Questions tagged [matlab]

Questions about the numerical programming language MATLAB.

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Solving condensate density problem in MATLAB

I want to solve for $n_{0}$ for a fixed value of $n$, lets say $n=1$ $$ n= n_{0}+ \dfrac{1}{2}\int_{-1/2}^{1/2}dq\left(\dfrac{e_{q}+Un_{0}}{\hbar\omega}-1\right) $$ where $e_{q}=2[1-cos(2\pi q)] $ ...
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2answers
302 views

Why do structured and unstructured discretizations give different errors?

It is necessary for me to solve a Poisson problem with a numerical method on a square domain with two types of triangular mesh: uniform triangular mesh (using uniform distribution nodes on square) and ...
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1answer
647 views

Interpolating 3D Array non-monotonic data in MatLab

I am working on creating a program for simulations where three variables are parametrized, and we modify one parameter while keeping the other two constant. An example array looks like this when ...
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1answer
621 views

Dirichlet boundary condition

I am trying to solve ODEs in matlab using ode15s. Instead of specifying ODEs in the format M * dC/dt = f(C,t) where C is a function of x and t. I want ...
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1answer
104 views

For loops in matlab with a specific starting point

I have the following definitions long = 1000; init = 500; N = init+long; T = init+1:N-1; T1 = init+2:N; I then fill the vectors ...
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2answers
211 views

Raising elementwise a large symmetric, positive definite matrix to a power in Matlab

I have created a large positive definite (thus symmetric) matrix in Matlab. For sake of simplicity, let's assume that the matrix has the following form: $K= \left[ \begin{array}{ccc} k_{11} & \...
2
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1answer
132 views

find the exact solution ref The finite element method using matlab by Kwon and Bang [closed]

The results found are as under how do we find the exact solution ref The finite element method using matlab by Kwon and Bang.Page no 280-281 Example no 8.10.1.
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0answers
90 views

Bracket Algebra, Straightening Algorithm

My apologies if the question is simple. I need to write a code for straightening algorithm. Which includes defining bracket algebra. I tried to write it in CoCoA-5, but it wasn't possible because ...
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0answers
415 views

3D animation of a vector field (ParaView) [duplicate]

I am trying to create an animation of a 3d vector field in ParaView. All my data is in three matrices (201 x 201 x 201) corresponding to vectors components in x,y,z directions. And it's calculated in ...
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1answer
590 views

Is there a faster method to compute the geometric series of a matrix?

I want to calculate the geometric series of a matrix $A$: $$S=I+A+A^2+\dots+A^n$$ and then apply to a vector $v$, $Sv$. I've done it in Matlab with a loop and I think it's quite efficient applying ...
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1answer
159 views

Simple way to derive transpose of a vectorized operation

In a program I'm writing, I have a sub-routine that does some vectorized linear operations (specifically differentiation). Say for convenience I have defined the following inline function, which ...
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3answers
2k views

Solving a double integral in Matlab

I need to solve this integral: $M = \rho h \int_0^a \int_0^b N^2 \ dx dy$ where $N$ is defined as: $N = sin\left(\dfrac{\pi}{4}\eta +\dfrac{3\pi}{4}\right)sin\left(\dfrac{\pi}{4}\eta +\dfrac{3\pi}{...
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1answer
717 views

eigs routine in octave [closed]

I am using octave and observed a problem with the eigs-routine for non symmetric matrices. Using GNU octave version 3.8.1 the code below gives significant difference of eigenvalues although same ...
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1answer
1k views

Difference between eigendecomposition and singular value decomposition for Hermitian matrices

Let consider the following Hermitian matrix ...
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2answers
1k views

Projecting Finite Element solution onto new mesh

I am implementing a finite element solver in MATLAB and I have the following problem. Let's say I have a mesh $\mathcal{T}_1$ with triangular elements on a rectangular domain $\Omega\subset\mathbb{R}^...
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2answers
521 views

Bessel EVP and fzero

I am trying to solve the Eigenvalue problem $$ x^2 y''+ x y' + x^2 y = \lambda^2 y\,,\quad x\in(0,1)\,,\quad y(0)=0\,,\quad y'(1)=y(1) $$ The differential equation is the Bessel equation. The solution ...
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1answer
640 views

Importing results of FEM analysis into Matlab

I need to import in Matlab the results (like time histories of diplacement or frequency response at a specific point) obtained from a FEM analysis in Nastran. At the moment I ask Nastran to save the ...
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1answer
2k views

