Questions tagged [matlab]

Questions about the numerical programming language MATLAB.

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4
votes
2answers
271 views

Fastest Way to Mutiply $10^4$ 2x2 Matrices

In a code that I work with (written in python, but also tagging as matlab because numpy is so close and I could use it if need be), we use a transfer matrix method to compute the properties of a ...
4
votes
2answers
151 views

Effect of mesh size on solution curves for a 1D problem

I'm interested in studying the effect of mesh size on the behavior of the solution curves of 1D convection-diffusion problem. $$\frac{\partial C}{\partial t} = D\frac{\partial ^2 C}{\partial x^2} - ...
3
votes
2answers
251 views

Solving ODE with “Jumpy” Coefficients

I'm numerically solving a linear coupled ODE of the form $$y^{\prime}(t) = \hat{M}(t)y(t)=\left[\begin{array}{cc}0& A(t)\\ B(t)& 0\end{array}\right]y(t),$$ and the difficulty I'm running into ...
1
vote
2answers
106 views

How to understand the storage of the Hessenberg matrix of Krylov subspace matrix?

For the Krylov subspace method to solve the large sparse linear system, we first need to generate a subspace Km = span{v,Av,...A^{m-1}v}, which indeed a process ...
-1
votes
1answer
99 views

Finding derivative of Matrix at different grid points using Finite difference methods/ Cholesky Factorization

I want to code this problem in MATLAB. It would be a huge help if someone can suggest to me how I can approach it. I need to solve the below-highlighted equation, I need ...
5
votes
0answers
65 views

Why the two Gram-Schmidt algorithms produce different results for qr factorization?

For the qr factorization using classic Gram-Schmidt algorithm, I found the 2 different implementations below. The first one uses the for loop to compute the upper ...
2
votes
1answer
122 views

pdepe or Crank-Nicolson? How much is pdepe good?

I am beginner in MATLAB and similar. I sow and discussed with my professors doing simulations some times: they wrote down a lot of calculus, most of them using Crank-Nicolson Method and so implement ...
4
votes
1answer
91 views

Why the solid FEM problem can not be solved after constraining 3 degrees of freedom?

I write a simple MATLAB code for solving solid FEM problem. The problem looks like that (1) (2) x-------x | / | | / | | / | x-------x (3) (4) ...
35
votes
2answers
12k views

why is A*v+B*v faster than (A+B)*v?

$A$ and $B$ are $n \times n$ matrices and $v$ is a vector with $n$ elements. $Av$ has $\approx 2n^2$ flops and $A+B$ has $n^2$ flops. Following this logic, $(A+B)v$ should be faster than $Av+Bv$. Yet,...
0
votes
2answers
131 views

contour plot of cloud of points [closed]

I have a cloud of points scattered in a rectangle and some data in this points, a bit like this $$ x(:)=[x(1), x(2), ..., x(N)] \\ y(:)=[y(1), y(2), ..., y(N)] \\ u(:)=[u(1), u(2), ..., u(N)] $$ ...
0
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0answers
73 views

Comparison of diffusion time - theoretical value vs computed

This is a follow up to my previous post I've been trying to compare the diffusion time obtained from theoretical derivation(answered in my previous post) and what is obtained computationally, for a ...
0
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2answers
191 views

What's a nice simple PDE to play with in Matlab?

I want to learn a very simple PDE to gain physical and mathematical intuition—a PDE with just one spatial dimension $x$ and a time dimension $t$. And, I want to write code for it in Matlab and use a ...
2
votes
1answer
89 views

Solving system equation

Given matrix $K_{n \times n}, H_{n \times n},M_{n \times n}$, I want to solve for $B_{n \times n} $ and $V_{n \times 1}$ from the nonlinear system of equations: \begin{aligned} &H_{i j}=\frac{B_{i ...
11
votes
3answers
5k views

How much more work is it to code math models in Python, compared to working with Matlab?

If one had to code up a new dynamical system for a research group at a university, and the university has a Matlab total headcount license so that one could code in Matlab, are there any benefits to ...
2
votes
1answer
90 views

Could the convex problem be tackled by CVX?

I want to solve the convex optimization as follows: \begin{align} \underset{X_1,X_2}{\min} &\ -\frac{1}{N}\sum_{i=1}^N\log\det\left(I+H_i^HX_2H_i\right)-\log\left[1+h^H(X_1+X_2)h\right]\\ &\...
3
votes
1answer
841 views

How to implement flexible gmres in matlab?

