Mathematical vectors, operations on vectors and vectorized programming.

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5
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820 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 ...
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239 views

Extract common factor from vector or matrix

I can't believe this hasn't been asked before but I can't find anything. Is there a way to convince Simplify or FullSimplify to ...
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0answers
93 views

Compile issues, scoping and order of evaluation

I have a few questions about compiling functions, which I think are all related to scoping and order of evaluation. I will illustrate them by a minimal example of the problem I have. I'm sorry for ...
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46 views

StreamPlot in 3 Dimensions

I would like to plot the vector equation $\left( {\begin{array}{*{20}{c}} {\frac{{ - a + \sqrt {{a^2} + 4bc} }}{c}}\\ {\frac{{ - a - \sqrt {{a^2} + 4bc} }}{c}}\\ 1 \end{array}} \right)$ as a stream ...
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226 views

Solving Symbolically Equations with Vectors and Matrices

I want to solve equations with vector variables and vector/matrix parameters symbolically. As a basic example I would like to be able to solve something like $[I-aG]x=b$ where $a,b \in \mathbb{R}^l$ ...
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95 views

Ray tracing: Insufficient precision

I am writing a ray tracer to find the intersection point between a single ray and a cylinder. ...
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120 views

Manahalobis distance between two vectors

I want to calculate the Mahalanobis distance between two vectors that represent two points. For example: ...
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93 views

Solving for vector elements in a function to which the vectors are not passed explicitly

I want to define a function which takes in two integers (indicating the lengths of 2 vectors), and solves a simple set of expressions at a set of points to find all the values in both the vectors. so ...
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21 views

Transform a vector DE into a set of scalar DEs

I have the vector equality: {{a,b},{c,d}}.D[{x1[t],x2[t]},t]=={{e,f},{g,h}}.{u1[t],u2[t]} I want to solve this using DSolve. ...
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22 views

Vector field plot not appearing in VectorPlot3D

I am having trouble in plotting the vector fields - Bfield and Avector - with the VectorPlot3D function. Here is the code used to Compute Bfield and Avector: ...
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41 views
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17 views

PolynomialGCD in complex numbers for vector simplification

I wanted to define a function $f(t,\vec{r})=e^{i\omega t-i\vec{k}\cdot\vec{r}}$, and take gradient of it. With, ...
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28 views

Working with vector-valued functions to solve an ODE

Let's say I have a simple vector-valued ODE given by $y'(t) = K*y(t)$ where K is a matrix $K_{n_{X}n}$. Let's assume that the matrix is $K_{21_{X}21}$, $K = \left[\begin{array}{cccc} k_{1_{X}1} ...
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46 views

Controlling scaling of multiple vector fields in VectorPlot3D

I'm trying to plot the electric and magnetic fields of a relativistically moving electric charge using VectorPlot3D, and apply "Manipulate" to change the velocity. The code I'm using is as follows: ...
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46 views

Find the point of intersection of A,B,C-plane and D1D2-line

The problem. Five points A,B,C,D1 and D2 in R3 are given. (1) Determine whether three points A,B,C are collinear(i.e. lie on the same line). (2) If A,B,C are not collinear, find the plane that ...
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67 views

ParametricPlot3D doesn't work with components of a vector input

I can't understand why ParametricPlot3D works, when the input is a vector and does not work, when the input is separated components of the vector (it returns an empty plot). The same happens for ...
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48 views

How to solve a multi-vector optimization problem efficiently?

How to efficiently solve a optimization problem which involves multiple vectors? My optimization problem is: $\min_{\bf{K}_{i}} \sum_{i<j}\left[\bf{t}\cdot(\bf{K}_i-\bf{K}_j)\right]^2$, s.t. ...
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50 views

Get rid of external library dependency

I am trying to generate C code for some functions, which I do not post in full because they are a few hundred lines long. The functions do nothing too fancy: a bunch of dot products, powers and roots. ...
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124 views

Gradient from Vectors type

I'm working with Vectors type in Mathematica 9. For this purpose I use the following command: ...
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179 views

Any way to fully expand an expression of two operators?

I am looking for a way to expand a complicate expression like the follow (A o B + C o (DxE))*(D o (ExF) - ExA + A) Here o and x are the operator. I want to ...