Solve poisson equation with Neumann b.c. (matlab or octave)

I'm trying to reconstruct an image given its Laplacian, which results in a Poisson equation and I'm using Neumann boundary conditions (derivative at boundary = 0). What I have is the laplacian (f, ...
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2answers
1k views

Solution blows up when using Runge-Kutta to solve simultaneous ODEs for liquid film equations

This is a continuation of a problem I asked over at physics exchange and math exchange. Basically I have two ODEs that I am solving in order to calculate the radial and tangential velocity of liquid ...
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1answer
153 views

Approximate $h$ in $F(\theta)=\sin \theta \int_{-L}^{+L}h(z)e^{-ikz\cos \theta} \,dz$

Consider $$F(\theta)=\sin \theta \int_{-L}^{+L}h(z)e^{-ikz\cos \theta} \,dz$$ $$|z|\le L$$ $$0 \le \theta \le \pi$$ By having knowledge of $F(\theta)$, how can one approximate $h(z)$? In addition, I ...
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3answers
173 views

Meshing of polygons

I need to generate a sequence of increasingly denser high-quality triangular meshes for some pentagons in MATLAB. I want to supply as my input The coordinates of the 5 vertices of the pentagon ...
4
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2answers
23k views

How to find all roots of equation in Matlab?

How to find all roots of an equation in Matlab? I tried and it gave me just one of the roots. For example: my equation is $F(x)=0$ where ...
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0answers
172 views

Find the solution of linear equation using Wiedemann/ Krylov method

Let given $M =$ 1 0 1 0 1 1 1 1 1 and $b =$ 1 0 1 How to find the solution $x_3$ where $x=${$...
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2answers
4k views

Determine unit outward normal vector for a curve

It is necessary for me to find the unit outward normal vector for the curve: $$\gamma=(x(t),y(t)) $$ where $$x(t)=\cos(t)−0.5\cos(3t)$$ and $$y(t)=\sin(t)+\sin(7t)+\sin(3t)$$ I know how to find ...
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1answer
168 views

How to construct the matrix like this

"We consider an unstructured planar (undirected) graph and calculate the stationary probability distribution of the random walk on the graph. The graph is generated by choosing n random points in the ...
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3answers
945 views

Searching solution for solving huge linear system in MATLAB or C

I am encountering a problem that my MATLAB code ran and an error occurs and shows that it is out of memory. My code is using finite element method to solve some complicated kind of integral equation ...
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0answers
312 views

ARPACK gives different answers from Matlab and NAG

I'm playing with ARPACK. I looked into the examples they provide, zndrv4.f illustrating the usage of the routine znaupd, in the directory of ARPACK/EXAMPLES/COMPLEX/. I also came cross NAG Fortran ...
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1answer
108 views

What is the best method to combine multiple vectored results into one chart?

Currently I am working on my research report where I've done a lot of measurements. For now I have uploaded everything into Matlab and visualise each on chart. Each one consists of 4 lines drawn with ...
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0answers
413 views

how to pick a submatrix of a sparse matrix quickly(matlab)

I have a large sparse matrix A and i want to pick the submatrix of it to do block jacobi iterations. For the blocks, i have get a matrix Q that contains the index of nonzero entries in its Jth column ...
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1answer
2k views

Switch between 2 equations to be given to ODE using events

I am trying to simulate a system with bilinear stiffness described by the following equations: $25\ddot{x}+15\dot{x}+330000x = p(t)$ if $x < 0.00072$ $25\ddot{x}+15\dot{x}+930000x = p(t)$ if $x &...
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1answer
140 views

Help me analyze the computational cost of two kinds of operations

everyone, I have a question about computational costs for a algorithm. That is: I have two vectors $u_n,\ v_n\in \mathbb{C}^N$, a matrix $A\in \mathbb{C}^{N\times N}$ (can be both sparse and dense) ...
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2k views

How to solve an ode with stochastic time-dependent input

I am trying to repeat an example I found in a paper. I have to solve this ODE: $25 \ddot{x} + 15 \dot{x} + 330000 x = p(t)$ where $p(t)$ is a white noise sequence band-limited into the 10-25 Hz ...
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2answers
3k views

Eigenvectors: MATLAB vs LAPACK DGGEV or DGGEVX

If we call LAPACK DGGEV or DGGEVX routines for two badly-conditioned matrices in a C++ code, will we get the same eigen-values &...
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1answer
901 views

What is a good way to take fractional powers of a matrix in MATLAB?

