equation, when I visualise my output in Paraview, I see a separate solution in 'x' and 'y' direction for each node on the mesh. Therefore, if ...
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1 vote
759 views

### Find a permutation matrix (using the Matlab's function $symrcm$) of a matrix $A(2:end, 2:end)$

I've the following Matlab code: r = symrcm(A(2:end, 2:end)); prcm = [1 r + 1]; spy(A(prcm, prcm)); where A should be sparse ...
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### Efficiently approximating sum of 2-norms

Suppose I have a real vector $\bf x$ of length $KN$, where $K<<N$. Let's say I break this vector $\bf x$ up into $N$ vectors each of length $K$, $${\bf x}_1,...{\bf x}_n.$$ Now I would like ...
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### How can I efficiently position the different segments of a large vector in Eigen C++?

I have a very large(up to 9 000 000) VectorXi vector defined in Eigen C++ which is read from a data file. The vector consists of 0, 1, 2, ...n segments with ...
150 views

### combine $n$ vectors using $L2-normalization$

Suppose that I have the following vectors $v_1$, $v_2$, $v_3$ $\in R^n$,$n= 9$. What I want to do exactly is to combine these $3$ vectors into $1$ representative vector $V$. According to the ...
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