Mathematical vectors, operations on vectors and vectorized programming.

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28
votes
2answers
2k views

Animating a Voronoi Diagram

edit: Excellent answers have been provided and I made an animation which is suitable for my use, however, all the examples rely on bitmap/rasterized data; is there a vector based approach? I would ...
20
votes
7answers
831 views

Make a huge vector in a wise way

I need to construct a vector similar to: v[x_]:={0, 0, x, 0, 0, 2*x, 0, 0, 3*x, ....., 0, 0, n*x}; where n=10^9. How can I ...
15
votes
2answers
2k views

How to represent and manipulate abstract indexed vector (or tensor) expressions?

I have a couple abstract indexed quantities, both differential elements $dx = dx^\mu e_\mu + x^\mu de_\mu$ $du = du^\mu e_\mu + u^\mu de_\mu$ I can compute the expression $(dx + du) \cdot (dx + du) ...
14
votes
6answers
2k views

Why can't I define vector v as having subscripted elements v_1, v_2, v_3…?

I'm a very beginner in Mathematica 8 programming. While trying to play a little with tensor analysis I encountered a problem. How to define for example vector in such manner: v={$v_1,v_2,v_3$} For ...
12
votes
4answers
469 views

How do you decompose a polynomial matrix into its matrix coefficients?

Let's say I have a matrix, $\mathbf{M}$, that is polynomially dependent on a single variable, such as M = {{15 + a^2, a + 5 a^2}, {a - 5 a^2, 2}} and I want to ...
12
votes
1answer
1k views

Persistence length of a polymer chain

I'm trying to calculate the persistence length (Lp) of a polymer chain using Mathematica. The first and simplest method is to compare the EuclideanDistance between ...
11
votes
4answers
3k views

What is the cleanest way to prevent divide-by-zero warnings?

If I evaluate {1, 2, 3, 4}/{5, 6, 0, 8}, obviously I get one warning: ...
8
votes
2answers
599 views

How to declare a 3D vector variable?

How can I do vector calculations without telling Mathematica the vector entries? I have very many arbitrary linear combinations in $\mathbb{R}^3$ which I want to perform some general calculations on ...
8
votes
3answers
1k views

How to find the magnitude of a vector?

I'm doing this exercise in Wagner's book (p.78) , and this is my attempt: ...
7
votes
5answers
1k views

Vectors with a certain magnitude in Mathematica

For a user specified magnitude, is there a way to have Mathematica produce any 3D vector that fits that magnitude?
7
votes
3answers
282 views

“NotAvailable” and “NotApplicable” data points returned by WeatherData[]

I am trying to use ListVectorPlot in combination with WeatherData and CountryData to show ...
7
votes
2answers
3k views

How do I simplify a vector expression?

I am doing vector analysis. I have figured out that the following expression won't be simplified in Mathematica: Simplify[Dot[x, y] - Dot[y, x]] I think the ...
7
votes
2answers
485 views

How to make a point's position time-dependent given a formula for the next step?

I've made a program that is just some points on a plane. Red points are cops and green points are robbers. Each point has a vector indicating where it is going to be in the next step of $t$. Right now ...
7
votes
2answers
727 views

Integration with vector coefficients

I asked this same question in Mathematics, and it was suggested I might try here. I'm more comfortable with Maple, but if I can get Mathematica to do what I'm after, so much the better. Basically ...
7
votes
1answer
438 views

Estimation of vector autoregressive (VAR) process

To estimate 1-dimensional VAR process (which is AR process) you can easily use functions EstimatedProcess or ...
6
votes
2answers
181 views

Reduce data by taking averages

I am trying to implement the following: I have got two vectors x and y of unequal lengths. The length of ...
6
votes
2answers
1k views

Plotting a path in a vector field

I am trying to make a visual representation of the curve $y=x^{2}$, with $x\in\left[0,1\right]$ in the vector field defined by $\vec{F}=\left[-y,x\right]$. However, as far as I can tell there does ...
6
votes
4answers
170 views

Define Function with Sum over a list

I want to define a function that would symbolically look like $$ t(s,\underline{a})=\pi s + \sum_{n=1}^{n_{max}}a_n\sin(n \pi s) $$ (something like a finite Fourier series). Here $s\in [0,1]$ and ...
6
votes
2answers
588 views

Animated Vector plot

I'm trying to make an animation of a time-varying 2D vector field. However, I'm got a difficulty in that Mathematica normalises the length of the vectors with each call to ...
6
votes
2answers
106 views

Complex result for Real vectors in VectorAngle

I was expecting a real angle using VectorAngle when passing real valued vectors, however I obtained a complex angle. ...
6
votes
2answers
198 views

VectorScale Explanation

I'm having great difficulty understanding VectorScale. Here are the definitions from the documentation. With the explicit specification ...
6
votes
1answer
1k views

Smoothing/Averaging 2D Vector Fields

I have a list of 2D vectors defined by {{x,y},{u,v}} and would like to smooth or average the vectors. For example here are 2 vector fields, the second has noise ...
5
votes
2answers
516 views

Plotting: Is anyone familiar with gradientfieldplot command?

I am trying to plot this graph showing the electric field lines and lines of equipotential based off the electrode configuration(in black) of two parallel lines. This is what I've been using for other ...
5
votes
6answers
881 views

A matrix-vector cross product

I want to do a cross product involving a vector of Pauli matrices $\vec \sigma = \left( {{\sigma _1},{\sigma _2},{\sigma _3}} \right)$; for example, $\vec \sigma \times \left( {1,2,3} \right)$. ...
5
votes
2answers
1k views

Plot 2D Vector function in 3D

I want to plot a 2D vector function such as $F(x,y) = (a(x,y),\,b(x,y))$ in a 3D graph so that the vectors are embedded in the xy plane. I tried to do the following: First I defined a piecewise ...
5
votes
1answer
111 views

How to define an orthogonal basis in the right way?