About the flexible GMRES (fgmres), we know that it is a variant of right preconditioned gmres. And the robust command gmres in matlab as follows: ...
0
votes
0answers
64 views

Fast algorithm for computing lower mode shapes and natural frequencies in MATLAB using sparse stiffness and mass matrices

I am looking for a fast algorithm for computing eigenvalues and eigenvectors from sparse stiffness and mass matrices in MATLAB. The eig(K, M) doesn't work with ...
0
votes
1answer
492 views

Multi-domain 3D Geometries for MATLAB PDE Toolbox

In principle the PDE Toolbox in MATLAB can handle multi-domain 3D geometries as noted here. This feature and the associated function geometryfromMesh were introduced in MATLAB R2018a. The associated ...
0
votes
0answers
62 views

Can't plot correctly precession of perihelion of Mercury in MATLAB using ode45 or ode23

I was trying to plot precession of perihelion of Mercury using matlab. For this I am following a book Computational Physics by Nicholas J. Giordano and Hisao Nakanishi 2nd Edition. In that book ...
1
vote
0answers
39 views

Using nondimensionalization to solve an ode in MATLAB [duplicate]

I am trying to solve an ode that uses some extremely large numbers and some extremely small numbers, namely $$ e = 1.6\times 10^{-19}\\ E = 10^6\\ \tau = 6\times 10^{-24}\\ m = 9.1\times 10^{-31}\\ c ...
2
votes
1answer
54 views

How to store all solutions of an ODE on Matlab for multiple values of a parameter

I would like to solve an ODE for multiple values of the parameter p and most importantly, save all the solutions for all the different values. Till now, I have ...
2
votes
1answer
179 views

MATLAB's ode45 not dealing with initial conditions well [RESOLVED]

*Concern highlighted in yellow *Solution at bottom I have a differential equation to solve for the motion of an electron: $$ \frac{d^2v}{dt^2} = \frac{1}{\gamma^6}\left( \frac{eE}{\tau m} - \left( \...
-1
votes
1answer
21 views

Plot sinewave on ZX axis [duplicate]

I am trying to plot a sinewave with a bit of 3d perspective along the ZX axis instead of the XY axis. I have so far been unable to get anything that works, and have been unable to locate any examples....
1
vote
0answers
72 views

Using MATLAB to simulate the Ising Model

I am using MATLAB to simulate a 1D Ising Chain. I am running into an issue where when trying to find heat capacity, my system has a tremendous amount of noise. I'll post my code and an image of the ...
2
votes
3answers
229 views

Is there any other sparse matrix data in matlab built-in file?

I want to do some numerical examples solving large sparse linear system Ax=b. And I want to use some data from Maltab itself because this experiments are easily ...
3
votes
0answers
63 views

Why GA convergence curves continue as two parallel lines?

I'm working on a optimization problem and using GA algorithm (in MATLAB, ga function). As you know MATLAB plots GA result with two curves, one for the best values and other to show the mean values ...
0
votes
0answers
54 views

Simulating flow in a branched pipe

I am trying to simulate 1D advection and convection of a solute in the following blood vessel segment. I would like to know if this system can be simulated in COMSOL or MATLAB. I have used pdepe ...
1
vote
1answer
112 views

Solving 1D convection using method of lines

I'm interested in solving the following 1D-advection equation using method of lines. $$\frac{\partial C}{\partial t} = - v\frac{\partial C}{\partial x}$$ The spatial domain has been discretized into ...
0
votes
0answers
84 views

Why does the matlab command **chol(A)** slower than **chol(A,'lower')** for a large sparse SPD matrix?

For a SPD matrix A, there exists Cholesky factorization $A=LL^T$ or $A=R^TR$, where L, R are a lower and upper triangular matrix, respectively. Also in matlab, there has a command R = chol(A) which ...
1
vote
2answers
53 views

What's the difference between the 2 ways of definitions of function handle? which is robust and better?

Recently, I have been studying Krylov subspace iterative methods. I find the matlab robust command pcg and the new concept of the function handle to return a matrix-vector product. Then I use help pcg ...
3
votes
4answers
299 views

How does gmres method iteration behave for this non-diagonalizable matrix?

Recently, I have been studied my lessons about gmres iteration, probably the most popular iteration method for general large sparse linear system of equations Ax=b. And the convergence is obtained ...
1
vote
1answer
278 views

How to compute all the eigenvalues of a large sparse matrix using matlab?

In matlab, there are 2 commands named "eig" for full matrices and "eigs" for sparse matrices to compute eigenvalues of a matrix. And eig(A) computes all the eigenvalues of a full matrix and eigs(A) ...
1
vote
1answer
272 views

What is the format of saving sparse matrix in MATLAB?