I am working on a problem that involves taking fractional powers of particular matrices. For the matrix A with 2 on the main diagonal and -1 on the sub and super diagonal (the finite difference ...
4
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1answer
4k views

Why is my MATLAB code for back-substitution slower than the backslash operator?

I wrote the code below to invert an upper triangular matrix, avoiding any possible multiplication/subtraction by zero. It just uses $\frac{1}{6}n^3+\ldots$ flops instead of $n^3+\ldots$ flops. ...
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0answers
355 views

Optimizing rank computation for very large sparse matrices

I have a sparse matrix such as ...
2
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1answer
6k views

Nonlinear ODE to solve Duffing's equation

I am trying to solve the Duffing's equation in MATLAB. $ m\ddot{y}+c\dot{y}+ky+k_{3}y^{3} = f(t) $ where $ f(t) = A \sin{\omega t}$ To do that I wrote a function to be given to the ode45. ...
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1answer
281 views

Why doesn't the integral of a smoothing kernel equal 1?

I was checking the unity condition on a smoothing kernel for SPH, however I don't understand why the integral is not giving 1. The kernel function is $\displaystyle W(||\vec r||,h) = \frac{315}{64\pi ...
3
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1answer
2k views

2D cross section from 3D surface

I am trying to apply the "restoring force surface" method to a dynamic linear system. The idea behind this method is that, knowing acceleration, displacement, velocity and input force it is possible ...
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1answer
1k views

Scaling factor of the inverse Fourier Transform (for convolution purposes)

I have a certain 2-D function. More properly, I have not the function itself, but the matrices $[X,Y,Z]$, where $X,Y$ are $1\times n$, and $Z$ is $n \times n$. Now, I want to calculate a a new matrix,...
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1answer
292 views

What kind of test cases are convenient to use for testing the code for Euler equations of gas dynamics in polar coordinates?

Consider Euler equation of gas dynamics in polar coordinates as $$ \left( \begin{array}{ccc} \rho \\ \rho u_{r} \\ \rho u_{\theta} \\ E \end{array} \right)_{t} + \frac{1}{r} \left( \begin{array}{ccc}...
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0answers
2k views

Piecewise linear approximation of an experimental data curve. Knots position constrained

I need to fit a curve, obtained from experimental data, with a piecewise linear model (4 knots and therefore 3 lines). I tried using the MATLAB function ...
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2answers
920 views

passing arguments to ode45 with 'flag'

I want to pass additional parameters to the ode45 function in MATLAB. There are many questions already on this, but I also have a 'flag' argument in my function. ...
2
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2answers
1k views

MATLAB: incorrect computation with pdepe for parabolic-elliptic system

I have found that MATLAB solves 1D parabolic-elliptic system incorrectly by using pdepe function. Here is a system: $$ u_t = u_{xx} + 2, $$ $$ 0 = v_{xx} + u. $$ Boundary conditions: $$ (-u_x+u)|_{x=0}...
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1answer
208 views

How to write a function-generating code in Python/MATLAB?

I want to write a code that generates a function I(t) that satisfies the following condition: $\frac{\big<I(t)^2\big>}{\big<I(t)\big>^2} > 2$ In other words, $\frac{\lim_{T \to \...
2
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2answers
241 views

single-variate function variational Intensity Plot for Matlab

I'm wondering if it's possible to create functional intensity plots in matlab. Examples of what I'm looking for are below found in this paper: These figures were (guessing) probably made in R, but is ...
2
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1answer
5k views

Plot a surface from data sets in MATLAB

I tried to plot a surface in MATLAB but, since it is the first time I had to do something like this, I need a confirmation on the process I followed because it is important for my project to plot the ...
3
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0answers
3k views

Numerical integration and filtering of acceleration experimental data

I have a vector containing acceleration measurements and the corresponding vector of times in which measurements are taken. To obtain velocity and displacement I used the cumtrapz() function already ...
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1answer
219 views

Can anyone give me some suggestions about optimize my Matlab codes?

recently, I try to write a Matlab codes to implement a sparse approximation inverse factorization method proposed by M. Benzi in his paper http://www.mathcs.emory.edu/~benzi/Web_papers/ainv.pdf this ...
2
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1answer
800 views

Saving symbolic function to increase efficiency in Matlab

I have a lengthy expression which is calculated using symbolic differentiation of a rather complicated function. I now intend to call this resulting (symbolic function) in a for loop many times, and ...

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