I am trying to work with the vector notation without defining vector components explicitly. $Assumptions = (x | y | z) \[Element] Vectors[3] The vectors ...
4
votes
5answers
334 views

How to generalize and speed up this program?

There is a vector whose length is $n*m$, we can part it into $n$ sections in order. I want to define a function to compare the $i$-th and $i+1$-th section and find the minimum. The program for $n=m=3$ ...
4
votes
2answers
4k views

How to combine two vectors into a matrix by columns?

I know it may sounds idiot, but I've been looking through the document, and couldn't find a way to combine two vectors say {a, b} and ...
4
votes
2answers
169 views

Assumptions for RotationMatrix

I'm making C++ program, and in my program I need a rotation matrix around any vector. I wanted to extract RotationMatrix[fi,{x,y,z}] output and put it in my ...
4
votes
1answer
1k views

Visualize eigenvectors at specified points?

I am very new to Mathematica and I got stuck about visualizing eigenvectors 2D and 3D. I want to visualize my largest eigenvector field of tensor data(15x15). I wrote this code for instance : ...
4
votes
1answer
193 views

Orthogonalizing without normalizing

Is there a way to make Orthogonalize do the normal Gram-Schmidt procedure without normalizing the result? As far as I've understood this was possible with ...
4
votes
1answer
99 views

How can I implement this recurrence equation in Mathematica?

I asked a similar question yesterday but today I realized that I was implementing the wrong function. I have tried changing the implementation but I can't get it to work. Problem: There is a river ...
4
votes
1answer
306 views

How to fix errors in Gram-Schmidt process when using random vectors?

I first make a function to get a random vector on unit sphere in a swath around the equator. That is what the parameter $\gamma$ controls; if $\gamma = 1/2$, the vectors can be chosen anywhere on the ...
4
votes
1answer
63 views

How to use DSolve with vectors without decomposing into vector components?

Given a basic, two-dimensional ballistic trajectory problem, I can solve the equations of motion using DSolve (or NDSolve) by ...
4
votes
0answers
698 views

computation of gradient vector field in 3D using GradientOrientationFilter

I want to compute a 3D gradient vector field of an Image3D object using the built-in GradientOrientationFilter function in Mathematica. From the documentation I ...
3
votes
3answers
310 views

Multiply (not divide!) Vectors in a List by Their Own Norm

I wanted a set ("list") of 100 random vectors of dimension 2. I accomplished this already by generating a "list of lists" where the elements of the overall list are 2-dimensional lists consisting of 2 ...
3
votes
2answers
176 views

Simple Plot of Vector

I have a vector $<x(t),y(t),z(t)>$ constrained to a unit sphere. I am trying to plot what the vector looks like as time progresses. What would be the easiest approach to visualizing this? I ...
3
votes
2answers
173 views

Orthogonal vector in two dimensions

Maybe this is really basic, but I couldn't figure it out. I would like to find the "hat vector" of a vector I defined: it's a vector orthogonal to the given one, assuming two dimensions. So for ...
3
votes
4answers
131 views

What is the inverse of CoefficientList?

I have numbers in vector notation. I need to get polynomial notation from them. My numbers are {0, 1, 23, 5, 15, 0, 0, 0}. I want to get x + 23x^2 + 5x^3 + 15x^4 ...
3
votes
3answers
436 views

How to pull scalars out of a function that should act on lists?

Suppose I have A = a vecA B = b vecB where a and b are supposed to be arbitrary scalars ...
3
votes
4answers
169 views

Pack Solve results into a vector

I am currently using a really easy function to get the eigenvectors of a corresponding eigenspace: ...
3
votes
2answers
964 views

creating vectors with normal distribution of lengths

First consider vectors of unit length, say on the unit sphere. Now I want to give some magnitude to these vectors and I want the magnitude to be chosen from the normal distribution. In one dimension ...
3
votes
1answer
739 views

Plotting a complicated vector field

If we consider the vector $\left ( A \cdot \nabla \right) \: B$, we have in Cartesian coordinates $$\left ( A \cdot \nabla \right) \: B = \left ( A \cdot \nabla B_x \right ) e_x + \left ( A \cdot ...
3
votes
2answers
143 views

Is it possible to specify the direction of rotation in VectorAngle function?

If I use the function VectorAngle[{1,0},{1,-1}], is it possible to obtain the angle generated by rotating around the axis counter clock wise? In other words, I would move from the first vector to the ...
3
votes
1answer
387 views

Plotting a Gravity-Field [duplicate]

I try to plot a 2D gravity field or something similar in the form like $r/|r|^3$ with the standart builtin VectorPlot function: ...
3
votes
2answers
148 views

Vector Plot of a linearly varying cantilever

I want to drawing with Vector Plot a deflection and slope of a linearly varying cantilever. And with Contour Plot it works but with Vector Plot it didn't. Here is the code: ...
3
votes
1answer
149 views

Introduction to Vectors and NDSolve

I want to use NDSolve for a complicated equation that contains vectors. I am still new to Mathematica, and have really enjoyed what I have learned thus far. Concerning this question, I have already ...
3
votes
1answer
493 views

NDSolve with vector function

(Possible duplicate yet I still can't understand.) Basic 2D revolving around origin: ...
3
votes
1answer
123 views

Center of quadrangular

Having 4 points A (ax, ay), B (bx, by), C (cx, cy) and D ...
3
votes
3answers
136 views

how can I make a control for my vector equation in my simulation?

I'm trying to build a control selector or menu for equations to put into my curvature simulations. However all the code I've tried hasn't worked.Does anyone know how I could make a control selector or ...