We know that for lagre sparse matrices, we can use compressed sparse row (CSR) or compressed sparse column (CSC) format to store the sparse matrices so that we can save CPU memory. And the coordinate ...
1
vote
0answers
70 views

Solving diffusion equation using finite difference method

I am solving an 1-dimensional diffusion equation with Neumann boundary condition at outlet and constant concentration, C, at the inlet. In the end, I want to observe how the concentration diffuses ...
2
votes
0answers
243 views

Extracting FEM matrices in matlab pde toolbox

I am trying to follow the dynamic linear elasticity in Matlab, link here. My goal is to extract the FE Matrices using the function assembleFEMatrices in matlab and solve the resulting system of second-...
-3
votes
1answer
89 views

Does a new proposed method for solving Ax=b must beat matlab command 'A\b' be a successful method?

I have a question about direct and iterative method. Many people including me often say that for very large sparse linear system, Ax=b, an iterative method is necessary because of cpu memory. I also ...
0
votes
0answers
41 views

Solving Parabolic PDE using Matlab

I have the following pde (Burger's equation) for $\epsilon>0: u_t+u.u_x=\epsilon.u_{xx}$ and $x\in \mathbb{R},t>0$ and the initial condition: $u(x,0)=\phi(x)=1_{(-\infty,0)}(x)$. I want ...
0
votes
1answer
784 views

Shooting Method- Boundary value problem starting from -1 to 1

The equation is $\rho \frac{d \bar{u}}{dy} = -\frac{d\bar{p}}{dx} + \mu\frac{d^2\bar{u}}{dy^2} $ with boundary condition $u(-1)=0$ and $u(1)=1$ I am to solve it using fifth order runge-kutta ...
1
vote
1answer
68 views

How to avoid unnecessary checks when inverting this LU decomposition

Background for the question I am currently working on a Matlab code in which the systems of linear equations $Ax_1 = b_1$, $Ax_2 = b_2$, ... have to be solved. As the matrix $A$ is constant during ...
2
votes
1answer
100 views

Passing data as arguments in ODE45

I need to import data from file in order to describe the structure of a network. I used the following: weights = readtable('weights192.txt'); W = weights{:,:}; ...
2
votes
1answer
141 views

1-D boundary value problem: How implement mixed boundary conditions using a FD method?

I have been given a convection-diffusion ODE modeling the steady state temperature of a pipe (through which flows a fluid) as $$-\frac{d}{dz}\left(\kappa \frac{dT}{dz} \right)+v\rho C\frac{dT}{dz}=Q(...
3
votes
2answers
168 views

ode45 with matrix initial conditions

EDIT: We have a coupled system of 10 ode each. The coupling presents in the last equation. I thought about using a matrix 10 by 2 as initial conditions. I also followed a similar question with the ...
3
votes
2answers
330 views

Why iterative method: AMG preconditioned PCG is slower than Matlab direct method 'A\b'?

Recently, I have met a question that a saying goes that for large linear system: iterative methods are required because of memory problem of direct methods. But when I implement some experiments ...
1
vote
1answer
192 views

How to use QZ decomposition for single matrix in Matlab?

Can I use QZ decomposition on a single square matrix in Matlab? Like, [Aa,Q,Z]=qz(A);
0
votes
0answers
77 views

Reducing run time of a numerical calculation using a mex file in Matlab

I wrote a Matlab code that involves doing a numeric calculation (relaxation), but it is quite slow. I learned of the possibility of using a mex file to run a C code and integrate it into Matlab, so I ...
1
vote
0answers
167 views

How to set the errorbars in a different color from the plot in Matlab? [closed]

When making a plot in Matlab using errorbar(...) the color of the error bars is the same as the plot. How do I set them to be in a different color? I tried looking ...
0
votes
0answers
210 views

How to do a Hoshen–Kopelman algorithm in Matlab with periodic boundary conditions?

Say I have an array s with elements of 0 and 1. From my understanding, a Hoshen–Kopelman algorithm for s will be (in 3 ...
1
vote
1answer
105 views

How to implement this even-odd matrix decomposition efficiently?

Note: This question has also been asked on stackoverflow - see https://stackoverflow.com/questions/57197910/how-to-implement-this-even-odd-matrix-decomposition-efficiently?noredirect=1#...
12
votes
2answers
2k views

What is the most efficient way to write 'for' loops in Matlab?

I have read that if, for example, I have a double for loop that runs over the indexes of a matrix, then putting the column running index in the outer loop is more ...
2
votes
1answer
68 views

How to pass matrices to parallel workers quickly in matlab?

I am trying to solve many different linear systems in parallel in matlab. The problem is, each linear system has entirely different parts and are fairly large, so passing the information to each of ...

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