# Questions tagged [matlab]

Questions about the numerical programming language MATLAB.

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18 views

### How to implement the gmres method using Householder transformation instead of the Gram-Schmidt?

For Generalized Minimal Residual method GMRES, we usually use the Modified Gram-Schmidt MGS to generate an orthonormal basis of ...
37 views

### HSS preconditioner with gmres [closed]

I have a question about HSS preconditioner with GMRES method. For implementing the HSS preconditioner with GMRES, we need to solve the linear system of the form (I + H)(I + S)z =r, for a given r at ...
44 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 ...
48 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 ...
58 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) ...
11k 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,...
39 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 $$x(:)=[x(1), x(2), ..., x(N)] \\ y(:)=[y(1), y(2), ..., y(N)] \\ u(:)=[u(1), u(2), ..., u(N)]$$ ...
52 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 ...
82 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 ...
79 views

### Solve a nonlinear system of equations with condition symbolically

Consider the following system of nonlinear non-dimensional ODE : \begin{align*} \frac{d\bar{x}(\tau)}{d\tau}=\quad&\bar{x}\left[1-\bar{x}-\frac{\bar {y}_{1}}{\bar{m}_{1}\bar {y}_{1}+\bar{x}}-\...
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### 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 ...
4k 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 ...
40 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]\\ &\...
135 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: ...
37 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 ...
99 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 ...
25 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 ...
19 views

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### 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....
52 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 ...
113 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 ...
50 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 ...
41 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 ...
69 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 ...
32 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 ...
51 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 ...
115 views

### How the gmres method iteration behaves for this **enfant terrible** 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 ...
16 views

### Offline Parameter Estimation for second order system - Ordinary Least Squares

I have a second order system which is described by the following differential equation: $\ \ddot{y}+α_{1}*\dot{y}=b_{0}*u$ where $\ y$ is the output of the system and $\ u$ is the input of the ...
57 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 ...
22 views

### Interpreting results of using no-flux boundary condition

I am solving for solute transport in 1 D. $$\frac{\partial C}{\partial t} = D\frac{\partial ^2 C}{\partial x^2} - v\frac{\partial C}{\partial x}$$ No-flux boundary condition is imposed at both the ...
61 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 ...
85 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-...
81 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 ...
32 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 ...
62 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 ...
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### Controllability - Maximum Matching

I found this image on wikipedia referring to Barabasi's work on Network Controllability. I tried to verify it. We have a A matrix of dimensions (20 by 20) made as the image suggests. According to the '...
55 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 ...
47 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{:,:}; ...
75 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(...
89 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 ...
176 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 ...
69 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);
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### 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 ...
43 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 ...
75 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 ...
79 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#...